Engineering Physics - Uma Mukherji by Blog da Engenharia de Produção

Engineering Physics Second Edition

Uma Mukherji

Alpha Science Internatio nal Ltd. Oxford, U.K.

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Preface to the Second Edition nu, fHW:ll.. ' ' llltl"IHj~d :u a ICXthovJ... f'vr lht.: 'lt11.ll.'lll' til (Ogtnccnn~ ph)'SlC' l'Od un cxpcncnl!c:<.l tct.u:: hcJ vf phy•m:Ycnpn~.·vnng. physacs. I h:tv\.'1 I ned 1u ,ejcLI .mel ;Jrrnnte 1he m:uera,1l Ht ~uch a \\it)' 1h.11 the studcnl~ would no l fa..::e ..~h..'lh..'l..' . ,.\"'

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tllllkul1y '" fo llowing the book

Tlu:-. ctdiliun. ahe ~ccond. ha~ l"lccn lht1rou~h ly rc\ i~ed. l::rmrs ~md mis.pnm.s lmvc l'l\·cn ~orrec1ed and some dangraml' hu"t: hi:cn mPdl ficd and unproved hlr iHop·cr rC'prc:scnt:ilhJn of' I he thc<n'y To fulfill hc rcq turcmcnl~ nt' students (on Ihe h~"i' ul t\11 lndau Sur\'t:y) . .;,omc mOI'e wp•c.; hot\C h..:<:n •ncluctcd 111 ahe \C...:ond ctJu •on. Nc\\ topics including conducu\'ily vf rnl.'it.tl :md "-Cmiconduc:wr. Hall C1 f~l.·t. m ag,UCIIC llHHCII:tl~. puJ:Ift~fll iOil . /OilC p l:tl (', c J~CII'O·OpltC' cf(CCI.

pfl,,tu..·l:-t:-.lit::iLy, CIC. h:w: bcl!n .ldded.

I ' IHmt-1) hop.: thai the !!otudcnb from t..hiTcr~ot UIU\'C~rlh::~ Wlll lind 1h1~ \!lllli\UI of tlu,; bout.. mul h more useful

I .uu ~J. It\!ful the

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1up1~!\ IU 111lJll'm1C ch~.: .\landanl or Mr N.K. Mehrn. M/ s Narosa l'ut>hsb~ng llousc

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\\ ho C(.lrl\ ~.·ycd alltho'c ')Ur'\'C) repnl't.:s l l'l UIC r .un t;mldullO MOTI Il;R whose '\llt.~lll 'UJ'J)I"n ga\'~ me strcnglll h)t•nmplctc the rc' ''tun work. I nm nlso thoflklu l IHt\botn<.l Pruf. Shel har Mukhcrji ror cht:d·.. inJ! tWCr:tll p i'C:'"!Cnt:uion .tnd for P:" 111~· Ilk .1 UC\\ pcrson:ll compuh!f. oron th:u 1 c nuiJ "'' my '"'t.'lr~ ~moothly nnd nKd} . Ill Ill)

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Preface to the First Edition rhc cuurM~l'- pwscnbctl for cngmccrm}! phyl'ott' by vanow.. uru\cf:)lftc~ arc nt u ;•d\'anccd h:\·c.·l. unJ constdanbl~ tmpor1lllli:L" 11'1 g t \Cil m every tQptc fmm dH! \ ll'WJM1101 or us applkattOn 10 pr:tcuc.tl hl'lds_ Hut lc\\ books prO\'tdl' alL \t'r)

lhnt 1'- \'~pCC'I~d ('(them The prc~<'nt ht)U~ :HIC111Jli:O.: 10 lulfll COUntC ObJCC11VCS. SotlH! vf these topu:' nrc: for.t dJ ~at research lc\'¢1 , hk..:: holn~r:tphy (producll()n of \-dlmcn...ion:.l ph<:ungr.1phl. fibcr·opltcs communu:mton. "'upcrC'onducli\·ily. ~md ...o tonb \Vuh rercrcnce w 'lluch od,•:mccd toptcs. Lhl~ cmpha-;ts m the courses ts ~·'·en 10 numcncat problems. In the pr("scm syMcm ol' \!~nmmntton s. about lifly

nw reh;\ iti)CC h,) ..:;uch numcrrc:al pmblcm' ;.•ntf uhJcCH\ c f}'IX!- quc~uun~ h.,~ hcr:n l.tlcu hom tbJiy hr~ ~\pcn..:nces. t l•a:.l"~oOl. i111tnJcd a"' a ICXlhook f•,r.:-ra}!inecnn!.! phy:..1C" ••nt.J s~.:iunce ~•udcrn:... lric' hl select anc.J :trran~c 1he m:uer~:~l an "tu.:h a "·a~ lh~u a \HJdelll '"'cl\tld 1101 per ('Cnl emrhaSt' 1\ (.)0 p t\tbiCtll·SOI\'IIlJ; fjUC(,ItnJh -

f.tc~

noy d 1mcuhy m understanding the tupt<''

TJw., bonk IS 011 O UICOIHC OJ Hl:\rl)' ) (;U...., dl fll)' ((;(l~hm~ ~'<pc!r!CI\Cio} rhc (C:\1 i' h::"cJ on my kcturcs- gh·cn 10 Jht." untter~r~h.luaft.' engineering qudcms of Bomhay Univcr,.uy from PJ90 onward,.,, Tbt! 'UbJCt'l mnncr i 10 :u·mngcd and so ~s 10 muke the le\'el ol 1reu1ment progrt.>SSI\'ely more dtfficult nnd

dn::cu!>s~d

lh-: matc.n.1l more log1cally accc.p1ablc. i'J'(Ipt;r tccttb:.u.:~ rrolf\ 1he-.studcn1slu:Jpcd

m.: w c:lan{y dtfl'Crcm mptcs Thl! hook'' d1vidcd HHO 1\\'0

pan~

·nu.: 1an.a p:1n Jt,..CUSS\:~ bablc 1hcorie~ likl!

.:ry~taUogrnphy and cry~u\1-lmperfecuon. shemll'l~leetricuy~ t ht~rmJOnu:-emt"StO~

ultrJstum.·. :1cousucs :m<.l semu:onducwr 'nle 'ccond Jt;an cO\'CI~ udvtmce toptQ hkt.: lhm flllllllliCrlcren<:t;: and dtffnJcllon. x·ray~. mouon or 1hc charged pantdc an clccmc and m:-tgnct..k fie1d. quamum phy~l(:!<. nnd SchrOdmgcr w;we t!<JUI1llon, l!u.t!r. hot('lgmphy. liber-opUC'"S. r::tdtmlCll \'it..y nn~tl ~uperc<>nduc ltVI1y.

The: purpose ol 1hts oook •s 10 i;t''~ 1hc saodcnb ~ c leat' undersL:u1chng or which are l'ehucd 10 thetr cour~c uud J1ay ltl du} hk 10 diffcJCnt wuys ~lou,·:uh'n \\:t,lherc, ~md 1hc '>timulul\ ~:alllt' fumJ my Jw ..b:aud. Pttlf Sh..:kh3r MulhcrJt My studem.... 3Im gu\'c me tnoml ...uppon nnd proper f~edh:•ck rt.l.gurdm~ lopu:~

the Mund:>rd ol Uus manuscnpt-as they hnve used my cluss notes during la.~t

lew y~~·r.'\. I .tm thankful1o Mrs S:ti1ap \-.•ho did .,11 ahc aypu1~ \\ftrl.... :) l'lc.l 10 Mt Suh~~ N~trkhcJ~: lor nil lhe conogmphic help anL1 1o makt! I he maucr presentable. I am :tho thnnkfult" Mr N.K. Mchr.1. M/s Nnru"' Jlubhshmg I l ouse. for bnngmg out the book in II$ pri!S\.!nt ft)nn.

Um:• Mukhcrji

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I ~td h'r Sinttlc: Slit 101 fnr Dtluhk Slu 2fl~ Oiffrm:IIUO Cir.uint; 1.27 ;\b'-4.!UI Spc..-:lfll 20.< l.~fJ2

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20'1

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211

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in Elcctrk and

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141 :t,'!_

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Physi~s

\\'a,~ ~.<fOal ion

und Schrooinj:or

!78 I , (,lunnHml Thl!t"11') ~~ Rth;h.itum

l'h•\~t' l• lcl"'tllt.."

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114

4 Ht l'lllN' Vclocuy nuJ Group Vdoc•t) .:tJf• ... '. - Sdtmdm~~r \\..t\~ l:.t.fUOIII(IU (Time o~:pt:ml~:ull .JO.It I ll( 'u,hrtkllll~tl (l unc l!h.lt.'J~Il"Ciitl Wtwt hqu;Ut•ln t~Ti t:J -1 fi• b~.:n V:th•e f...q~u,thlll l/'1

I 2U J 11

t.;t.Jt am:.u')

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v,,.,,,,"' .r!1

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hllluduclii>U-L~er JZ.' ~ I I Ah~OT)lttclll ul RadhlltOII J1J ~ 12 bnm.<lfln of R•dmuon JJJ <; 1 ~. I 'lJK)n l,ul~')\IS l:.ln t ..>&\ln I)!

R,.,J!.ttu•u .~2 . 4 itnnuhtll!d Emts!-lon 111 R~dl:llton .uh.l ~s m~ Au ion ll<~ Populalinn tnvcr..iun untl Pumping 3.!5 OpcnalitliJ- Pnnctplt.• in La<ier JZ.~ .; _ 1.2.~

:...:! ~ '1.

\htHUClcn...ltc Prupcrt..t c.~o. o l 1-'l..o;.cr Ltghl Kuhy user 127 ~.fl lh:llum-Nc,m L.oct J2..9

:t-.·1

4!7

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10 Scnma.mt.lu\;lor L.t..,~o:r ur l>1odi: L;l-.<'1 ;anJ J.o.~phl 1--nullm,t;

DI,>Je tLE,DI

.<.<~

ll'l!tOoltJclion Hdngr:tpby Uc) 5 I I I Rccordjni! Of 1-lolol!ro.lll lJII ~I 1.2 kccun...u'WciiOII ltl l.he Jumgc HI

~ II \ lJ~c~ c.1t' lt•,lognsph) l<J/ llmothll'Lion-Fibc:r Op1iu 342 .tt I \ T.)t.tl lnlcnml Rcftcc lion .142 !l 14 p,.,pagouon ol I 1glu 10 F1bt:-r .f.l·l c; I Iii I"Mkn:nl Ty(>'!~ ur Opllc;tl Fibc.r f.Jr, ~, 1~.1 Cia~ I<>> Fibc1 J4~ cll qo ' 1~.:\ Step lndco.\. Fiber 347 5 1~ .•1 P.l.SSIVC and ;\ c t•ve Fiber J.J7 ~ l~1 Type' o( R~t)'~ fMcru.lion:tl and SLn\ I<My-.) 14'1 'i 17 ,\1udC's ut' l'rup.1g.s11on m F1bcr f->tH

~ 12

5. 1R MullmuxJc: nrnl Monomode Fiber.. _t5n S 19

I)I'OJX'r''ion

ln1<:1 Mudnl l)l~persion

J.m

~.2n

l.u-..'e." m Fiber Coble JJZ ' :! I Pll\."110 Oct~C:IOI J52

!U I I Mech•n'"" ot l'hoto-DiOde .IJ2 .5 11.2 Quontum F:ffictency :.nd Re.,ponc;ivn} JJ.J '\ li.J Long Wa.·e Lc.ug l.h Cur.OIT fSfl \ 1.2 Componc:.nl$ t)l =tn Oploe11."'CliOOIC COJllU\UDI("GIJOil sy .. tcnl fBiod·dl.tgram) 354 :\~3 U..e, ol Opu,·:al hher JJI$ s 2·1 Ath unHtges or Opci...-:al Fil~t 357

Problems 357 (!m!.\tirm.'i 15S

3~ 1

6. Radioaclivil y llltd Nudcar Rcacliuns C.. I llllrl'<lll\'llt'n .fr, f (•..! H«nl!.:<~lln.. tmm~·nh .:n. Ucll:dm-.J(;~lj:Cr · Mull.: r Counter it :l K.uhu.Jl11\\.' u ... mtq!loUI•IIItll l lc:\.o.J) Jt,i t, 4 Nnt ur>~l R.uh'l f.,,,turoJ" lr,r, (•.:\ L:lw ,,, Ko..~\liu.._~h\'\'

Uti

u .... lllll!~li.IIUIO u,;-

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f,'i.l

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J<efcrellccs S ubject l lllfl•x

JH::!

PART-1

1 Crystallography and Crystal Imperfection CRYSTALLOCRAPHY 1 In nature. clement~ .snd Lheir chemical compounds arc u~uully found in three nnmely. c;ohd, liqutd and gaseous. Differe nt solids bavc t.li flt·n~nt propertic..-. If the utl'tn; or moleeul«< in a solid are arrJng~d in sume regular r:~>hion. then tL i~ kJ1own a~ t·ry,\tfllliur .WJiid. The mfljority u f -.olid<. :1r~ e ry~lltllin\':., with the

~Hth;..-:,

or mol¢culc~. of which 1hey nre comp<,sed of. armngetJ imo regular 71u~ pl't.u •m.'t.' tJj /tmJ:·rl11l8,,. uu/t!t i.\ t/IU.J.. th•• dc']illill.~ /)I'IJJ'I'tly uj" l'f)'$1(1/, IJue to lock or lhis lo ng-rnnge order i n the

.unm.!<l.

mn~

R'J>e.th:!..J

lhrt:CwJitncu-.iunal p:mcmi:.

~lmmgt'm.:: nt

uf th~il ctuhlihh:nt pMtiel-.:s, lilhCr snlh1' m;•y ('lroJlC.tly be regarded

;a~ w rwr-rmllt•ti/Jt}ftid or t!llwrphom•sulid, whose stilfnc.~~ i.s due: to an exceptionally

hi,gh \' i$coSity. G bss. pilrh. tllld many plastjcs u.rc example" 'Jf such a morphous C''nhoul fonn) solid~. Amorphous solids may ..-xhibit.s:hon.. nmgc o rder in their •·MUCturc,, The umtlogy betwc~n an !lmQrphOU$ Stlltd um.l a liquid is '' urth pursuing. genera II} the)) Un not have h'mg rttnge order. 3~ X-rny diffrnction indic.ltc!; !hat muuy lit)Uid molecule:-. tuc cnntinually shifling. 1heir positions. Amorphous solids have nu ' harp melting pt'lim w herea.~ for cl'ysrnlline so lid. melting occurs ut a pr~ctsel} defined lemperutures.

l.l

C rystal Strucmre

In u cry~laJiinc s.oHd. t·t:c:h tltom or m(1/ecuh· i.r ,,iiUatcd at a dr}ioilr pouJI in ~pon~. fit a rlt•/inite tlt.tllllfCt fmm rmd in u tlefiuir~ angular orirntntion ro m!Jrr mmm m mo/cntlf'.\ \urmtmding it. Thus. ~ perfect crystal is considered 10 be C(llll<olfiiCtcd by the mfinite. regular repetition of idcruic.:.1l s-tmctura.l urHIS or huilding blocks. The oc1ual m:uerials are made up or agsrcga1es ur 1hose cryswls. Crysmls 1. an bl! .ringle or pol.\TI)'Jtallim~. In a single cryswlth~ orietrtathm a/ the atoms or molt•rult•,f arc''" mri/rmu mrd co,tbuu: tllmuglwut tht.• rlllil't' cryswl;~s ~hown 1n FiJ;!. I 1. lllcre ure no discom inui1ics:. 1hc bound:•ry o f 1h:u t}rpe of c rysml is the boundlll')' ror ~1e enure crystal . there nrc no subdiv1s1ons. no 1n1emul gruln huundarics. for exampl.:. diHnwud, ruby. ¢1C. Whereas for polycrystallim: malerial \dmlc r t·)·swl ,-., umd~ up r.if.wmllf"r crysmllites a~ shown rn Pig. 1.2. Eac:.h small 4

f;fl.<:tnt'<'l'l" '-' f.1Jn·sn·s l$ ••~...

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:m.l..: b) SHic ''' lorm :1

'' hul(! pol' en ~ltdhn~ m:Jil'rml t h~ I 2). ltkc 111 <.(\.Hlfll.

1'1 1ct can.: J,:I4Hn hciUthJ,,•n!',,

bel \\'Cl'll I WU p111i ll\ rfh trlt'JIIIIIitiiJ •,, tllmm witftin

parlicufur ~mm 1\ ufu·m ~

tmiJol'm, I.e·.• 1'01 II .f.:l'ollll IW,( tltt .\ tWh' latwt' palu.•rn but snmn 111'1' l,'t'llt 'Ut/1~ nn'<' ll/('11 itlllrl.uu/\ uud tlttt\ J11rmm-: ~roiu homulatw.\ m po/\'1; \.\lullrm• \rllttl .Sm~k " ' >'' ;'I' M l ' tn•u..: P"" h~t .•hit' 1houl polycry~htl hn..:. , ,tlitl, 01~ na.my propi!mn ttf , ,,Jitl!\ :trt• h,.,, ~ • mhctt \\ irh ,ju~lt• cry., t . t l~. TtKby .tin ami ..til n:ttur.•ll) u..:t.:ut t tnp t:•Y~ I ol ... h.l\c hcl'll ' Ynlhdill.· d 111 the hthunuury under conuollcd L' ltlldtluUI' Sm}!IC cy~Htls nmy h: dll~l'-i ft~d ;, ... ,•J;.·m~·mnl ('1..,'.\'tu/ (e.g.. A I. h :. Cu L'tt• I and ,,mic ""'-'itnl c~.:.!! , 1\};CI t eh .l.

·,,sn"'

~;nun

Fi~.

1.2

1.2 l'ul~cr~ ,1.altiu•· .. tr-m turc \\ ilh g raht~ tend ~min houndan

Dcfin itiCJn uf l"rys lal

Struttun~,

Lat tice l'uinl$. liJllln

Lallicc. Lalticc J>Jane. B01sis. Unit Cell A ny-;1a l Jl'- :1 1-duocn~umal hfl·d~ f~ct=ul:ar a nd ('ICfn)c,hc- tarr;u lg.cml"JU u l ~ ~ dirncn,lon~ll p atlc Jn nf alnflh or mnkl."ull':S in~~ pace. i~ C'~11lcd crystal s1ructut·c. u+lll'rt.' vndt muf ;·,·tw' mow ,,,. mnlt•,·ult• how• th.· tmll'' t'lll'iramn,wt ~'Hiun cry;;.tal 'IOICI \If'~. p1tS tinn ... ol :ttom tll' m•,lccufe or group uf at tuns wlt~.:re th,•y ~1r\• lt.x;ntctl. tcpn:wntc~11ur ... nnpll(lt)' II\ .wmtt 1minh·, '' htcll Hrc knt•\\'n ,_,, ' hlt t icc I>Oints ' a:-. sltt)\\ n 111 Mg. I .3. A pumlh·l m•t.Ji~<' armnx.t·nwnt oflouin· 1m•'t~t, ;n 'fmt't' (Fig I 3), b J~;lirh.:d n-. SJ>:)C"c lattice. whi~h provide the cnvl.-onmenl nround any par1icul:1r llmicc poinl and is in every w•'Y Lhe :i-tll1\~ us around uny other lauicc p~unt Wilbm ay!'tal ml\ phmc p a $t-UI}! throl•;;h ;11 I\:~''' unc 111111\'".

rxHnl i~ c.tlt~d Latlkc t•lane. h IS ~!\'J\!nli:l~ l() IJI',Illl!:UI .. h "' I:Uttcc J>UH1~. IW ill tl cry!<oHI I 'UUCIUrC Acryo•t:tl 'tniCiur~ II ~U I Fig. I I ) , ... funned hy ol!'o'otl\:lilhll)i! \\llh Cll'l'\ l.t111l'i:

pnim u'

m ( h~ I

\h0\\11

.l},

anum/ ra·,wmhh o(mom'

/, -+

lr'

,-+ (

,,: Fl)!. l _t ~hl>lllllll

l..u11.1 I"'"''

l /1

--;-

Sp.ac~

hg 1--' \\hi"'h

•lt '''"" ,1\

lnlfict"

~md

1...1llt:ti .J ...

I unit cell in two dimt•nrion

Basi~. lh-..:)'

.trc

h:lculk~tl

•IN Jn~<Uh.'l11 .1ml url\!nHlltUII f h:: I -l l, He.n.:c. Juuu ·t·

Jl""''

in l.:t•mpt•'llll'll •

+ bmt\

-e ''"'''"'

:.trur Otr't'

Unit C'l'll: ll11.' ~~·ru:r01l :!-,lnlll.:n,luJwl h.111kc tFaF I _lll\ nn 111lm11C" +trrn~ ,_.j J.tll h:.C p 11111h. \lhkfl f\.'plC,C111 lh.; ;thmht.· ur nwlc,ulur pc~o..,uwn~ 111 the ~.r~~tul 11tt:'lt' ('H.IInh uh~) Ihe lullkc

()

•• I

,/multi lht \111111' f'III'/IIJ/IIIIr-111 fit t/u• Wmt•

cnndiiiLIIIIIHH. t•un fwtll'( poult ft1H't

m ll'trltlltml

li.!l u~ -:~H\'Jth:r 1' 1.\-!. I.J. wh~:h! vet.:lur:-. a •.ud /; ouc IJU'"'hk dJOII..'I!"~

Fi~. 1.4 IJasi' r.,r the Jli11H1(h...- tr:JII\I o~llunt~l \C~h1f nf the lattkc. The gcm:ro.~l p.lf,tlldog.r.llll ..\IJClJ tl~fmcd h) the pnnHII\'r: vc:CH.trs ( I ond b . fonn:-o u pnrnthh' ~."ell '' h1ch I\ t:;tllcJ tht· unu -:dl. I11U\. :t 111111 t.•f'lt L~ defined a.~ lhc wrullt'.H .&rrmm ·u r, ji.;urt._ ,,,. "''(JillfWII\" of ll•/u,·t, grw•,\ thr m•wnl ('ry,o;wJ .\'truc.:run•mul u ~lwu/J luH't' uJJ

1111' rltm·m·t,'fl:>llf.~ of llw J1<lmculur t'l'\':rwl. It c:m al~o be deli ned as the Iunt.l.un.:m;d elcmcnll() p:Jtt\!m ol ., uHnunum number of atom.;; o r auolct.:ulc" m t '''liJl 11t muh:~o:u h;,, ''h1ch n:prcM.'ttl l ull\ all 1hc ~.-haraclcri,ucs of ihl? d)\t;tl F• u th.: J-dm1cnsinnal c:L-.c. 1hc unit cell eli a parnllclopipf"l"!U f\)HJh:d h)' the b;t.,ll \'.:ct,,~ ii. ''. , . :a ... concurrmg edges: :md inclmhng :Jngfc, «. fJ. y QS shown 111 Fit=. 1..5. I knee an ~r-ncrul. a ··umt cell~ rnu) bt· defi nea.! ~'' tilt' Mnalle.,t ,-.,fmnt• oj 11 '''luf.Jmm u l11ch lltt· ~ndre '-'I)'Jllllmu.\ l•t• rmntwt•u•d In '''''' \lt1lwn.J! ' ''!U'Illion• m .i~tllmr•mmn mul whi1•1t n."/)l't'.\ c!nl {:1/1\- till durr.lt 'ff'f"l\th',\ t)_j ,,,. (Jllllh:utur t'l)'~flll.

Th< clllliCC tll wul cell" out un1quo. h nmy be ABC'D o r A'B'C'D' IF•f l..l! h +::u~ h.: con!!oUUCtcd 1n ll nuaHbt!.r' of w'')'~. but the mut cel l ~hould he ..: hu~cn 111 " UCh :t \lilY th:lt it CCIIl\C)'' all thC' ~YilllllCH)' or :1 t:I}'M;a1 l:micl.!. by h11V1111;;

shoncst possible >~Zc. which makes the mathcrnatica1 cnJculut10n~ eM>~ . For c.\Omplc. AllCD wall be the u n ll col i fl'l l Cuhic~tl ~ry~ml '' hcu (tJ = lrl. nm A ' B"'C'D'. E~1 d1 :.Hunt ur lllulcculc m n unu t:cll •' roo,tdcrcd u~ i.llmllce- poinl.

Tltt• d1 'lllllf t' u he1u ' '''" twn uwm \

--·

~ "

,,' l .

''., /r

Wfl.\' 0/

tilt• JlUIU' 1\'f't.'

tfw mm nil", uml

f\'

tJI

1/f,. "ft•u~_•lh uf

~1\\l\'H ..t~ lanhr

fUIHIUtt'lt. f

1.3

Lallicc l'ara mctcr

In a 3-dlm~miou:t 1 c.JM.~. tht: Utul L'ell t s ~hown "' ;, ptU'•II Idnp 1J)J>cd In l·•g. t ~~.

Fh~- 1 .~

Unit c·C'II In 3-dhncnsion :.re ll'!t!' b:"ic \'CCtors ~long, ~ .).: tlXC~ t.:alkd cr~·l'!1aJioJJ.mphu: :tXt'" The !HIJ;IC:-. bctwc.!n thC!'C axes ttrc c~11led ant~rf.ICtal ;.~nl!l~;-. wh1ch ace a.{J. i~ bel\\ ~:t:n 'ector!\ t/; ,: ) (t~ - ii '· ( ii J~ I. Pnmtlll't· 1 rc:tt.n' ii . b • t-: (nultht• mrc·r/i.u-iol rmRf• ··~ U, fl, y, an~ IIIJ.!f'lh rr rullnl 'lauit'i fJIItllutf.'tN' t{ til«' t'Y\'.\'tal. T,, ~eterminc: the ac~t~.sl ' s~c of unit cl•JI. Ihi! ai.'LUal ~·olu.:' ,,1 \ C1.hll' ,i. h . ,: ~and rhc lllh.·rf.,...:wl ungll·... nm~ l he knuwn

1; . t

vcU flP•· a

1.4

l.a ll ice Vector and

Din·cticm un.Jcr Itt 'pecrfy ~· C"Cflrllll pl'tUlL ,~1) I hI or ;,t CCII.Iin dir\.-.;lion. ~:&) OP iu .a tlfllt cdl. \\'.: u~c- ht~.sie vcc1ors I ll

r f Fip

\\'ht'll \CCI of:\ ~cc. tor ..

ii /;

Hr t;

IIW h t1"h:

lh.: unil t.dl. then point/',., rdutl'd UJ lhl' on!_!in by \'eC.."tor lmnsilion Iii

01.., - f -= n,(_7 -t \\her~ HJ•

1.5

IIJ

,21; + n ~c

•IIIli ' h oil\: lhtl!t; intC.~CrS,

Se,·cn Cr ystal System w the d,n.:r;:nt h'rmcll !\') ruiiO'.\ ~:

.'\cc~lr\l r ng

C:'u, h~ ~

Nn.

f"r~ '-l:JJ

S\Siem

'1u luc~

tJf t h+: Inti icc p:uiii11Cii!J , ~C\ot' n ... , Y'l:tl

V~ctors

B:aslc

Cuhn;

rt:b:i

~100\k.:lllll~

,,.It~.

'~ !!. ! em~

lml·rt;K: tal Antzle"

o= 1hr= 90 ' "~ 114 'Ill""' r r>YJh r~w

1rn:Junt-

il 7

4 5

l'cuag,ln.al

a=h"-i

r.t r:JJcy-:=90

OnhorhomhJt:

a.,r.b~t

a;J!;

y;'l()"

Hhombohcdml congooall

o= h=•

(t • {$ •

't"t)()'

l lc:tiiJ:!UIMl

u=bF-c

T I

«= JJ =YO'. r= t!cJ•

The ~haJX:S o r the unil ~ll~ :Ire ShU\\.' II in Filt I 7 or l hc~e ~·.vcn (.'f)'Stal !')'$h.'nl~. the cubic sy~ICIIl i1i rht simplest :and JlltH1 synunctrleal in which a h c- ami ll. fJ y =- 90°. h i .. inlc rc~tin~ lo ntHC th:ll 11101c than hlllf uf the..· llotturull} cw«.:umng t:l}''l:tl~ bclon!:! lU the cuhit.· <r~h.:m.

= =

/•

QJJ I

i •

v·· · v

,, Fi~.

1.7

Sc , ~n

Cl'):.tnl

~)~tetus

1.6 Bravais Space Lattice1 tn tiJ4.5, Bro\ui .. <>h<.\wcd thut tht.•r.: .Jf'\' ••nh· l.t \\.t~s ofurrllnJ.!tng ('K1im~ 10 ~pJt.:c so lhO.I the cnvironmem lc>Ok~ th~o~ ..,itmc frun' t:.&dl pvmL 111l:Sc I .:.I lntticcs arc railed Brm·ai.J .ffJltc( lattices. each ur which hoh tlw 'nmc:: et.'tllccunn of ~ymrntll)' clements at lhc lnuicr: point.\.. For c ubic system. three Lypcs: u t nr.J\·ai.. l:uucc..: un.• l~,..~iblt•. \.ii' • (i) Simplo cubic tS C.) (e.g .• pallttdtuuo) Cii) Booy·ccutred cubi<· (B.C .(.) 1~.g.. molybdenum) Ciill Fncc-ccn<rcd cubic tF.C.Ci ~~g .. Ni, Cu. N:oCIJ

. i 1-{~ ••• ••

lA)

obi

•

. ~

<•)

Fi2. 1.8 ( 11) .Simple cubiC' slructurt" (S.C.~. th) BtwJy..c:c.nlred cubic struc.•uu·~ ( U.C.C.) and (c) ~~act·cmtr~d cubic slructore n-·.c.C.l

S Nn 1

( ·ul11t: Tc~t"4-1'1111.al

f)J1hncl ll)llll)ll:

l nEHI1.:.11 \h•ntXIilti~.

lo 1

lk"<tlJ.!Onlll lnd uln.

h14.d

1.7 The

Sy mmelr) Elements vf ~• lh;UII ' ) ll\IUCifY dceUt.':UI~

f~lf1l.1nc'

<•I

ttf a

Crys1~111in c Svlid cry..t:tllinc ~l.J1hl urc ( I ) uxc~

ul ' ' llliiiCir~.

\V1111llCrl'\' .uhi (~I c,-:uta• nfsymniL'If\

I . •\ xe.' uf ") mmetry· ·• -.:ty ... l.JI;.. hdnJ! rotmcl.l around :111 .t\1' llt lw f.:t~..,l.tl t•uupll'' ''"""r

Ct~tt..,itlcl

mutt;· u.l~nlh:.tl P'''ni ~•u' tfunng it"" rot4tllon lhmugh "\ll41 • lhL'Il thai .t\1' ' ' 1...tl11!J

th.: cUI\

flj \\'IIIUh tr\'.

I•I.Jtion,•f(}() brin{!\ it illh\ u.f~nlr~ul 11r t.'~l l ll!tii\.'Jl l pn-,ith·,n pn,llmn' lfllllle! t.'Ornpldc filhiH>O. fl '' ~:.aiJcJ d I f,,il/ U.H\ n/ ,wmu tr\ ln gcnc-rJ.I. if .a rnwlion thrt1ugh dn .m~Je f\hHhH .1h.1ut ;m ·'''' hrhiP' J ll~urc Hill' I.'Ottgrucnl po~hl~m. then th.tl ot\1' 1' l't\llc,l •'" n~f,ftl ft.U.\ of

In .1

t:Uh~.C,I!.a~h

1.\' ., ~ i..III1~1UI!tll

uuur·tn I h~r~ .m: I :\ ,t\l'' ol ,,, "l ol\~!> .ln.

\ymm~try

tor ;a cube

h.'lraU 1 1-f~•ldl fFi~ I'}).. which P••" fhruul-!h

iii"'P'''III."

'·"C

(t'lllfC\,.

1Jl J -l .1 \l'' ..l.h.' 1r1.d

I '~II 'IUJ(t'Zig I 10). whk h p;"' tlm•u!!h th.I!J.l m.tlh t •pf" ,.,,~~;

~~Jr0\!' 1'~

l ml f• .1\l!\ .IN" d1.d t:! ltJh,h (Fig. I II ), whidt p:~\...,lhluugh u.·nth~... ,1l t'Jlr'l"'lh! !!t l~~'

•

f •

11 = 1~1)'

Fix. 1.9 ..a-rufd ftxts of syuuudr:o

Fi~.

I. HI

V I~H j.fold u'\c~

.-.r . .,numetr~·

. Y F i~. Ll J

2Auld

---- -- ~

m ;t\.(-~

ur ..ynlllwrry

2. J"l:mc:~ uf symmdry lltlu.• cn~l!l l i .. ~o:utlnu I\\U h:.Jv('s hy tt plan~ ~u 1hn1 unt.: hall ht."'-nnll'' 'ht: milror

11111Jl!l: t\l th~ ._-,ther h:1lf. ~h~n th:Jt pl:me 11- c:1lkd pltmt• ••l l\'"'''" tn For c:uhi' lhCI< al'c 9 pl.mt'' IJf .,ynunclry

"') .,(l'UI.

111 3

l,l,tn~.· ..

r:..r;lltt•l t<• the faces of llle -:ubt.:'

lf-'1~.

I 12).

t li 1 h t.h.t~chm1 pl.tllt.:\ p<~'t:-.ing 1hroul_!h Lliu~onall) uppu:-.Hc p:smlld cJgl'\ !1 1~ I 111

l. Ctnu·c (If symmetry II '' ·• fl'll l llt 111 01 ~ry... IJI ...uch tlmt if h li l~t' ,.., t.lnw.n l mm .my J'kllflt ••nlhccrv~wl lllnlU;!h 1ln·· puinl oud produces C()ual c.Jt,lnn'-'1>!: on lht< other 'Ilk ol lhi" u:ntrnl J>tlllll. 1hcn it meet" .en 1Jcmicnl point. Feu t.uhi~..- 'Y'tcm th\."l't! ' ' uuc n·ntrc u( '~ mnu.•1ry 1 1 · 1 ~

I 1-1 ,

• Fie. I. U

1.11 t ,,.

ft-dia~flnul

plant· of synundr)

Courdinalr.'> of Lallice Point I he

t.·ounli mtW~

'Y~tc nl'·· 3 1'C

•'f

Ihe corner

co. o. m Any

l: tll kt.~ pt_1Hit:-. f(1r

S C.. tJ (' C J lh.l l...:.l,,',C,

on~

o f lhC:\\• li'H.)r'di n:th:!o (.OIU ht: wk~n .,,. oflgln \\~c.-,l.l mt; w thai ori;un. Lh\! cunrdinoue~ nl oth~ t l.uticc p~lllth .u.: dt:lt:rmnlci.l 1Fir 1. 15). Ib) Rud) ~ccnm.:d latlln~ point in B.C.C 'YMCIH havin~ l:U,,tdln;Uc'\ 1-!-. !1'1~ I l (iJ,

Jr.+ J

- - -

rt:)

Facc..cemn.:d lttttirt: points in f7.C.C. :-.ystem hnvtng coordmatc-s t ~-.

Ill.

H·J. and r-t.O.-lllf'ig

1.1 7).

!· H).

• (I

/ Fig.

!11, II,

til Ill I

---·

.' "'

I . J~

f-ig. 1.16 CCJordiuah.'.S or bttd)•C\.'IItrt:d hllll« points

('onrdfnnh·•qof Cflrncr lnuf«

twlnt-.

1.9

Numhcr of Aloms/Molcl·ulcs per Unit Cell .H'''~~'"

Per oni1 cdl number ul

cryst!tl di!H.'rnunc'- how ~ln,~o·l}

( 11) 111 i.'h:Uh.:nl!\1 or mu11ll...·r ~·f nwlt!cule, 111 iotHt,; lhc p;,1rt1culur i:oVhd 1'- packed up

1. S.C. Cn•\WJ lu SL ll)'l~llhe!rl!

nrc 8 U~\lll1'. nul.!' nt c..u.:h ~.:urni!r. Eu~h corner t1Htm j.,. .. h,ared b) X uml.:clb. Th~rcfrn c. lhc loUtlnumht.·l ul at01lh

•

peruni1 cell NJR=IVS= 111'1~- l IN). Cn·.<r<~l: ln II.C.C <ry>l:ll. thCI'C i~ one atom :11 th..: ~t; 1 11rc ~t n(l S

2. n.C.C.

atom~ 01 ~ eorners. Ea<"h

t:Orncr ai~Hn

is shared h)' K unn ~.dJ, s~• thl" wwt

number of :uom' per unu 10 hg. I 19.

.,:~._•II

\\ 1JI ~~

.t.'- ,.hown

N;1 + N1 /'A -= 1 + I =- ~ In

huH(' t'l'_l HnJ, tnt tl(' l

('('11/tnitoll~

J'lum/(/ he nj

mul lunb· \'llmt• l\'f'l'

Fig. 1.17

Coordinnu:s or ra ..·t-C(lntn. d l.u1tke points

Jn EC (_' ITY'Ull, Ihen: .are 8 ulom!\ a1 ~ com t:l'\_AI tht! ..:cnuc t1f (l f:tc\!!\ then.~ 3n: ;mnl hcr tl :uum ... Each corner ::ttnm iJ.. 'hn r~d hy R uni1 ct:1h.

J . 1-:CC. Cr;. WJf

Fig. 1.1& Numfx:r or atoms/ onh ct•ll in S.C.

fill. 1.1.9 Numbt r o r AIOm$/unil edt In U.C.!;.

Cr.uw/logruplr,\' ami Cr"uof hnt'erfection

~~~~ ,,,·h of rhe h file< ccmrcJ aroOIS i• shared by 2 unit cell~. Hence. rhc tor:tl number of arom, per unit cell for F.C.C. Is equal to (Fig. 1.20).

N1 1'1. + N,-1'1

=8/S + 6f2 = I + 3: ~

\\hen: Nr i-.. 11u: number of comer uturn~. Na I he number of body·ccmrcd atoms •111 (1 NF the number of fnce-ccntrec.l ;uoms. Jn iouir • n\tul, cm·nrr mrd fm.:c••t'l'll/rt'fl ums .riJUuld b~· OJ t!J~ Sllmr 1\'(J~. So In N;u:l e-n 't.'l whu:h 1!1 F.C (' all com er:-. and face cemred 10n~ ~u·t: Ncr' CFig.

I 201 whCJ:e," Ill bdw~en 1\\'0 Nil' there wrll be ODC Elich IN,,) whreh ;Ire 1hc mJtldlc ,,r 12 cdscs (i.e. Nn = 12) of the unit cell is sharod by·I uuit

>~lllate<l :u

cdh as ..:lenr ll\mt Fr,t: I

:w. where as one Cl

1on

t J.e. Nit=- I ) as

fll

the ccmrc

uf rhc "'"' .:.-11 Hence totul number of NaCI molecules per un11 cell will be (N1 / 8 +Nr12)N_,. + ( N,/4 +N8) 0 . = (8/8 +612).v,,• + (12/~ +I >..., = (-1>,1... + i·llr1 =HI N~d n>olecult.• Hen<:l.', 1h.;- numhcrol tHom:- or mokctl1C..'i per unn cell is ~. which is higbtcst '"F.C C" cry<talo e. FCC cry>Jal i:< more closely packed than O.C.C . •md S.C

1.10

Coordination Number

In 1h~ cry,tJII inc C..(Jhd cuc::h awm or io n I) surrounded by 11thcr :lloms or ion\. Th~ nurn~r Ul

l'4uidi!<ll:tnt nc.arc~1 m.·ighbour or the sam!! type lhllt an ulom nr inn hll ~ tn ,, g•''cn 'tnltturc is enlied <'ncmlilwtltmmunhrr. whkh will be daffcrcnt

foe th rret~ nl

~ trucaurcs.

Ji1g. 1.20

~umber of :tlomS M'

mnlecuJes pt'r unit t'"t'll in F.C.C.

I. For S C •·nsrul r.oonfimmnn 'wmber u. 6 (Fig. 1. 18). ThL" comer ::uoms are lh"' ncarcl>l nc.:•ghbour~ of each other and connected wnh S unit cells. llencc. c:H:h comer :uam b:1.s 4 nearest ne1ghbours 1n the same phme. Olll."! Vl.l'rtacally ubove and t•nc vcrllcaJiy belo\\ Hrl'r' unJt'r,\ 1 n~1ghbour tliMcm rt! '' " · 2 . For R C.(" t' f}'Jta/ cmmlmmwn mmtbl!r IS 8 (Fig. I 19), Here for any corner atom 1hc n~.·:trc~t ne1ghbours arc 1hc body c;entred atoms. Sinee there: ,;ue eigh1 >tJrroundfng un1\ cells for any corner atom M<l c~ch of them have o body ecntred otom. so the coordinnlioo number for any comer nrom is 8. Similarly the cen t r~ i.1tu m 13. surroul'de;d by 8 comer utom.Jt so coordination number for ce.mre :'11om i." .1. ~

1-1.-- ...... - .., ....:..,&.a.. ...... .1:~..........

••

17---:n

_, Fur I (._ C en \lol (HotduiiiHan m1mlwr '" 12 (Fig. 1.20) llt!r..- 1hc ltC"tu'C''I Uctghhuuro. uf :ua~ l.'l!tU~f .UUin .tfl! f;u:,• \.\'1111't.:d .lt011h ~•f the \llfiUttnllmp unit c.,:olb. For un~ l.'OI'IH~r .tH•rn th~t,•nn.• 4 l n~:,·•t-'!.'lltrc,t nc:~rL..,t nc•t!hhuur Ul it' "''u pl;m~o: -l 111 ,, pl.uh: ,,h,)\i.' 1t. oll1\l 4 Ill ,J lli.Hh.: ~luw 11. lll'li' lll'flit'.\1 th tgM•t'tll th Hllllc'r

J.ll

'''"~

Atomk Radius (rJ

lu ~akuhlltng .tiPtnil l~nliu .... H '' .t,,Uml'J th..tl thl! .ttum' a rl! 'Jlh('fC' .tml .tit.' in ,·.,nt.•<t with <t~th mhor tn u <I;'Mul I h< .U<IInl< r~~tliu' i• d~liu<d "' ·J,/Jt/w r/i \lmtr ,·lwtu-('t'll t/w llt'lll1' \l m•t-:,Mumn ;, u f"ll\tu/ o(purr r/,•mf'ttl ' nh· .ltOIHh:

rm.hu"' t j.., nh\\'>.., C\Jln:\~1.1 rn

h.'r!lh nl

t.; Uh.:

t.:tli!~ 11

I. S.C rl'\ Hal: Tile frmll \ i-:\\ ol.) S.( .. ry ... t\111~ ~hown ln Fi}!. I 2 1. t ln.:rt: ~Ill' S :unm~ ...hu:ucd :u S t:om,;o. In S.C nyM.tl. Cl.,rner .tlOUi' urc Ill<.' m::.uc'l nc1ghtmur oll.!uch tltt~~.:r. ~\•lh~ 'um~r ,,toms" 111 N in w uch with each tllht:r 11 u i' the ,jl.lc ''' Llll' un11 .:d l ,wd 1 lh~: r.uiJtt., olthc.• lltt..un, tlwu ftnnl rig 1.::! I

:!.1 = (/

t -=- o/1]

1 IJ CC CnMal' In 11 C.t u)'!lllll .;~.1n11.'1 .lhllll 11Hd hod} ,:cntr~d .tll1111 \\I ll ~ m tOth:h. hc.::tu~c 1h~o.·~ .tr't' the n.:;u.:'f ndghl'Mm1 \tumic mdiu~ r t.;•;.m l"k· cakul;ttc'"l lur I he B C C' Cr) ... tal tnth ..· fHihmiuF \\ :1} ' 1.1.'1 11:- t:ntl'-Jdcr h~ 1.!2. wh~1 ..:0

1 F.C.C CnM"I: In F.C.C cl);;;tal comcrntom and tac.:-centn;d atnrn \\Ill hem touch. bccau ~c they (W"C the nearest neighbour. i\tom1c r:tthU)Io rt:tm he cah:ulntcti for :an F.C.C cry,.rul n~ lollfl\\o":~t:

/" /J

I /\

'" l

" ,, anrnic r:.ulit•" rnr H.C.c.

I'if.:. r .!!

t'nn ... ulcr F1~ I 1J. \\ hon: flllJr' :

Neau::o-l lh!1.g.hbu111 l.ihl.ll",:e 111 I (' (

uwr

wn'

'' .!r - aJ":!

Fi~.

!.12

Packing

l.l-1

Densit~

tmnit rudiu. . for

r:.c.c.

or Atomic: Packing Factor

In rhe \ludy of t'T)''U'I Mru.:lurl!, one nt the 1mpon:mt concept.~ a~ pn.ck1rlg cfficrl.'n4,'\o c1f ••rnm~ nr 11.111 .. 111 ,II.!T) .. t;tl H1ghcr p.:..lc kmg dn~umcy pto\'adc~ crCiclem pa..:lt.•n~ of nmm~ 111 .;ofah._llh.' concept of po\eh..ml! ,., undcr:o~tOlKI b) 01 paramctl·r hJHm:n Ol\ ·•tomic flOtt l-.ing lncttJr oflht· &:rysml PnrJ.inJ.: dt·1~.nn• ormomit porkmg /ltl'tm n rlrfinetl u,, tlw mtm of rJw \'ulum~ m t·utm•tl hy tlw tltom.\ fJrr mut rr/1 to thr

total ,.,,/w,r ot sll,- un•t f<"ll

;\.P,P.

Volun1e occupu.--<1 by rhc arom:,. in rhc un.ir cell _ ~~~-lfr ~ c

.••

r.t..

·•

I 1'1 I.

S.C.

"'=

Vt)lllrlh! t'IC:<!Uf)U;tl by th.: 1011'- Ill l hC UIHI

ct:ll

Volu111c of fhl.! uuH '-·ell

Cr~•t:d

Nt•

Clr olh.'111'1Unlt \!ell :. I

Volum\' nf tml" ~:llum ; ..JIJ m ~ 5u.lc uf lht: 'J IIit ~.-dl =a :!.r \ 'ulum(.' nf lh\!' unit cell 11; rhu<. pa~klnJ! ti<n<lll'

= =

4/.l Jrt \ A P.F. : -'-':....,.,, 1

- tr / 6

IU .C. Cr)<ml l'\umhcr o l awm~umt I.!CIJ : 2 \'t'lum~ uf h\t... mom~= 2 ~/3 trr' :\a.f\' of unnt.~dl: a = -'rl .. 3 V(llum~ n1 unit c~.•JI =-a'

I kn«. p.tet1ng Jcnsuy A P.l' •

:! 4f"!.nr' <I

1-'.C.(..". crptul Nn t 11 ;ttnmVunh cdl :: 4 \uhmu:. of tuur :nom'= -4

\td..- ••I

unu~.·~.·ll

40 rrr' :- ,, - 4r/ .., 2

\uhunc nf unll \.:11:. , 1 Sn, P·•'-Jr..iug d~:rhH)

4 4/3 r.r' A.P.F =

CnM.•l ~c

, !Jr (4ri,/'iJ' = {, -

Cttvrt!tnu1uut

Ah:tnllt.

NH. ICNI

R:uhU!i (rl

,\t;'ln"'

()1:1

·\P~

Un11 Cdl (JJ)

nee

\ 'J.n/4

EC.C

.fiut4

nih ~

\·3 r. IS 2111'~

1.13 Cakulalion of Lllttice Constant M Crystal Dcn-:ity In the.: ..:M\! tH cubic 'ry:->tnl, lnU1CC constant IS''· It lJ 1!<. under cnnsldcr;shon. then VoJumc of 1hc umt cell

th~

dcnsuy ~,_,t

th~ Cl'}'!<~tul

= tl t II I I

Furl her. 1f there arc 11 number nf nwlcc uJc, or a to m' (lattice J)tlinl:-.1 per unit cell. M Mol "t and N A\'Ogildro nurnh<r !No. t>f molvgm mnlc uf >ulx10nce) then }1·1a:t~ \tf em;h M ~t.'~ ln

nwl ; MIN

cuch uni1 cell -

MIN

Fro Ill (I 11 and ( 1.2) we get

Dtr'

II .

MIN

tr'

(llft///1.-{1/

0 = nMINa' u :; Num~r or atoms or mollonu c~ll. M :::- MuL "1 or AlOnlic WI ., N .:s: A\'~)~Ud ro number = 6.013 x I 0~ No. ol mohJgm molo; = 6.02~ x I No ul rm~bl\g mPis

1.14 Miller Indices 1lh: l'fy•anl -.truclHI'U mny hoc: n!l:nnrc,l u.. tnm.!~ ur ''' .m u.:l:fc,galc uf n -..ct r,f /"ttlrtJI/d nJttith'\'Umt plniit'\ fU"''"S rluWH!h wIt 11\t om lmucr 1milrt t~r u mmrlwr nflmnet• tmmt,\, ., hit'II nrr t.nrtwll H\ "lmrit•t-fl/tm,.," for a pi,·~n Ny-..Jul. l:tuh:c plam"> cuu l>c chosen in dtffcrem way,, e.g .. lui. lhl. I c) 'hvwn In rig. 1.24 .

•,

•

(ll !

•

ld!

rig. 1.24

m rrerenl laiiiCt'

J)lune~o.

In utc.lcr lt.t clcsignutc J hHtice pl;:me sci~.:nutkaiL_), Milkr J c\clopct.l u mcthud l>y throe numbers (/lk{J. whkh arc IJlown 'L' '"M11/er md"·t'l'' Thi~ mclholl j, """ er<all~ cmpl(>yed Miller Inti ices can 1>e <lclinctl in the f<~Howing ""Y ··t.trlh·r lm/ltes.. tJI't' rht tltl't't' Jlllil llr.u fkh:.t/Jit• mlt'xt''' I;. /.4 /, wJnr-11 hm•t•

tJ/ ;,lto'l"t!ph L'f tht+ nmL'r!nh,·ti plm11·. m1 the MJIIl!r indicc .. for a panJcular t:ry~wJ plo.tnc l.lfe det~nmncd ln the

lltt samr ratlos w th~ rtcipn.>t:all thrt!~ tUt1 J, The

loJiowing way l l ) F•rst. detennlnc dlc intercept> of the plono un U1c three coonlintotc nxe~ say p, q, 1 , 12) ScconJ. toke lhc rccipro.:al< of ll1csc numbc"' wul by taking LC.M.

rc:duu.· tht:m to the i.fll.tJic,t three integer\ J.~ h. k. I. ~uch tluu It A I= l 1 ! Jl ,, , The 1\::..ult 1fi. then l!Jh lo...cil m p:trcmh~.:o.C $ 3~ thJ./}. (1) Th~n th.: cun.....-rm:-tl p1anc ts c;sllcd tn ha-..·c the ~·tilln tnili"c' Ch!IJ A' au i.'Aamph: lt11 .1 plane whusc lntcrccpl' an.· 2. 1, J .-t~m,; ' .uw' lh1.• ll!l lprttt.•ul ... an~ Ill I /~ 1/.t llcucc. oiCCC1rding 10 th~ dcllnl1tfii1Hf ~fl l kr hhlh'l'"

•1

1.15

I : 111

1/1

1/~

= !1

Different Crystal !'lanes with Mille•· lndic"s

ntc Mtlkr tndt~C~ tltJ./t ..J~I\Oh! lJ '-Ingle plane t'r tl ~Ct c.lf JUr:tii ..·J rlan~ ... It·'

rtlune t.Ul' dO \1\1., (m the OCi!all\ ~ ,UJI.: uf Ihe 0ri1;111, I hi; n\tr.:,f)Wiihng I nell:\ Will then be nc,g-ali\ C. ~' mUicutctl by pltlciug o bar <~bove thou tn<kx. e.g.. Chi._-,) ~Iiiier lndk\.''- foJ o.i\ J~t..:t.'' u( n •l.,ic ny.<rnl !tf'C $hOWIJ in 1F1~ I ~'i(:J)t· IKGI·tiiMIJ. r DHG (010). ABCD (001!. " .r.t " lij!ln .u E.

ADIIL I IIMI 1, -\U rt; t i!Tl!) , l:IIGF COOt I

\\ .rt ·111~111 .tt

rtww \1.\ pl:tlll''- .lh' ~·ttttl\':ll~tu 11) ~ymmc try. whkh ttlgciJtN Jh.' th.:onuteLI h} ·urly hr.Jclch amunJ /.hiler lndtcc; ns 1100). Hgure I ~~ thl and 1<1 <hm" plane' "I \I iiier lnJ,_,., IIUI!nnd 11 11), r<!>pcoh\'cl)

/1 II

ill.iflll

f •

,,,

,, .~.

• ICJ f'i~. 1.!.~

!ol HCG Fplone: (1001 Mlllerlodl<es. (b)ADGF plano: ! IIIII Mill•rindirc.<. 1"'' Al ii' plune: f lil t Miller indit·e..~>

h 1, 111\('Wlrtunt 10 nt1h.• 111.11 p:ar.tllcl plunc' whtrh au~ cry\tallngrnphu.:oall~ c:qut,al.:ut h.t~o·c ldenucul Mtll~r mdJcc\, 1 r tlUU) as e4LH\.:•Icnt u, rU.lU1. 1J 111 0 ~·!lli'..tl~·ut tu f~:!.:!t f I lUll\ cqua\";tlcnt tu (.!.!0) .l~ 'ht.l\\n m h~ I

:u,

l{~tl+

IIJICI

! ...

[; ,I

• ,,,!.,.,., ,,

: ,;f:\~

: ! .. '.!..

'"'

••

;:: I

•' f. f.(, l.lloi

ro~t f>lrTt'nnt tHHH Miller pl~u)t'JII, fh l l>int'l"l'hl Ill Hi \llllt'r- pl.ut~. 1d Ulrr,·n nl t lll ) MiH.:r- l)hmr' 1

Fumtt'frl

r>t1t" tht-!uii1'"HI~ MtJJcrphtrh..'' CU.1(1~1),fhJ ti~~J.ft:IIIIU!,

Ill ~ltll<t plun.· "I 1211 lntC'h.:t:ph tLr.:

I t/~. l

I kn,c. the plane ALIC h 1121) ptnne ti-lg. 1.27t.I)J 1~1 Mill« plolll< Is 112.!1 ln~<••cpt'""' I. l/1.

Tim

1121

the rt•n• i\ISC " t 1221 pl.m~ (lop 1 . 171~11.

PI Mi ller pl11nc ;, 1TIUJ hll<t«p" 4t< 1- I. I ...,

Tit<1clun.-. ohc pi"'"' ABO> " lliOI pl•nc (Fig I ~71<~1

£.wmplt- 2 Or..tw lhe t.hlf~:rcnt ( I I I' phtn~'

lhc

11111 1

t.:t!ll uf ' ""J,IC ..!ubi..;c

'Y~lcm

't}l"l~f11

l<igure L.l? (d ) Show!<. lhl! unit tciJ nJ tbl! \implc {'uhic plull<' ar< AFII. CFII. ACH. ACF

: c ):---------, \

111C

rt'Hif (

Ill)

·~·

(.lj

•

II'-'...

~~· " -.

~..it·£_( -

••

•

--.... '

' (\h

(<I

l·'iJ:. 1.17 I:•J AJU: plimt': ( 121) ;-.untr lndkb. fb t Auc· plune: ( Jl2 l Milf~·r indic,-s. tct A.BCO Jlhmt>: ( J ill)

1.1 6

~tiller

indiri:'.s. 1d1 Four I IIJ ) t>lunc inn

cubt.~

Diredinn of a Une (Luttice Vector)

or tl Ime in ~pace cnn be 11l1CCifteJ ~Jtl!<o.lactnrtly hy gtvmg thl." -.:<•urdinah..'\ thrnn_gh \\ lucll cad1 lhtt: J><:tS:'\l'' 1 h..: \qu;m: hnLckca-. ilft.! u~u>~l ly u_,cd to am.lJ ... .tl.t ..t1lin:claon. For t:uhic 5}'\h:m ttol tH.Llto the plant.· \\'!lu~ Millt.·t mdicc~> {hJ..I) I' the fhrc~uon III HI 11tc: d ucrtinrt\ f lt '.IM41U~ hnes of Fig 1.18 nrt" !'II. lnllml ·· Darc~11nn

OA =I IIIII

()R = IIIKII

ClFl = 111101

00 = It· II or II llJ QE: 11.0, t l or IZUI I

DC= II III

!·

OP: 1{- ~-IJ or( l 231 OG:I IClll OH

=I l· t . + I or 11211

l'ic. 1.28

llirt<clicm or u linr

I'RO('EI)lJI<.£ TO f1NO OUT T il£ ~ILLLER.OIRECTION (hkl) (SA) FOR J,.Xi\Ml'LE [ 1211):·· S tep 1. flivid<' oil thr.:c int.:gcr> h. ~. I b) the highest number (SO) l. J Step 2. Su it w111 be lvk. IJl.. Ill. 1.c h/l. IJl. · 111. = h: I.· I ( <Jl.

f:~

±=1.1 . I)

Seep 3 . flraw thrtc Jllunc> u~ >htl\\'ll in the Fig. ( 1.28) at hlk. kll. & Ill.

( C£. at~·

t- ! )

·~ 1hJ IXltU1 wlh~rc chose 1luc-: p1nnc!' '"ill 1n1~rsctt Ju:n d h wuh ong1n !01. then 1llH 1 \\Ill be the Mdlcr·dirccuon [h l ll. leg [ 121 [)

Sh.·p "'· No'' HH

/Ill I dt'rectitm am bt aLffl dont b)' an oasy method in Lite fallowing way: s eep I. Divide "llthr<e imcger> h. k. I hy the hr ghc~t number (Say l.J Step 2. So it will he blk. 1./1(, 1/k. i c ., hlk: k/k: Ilk= h: k: I S h'p 3. From origin 101 g<> a di"nnce (hlkl (i.e.

from thou

ptll!ll (it ~

t o .1

d1'tm1~t' (~/~)

~c) i~

the pniru ..., hit•h ''':lOll'!

fi(

along >·:rxi' (<>y 0 a),

(t.c I) ohm,g

frnm tbt~l p<mtt ( bt ~l• tu a tlbtam.·c (1/k) ( thea

Y~:•:(i~ t 'i<~y

.; h)

a.c.-} ),lh.lll~ Z-.L\h. (~;,ty b e ).

j'l(Jillt fH)

~~.s discu~.cocd e~u'LH!J

Seep 4. !Inn fO H 1 whtt h is tll~ Miller dir~uon lh k 11. (C£. 112111 Say fo1 ;mother example nf the Miller-direction II 2 3 1~ 1/3 : 2/J : I = I : 2: J. >o go 113 olong X. 213 alon~ Y und I !dong Z. You will rcuch Co the point (P). l o1n (I') with ongin (0). Then (OP) is the II 2 3 1 direction. Some point (Pl will come by 1hc 1" mcthW ;,Iso. as shown in the Fig. 1.28.

1.17 lnterplanner Distance ·n1c ''lntt·lpfttmu•r Spl'<'IIIJ; or dl.tltut<'t' '' 1.. tltt• (lt'Tf'<'llllu·ulr)r tltJftlllt'(' il;., 1 h<•tl~'l'tm ~"""''Jtmmlim: (lu.{J plmu~s. '''hich t.m he \:\lmputctl h~· t •• ~tn.L' the Hl'lll.'loll t.'<I'IC J~ folio''~· It b abo the perpcndicul.tr dbtunt:~ rmm L•ri!!m h• thoi wt ul paralle-l rhmc~ (ltJ.II Let u~ COO:\idcr Fig [.~9 whe-re th~ pbth." ABC (11 a cuhtc ..·ry,t:'l bt·h,ng' to 11 fttmlly of pl:tocs ''hu...~· Mtller tndJcts .1rc fl1klt Let the pl~lp\!'IHii~·ul.u ON h~.• tlra\\ n from onJ;n'l It~ Ul~ plunc t\JJ('

tlu•

"' •

•• ' I

Leo U' >UpjlOSC ON onnkcs ""angle IX', {f.t (hg>. 1.29 :ond I.JUl. woth X, r. lnlcrc.epb nr plunc ABC\\ bo:-.c l\1•llcr Jndicc...' arc fIt~/)

otXC:-o. fC"J)l:thVtly. 'Tht

~~n 1he:-.c ti,\C:\

M<'

OA =olio. 08 \Vh.:r~

o -=

l.:nu~c

= u/A . OC = all

corumm.

Ntm , lnuu Fit; 1.2CJ. co~

u' = ON/OA . coo {l' ~ ONIIJB.

cO>

= tJNIOC

( 15J

I tH.: i.JI,tance ON rc:prescnL~ the 1ntcrplanncr ~padn}! d1,1 t11 L.hc 1amal)' or plonc:. chl.h Sn Jcllln 1 lA) anJ ( I 51. we- gel •

_J -

4.;0:0. f.C -

JL (:0), . p· -- ..!.L /''·.

II • ar

al\

-./ -- .!L II

CO!\ l

( 1.(1)

... 0. N

11 •. 'I

-! · fl~.

1llc: hill' ON lll:tl..e-'

1.30 EniA!"Atd ' 't:rsion ()f t-ltt. J.l!l

Jfl

::m~h:

ct.JJ'.

rON I'= !dl·

~I-=

r \\

llll X. ) . L J:Xl'\. r~'iopt:CU\el) . .Sn

= (t- +

,.r,-J... - <.'os-.. fl. , 1 ,,... c, •.., ' {J • + ,J ·' -.:n:..

cos1 a·+ co~! If+ ..::o:': y'

Su.

Sub:-1HUIIO)! the values ot cos~

!1.71

,.- , -,

( 1.~ I

= I

I LlJl

a. CO$: /1' .IOd \:.0; y· lnml ( 1.6), \\'e get

(t/lr/(1) 1 + (t141o)2 .: ~d/1111~ e

...

<llt!+A'+I"I=I

( 1.1 Ill

Tlu!t '' tht.• ~Xfln!:..!'ttOn lor intcrplnnnct ~pactn~ 111 1crm .. ,lf l.tllu.:c con,l.ult tl uml M1llcr m,lu·c, lt. /.. and l

I. II! lnterplanner Spacing for Cubit Sy~tcm I.

S.C. Cry>tal

(IIJ

(iii)

Jilt!=

..[/;! +k:

+I'

" + /2 ''Ill ; ,IJ,z +.<l

= uJ/2 = tJJJ3

Enxmeermx

Ph_,, ,.,c~

So. lc/ 1,. 1 :

tlmu

r/110 ; 111 1; I : ll ..f2 . II , l = I : (1.71 . 0.53

I tluu

1 J t/11•1

= I :, 2

, l

Jo'.C.C. Cry,llll

Th~ ( I C)O), ( II 0) !.inti (Il l )

pl:lllr.!S lor F.C:.<. I. ttl u•c :111! ~h ft WII in Figs. I ll f tl. h. c)

LJuc Ill U•• prc;cn~c <>I c<tulnti!C~ pOint (II\ ~~~h rae.: o f F.C,C. ~rysr..lthcre will hc 'omc ut.ldtllonal plum:' tn uddltmn lLt the unginu.l phanC"'\ in S.C. cry.:.lnl (i) 1100) Plune: In FCC U)>lill ! Fig. l.ll.,) it ;, doJr that an :ulditiun:ll t 100) pl.mc urises hulf~ '.\'il) bC"L\n•cn twu t lfiHt pLtne~. ~11lese plane' pa-..:: lhrou~h the cerun.::. of the frc.mt an!J h>t~o'k t:&\:'e ... Nu" tht lnt~rplnnner di~lan~c vi n~o'\\ !I 00) pla11c' f.,r F (' C ny't•l ;,

'"'

dill

fig. I.JI t o) i\dditlonnii iiiOI IIS 120111 plant lor F.C.C.. (bJ Additional (IIIli as 12201 plane ror t:c.c.. 1<1 Original (Ill ) pl•n• ror f.C.C..

Cr\'stafloxraplt)· and Cn·.rtal lmp~r(rctiou

""" r1101 : (d100) P.C.C.

(t111.,)

S.C

2.l

=an.

<·"'he

Th•' n<w ( 10(1) pl.mc c•llc~ "' (200) pl>nc w.n ong111 0 (u) c 1101 pliHl\!: 11 i•q,:Jcar fnHn Fig I 31(h) 'hm lhCic ;•rhc .. tm :tddiiiPn:tl '-Cl vf r I I()) pl.mc> p.r.•ll<l lll lh< Firs1 '<1. Tht~c plnnr, c<~m< h<lw.:,·n 1wu JIHli 1,J~ne> Su. lhc hnc'l'l.mncr 'p>cing for nc~~o 1 1101 pl.mc fur FC.C "'l'''·'l j,

""" ''""- itl:_""l i'.C:.C.

(tlowl S.C.= d/2 2

Th~> n~w

1 11\JI plane Cilfl he called ru; (22Q) Plane. w.r.l , Ongin 0 11111 (I l l) Pl.mc: Figaro. 1.3 II c) clearly , hows rhnl in rho oi filii pl11nc

"'"c

m•

n~\.\

pla11c uri'c' t.luc: tu rucc c~nlrcd point So. IJII,I F.C.C: (d"''

S.C.=.,,,..,

Su. 11/J,,., 1/tlnn l/d111IF('o = I :

/ ·~

../'2 ·

,: 112

()

,..

\l.ldlh.,n<JIIIIh

lllUl

'"'

Pbtlt' (<)

d!!.:.

..) g. 1.32 (:l l Addi1ional ( 100) us t 2UO) plane f(Jr B.C.C. , ( h) Orig inul ( JIOJ ptunc for

U.C.C.. (c) Mdilional (lll ) os 12211 plane for ll.C.C.

3. D.C.C. Cr)stal The 1 100). I 1101" '" 111111pl:mcs lhr fl .C:.r. arc ,Jouwn in f'i~'· U1 (a). (b l.lcl Oue 10 un extra luHtet: J>t11111 :H th~~ blxly i.'cntl'c uJ the BJ .C. lf)1"utl. here <~I ~• • '"me c~••·• ttJd111un.al pl.u\1..~ \\Ill ~omc. 111 (I(Xl) f'luu.: Fn1111 l11;. 1.3~(.11. 11 "LicJI ch.11 ''" Jtltllll\111.11 riOOJ l'l.mc .lri"-C'

lmll\\.ty

bcl\\t.!Cil I\\U I

WOJ rl .uti!:!l. H1 u

c.c

s ...,,

nu-. Ol'\\ t ltiOJ plane J.:.m he l"JIIcJ ··~ llOU} pi:.Ull.' w_r.l. ongm (') UU (tl 1,,.d 1-'lmrr• hum Fag.. I .\1chJ. 11 '"'~lear tlmt nu 1.!:\lr;t I li th pl:uu.•

"'""hie lt•r ll (' ('

s...

tiiiJ till) Pltmr: l'rnm Fi~ l.l21CJ. 11 ' ' .:!tar lh:u ' "' ~.C.(' .. n<ldiu"""' f I l l) plnnc!i un-.c muiWiJ) hl:t\\l''('IJ I\\ {I {I J I J pi.IDC'>. n u.. new ( I l l . phlnl" \,:lUI he called .t:i •1~• p l.&iOC \\,rt ongm 0

lienee

1.19

Important Featu res nf l\liller lndices

l h\! tmpmlimt IU)

lcatun~s

ul Mllh:r nuh\:\: ... p;utu::nhlrly for the cub1c

sy~tcm

ar..:

r\11 equn ll~ >raced pnrolkl pl.•n<> hnve 1h ~ <nmc mde~ numh~r 11•411

tb) .-\plum.· par<~ lid In un(' ut the.· .:non.hn;al\" UM.• , ha>~. :m mtcrccpt ol 1nl 1nth and .Mllh.:r mi.k-x "d l be ""'n• lw dmt .i.\1,. lC' MBII.!.T IIUJIC('' clo nm d.:fm.: a parlicular pliiOC.' hot :.J. Wl nr p.:lrallcl plunc .. h i> IC ~ ~ nnl) 111~· r.ttm ua th\· uH.IU:\·~ wlm.·h 1::, ofimp~l nitn ~c.:. (-121) pla11C' ace I he ''' 'nc ;1l'o (~ II ) pl~uh.;s. Ic) A pl:mc pa,SIIlf!. ahrough un!ltn i' Jdmcd an tc:rm' l•l u pan1lkl plunc havll\g non-7.t:ro 1mcrl·ep1 (iJ For t·ubic system. nurm~tl H.' the pl:mt.• w1th 1\·llllt:• tn\h~;c' tltUI ''the d1rc~11un

(~)

lltA/1

lmt:1 plan•lcr ,j,'Httll'C ,/ bcp,\.·c.·,:n ndra~nt pl.mt'!\ or n \1.!1 uf pantllel plane' or lhc Mil iCI ln.H~.:c, thHI I!\ gi\L'Il h)

CRYSTAL lt\IPERFEITION An idenl cryslal is or.c m which ~~u..-11 uwm hus '-klinite eqUilibrium loc:u,un m a r~;gu lur arruy. SUL·~ a try~loll 1s \'Cf)' cJifficuJt m c.buun in prnL:IicC. t\11 r.:.tl

tryst:al!t nru in ~HOlt: 1\:'J>crt 1mpcrlt.·c t. A11 Hllll~rtcc.:llon mc:m~ •.my dcvinttnn from perfct:t r~gul.•r lntucc ur ' lrucw rc

1.20

EITcct,; un Crysta l Due to Presence of Imperfection

hnperh:•.: hon nr ,Jef,·~b in the '-I"Y~tal ~tructur'-' nh.:otlb 10b~1ng JliOm">, ato nh t1UI o t pi:Kc. ltTcgu l,arilics 1n the 'P•tdn)! ,,f ff'"' nl .unm~. prc\l'Jlt:c uf impunltc,, etc .• whu:h h.t\l! a a.;,•n-.lt.kr.lhll- d lt:-(t upon tlu: ph~''ILJI prorxnk.' u f the Cl)''taJ

A number unJ~'nant prnpcrue, uf \(!lid, illl' ~nmrolled far mor~ b} 1he nu1ure ot the lnlJXrfectton~ ' han b} lh\: nu1urc ot llu: hi'"-' ltltllce. wh1ch rnay be onb• t.1 vchtck for lhl" in1p~i ft.'\:llon 11l.,. l••llm\'tl)g. .m: llllJMtrl;Jill eff~cl.$ nu ny..tal du~.· to th~ prc.scm:c uf i lllpl!lfl't::IWII'-o 1. Conc.lucth ity o l utril hiC ~flll •conducW f'. m:1y hi? dictated cnurely t>y lhl! 1mcc dntount o1 c.ht!rniCal 1mput11•c-.. :ts n or r ·typr scmt-com.Jucl•''II'S, 2 Colour u( the t'J')'WI tun<' .Ju~ tu llllll'Crlcctinn \, Mcch~mk~l ~·nd pl:t . . tlc pwpcnico; uf ..otid!<o arc u~u>&ll) cuntrollcU b~ tli.SICX:all(ln. 0. ' J)CdaJ I) J>c! Of 1n1p<.!ffOCiillll. -l DtiTusion thmupt "OH~~ rnu~ b.: ~cc~J~ratctJ en()rmously by tht: prc~cnt:~ n1 nnpuri1ie~.

5. Lurnmc.M·coc-c orlhc Cl~''·•l•:o. nc:•rh oiiWliY' .._urUl t~Ch:d wtth the: prc,cn~.:c uf impuritiCf.. (l. I mperfection' !1-hm\ s murJ...l'tl mnuencc on and on h ys.tel'1~1$

l'l~cLm.·nl. th~rmul

conducuun

7. lmpc:tfet:t•Ou t l\ .o;;llll~ L"n'C' ptoduc.c' 'u~ututt' propcnu!' like mtn:~t\.l' tn ltanlu~"' and 'trengd1.

1.21

Cau~cs

1Jnp4;nec1 h)U' 10

of lmperfeo.:tions in Crystals :t cry~ t :JI

.m'c' Ju~,.· tu folluwulp n.:a,ons:

l. Thcnnal ., ibrationo; 10 ot. cry~tuJ .11 ht}!h tcmpc r.llurc 2. ParhclC' rod1a110n in a nudcar dctc-cit."'r. 3. Arufidal doping ol impurfl t.._~, "" Ph1Mic c:lt:formati :m . 5. Dunng s.rowth b. By l!Ucnchmg. 7 By <cvcrc Jclom1~11nn !h~mmering. roUing. e1c L

1.22

Different Types of Cr) stat Defe(ts

1.22.1

Poinl Derecl

Tilt; :timplcsll)' f'~ or irnpcrh:l uon

gcnc:mllr

or lh~ following l)'pc~.

(U) Vacancy

Ill·' solid 1!\ thl' p~llnl ddecl. Puilll defect~ ttf~ ( b) lnocmilial ( i.J) lnt~r~Htial tmpurittes

m Fr,·nkcl dcf"cl

The first tour l)'J>c!S of dd~ct~ uccur in demcnt:tl cryMitl!-. " 'hcl\.':h tlltt l:tf. t

l'-"u

L)'JX::~ l'ICcur

in tomt: \ry~tab. fa• \·hnttrrJ V;t\.iiOC) '' prnduC"Lcd due to rhc n:mov:tl uf ~u1

othlm fmm II\ puMthm m the l;ttlu:c • Fi~ l.:\3a • C!.!naln :.unuum of t!ne•g) '" rcqum:·J h l h1c.a~ tlw hHtH.I t111tJ '"' Ire~: 1hc :thnn l'rwn il~ po~i1lcn1. Usu:ally. che~ 1, .1 reductwn m

the.~ ...trcngth

of Pnndm.g_ .uound th~ vacnnc) region~ In ~l.! n.:ral lh" l;•tlict: tlo!uds thi! n:gmn nt vm.·.anc) whkh c;ausc..-.. dl::o•lt •r11nn in ths: l ot111t."i: l"o L:tc;nc ':u:.lnC) lht: en erg~ rel(uired 1~ nf the (lrdcr 11f 1-2. c\'. whh:h •.Ctur' m

coll:ap~c ..~round

all el~mental Cl) ''al~ Q' a re;ull ollhemml exci1a11on and mrre~o;e, wnh 1nrr~:L'c m lcmpt•r.tturc:

1 ht fLHHtvt<d utum docSc nol vanish. II truvch wll•~ 't•rhtce nt the

nut~.· riul.

(h 1lmt•n.wwr Here .til extro :tlom 1s (jued into 1hc ''uu.lt-H:•,,.,.,.. " 1hc n:gul.trl~ occupacd s1dcs m :• crysu!.l {Fag. 1.33b). IllS also ~:r..:ah..'{l b)' lh~nnul agmuu)n Dntl c.tuses di ~h)fiW11 1 1'1lhc l-;.1ll1Ce nnd produces local str:un. Sint:e 111 ~c ncJ.lllh~

••f JIOlll l ~ l.u~c1 th.m th.: void lmo which i1 is littcJ, so the L·oag) rcqum:d uucr'1111al lc.lflllttUon h Iupher 1hnn 1.ha1 of v:.canc:y (orrn:mon «c) SuJ>.,titutumal lmJftnmc•.\: In thiS. n foreign mom IS oc~·up y1 ng u ,,·guhu ~•tc 111 a cry~t~ll lanir: f h g 1..\Jc)

,jzc lm

(t/)

lnlf'ntllmllmtlfttll;n: lien; n lon:•g.n ;UOill Ot 10n OJX'CU(11C' a JllrH.:I! IntO

the w1d between rcgul.u-lv o.;rupic<l silc> in crystal< (Fi~. I 11,h The lun!IJ1n OliUIIIl'all tw fith·J wc!l1f ah '1/C "n.:l~1th•ely ' mull compare•ltu llw L')'ol:lt .JWin ~~) !khouh· lh/at. In wnu: ~rys:tnls. :t. specific type of lmuce ''ttcancy 1:. nflcn culled <t"~ .Sdmttl~ ..tcfcct Thb point unpcrfechon m mmc c• ~ ~l.tb fK'l'Ur' 100 \':tc:.tnt:• I~ 3S!'Oci!ned With 3 po~itivc 10 11 \.tC~U14!\' (Fj~ ll j'l;: «hu-. Olc>eall'ied V:lc::mc)' p31f Of poSitiVe,: :md lh!j_l.aii\'C Wll". J\ L'!n.lpf«!d p:.m ul ' ·'l."~utl) ul "f'Pm·•l.: Mgn b a1~o ptts:c..able '" S\:ht>ll~,. ,lt:ft:'"t. w lu~h nnunt.lln' Lhc lc.•uh. '-".)' .. 1.11 dectrically nC"mral When

ol 01."£DI1\'c

I .J~I!),

fhC l'\il<>h:l\t. It ,1t!inl t]()(CC1 jn :1 CrySl:ll 4)( thl!' type 111at..c, (MI\'olhk !ht: c.h fltc"-JHf1 nl :1WIIl' u1 HJI" v. trh1n 11 e~sily. \Vhcn vac anc tes Jre prc...~m- dutn"'1011

,k.,-u,... b) .ltuupin!! uf •til .u.IJ:ll!ent ntom into the vacancy to lea' c a nc" ,·ac:ml·y hclund. 1t1tu whkh doothcr ;tlum or ion may jump. h 1:, bchc., Cd th;.11 the (Htlplcd patr uf po,uin- unJ ncpali\C io n:. muy c.hO'u:,c !"ttSlCI limn 1\\llulc..,l \'UC&.~th.. h~.'\. In clo!-ety paL'kt•tl xtn1c\urc lF.C.C. and H.C.P.) vacuncie'< and Sch,ltlk~ tlell."~'""

()Cl'ur m,wc: Fo1 mntt ay!>l:t1 numhcrs of ion pnir production

•~

11.11 I "h~·e

N = nu • •I hill tee 'IIC..'

1\ =

Buh/111:111 con\I:Ull

J-. 1 ~

C lh.'IC::• W t:rCI.IlC U pajr uf 10n \'lll'.JilC) iD'oldl' lT~,I.t l l.tllh.l'

r :- lt:tnpcntture in

(f) Fl('lll.t!l df'[f't"J" In IOnic Cf)' S13L a '\pcdfi..; lypc or tnlt'T~ll li.tl ,, .:t~ lkJ Frenkel deJect tn Jnt,! tSIHit11 de(etl. an atom is trunsfc.rn:d irl'nl :1 lamcc '"e to an anterstttinl posiuon. II ere for ionic crystal when u ncg::HI\ ~ inn ''~•cuney t\ us!totmlcd w 11h an udt:tMtl~>\1 f- ve) ion or 3 p<'t~iti\'c ion voc-nncy ~~ J$Suca:ucd

0 0

'"' 0

•

'"'

ED +

+ G

--t I)

I+ I - I

-t Ill

fll~.

1.3J Point ddccts: (») UI~OC') . Cbl intr.rMitiul. (e) sub,.titutiunul irupuriUcs. (d) ini e~iiti;d hnpuritio. lc) SdaoHk) defl•cl. (() fn:n~tl ddl~t.

wath :ln tntcl"\hll:•l (tve) aon chen il ·~ cnllcd Fr&:nkd defc~t tFag. J.33n. It maant:uns Lhc tome cryst:tl clec1rically ncu1ml. Such impcrtcclum '" cn·ntctJ -when !J poSiUVC 01' llCSatiVC ion iS IDOVCd frnm llS normal JatttCl' \I{C tO U ll(:t:trb)' un~rs.wi:.~l po:-.niom. When such type or mtc~tatutl~ arc prc:-.cnt. thffu,,~,n ,x;cur' as they n11grm-: 1hrough che cryswl ,.\'!, \H! would exp.;cl thai d1ffusaon an a :-ohd &')

"'t.rongly tcmpcrnturc dcpendam. H

incrc~L.~es

wnh increase m temperature In

rdau vcly open qruciUre (e.g.. B.C.C.) interSiitinl ond Frenkel defects gcncrully occur. Number of Frenkel dcfccls creauon IS

, = f NN~ l ~ ~...,.;n,.-,·

11 121

N;; Numbn ul lallh:c \ Jh' " V' = Num~t ul H11(t"''llllill :-out.:-.

\\ h..:1t.:

/- =l,!ltl"l!!)' f'-'l fUII'l!d hi r..:tllH\ L" ttn .thUI1 (mm fatt iu! ,jh.: h J .IH IUIC:f'\llli.lf r""1uo,

S HH.'i.' tlu.·

, ... \cry

'"t.' n f 1

h'tii H\ l' l:•tt!l' ,.;ocm t~·mrcd lU (+\'C) ion.lht.• l \'I.' I II HI

HIH.'I'-1111.11

l olf1:

1.22~2 t)i,JcJ<:a tiuu - l.i ru.• l)cfc.:-t 11 '" :1lim: Lh:fc\'t m \\ htt.:h u hnc ''' Jtnm~ 1~ not m proper fl<''Hion 1)1\lt~·.twtn' nrc I incotr ,lfl.l) nl Hh nh \\ ht:l.: '-=uonhnation chnructcriMtc:- dtff~r :.)' '1i.'nl.lth.dll) fmm the td~.11 one l'lw.w dt\lnnllmm mr> petft'l'l u'ttiJiuthrmrrl\'t!,f httl mi mum ltcd

wi1lt ''m h mhn I . l:.dg,·/)"frl'l·rtflllll: h c;tn ~ \'huahsed m term.' ol r.:mo \ :\1nl one lot~li'T ill u1tm1' auJ lh,· :.ub'l4:llll\.'11t •u:~u111ufllllnn uf llw arrc_ty to tlw dde..:t . ,... ,g. I '\~a )

.L l.li,h•r:•thm. the hotmtling of

Ot,ltti.:allon" lf\t:lf nnill'ilh:d h) tlw 'Ymhol

Aruuml the-

h.'~Hitl

rltlfllhll "und1Unn. rht.·y

1h~

;lfc.'

lht: ~11\lnl' <~rl" nol til

uml1.·t ..u:un, wh1ch '" e h::ltly l(lund h o111 h,t.: I qtut

und~r tlh' ~•pp li c:.Hhm ,)J ntod,:_q pJtr ot rorcc:-: the cry~tul \:Uil b.: p,:rm;IO~!nt l y dcformcU CFI!!' I J4h outd c.:). !-Jmcc tJ1c da:-.location ts occurnn~ OJ!Onl! tli1.' .:til!'-'

;>-

•••

(<)

tdl

r1 I

th'-'refuu.'-. it ,.. ~JIIcd .:dgl! dishlCauon. Tile ent1re process is C3llcd the ... lip. The plonc nlon1t wh1ch lhl!"'lip to.kl'"~ place is cull~d theJ/iJJ phme {fi~. I 3•1:,, I ~4cl 1l1C QIQIH' ribtJVC the 'lip plane .trc HIOl SlnlC I!OillJ>fl!~\i~IO l1nd tho~C hdtl\l' lh~ ~~~r prC 1n tCI1"tllll U 1h..: c:<tr:t IMif pl.nll~ i~ :•b,we the :..lip pl.1nc then 11 i .. ~.:.1 II~U pr•sll i\ c Lh,h>tauon ~ .L I If the c:<tru Ill one i~ hch:m the '<lip pl:tnc tiii.'JI 11 h \::tllt:d Negntl\ c "h ,foct~Uilll IT). F1gurc,, I .34 fa ). (h). (C) .;;ht;w po~i~vc lh,luL.nuui nlt: $1/C nf lh~ di ..hl\. Hinn j, dcM:ribcd hy the Buf'l:t'l'\ \"1'41nl', tFi);! I ""'Lkl h

lnl'J ... UI\!'

tht:

rd.UI\.l'

tlt ... rl.s.:eml!nt' ;jlong <;lip pbnc, ;I

r~lll

td I.IIIJ(..'C

l,.llllloUIIIII~

di.,Jucatinn. m~l" lh~ ~nher pans. In r:l/p tht mmnh· bmul\ ltufJm~ mh lu\t'l 1t1 thf "" u Mt' hmlu'll 1m/\ mlf ot fl ,,,,., \\.lll.:rc:tc. in n pcrjf·t·t cruta/ all tilt bonJ, /wluerntWii Jr~ren wuuhJ /tm t' IU ht' bm~cu \mm/UmrmHI\' jur fliU\fi,· J1fl\l fO on·1u: uJudt nc•c.·c/\ llf+l• It mon: (fun• Tluu thr prt'H'rH c- H(11i•lt•t tmmt mo.lt·., II pn.n'lhh• ro mu/(or,-.;umtf H'/r\' mluf,· urr le.u: ~·tttm~. a .. tltr\' ouRhi tn ,,,. ,m tiU' hmtt. nj prr.Ject n \'t/fJI \lrJh ILII'c' 2 .\, u·w t>t11tJtati,m. Another lind o f lliliilncation j, ..cre\t. di\llK.:.Hu1n rh.1t cnn tx· \I..,UII~d hy unngming that a l'UI i~ m::ulc. pan-"-'> mto .t l''-"lit!t:~ t..'1'';~1 arul on~ :-1dc HI tht.• ,u, , .. th\'n t.li~ rhtc\'t.l relttth .: to th~: othl!r (~i~. I ..'-hi• ,tWIIHt.. lot)...::f' "-Plntl ;.utlund llw ,ls ... ll"'-~;,hnn \\hich ru..:cuunl:-. lor the numc ' Mt \,.,/ IJt ,fof tltloll In .u.:IU.ll L:.l) \IJI\ t.H'Ih:k.'ollltllh a n: U\111111) th~: \.l1llll111111tiHII oi cdg«." anti wrt.!w t.h•lucottillll,, wh1ch b. c::~llctl mh:cd tli,hK.."~ttmn

1.!2.3 Surrncl.' 0«!-f\•(·t~ I Thc...t a1~ due hllhL' tni\11Mtr..h nf ahlmk Ia)~" ft'"lr the :1h~~u~.:c 111 :n~ l~·~,·r Pll the .. urfac..: 111.:. mi~m.tlt:h may be: !!e ms\ the em ir~.· C.l)'~t ::ll 111 p:tll u( it 11t hctwccn twnutlpt:cm c.ry~ml hte~ within n poly·l'~lnllinc o;olid :! Sta~:ktn~ fault·l ht ... r\'~ults wh...·n one ::unnm: plane t\ pil<-d nut ''' ...c:~u~·n.:e on ,u101ht'l, Y.h!!ll li1111~~ llU tllhl!t :.tdl: of tht.: f,,ult l"o f'h.' IICL!I, "\ GrJtn l,.•unt.I.Jr;t r'nmml'rci ... l metal!. :m: usual!) ptll) u'o~t.IIIHh... I .u.:h UlniJ.in' lafl!.C: number ot ..:ry~t.tlhtc' each h;to,.mg the \:unc lattkt.~ ftJIIt::lll hut t.lif(.:rtnll~ 111 wntctl I he intcrfJCL' t~twccn the region of (I)'MalhnL' ..tru.. tun.• 111 a pulv-t·C)' 'I~tlluw 'olld '" called gmm houndm')'. Along the gr'am boundar. nu ..m:ttdl

ean occur which g1v~\ ri\t.: m imperfection (Fig. I.2),

l.ll.J \'ulume OcrrcL' lllc\C oc~,;·unJu'"· u•atltbiH'n o f v:tcancics in a small n:~1u n which can ~lt lh.:rpro~o.lu~\!

voad' an o1 ~ry~ldl na 11 ~ pr~'cncc of foreign n1om~ of lnl)l~ ihlll<'"""" <••mpaml In lh~ .1\."tU,II \.T~ ... tal olhlllb Vnu.b pr,,Jucc dl'cr~a.slll~ dc.n'H~ while fuh.'l~n ..dunh 1ncn:a'~ ur dt:L"n.:.a'c thr <.l!.:n~it~·. Ruth crc.atc imperfl'CIIon in th~ LI") .. tal

1.23

Diamond Structure

~1any el~m~nL\ .md \:\lmJ>cHuu;l-. l"lin ,,dopt mm-c thnn un\! cry~'>t,11 MruciUn: hl'\.'",tii'IC

the pnn1cular \lruccurl· t.h:tcrminc!t..l hy 1he encrt!) hand mcKicl (Fig . f1 I I. Sll it j, JX"'ihll! lhJtthc: .. ame t. > lcmcm or con\JX"luntJ tlchavc like a mew I wh~n 11 ~,;•1 >· ...wlhi.C!-> in one ronn and like c non-mct.nl when iL adopr.s another. for I!X:tmplc whue un :tnd gr\'}' un. Simil:'lrly o n..: forrn mny ~ on 1n::.ula1or and the other u ,cm• <.~tuiductnr. llkl' dirunt'II'U.I :utd gr1.1phit\! hut f\mdnrnl!ncttlly hi;tth nrc l'UII"Mm

·n ,e dt•ml•mJ r·arh.-m ..nltam, gt•rmamum am/1m

():rtl\')

all c:rrsw/t;:;f! wu!J

d;amond .wrucmrr. wluclr rsfac:r-c:entrt'll fflbtc struc·ture ami thr atomw b<IJ'I~' is

two 11Wm.' tu·r tm;: lauicC" poim, Each I:Ht1Ce poltlC corrcl)pond~ to I\HJ identtcal awm': une loo:ntcd .u <CI. 0. 0) and other nt ( II~. 1/4. 1141 r 1'1~ 1.351.t)l, nt a pomt one qtJ:tncr c•f 1hc w:ty a long 1hc body diagon:ll. So in a di::unond \lntc1urc c1gh1 0

II:!

1n Fig. 1.35

t )

(a)

Oiumond $lrut·lurt"

Ct1m.!r ~tnm

• 1·.1\ ~· l.'"ti!CI~·ll oUtUU

• '''"'"

\' 1 •

.•\ tum

.at tll-1 I ·-1 I ,J 1 l\).. 11!00 'lA. r I , nmC'f ;ol«•fll

.u til I

I• I. I1.&J l~Jt k•n

tt))

r t L.~e ~:cttlt'"ICJ

..""~ :: - --

•l•ltll f

tr:

---

.•

i I'

-------- ______...........

fii'ig. 1.35

(h) Diamond MI'UCiurt'

'"':•

Crntflllogropln· mul C,'"'l ..\lal lmprrfi·rtum

.uoms at c1gh1 t,·pr,h;r,, su. (,u:t.> cc111n.:d onolll\ :.t 1he ccntrt.! ~,f .:;tch nf th~ :-.1\ tucc:-. ::md four ntmns ot (114. IJ.l. l/4) urc pn~nwnc:d on lht.• wuy ulnng rhc b4.xl} dh•gonal m!\ltlc lhL' tlflll cell , 10 suc h ~ wuy thai each Llf lh~ltll!-1 linked te tra hedral~ une COnlC.r ;m.J l llfl~C l.u:c~ccmrcd Sn Hl <hmond ~truc1ure

\\Jth

Lt(OIO:o

If'.. 1 .:\~h)

f 1) E.;tch mom ha\'C four nc~n:~l nc1~htwur~ 'o the c')nn.lamtlutn number'' ruur wh1ch mc;m' •~.:lat VL'I)' upcn "'lru~cure~ (2) 12 O~XI n~:lfC\1 neophb<1Uf\ (3) Th~JIC :1rc l.!l~ht alUm' p~o:r mut ..:.:11 111 cJmnwnd L'tY!-.1\tl ,tructurc. -1 lrmn

. ( I I I 11 rig1nal F.C.C. 'lructurc + J C\l r.l \~r'hu.:h .trr.:: cnl •cly m'itk lhL· ~.:ubc; ,11 ~· 'J· 'J

(..$)Two ~tum:-, p~1 ba~1 ~ 1.c. per one l:li11CI.! pouu. along the hody cho.~onnl ~itu.tt.:d

:tL qunner d1sllancc. As the) .:tre lh<' neurest nl:!tghhour. 'o Lhcy arc m

wuch "Hh ~nch other Cl:ig. I ~!'a and hJ Soard'" tbc atomu.: db meter :tnd 1 the JWmi..: rudn1s. lhen

d llen~:c.

=lr = 114 fOOd)' doJgonall = 1/4 h rl., 1

I hi.! :awmk radius

11.1'1

= ""ja/H

15) Ah>nliC p;;addn~ rucu.>r tor t.hanwnl.l \ilfUC:turc is

A P.F = ~" 4/_I,.,,,_J/X!' =

''"'If• = n lJ

rl 1-IJ

All the clcmcn1s htwmg dmmtlnd o,;uucturc ll:t\c lour \"Uicm:c clcclron m w htch two cl e,lron~ will be in ~-state ,.,.. hilc the other 1wu will be in p-st;nc. The b<>nding hctWCt.!n the U!om... '" o.,:twn~ly l..:ll-valcnt So \\C ucccpt thm u C4.!rttlln .tmount of cnl!'r,!!~ •~ r~>'qU1r~:d m ' 'l'dt:r h"' 111t1ke 1h.: 1!1\:'~,.:trtln:~ I rcc \Vh~n thl!~ l c.~ .. C. S1. G..: ..:tl,) t.akc parr 111 \.'lttt<_ h u,:IJun l'ht' ~~ m otgn.·~mt'nl ,.,,Lh the lad. that ltl very h>\\ tcmpemture .til 11h.~,c clcltiCtllS h,l\'lll8 duunund ~tntcwrc :m: in~ulawr. Bonding i'i stn.lngcst in di:.ummd ay~w.l tZ (l) So u j;o a \C:ry hard msulo.tor. h:l'''"g bagh ftlehing potm Bondmg 1s "~a k est m gray un <Z =50. Hccausc. as ~u omu: number mcrcas~s. lh~ amer:nomk d•sumce.l\ ancreases. bmdmg force becomes '"caker ;.llld dcrni.:nb hc:\"omc more- mt:LaliK whc1·~ vakm:c clcc1ron' become more :mtl mort frcl.!. \Vh\'rc ~~~ fur irucnni.!di:ue \'3Im.' of Z. ~:1y fo1 Si = 14) :tnd (ie <l .32) elc:rncn~ bccvn'lc !'o.Cil11COIIdUCll'lr. A'f. honding bccOinC' \\'tAker. then wtlh 1ncrense o l o.tom1c number.

(:tJ Forb1dd~n cner}ly

g:tp!. "ill di!C'ft'tt~c. wall ancrensc. (cJ D1elcctnc con'-UOl. mciHnl_! fk•tlll. :tth.l l)chyc tcmJ)I.'r~turc w1ll dcct\1-<.l~c

(bJ L.nuicc p:.lmmcter

1.24

Barium Titanate (BaTiO,)

UaTiO, as a tcrrocJecLric crystal a:-. ,h,.,\, ;ltn f•!t· 1 16. '' Juch .;xhib11~ an t:lecl t'tc dtpole mom em in l11c ob.;cncc of :m ex1cnual dcctric field. In a fcrmclcc1ric cr)'stal lhe centre of poSlLi ve chrgc 1i'h- or 1h.: crys1al doc!r. not coincide with th~ centre ur ncgnuvc charge(~-J.dul! to which a dipole: momt>nl wi II from. Thisspontaneou.c: dapolc moment can bl! uhcred b.,• {ti>J>Ivine. !<>Ufticicnth· strum! dcCiri,• fit·ltl

Fi ~.

L16

u.~··

U11rium ritnmtiC! "lruclurt'

l11 !hi.' nun ~ JNII tUIII.!d l"h:t'-C l3:lTi01 11\1<. C.'UI:m.• ..um:lur~. \\lth I:S01

11U1<. otllhc

Ctpht "'Uhc ,•• \fllC.,... {h,g. I.J6), 0 .! ions :u th~ ~~ntu.· ol lh\.· ...1, t .c~c:. .tlhl n-l• :tl Ihe Ond~ ccnlrc But ht-Jm, " Cun.: lcmpcr.llurc.. ( I.!Cl'"'C;;;; ·v.n- Kl cht.· 'truu urc ''not ~.·utw.: hut 'hgl111) lll'lnrnwd, \\hen B/ ' .uhJ II tun an· J1~pl.1.\. :d rd.unc 111 f >' HUl' •.tnt! thl'f\.'h~ d~\·elnping dipol~ momcnl Cry ...t.al 'trU\.IUlc tnr lh"£1( ), omd \ ;.ln:ttutn t1r d irt'\'IIOn ttl pol\lrtt.iiUon wuh t~:mp~o•r:uu r..· :m: '"t"' n 111 lahul:~r lotut tn T:ahh: I ,\Om c Curie I CIIlJ~ntltm:. UaliO, "flllll-lcrro.\.·l,·,·tl•\.· •• nd h." 1.'111-'ltC. ' l tih.:IUf(

A-..,, ki'Hk:lcc rr~~;; tTY'Itll. ~ I n\\' c"rh: ll:ltiJ)I.!r:Uun:.

lunf" t i'l~

1.25

1. ~7)

whH'h '' th\! stgn of u

tcrro.:lc..:m~.-·

l~aTr<)

..hn\\' th~o-• h~ \let~' I'

m:nc.rial

Interstitial \Inids

t-\ n} lhn:c·dnnens1onnl nrrang..,mcnl o l ~phc rcs of ollnm' tor •<m~) gtv...- ti~t In '~nd ~pac~ hclw~c:n Ihe "Phcrc~ . Thc~c: voHI ~> arc t:illlc-d " lnh! flllliliHI 'nid," T\\ u main l)'f>C\ o( inh:rstitiul void-. in clost:-packed Struc.: turc' :U'C ()IJ.\~ihl e.

Tahh· 1

(' han~t.·

urditrdion or pol:trisuliun \\ ilh h.'IH1h'nllurr. fo r H11Ti0 ,

r;lllpt:t.~IIJll' W:t".'it •n 1

Cr~ ·MI ~tru~o.UIIt

l•h ~

,, t

("ulou, II

u-/, Tf 1HI

11111 II

.! rflhlt'~·~·l

J-• "., . /1- 7•

! I a W1 K

i II I

II U II

'NI

()nhnlt111UII•I~

t.tu./J •l

IJ'I

Kl•~•n•h!IIM'\.Ir.11

II '' U

I J • I' H

'HI

I I• ll·<~lrc•dml \ ·l•ul Jl '' lun'rlci.l N!l'-"t'cn 1h1c&: 'r"IH.'IC!'

l•n :.. t'fn..,\'-I'•U..'I..&..•tl

piJIK mll.- lnunh ~plh.'ft.' un .m adjaccmcnt plane ccnhcr~1n IHJ' "'.tithe ''vllunu. m th~· c.t\r t~ ' fi.ICl ' tx•t"'"'cn the 1hree ..,pherc~ (Fig I 1~1 l'lll nome lt'ltllhnlml wul n dt•r·il'f'd f nmr tm• ll'Jtlllru ft•tmfu..tlrtm u·;tlr .J rou wn ami .J ltrmiJ;Ufru /il••' of r'rJiutl ,·i:.e It j, t1h1aincd 1:\y j~)ining 1hc ccrnrc' uf the tout 'f'hcr~ ... For ~\l!'r~ ~phel\' m thrcc-Jmh!nsionul army. th\!rc arc two tctruhcdrul \UH.h. h can ht• ..,h11wnlrom Equ I 1.17) Lhtll the larJ:_est .fJJiu::~ tlwt um {it m a lfJtrnllrtlml rnulll.1!5r when· ; j, tJw mtliu\ of tl1c .spht:rc~ ol the c lo~c~pad..cd .JrrJy cVi~'· 1.41(•1. I ~1(h )). 2 Or lllht•dwl \'tml h ,.., furntccl with lhrCl' 'l"hcfc~ ''" .1 l'lw..l.'·rad..t•d ttl:uu.·

.wd tin ct• mor¢ ~phcrc.s on nn ndjaccmem ciOM:·t>O&~kcd plunc . .,.,.., thJt 1h"· ..:"·mr"'' ol th.: three ~ t,hlo!h!.., ''"one.· plunc. nre direc tly nvcr the three to.m!!Uhtr \\tllcy' -.utruunding the Cl!nlrul Valley ur the (ir,.,t plnnc nruJ th ~rc I\ liH \ J1hl'fl! 11\'l'r lhc crntr.:tl \';IIIey (f'i!! I \9>- Tfut mmt,. tWIIthttlml 'ohl nmt' .\ jwm lilt' rq.:ulur ocwlh·tlmn (o Pf~lrhrt.lrmr h'flh sf.t conlc'f.f om/ e1~hr r; um~ufor jw nf #!tftUll \1;1'}. uba•.unt'!d by jt''lllllf1!,! lhc c~nlrc:. or l]tc ~i~ ~pht"rt~. l'hc~ ... om.: tlt.'l ;dl~dt.tl votd lt\:r 'phcrc m the 1hrcc"'duncnsional nrra)·· h r: un be ~hown tnun Ettn ( I 16) thut tit~ lorgest ·'l'"~'''' tluu n m fit m • oclllht'tlrnl IHJUI"' O•..S I <>it·. \' h.:rc r i' tht:

ratliu, o( 11tc ~phcre\ uf 1h~.: elo:-.c-p~u.:kctJ :unt)' t Fig 1.-lln. 1.42hJ

-- 'T~\ ~'-'="J. < /~

-1.26

1-1~.

l..39

Li!!llncy and Ionic

<letohl~rul

Cry~ta l

'nld

Str uel ur"

In general. I he smu:turl! n l no tnnh: " ' ' '1111 ~ ~ tlc1<:1ntuh..~..t hy thl.' rcc.JUin.:l'n..:ut 1h.H each aon be m conlut.!l wi1h ~11oo n'lttn)' hut~ \lf the OJlp<.,lo.itc sign n.s po~sihlc. su ~~~ to rc·J ucc potential Cl11.''l!~· Jnd tn ultain m.tximum ionic bonding. energy. \l. lu~.-h prO\'tdc~ the gn.·utc:-.t ~htbi ll ty. In tumc Cf}'~lal (+'vC) ion~ arc .;:mallcr in si7.C ttmn the c- v..:) ton:. l;tt>camc the SllC uf .m iun Increase~ vn :.tUding extr:a nudcar electron !ll'ld !-thnnk:<~ till remuving tht ~· lcc.· lrt111 So unliJ..c lhc mclnl lit.:. l!lcrncnl ;tl cry!'-t.ll strucU1rc. 1hc <liffcrcncc 111 :.11c of rhc l\\0 l)'pe' of inn!\. \\hich form the cryMal lattiCe 111 rome l7ry.\lnl. 'hould he taken m1o account in the gcnmctf} u l

thdr cJo,e ~p:u:lin~ In ll partu·ulor tom(' ,.,..,._\lfll Jtruc'nu·c, till! number of ( +\'t'J inns .turrotmtlim: «Witmll ~·~·J l(lllllml ~ ·rt't'• t'et':m n rli/Jrri ..U~tmn•" ln Hit rnnic c-ry~ t :i l hg~int,;y i!<o the numhcr of ncurc~t ncil:hhottr nf uppn!t.itc 1ypc (i.e :unund n Na• . hflw mnny Cl arc Lhcrc). Whcrl' a~ Cfldrdmulion number i~ the number of n~an: .. t

neighbour of the lo>tHm: l)'pc (i .e. ~tmund a Nu". how m:tn) Nfl 4 ar~ there or around A I. low mnn) AI are there). Sa (or imu• ''"'·'WI bt1th li~tJIH'\ m1d rot)rt/indtum trumber llll.. fiO.oibfe bllfj(Jrt'/~mcnwl rt"\'Stal tml\' t:omrlutllfitm mmrbrr tf (JO.uiblt·. Th u~ for stnblc configurmion in ionic c.:rysl:tl. the opumum nrrangcmcnt in nny crystal should be lhl! nnt!, .JIIowing lhe grcalcst number of opposilely charged

Crn•llllltJt;mpln• mul Cr\'SWllmp!'tfi•ction

u,nu:h (whi<:h give ~trong. honding), without requiring ~tny squet'lilll,.\ wgcthcr ol h.m .. uf sanlc charge' lv.:hich innea.sc 1\~pul,ivc forcel. Thi~ t;:m he eAplainl:d Licari~ for .1 binury cryMnl C.·\IH of .l~foltl ligunl'~ tL' ( 11 1),.,.~ In hg. I .40(:aj, three U h.m, .1rc in t.'Onl,tl;t \\'ilh ,A. • Ion hut nut\'- hh c;u.'h 41 mh"·r. So 1hi ... ,, a ~1.1bl~ c:nnfigur:umn accmding H•thc rtho\1.! condltn,ns. In~"-~!!· 1 .H}(b) '017~ A' inn ~ ~'muller 1h.111 in fig. I 40(n) and in aJJ B ion' .m: IU'1 m uJuch with c:u,:h Ulhl.'r and with ;\' Thi~ conl1guralinn i.; ju ..t .11 the hmll o l stabJiit) ur the crhk:•l ~:vndl1wn fPI Lig:utcy-~ tmd the r.•chu .. nf B .tntJ A· aun .. m th•:- ,onllsunuuln.., called the crillc:OJI iomc rmJio:,. t r( .md ,~·1 If tht• .... ,c of A • wn '' '1 111 become: ~•u;,lkr. Fig IAO(c) tltcn none uf lhc B 1011...,: lt.1ttlh .., ' 1011 und B ion~ Hr\! \.t.)UCCJL'd together. So the repul~ivl' force L... rnon· tll;m ::tttrw.~uv~ IUI ~C s~, lhl:-. -:onltfUriiiiOn Hg 1.40(\') bct·umc!l. un~l:lhh: ami unf<.~vouna0lc for hgaocy-3 und mor~ ra\'c)u l'ilhl~) (()( lowc.r lig;lllCY configunuinn. ~a)' hga nc~-:! Thu~ the relative ~~L~~ of the (+vc) ~1nd (-\'c) inns amoh·cd m .tn 1omc cryst:tl. )!overn the type.• ol 'he ~truc lurc ch:u occur.... \o tlw r·ruu·ol tfmu wtliu \ rauo/or A .. tun-:. '· • aml/1 ron = r, (Fix. 1 -IUh). t .t ·.. slw mtm 1, - h , br:tw~·tw 1/u· rmlu of 1tu um \ w m1 ionic cry.wal, rw1 giw• rhr WIJH'er t(' wlrr a JltU'tJC'IIitll' n miJU!IUII/ rn•,,·wlt;.t•,, m u J111frtl·u/ar Jn rm, w1ih puruntlar ltg,ann mutthcr. lwumH unw radm.'i l.'i wr iniJt'rem propl'r'ty oj tht• mcut•rwl

il)OS to

'" ('rltit:al cuodilhHl for Ligancy-3 a nd chungeo u(liJ::IIIC)' lb)

f1g. lAO

1\:J

numb~r

''itIt iunh+

rttdios

1.26.1 CsCI-Slruclurc (Li~,:un<J·RJ with Cuhicnl configuration l...e1 ll' ;umlyt.c t.hc ~itunlitm for (',('1 <~~trucmrc. of B.C.C lypc uf ligo~ncy·X CFig lA 1a), with cubk ''ructur.;o cunfiguca1ion. to calcuJatc Lhc cridcai ionk r.uiJu, r.ttio for I>· fold hgan.._,., lien~~ <.:1 io n~ uJ radwo.,: r. arc ph1ccd :11 ~ l,:nrn~...,-. ol llround a('~, Jon Wllh r._• mdiU!\ Ul1hC ce111re ofchc cuhc. ~uch 1hat (+\'\') •md (- \'e) ions allnre in t()uch in c ritical condiLion. S<l the A' 10 13- di'\tom~..·.: cfig. I ...alb) i\ ~t;'" + t; ltnd the adj:lC~I11 a- ic,ms arC !ll~fl Jl l'">l in lciU\:11 \\ith l!dCh Othc.r (Fig. 1.-l lh) :'II dle C rllJCal CllndiLion. Now to B distan.:c IS the liilli..:.: parumctcr rL which b given :.cconJing to gcomclrir con.strm;uon lor U (" C MrutiUrc as: rrom rtg. { I A I b). ln B .C.C. Sln •cturc (-vc) ions at S comer~ will be in touch with ( f.ve~ lOll at centre. i.e. :1!1 (+vc) and (-vc~ i<lO!- will be in 1ouch <~long body diagonniiFig. IAih l. ::t CUI-.e

a·

•••

I hi

Lht•lnc~ ..Mc uufi j::,untlluu

lht;;n,:lon:. lhc bod~· dwgnnal (hg. I ~lht '' ~tt=-1!r""+ ,

.uul l,utu:c par.:unctcr '' tt:J'

~>or,

u=-=-(t' +t

f.t.:

f-=-2t.

' l

\l.htch gt\' C\ thl.! crilicallonic t:u..hu' r:tlio

l,:•tr. "'

=, .l- I-=- H..,.!'J J

ltu

~~.UK)'·~

( I 151

' · ".' ; 1 :n

Thu .... 10 the: {Tit•cul ~•.:ondllJOn. the largr:-...1 c;u ton ol nu.hu' r· = 0.72tJ r, twhcrc r, t!\ :t rudtu~ ol th~: omon) c~n fi1 cxact l} mto u cul)tcal \'Old an a I..'Ubac:tl <.:ortligurmioo. where 'i£ttlll'Y h. 8~ No\\ if 1 'lr. > 0.73 e.c. r' '' 'hghtl~ hi!!l!Cr••L.. 10 the \.'a.._'-'! tll Ftg. I.·IO(J1 '' hu~h t:.. abo ~tuhle. 6u1 It the r:'IIJO ' •" / r, '' Je,~ th:.o U.7.' 1 e.• r' become~ ~1111 :;mftllt.:r :1:-. tn C~ii: of (Fig. 1.-lfk:), th~.!n tiMt cunfigunHion is not scnblc und unr:tvoumhlc IClr liganry·!> f'S.C.I smu.:mrc. hut mnrc rtl\'ournhlc ror lowcrhgaiH.') con l 1,gur~n on.

,,Jy l1g:1rh.')'--h

1.26.2 NnCI·Structuro O.. i~::tncy-6) with O<·tuh~drnl <.:onfigurution N.lC'I ... rructurc h:l\ tng hguncy~fl fhg. I A~''), F.C"' C I) JX!" 'tlnacturc. \\ uh ucUalcdrul conti.gurauonl\ Here in cri1 ical condnmn al1 [K''III\'C and ncgath·c lOllS urc jll}ll lnut:hiOB cOlch other b 1\ Otll ~(JliCCt.ln g. wilh r:u_hus r, lm' 8 ion :and r; · Ior- A • tOll. c, Cl wns arc suu.atcd at 6 Colller ~nh.t un¢ Na-<f 101\ ts :11 thl! (Cn l rc Qf the vcmhcdron Fig.. ( I A2:1). The crnu:nlaonu; rnd1u' rauo will come in the following w:.y (rom Fig. I ..S2(bl, which i~ 1hc 'lluare plan~.·r- crus~·~cc1ion or an uctahedi'On

I • o' --;!i-I

I .'

IJ.J

(l·cg. 1.3()) F\\r F.C:.t'. MructUfL-! \lllh Ud<lhttdr.J I~..: ..•nligur.llion (+vl') and ~ -\'d I(Ill~ "ill be In tom:h ;~Jon~ la ll u:~ J1:•r:un~h.·r u ~uuJ l ''l') con ... will he m h.lul.!h ••long 'urlace dii•gonal in cnlic;tl C<illlhllun. Hc.n~l!. Irom Fig. I A2{h) ..,. :!o=-1 ~l. l' .

2..fi. (t~-;- + 1~.

nnd u=.:?

) :;;

(1/

+t,

I + r..'lr;

=, 2 ( I 16)

r, lr • =- 2 ~..t

So the lnrgc~t C:.ltLon ofrndiu!oJ r. =It J l...t r. .~.:.uJ 111 t.::\;tc,;ll)' an ::1 c;Jct:lht!dr.d 'md ol oclaln..·tJral~..:~lflfigur\lhon wtw~c lcg;nlC)' ,.;: h, a:-, dc ...cu ... ~cd m :-;I!Ction 1.25. Thus. the bln:u·y ionic compounds ( ,\ B 1 wuh critical JUIHC r.t(hu:.-. ruuo r,_.. /r, hetw<en 0.73 and 0.4 14. crystallit.c onto NaCI structure with hguncy of 6. If r,' ~~~ is les-S than O...J 1~. then lowl'l IIJl~•ll<:). 1.1.!. -l ~ ~fa, l1Ufitblc :.tnd nm U.

1.26.3 ZnS Structure (Li~:an cy-41 with Tctralll'dr:ol Confi~uration If the ratio 't Jr..- Lo; less thnn tt.t I ..I for 'om..: n-ystnl~. the.:u h,gaJh·-y-6 .. \\ill bccon•t: unl"avuurahk and ZnS M!Ut.IUIC. lignncy ..o~. tht> JiumomJ \ lrudurc wllh alteratwtc Zinc und Sulphur ion will oc~:ur. (Hg. I A3a). In ZnS, which i$ having diamond-type Rtruetur~ with rc~ul ar tetr:thedrul <onfigur.tion. the (+,•c) Zinc ion \\Ill he Ul I he \ ~. posh ion which I!> mdkatccJ ._\~ (C); J Ill rig 1.-13(:•). :tl 1hc Ct:lllrc ulthc tctrubcdn:JI votd ( b~. 1 .~8 ). whet CitS 11s four ncarcs1 ncighbouh. louq-vc) •ulplooor i1.01> ill~ic:+ted "' tA , B • (' . D ) (Fig . I AJa) will be at each comer of the H.:tnlhcdn.m {t-lg. 1.38) and 10 cJitic:ll condluon all (-ve) sulphur ion will be in touch w11h each mher Ql'l well ns with che central zinc (+vc) i<m. tFig l.-13a, IA3b).

!. ! ),

l·ngmr.c.'I'UIJ: ('fl)..HC\

.-.

. ,,

C,H

(hi

In dh-1mnnJ 'ln•~IUr\! the f

''l') h•n t\ 1c (s -) al ((), U. ())and t +' c lttiO 1•• 1 c po~nwu :Hl-' 'l'Jl~Uah:d by a tJi st~mcc, om• fourth ut th.: twd) dm.gunnl. '\n 111 Lnltct:ll·um.ltiUHh (fn'IITI Figs. I A1u omd h)\\\."~~~

(Ln '") al 1

t. ~, ~'

, . " 0 -= r. \\hc rt:il\ 111 '-nlt\,;~11 Ct• ltlil1011 ,lt:\lotrlCc

+ ~

·na

-= ~-

hc.twccn

L\HJ ~ulphur c vc) wn ( A

dthl

Clos t\(.

t · ,~

whcl\' 11 "

Nn'' h)

the

1.111 11.. ~ p~t r;tnl('ll!l

1.1Ltn~

th\! t:nul uf the :tbCJ\C 1wo cqu:n1o ns we g,•t )

'·

.:!,2 ., - -= -,3 -= I 21:' a .2

So,

flir f1 g.utl) ~ Y. 111! h.'lri.dh•dJolf Ulllfi_guraliOO.I.?riliC--'d f ion1-: J"ddiu~ nil itt f I '/t ) r, h, --= 4 ~I m:ty l11.:t.:omc favour.1 hl~. So in cnl u; ;tl \"nmht .. m tht;.! lnrge't c;tUfiO \ll r:adlm 1; • -= 1).:!15 '~ can fit e:<:I.Cl ly 1n a 1etn1hc.drul n11d '''H"..: hg<~nC)' " ~. II A· " "•II , rn,JIIcr :1< in Fig. I A()(c l. I hen •.' lr- "ill he lese; lhtul CJ.~~5. thc::n li gan~.:)·..! \\til not be ~S ible: IO\\'f.'r lig:H\<.') ·'\\Ill ho: allowed. ThlL\

=0 225 01

1.2ft. ..S l.iJ!RilC>·J \\ ic h Trinngulur Configunniun Letu .. considc1 Fig I .s s which ~ I Hlw~ critic:d ionic ttrrungcmcnt for h_t.::tnl'} .y. X. Y. L. arc the c~mn:s or tlm:c (- ve) B ions ond 0 i s the centre o f C+\'C) A 1tlJ1 111 Cl'll1cal CClOdl tlon. From 6XYZ il ~ ~ clear th:11

XU = r, + r.' :md XN = r,

Fig. 1.-l.a

,~OXY:

l ..lt::lnc~··3

Ill ' ;md 111 AOXN. co> 111 :::

conO~uro.~IJnu

'v =r.·-'·-

IIX

u· Or

rhu .... 1111hc ~riucal condllat>n lhC l :argc~ l cati(Jil uf r;ttJiu" , .• =-I t 1:'~ ,. ~~.UI lit t:'i;\"'11} 111 :• manguh1rvoit.l who:"ie llg~&ltC) i~ '\. ff1o.uhu' ,ll1\ ~" .. malkr. ;, ..

uu ..

'" l•t£ . I ~Of<). then ... lr, Will be less than 0.15~. unu hgan<)·.1 \\ill n<ll t..: Jl<l'''hlt.·. luwcr hgnm:y·2 wall be ulfowl-d Thu ... Ill I hi\ :-onnph.: oppro;~unatmn or packing C(11)\;ldt:rJll011 t the arr;mgcmL'IH uf P'l''n" ,. :mel oc~;lli\'C ion positiOns) k:ttl' u' w ;:u.:L"C'Jll th~: \·anou' ''·•hie -.uul.'wr~,·· m term\ of ,·rmcal ioru~ ro.diU~ ru1io , ... h. s. \\\! ..:.111 £."-'th' I~IIIJ~ n ,,, l!I\Cfl '"Tublc::! 10 lh~ roii.JWing wuy. Tobie 2

r,-, ,,,,1 S1nac1un:

Cmu.ul l{.,lhu ..

.1nd Cctnti,gurull\_•n

R;11111

I. H '.\

' CSCI

--------------------------or HCP I ll

.mu C'"ul'2 (Cul:lcoiJ

I > r,' lr ' 11 7.1

..t nl'"ttJh'

•IJ.C.t '>f"'l \ N..iC'l Struc1urc (Ocl;.hetJral) t 1-.1'" (' l)'JIC:) J

htS ..,tu ~.,·w re: (Tctmhcdnll 1

t Ommond &;1JIJC1urc: h~ rcpt.&uns .ellcm.tlr cartmn ~ lomo; wish 1.mc Dnd •ulphor} S. 'rn:m11ular f)

Lirlc:tr

U13>r,•lt, >U-ll-1 ·I

0.414 > r,•fr, > U .2:!5

0225 > r,'lr, > 0. 155 U.ISS > r,'lr, > 11

•

Hem:c. <L'- the cnue::t lradtu~ t;"lr, rouu' d..:crca~c~. Hg:mcy decr(.)'3:\C:-.. Though lhc1·c an: a number t.lf t!XCCptton:-. hut to gcnl.!t;1J. the corn;lation hL"Iwccn rhc prcdicliOJh nl lhl' ubo·.~ t.kll:J and oh.'\t:r"cd CQ'SI:tl ~lructurC:\ .trl' good.

PRORLF'MS C~trl'-idt•r .t \u ltU~I;JI ll.t, tup I•.C.( ' •>lrllliUI\!, I I the inter.pl;anllcf diM.IIIt.'l ' 1l '' ~OX t\ lui' th.: 'c-1 1•t fl;tf,tlld pl.uh.:O: ~I ll J. IH HJ dl!tNIY ul ('u tnl'l. ll. ~1\'t'll th.11

.u "' '-'ll'u = i•l "-1 .mJ h•\~.ulm".... ~o :: f•.023 x IH~'tt! nn•k Snlmum: (}l'tt'-11\ - IJ

\\lkt\' 11

=Nu ul .thuu' ur mt~l

pet un_l\ u•H .- J tfur F.C.C. I

M-:- ~luk..:ul;u ''' :. 0\ ~I N: /\\ Nu : h.!C.\ x Io·' muf.. per rm rnnl ,,, ,uh~t:tncc

\. l

1 Ftnd th~

2.0:\

.1 U.

Mtll~·r tntlt ...... ,,,

1 tit••

n '-('I nl runallcl plane:. \4'hil.:h ln!lk(' thr lm··r.;eptt. Ill .111 ••u .\' o.~uJ l 1\.C ' .mtl utt: p:uallcl tu / :'''' ''· I• 1 .u.· t'"'""'

\t.'~li '""

Soltttum luw:11 p.1 r.un~ t cr- ut tht mtcrccpts of lh~ I>IUIJC urc in lh( 3u ~b .-.. St), 11)1: ntll\' IJI numcn'-"ul tmcr..:~o:pl-. ;m:- ~ 3 : 4 : '""'"} Ot~: l .: hm.~. lht.: ~ltlkr md1n:' .:tr~ 1/.l 1/-l · 1/.,.., a H1())

r~.Htn

3 In .1t.ryo;t;~l \dhl'< pnmllt\1.'' .trc I J ,w, I fl mt .1ml2 AU• •tpl,mc .2.31) '"'"' .m lnh:r..:t.·pt 1.2 \ .tlon~ X·o~.,\t..,, 1---'11\J the lcnj!lh ol lhc mtt!t-cCJ)L' :lion~ Y .1HJ Z·.t \C .. \'nlutron Mtlkt 11l;uu.• t 2. ·\1 1 \-\ lu:rc ,; -= 1 2 ,\ h ln!Cf<.'!.!p-1.._ .tr(' crf!.. hH. c / I l.c., ABC Jll:m\! 12111 tHtt I J~)

I )( /\ , :: t -, \

:)t~

Bvt intcr.-.:CJlh (.\ r\SC pl.sn\! .alur\!! X tr\ito. ~~ O.C, A. nol l.~ A. S1111 j ( nm the l't•q uir~d pJ:u1c lnt..:n;cl>l'~ lor I)U· plomc 1):\ntlld Hl ABC plan~ arc"· 2M3. :!c H1.'11C\!, ~hl kr inJi..:c... tor Dfil-0 rt:m.: ;11'1," the r.:~IPAA':tl'< .... , lhio! I. V2 112: (21IJ So DEF i.., al"«.t CB J ) plane tFi~. I -45). Th~ i uli!I CC:pl!<o uf lht'

nr:F pl:lllt'

lnu~rapl4t,

'·'"'

Cn•,tnllot<mph\' am/ C1 \'~ttl} lm(Jc.:rf•'< titm

• F l ~.

1.45

= II .:: I 2 ;uJ >.~lctn!_! ) -=- !bl' =- :!/'\ Joe I ~ -=- 1 :! :m .dun~ L ::- 2~ = ! o: ..! = ..t ..tu

.1h111)t ).

Thu:ot.I>E1·

t•

11:-.:

l""liUih:J J!lllnt: \\h·v~ tntch:~·pt-. 11lvu~' .111U: .a>.t:'

.m.· I .: \

h.' ·f"'~u .. ,·h

;.nJ .a \

pl~ulC'' I ht\\ .ar~ the );mice phmr:.s deS (' ribrd an tern•~ ul t..ltlll'r nulu::c'' Sfnl\1. 11~-e plane' r!lll .uW f J I I ) With a ural <klf;r:uu 10 S.C uml -.:dl

Wh:tl Ito. hallu.:c

2 Clunf) the l)'f'C\ of !lUml dc:(c..:l\ .md cxpl:.un hO\\ ll'~e)· urc pnx.luccd' 1 Otl1nc: tlte 11:1 nu l<~llllC ll.'U':IIlll'lrr ami unit cdl l)c.:dUI:e the- rc:lntivn fur atom'~~

unit '-dh und oawnw: pa~lin)! l'dcwr ot' 4.Ubic ~Y~lcrn and ('\l)lajn ILS llllportdlh.t: <-1

f1nd ..IIUUU<: rudiu' anJ .1 1Vnll~ p:J4;1.,int; f.1dm hu F.C.C \riven Ihe ),l iU~o:C <"HO,I.Illl

.l.biAU.

Wh:u '"' mu.:rpl:miH:r "pacmg·' lkdu..-e the

IC':m" ut Lmicc cum.t•mt .tml 6. Wh,ll

rcl:uion lor intcrpl:mncr

'VJtCin~ m

~IIIIL'J

ini.JII.."C'. ("qr..UJI tmfk.•r(('CIIun-• F\.pJ.un the •yper;. of ruinl th.•fecl\ .tlfuJ hm\ .\1-:

the~ produced~

For Ut!lh•nuc l:1Y!>Ial !'!t. t::1kul:ttc thi! alotmc p::.r.:~mg l':u:lur t.auu:e cothl:ml nl' !'t1 S.J;l Y 10 1 c:111

Solumm· SJ. the di.nvmt.: ays1.1l mom!>/umt ct!ll ~ 8

•~

h.•vmg d1.unond

~tnt cn• re

So. num\'(r Hr

[j x S.4J x IC) -[ju-= --

• l hu ... \PI f••t S1;; Mx "_....~ a, '

·t'' )' '

11 ~" '4'

,.;

--":--•----'...,,.....;~-

J-, •f S.(. • 1- ( · l ' l

l oll

-:U..'-4

B.C. C, dclemunr: lbC' h•llt,\\ m~ f"t\lnt-. rcr UOil \!dl.

.1111\:\•

1.10~1

lhl u~.,r;,.•_,t Jh.'lgbh~mr c.h:o.HUl..:'t.

h:.

'.Mdr.lng

AliUHH.'

f nl' lm

(JI f'n.nr<.hn;IIIIOil Numhe.r

'' C\•1'1"' n•et;lll' 111\'ln!! FC.C ~mu.:1ure It 1he 111h:'qll.uh:l JL\louu.:~ •''" '"'tu.tl 111 1 O.N Au h1rJh1! •c.l (ll p:u:tllclllnc~ rLLL! 11nJ the den'''> lll&:nppcr mc1od g•'en \1 WI : h' :\4 A\ugo~1.hu\ numbc.-r-=- h t):!J 'lo: Ifl="' per 1:;111 mnl~: Jo

If I~

l:.\pl.un 1tw term m1~rptnnn~r Sp:tctn!!IO u ~ - l).,l.tl .mtt .. hn\\ lh~•t the an1c1 pi.Uinl'l "l':.tdflj; u l COITCSJ>Olld111£ Jlkme~ uf $.(' uS I ICMh, t lith I I Ill .Hl" m ltu· r.lllfl I H 7 1 0~1 Wh.11 '' ~ r:- ..tnlunpertcCIIOfl ~plaw "11h \lmrr;tul ( I 1 \.,;hnule\ ..lett•\-, .uuJ t :! 1 l1cnktl tJdc~l ..., pumt dc:fcu~ Wnh 11 n(tH th.a~r.un !thnw ~,..-uge: dt'lhP\;.aiiHn t'.1l\ ul.ll\: .ahHnh· r.ulm .. ul H \ t I• C C•.. In '"r'"' \I Lmtic.;- constant " 1\1 ' ' ha\.lll~ F (" C ..trucwrc. Cnlcull,l.: the ntntnh' r:••hu ... A P.l· •nJ lila ..... "kn,tly Lllllt:c cttO\I:mt N ":": "\.:-;:! u.u. Ar. Wt ul ...:, = 5)>. 7 1 ;uult\\'u ' " = 1'\ fl!.l ., !()~"

'"I utuut

'\l•lllllfo:

RadiO' (F.C.C.) • ' '

" ~ .,

·l-

.t52 •.

1 --

:: 1 ~-ll A

A.PF

\t;,..,.. d~n~ll\

n = !1.!.\ J

~I x :'1-S.7 1

,\' ,, 6.U::J • IU :;. lo c' .~~ x w 111 • /):: tW3') l t:rlm 1 I I 'hu" IIW! pl.m"' II i Il l :md i l l 0) 10 'lmplc CUhlt; U} ~lui \\ llh 114.-'-11 dhl~niiU\ C..1h;ul:uc- Hlterphnncr ~pxmg tl.

l" In

J llhJiyblL.•nutll

Bc c

LtUJcc t.nnst.mi.J::' 15

(, o2..' x 1o1

!Otru~turc.

-:!lh.:ulate olh!IUh.' luJI\.a .. , .mJ m.t..... dcrt ..ll)

,\t WI u( ,\1o : '1~ qJ .snd '''"J!ill..lm·-.. numt"C'r \'::.

\Vbo11 '' ..:rpwl

anpcr-fcc-tJon1 Explain \\Uh l.ll<l(.rnm.,

clemcmal .. ~ well 11 t .-kulult=

~~~

,,IJ'nlU'

ro•nt

t_ldc:Lb 111

mmC" O)'Sfals.

lkUMI) ul C...a,\ s and S1 u~II1J:! lnllnwmt: c.bl01:

tlf G,L-= 69.7. lattice cvnst;~nc lot G~li\) = 5.6S )\. ltr'\rn AI \VI, n( ,\'\ ~ 74.t), No of t:Homs/UIUI celt for (;tv\1-.: J J-\1 Wt ul S1 .: 2X I . Luni~.:e <:on'\1- fflc Si e 5.·13 X I o-'~ t.'lll Nn t)f tth1111Vumt ecll tnr ;-,, :: X

,,, W1.

Wh.tll' L..at;BRC')' Show lh~t cnllcol 1\)nu; n'ldiu .. MIU, r,· h

\J-.·~· re~ ...._..., •L... I . •t:~•OC')

d~t<ri!'~l"C ...

I'.I

l)i~u"~

th:ummd l>ttucture and t"'Jlcul.:ur: AI\HIIIC

structure_

p~Lin}:

factm ftH dmmund

Ct\'.'Jtallo.~:,raph\· mul Cn'stallmpct:J~cllan

10 Wha1 '' the lipcdnh t)' 111 lluTi(), '-lnH;turc't Di'i C:.U'-l> 111 tkt;til with di:.~~rlun I Ill"" dnc' iL~ J'crrock~III(' l'ftiJX"O} dl,lll ~t.·s \\ith ICIU(':I .tUtrc"'. 2.1 C':tlcui::Hc f. rittcnl nu.JIU'- mttn r ' lr rllr Lig..tn~:y h und s 21. D•~tinFoi, h hct...,ecn nmorplmu' ~lui,, f'lr1hl.7n'-l.l11ne ...n lid' and ~HI~th: er~'t.tl 21 With a neat dJa~m 111 'ho" the foil" " IO[! 1\ltllct phutt.'!l ..and lilll.'t.~lmll l> Plane• ! :!.\4) and (I TII DJtt-cl • on~: (Ollt nnd ( I!.'> ~.J lkh n~ the te.nn' -.p.1CC lmtiu.•, u flll t.CII, l:mn:c ow.. and .11 (\1111~ ~.:'''' 15 A cC)·'tnl hnllrt' plillll' (11tH ma~c' .m mh.:n:epl ol I 5 A nn \'·:t\1\. sn a cry~Ltl hO\InJ% l:l.ltiCC ((10\l,ltlt-. t ~A ~A .md ~ •\ ""X r. / ;"'' ft:..j"'elll\d)'. Flml) and Z intcn.:cpt-. 20. Show th:tt nm~lrtuml lntt·til1R ul th.: uml ..:dl 'uhunl! \\ hKh c;1n be filled by ll.t.rU .. phcrc mthc B.C (' -.nd r· (' l Cf} \loll nrc H 51. U.(JJ( ,md 0.74. fr)'opcCllVcl) '!.1 A ccrt:un crysl;.al ha_\ l;.1lli~c ctm..t.tnt nl 4 24 ,\, I(J ,\ and l,()t'-1 A (lfl #"<. Y. L a.xrs re.-.pctli\'•:1) f'h):crmhu: 1h~ M1Uer llhh,·t!, Ill 1\\U l,utu.:c. J11..,"c:) 111 tJ,j, c •")'~tu l lun· m~ Ill\ 111 ~ nltcfC(.pt~ ut (il 2.12 A. I0 A. 1.8~ A for one pl.ono. (II) 4 14 A. -. I :!.2 A r('lr th.: mher p l ant S(llllt/Un f-kJc l.t.lUtc CU11'-IML.\ arc II - 4 2J ·\, f, .:. loA. i ; 3.66A

sr .

t i) For rif'-t plan.- intcn:cpl'- .uc

1· b

;

nurnc.m:;•IJmcrcclll~ :arc -~- I ~

s~· Miller inlhCC'\ Ufl' '2 12J ( iiJ For 2nd p lane inlcrcc:pt..

~tR" 1J, .... ,

,I\

i e numc:ru;;tl m!erccph ;trc I, • II.' 1c

.2X

so Muter ulGJCC.' nrc ( JO)) 'iih·er hn\'C F.C.C. '-lruc1urc ;mtl ih 'lH11111t." r.tdiu~ '' 1.44 1.,.\ h nJ lilt: \l).lnng uf

the

(~f)l

o1nd ( 1t I) l'f.mc'

Sululum. Feu I·.( (' :th•nuc

r.1d111"

,. -

~' 1

u;; ~~ .; ~t H!:: .J07fa A

..o

.['!

I.C

l.m d

lkn~h) (If CuFz IS _;I~() kg/nl '. A UJHt t.:cll cont:.m<, ruur n ..... amt '"i&h1 F 101\), Atvrnic wt of C.1: Jl) ;snd F = 19 C'.1kui,11C: d tl! laJUt.'C t:on!\t.ull tt f 1tm ct)'!.Ud. Soluthm A-. H 11.ru. di)'>C'U~'-l'J 111 't'lltun PJ, 1he number l'J ,,hc.ve 11U'nllunc(.) Cu.F! mulcculcl- per unit cell h fou r

dcn)'oity nf the cr)''t•tl Ca.F! : 0 :::

J.attkc

( M )" --NO.

COH'I..I - U -

4 X •~q b023xiO:'·x, UU)

tt=4.976x 10 '"m= 4 97~A

I'"

2 Thermoelectricity • 2. 1 Seebeck Effect or T hermoelectric Effect Thh.

ph~.:no1m.•non

''il' tJi,co\'crcll

h)' Scchec\: tn 1&11 mul

h~:n~c ~.·alkd

lhc-

Scd1Ct:l cffc\,_l 1h. h~und Lhal if /tfo h iuJ tJ{ di lSimilor mc•rr1h or,- r'tWIII"• •tnt. .\II co ru/;JWJ ttl hnn/ 1.. llt.<tit. tftot WI (',nt.{ ;, drt•t•/cJJU''' WI it omllu·un· n 1 tttll'lll {1ol\ \ tllum J:h tt. idlt'/1 /1 11 Jum·Iimr~ oj tlrt• lwn di ~-' imUm 111('/(1/_, arf' ummumu·d m tt•, df/(t-r,•mtt·mt)t•r·murt''' The m~tgniwdl! :wd di l'f'erion • 1hi' L'utTt."nl l ll.:pcntf, vn the nutur~ nt the I\\'O IU:III.:'rinl' u'cll tuut upon rhc cldfc • L'tlt:~ HI h!lnpc:"r.uun:

hch\ c~o.•n I hi.' lh 11 .tntiL·uM junctions. 11ti... t'fft'l"l i.J' ~Jtn11 ·n t1 tf~t-rmo,·/ntrw t•/t~·~ t , Sn/Ji ( /.. t•/l,•c I A potir (1f junc1ion' o r thi .. kind ~called ol thc:mll'lOUpk 'Ft~

~ 1l ThL· l' lit r 1:!\'llt:t:.Ut!d in a themwcouplc ,, t•aJkJ thL·nnu~kuric c.m I :.IT1d nm-.:111 \\Jw.:h llP\\' h c~Jictlthcnntx.:lc~.~tt·k current. Th1"' thcrmul•k•ctric t" ,. , I \\ill cx1't ouHI thcnnodc" Inc ~.:urrcnl will flU\\ :-,c) hull!- th\'tt b J 1\!lnl"'!r.atur-= tht'l'cn:ru:c ht'I\'-'CC'Il l\\'(' JUnt·ti~m\. Whcncvt:r the l !:ll iJlefillUI c ~-.t Lhc L'' u juncti•m' bt"cortw' ~.·tpral t' nl I "'' ill h.: Jcru mult•urrem "-WP' Ot~\\ tnp \\'uh th..: mcn:..,~111 lh,• h'111J1~o-'1.11Utt.• d1fll'l l'I1Ct.~ hctwc~.·n the m·o junt:HI.)II' thcrcn11• t•.m.f. \\ill uto:r~.·.~~" llw u tJw h.'ll\f't.!nHuro: <)I the ~.:~lid JUOI..''wn , .. tu.utlLun.:J ..1t o C, thL'" the t.:: m f tl\'\ chtpt."J \\ t•uh.l be. u mco~,ure tlf tht" t~Cmpa~lttu ~.· ·•I rho: ht•l lllfll titln t'u

<=::)>-"''' 1:~

fi~,

2.2

Or igin

1.1 ft·Cu Thcrmocnup1r

or Seebeck Effect

In ..uonm· term'> Seebeck effect c ~m be exp1aintd a~ follow,, It" wcl1 knc.1wn thai the nun'lhi:r nt tr~.: <le(.lr<ms per unil \'Oiumc ~1nd their :I\ cn1~t'! 't!lucuy \'Un c' lr<.."'~m u nc lllCl.Jiln unnlh~r. lhoug h ~~~I :u..! ~ood conduttOI''· Thu:-. at<.\ )llllCLhm ul \\\ o cJi,inti l~1r mct.tl\. altere m:ty be :1 lcmlcncy of c lcctmn' tu nu~rnlc frnm one m~.~tal to I he! mhct :1cros~ the JUnc tion, from higher conc~.·ntr:.Hion 10

low..:r conce!n·

tration. Blll ~uch 1n1gnuon <.'annot CQnllnue for long 3'- it <1Uic.:k1y scl!- up nn oppoMl..: clccLn~.. field lh~l J)l'tvtnts :my funher 111(')\Cil\Cnt of cl~t:tr<>n!' ucros'

lhc tmund:try. A" u rcs ah a fi\Cd p<.m:nual uri"'C" :.11 lhl• JU11'-'IIOI1 hc1w..:cn 1\\ 0 ..Jj.,innlar m~..·l~al, called us nmtac:r pott•nlilll. The \'cf()cl l)' nf nn clcclnll\ m a nH.'I<Jt LlcpcuJs w .;nmc cx1cnt nn h:mtJCrnlUrc. H'i n rcsuh the coman ['(ll~OIHtl tl!.: l\\<..~n .tn\1 ''' c' 1!1\'\'ll rncm~ ';u·~e, wllh tcmpcnnun.·.ln ~~g ~~ lhl· dtflcrcncc lx-l\\1,.""(-ll m 11 l:OnHu; l polt'llllab: \ ;111d \"'when I wo JUIICiion-. ;u~ kept a1 tWf) dart\!I'Cill ICUl!)~I'O lllfC'• \\til ol\. I IU dcnv~ CUJ'r\!111 mund the Cl fCUII l"h.: n:,ull.lnt \.•.lfl I. t \\ 1JI hl· L .:. \

\\ h\!n ICIIIP'4'1.:11urc uJ 11ul JUfiCIIOJl'. '"' ~:tnw. 1hc (.'t'lll~tcl pot..:nu:tl '' uhn "~:1"'"" 1w0 jun~.·tlf\ll'· i\ ' J result there IS no res.ullnnt e.m.l . tn Llll! llll:rllH•c••aiJlh.· ...o nc• cum.·rll lluw' mthl· t,:trnnt l lcm.:c. when one iuncwm nt a rhc1mo\:oupl..· IS ht!:U\':c.l up and u1hc1 •~ c:oolcd. Lhcn the l'Ontncl p<Hcnu.ll ~~~ lhl" ht:;ah:-ll jundhln bc..:oml"' num: chan 1lw1 of ~.·old junc1ion. and ;1ptJtrmwl tlifff'l'f!nr~· '' Ur' cln~J wlm:h liCI\ .as the r~sUIIUill C.IH.f. :\lld is re.;pon,thlc nu lhc n~)\\ HI nm..:lll Ill

.1cwv;,

th~o.• tUJil'f I.II(Ull

r-------------~~~-----

-,y.

....1.1 1

2.3 Thermnelcttric Series F<-'r ..a ;!t\'CU tl.'n\pt.:nHurc J.ut~l.!. thl" dirccti,-,n t)fthcunul.'!kdll\." m.l l111 «11111.-n:nl u unbino.\llOn or mclah may be pn:Jictcd by urmn1=ing lltc rnc1.1lo:. tn "' ...c-ttc\ St·du·d. an.mt:t•U tire IN<'Wh iu tt .Jt'lit'3 in .ruth u t\'0\ I lull •thf 11 WI\ ll\ 11 fmm o tlll'rmmuul''' , rlu..· ntn'('lll u Ill flaw Ul culd JWKllull, fl'ti/IJ the nnt fiCr lllltiiS: t'<ltlitr to thr otltt•l Ht l'WI'III.'! ftJt,•r itt t!Jr J:t"Ut'.\ . Thi-. , .. 'hH\\U 111 h_g . :! I

Ocl\\-C'('Il !he :!00° and llXlQC thCnTll"'C lcc tric scri..:!'o

I'll( IJ

,t!lct:tion

onlimouy. Fe. Cd. Zn. Ag, Au. Srt, ~· llg, Mn . Cu. Pt.

Cl),

l lf

ua.:w(... j,

Ni. l'll,lnUth.

I he mctnh tu lhc nght ..,,de nf lc:lO CPN :1rc c:111ed lhcnnnclt'"-' ' rically ("'!OM II\.: 111\'liil'-. \\hi h.' thu-...~ w ns Jell \ 1de 3tc called thC.rlnodcctru::;ll1) uc._g.lll \,• wd •• l:oo. At I he cuhl !lmCII<m. thc thcrmoclcclric (TE) c.m f. act' 111 'tu.:h u WU) 1h:u i1 tln\t.:.~ CUfTCIH fr~•m !he 1'lt"IUI. cotrlkr in Lhc lbiiO\\;trd' the 1hc mc l~tl l.llcr in 1hc 11'1 The ...cril.-.. .n gencr:•l. ui\O irulicatc~ the m{agnatudc ,11" c m ( 11lL' lurdu.o_J tt(l;&rt two m~ttlb ar.:. tht.• g rc~ucr b the c.m.f. 1hey produce. rh ~ largt!!-11 ... m.l ,.., ohuuncd \\ Hh :•n :mtun,my h iMmllh Ll:tem1ocouplc

2.4

Vi•riation of Thermoelectric c.m.f. with Temperature

ltl'a"' hcen t1hst:rvcd th:tt a~ we lncn:.ase the tempernture dlllctcncc ~IWI!I.ln t\\ o juncuons of 11 thcnn()C<Haple, 1h~.::rmo e.tn f will incn:a:!>C (FJ_g 2,_j l unhlll 1"\!achc,,

.,;· I

I I I

T\'l11P dtU

maximum limit fltt· ll'tll{lcrnltm• ,,j tilt" hot juurtum 1 ,., wlwt't' thr thtlJIIIO r'.m.f bt•c·mlrt.'l mtuimum H · ·r~lkil IIL'IIIrttl ,,•mpt•mmn· ( I") whirh 1\ nm.\'ttmt [m' u partlntlar pmr oj u:rlllh and Jl{{t•rnu (nr dilft>n'/11 lnur. 1\flcr the ncutr:tl tt•mp<nliUri!. lhC C. Ill r 'l;lr1' ch•cn-.t,ing :Hlll rll rl f'ilrlit"Ufllr IC' IIIJII'IWUfl' 0{ rJtt• fwt Jltllrlitm, t'(ll/t<t/ 11'1'1/U'Illltttc li}IIB rt urm ( ( J lflt1ntltt t!.nt.{. Ogl/;11 hCCtllltf'\ :.t.lto A/fl•r t~mpr'flllmt of im•t·r.;imt tlu: dint timt nf lhf·nuo •· m.J will iucn·au· in " '''t•t .W tliret'titm. n•.th th1• tllttnl\r> oj tt•mprrmurt! /urtJrrr 11\

Tho~ H h:'' ~~n '\."<11 thou wh<n 1h~o• ~o.'<\ltl )un,·tatm '';II ~:on,Hint H.'fl11)~.m•tutc .mJ hot .tunctu\11 h.'IUp\t.tllll\" ' ' "nhtah't:'l \,tncd tht•n th\! th~11t\11 \!.m.f. t/;.1 \\ill \':tr) 01111\0'1 fl~ .a J't.llolbtllll: hllh.ll\}0 pf th~.t h.:lllflCT.SIUfl' ditfC£l'llU~ bcL\'-t:'l'll

the IWU junCtion,, ill tile rn1JO\\ in.~;- \\ .1~ ( E =

lllb

knnwn

il" Scr:bf.'~k t:qUiU u.m.

-1

;

br-

(2.2al

\\ h ..·n t;uld JIIIICUtlfl tt:mpcrnturc j., 0 "C nnd Utn when cold junclion temperature

, cr i~ tht: tcmpcr.itUI'C or th.: hvc juneIiun ·~

1101 zem hul aJ r, f' then ,,

J{/ ~

+ t,l

where (t: - td i) the h!tllpcratul~.t diO·c-rcncc bct\\Ct.'n hot jum·tion und coll1 juncti(.10 and n. b :uL! knnwn ::t' Sce~~k L'Ocffidcntll.. 'fJw nFutmltc•mJit'fll.'Ur. (T,) u lmlj-wm bc•l\~t't.'JI tht.· (.oldJWU. tiVIItt•mpt•raJurr tmd tit~ tempc•raturr• t.{ im c:r:ritm CT,) Nnttrul t;omprrulurr "" ccm.Hcmt /Or tl gin·u tll~rmot·ouplr rmd it ,., indt•twmlr•tlf t~/tlu• colt/ jtmc_tion tc•mperature ( 1:) which is equal to

T, = (T, + T,)12

(2.3)

Thtrmrwlt•fftlt'tll' }fH'I'f.fiOil (('lllfh'Tclfllfl"

T, i,\

\'tuWhh•, II

hf'U18

II\

mm·h

••$?

n}mi'C' lflt• 1/('tl(t(l/

tcmpt•mttat• T, til tilt• rold junrrton is btlow tl. Tltu.f T1 dt!JN•mls (Ill T. . A' '-hO\\ n m Fig. 2.:; if t.:Oid JUrU.,IOO tcmpermure chnn~c:. Irom rl IO T,' then 111\'CniOn tc:mpc 1 alurt~ 7~ will :tl..,(t '-'h:m£"" from T, 1\1 T,' RUt in thai 'ituallliJl ahu T,1 will he :,.nmc (or·' Jl:trllculur couple.

2.5 Thc n noelrclric Power Tollll c.m.f 10" lhamrwuplc h a paraholic func1iun of 1cmprw1urc und c:m hr eXJ"'rc~::.l·d

,,..,

6=,, + I hr·'

f2 h )

l)iiTcrenuaunR equ:mon :2 (). we have tbcnnoclt'clric power (/tl gtv!!n by

[ I' =

:'fr =

r bt ]

1f T b the ll!m(h!r..tur"' nJ the hoi Juncuon nnd T0 chc tc.mpcr;tlurt \~t Ihe ~~ tltl ;unclion \\htch '' Lcpl ~on ..tant. Lhcn. J - T0 ;; 1. the tcmp<.·mturr dtffcr~..·n~:~· bei\H~4'n l \hl JUII\!Ium' an ' C. From t.:4UJIH10 ~ 7 \\ t": cunclude th:u th~ \ anmion of thcnn~b:UlL pm\·c..~r " 11h h'mpermur.: 1!- •1 'mughi line l Fig 2...1) c~tlled tlit"rmoclertrtc tli<t.r(fjJm Sud\ diut;rmn~ f{lr ,hffl'l\'111 nll!tnl!<. ~hown an F1g. 2A cl:1rify th:tl th..: r01tc '1f l'hung~ nt th..:rmo c.m r. \\ ith tc.·rnpl'l"iiiUrt h (X1\III\'C for lhcnnoclcctricall) IX""".: md.lh like Cu ami II 1t. nl.'garh~ for th-.:mtoclt:ctric:slly ncg:ttivc mew!' lilc h· Cu I'

lt;rllp IIIII Fi ~.

2.6

Z..J

\'uri:Hion nr

th ~rm ntl«trir:

pn"'t'r " 'ith tN11Pftature

Determinati on of Neutra l Temperatu re (T,) and Temperature of Invers ion (T;) from Seebeck Coefficient

At ncutruiiCIHJlCmlurc tT,l tlll.'rnt~) t.!.m (. i\ nmximurn. ~c.• change (1r lhermo c.m.f. £ wuh tcmpcn.uurc il\ zcm. So.

" =Ill+ •:.

I ' 2bt•

:11 1-==-

I" tht.•

r.1ll.' •''

[ I,=-~

thai''· ,\t

1 -: ·1~.

!2.Xl

th,:nnn c.mJ /:. J, /ern .So,

"' . L

'lilt '''

3_hT;

!2.9)

th;u "

1-k ·l

fiJ!. 2.!\ Fr·Ph lhf'nnrH;"nupl<'

2.7

Seebeck Coefficients

IIH.' \Uiuc.. ur Si.•cbct.:~ ~;ucHit.'h.'OI .. (I anU hom.· ~CIU.'lOtlly ~1\'CO with I C\pcel Ill lc.1d (Ph), 11 c:m be pl):,tlt\'C ''r nc~alin: fRg . ::!.5) For u lhc rmocouplr. rormcd Wtth metal -. X .mt.l \ s~cbcd•. cocflincnl ... c;_mhc \HIIlt'n a.... a, • and l1, , and l'tprc.;,cd :1' fl

" I'' "'"'' Sumlurly

12 lllJ

,.,., 1 - ~~ "· .. ; lh,

,.,

1 -

a.,

1,.. =--

11\ •

1~ . 111

h,l

liH:. Seebeck cocffu.u;m'!l- \aluC' \\Ill bl: pn"''' "' \\hen jut11:1h1n frum lead 10 oll11.:r mct.th u... cd 111 thnmouwpl~.

2.8

Ia, -

CUITCJll

nm"

.II hm

Law of' Inicr mcdil1te IVIctals

In pmcttcnl usc the circuit nwy not conwin only thl" thermocouple mcLah. 11 nttty hn\c :tddiuorml metal:-.. 1.c •• Cu or other mctul ' u~ connccr rng Wtr'CS nuJ :tl~o 111 the cml ufthc g:ti''~IOOIIII.!LCr Llr\·olun-:tcr to co mplct~ 1hc ..:tu.:uil. So i1 j, •mtxm:ml lO knc)\Y lhC crfccl or :tddition:al JUilCiion~ The crTCCI of nddiuonal melul ... II\ f.. new. n fmm 1hc 1nw ol intcnncduuc mct.at.... It '"t:ue~ lhm tfjunr tiOif oj thernu~t~twf)lt oj n'" mt•tal,f A and 8 tJ' O!Jl'llt"tltmd a rlwJ mt·wl C iJ itiSt'rtt•d iu b~..·twt't'll tlu·m.

llw n•.m lumts/wrmn ,•.m.f ,.,.maws t/Je .mmf! iftJJtll bmiJ JlltWIWil.f ofnwtal ( on• lit tht· ~·wut• u·mptratt~r~,•, 1'hl"' can b..: cxpl;uncd ~'' ft.,llows: ('ons<dcr a circuli oonwinmg 3 mctub A. B. (' ! Fi!\ 2.<>). If 111 tho t~rcull ull JUnt·uon~ nrc ;H the sarnc temperature then there will be no poss1blc ..:;ourcc ol energy 1hm could daivc current in the Clrt'UIL So algcbnc l\Utn o l the 1hree

,, ...iJt. 2.1'1 Juncllun ur

th rt:~

ruet:tl\ A. U. t '

12.12) ~uw.

il th~ 1csnpcra1ure o l llllll~uon AB lt. changed. 1h~ com:h·t polt!llll!tl :u th:n

puint dtrtng_c-s ton new vuluc

v; bul l'2 and \

, rem:un!- ~arne Tlw 1hcn11u c.m.r.

/! ut.•tut~ in the circmt wall then be I!= IJUI

frctm

C4UaliOU

v,· -+ ... t·, v.~

(2 .12) V~ + \', = V1 1:.

So.

= I '( -

\\lhch 1;., 1hc same tL9 '-"'C should g~·t. tf meUIIl' wa .. chmm~ttcd lmm tlu: cm:uH b) hnn!!ang tis Junchn n~ wilh /\ .uuJ llm1o contort I hu:-., /n-ruAru~.: thr nn·utt 111 Hum• 1mh11 m· 1uM'rtm.e " rltm/ mt·wl. wlm.H' rrmp~ratu((> '·' rlw \tiUU' tH 1IIm oj fltr wmi 111 the break, dol'S 1101 a/tt'r flu• row/ • nL.f lu rltr drnm

2.9

La w of Successive Temperature

thl'nnncoupJC, tilt• ~· m.f Jtt'TU'rtJI,•t/ ltt•tu nil IOII!'l'llllttn• J1flncm t' f11 mu/ (1,, 1\ i'i/llllltn the .umr (if Ihi' f' m ,f far um uumht'r 11( "'' n•Hn t \lt'fl\ ;,," 11 lrid1 for

lit( l'""rt! rtlll}:l' of trmfN!mturt•lm\ ll('t'll llf'wdnJ but tlrlll mt;•nm·;/tm,• lt'IIIJWnlrtot• ~llout.l

fu· /1.\t!d al 9"' Jwmx tlw

fi\ Jif.'fiUJOII

f'tl. ('

(~.1

'\)

Bci\\CCn n(> und IOO..)C. three fixed l l'llll'>l:nnurc' can h~ pu~.. iblc. fl '(', ffi{IOI lt.'lllfl'.'l.ttur.: (~ay J0°C• am.l 100°C, whkh will nul chom~c during cxp.:rimcnt. So m tin.· l:.thorawry. Itt"' af "llt.'CCI<('tiVC ICJI\ JJCnttut~o:" t:o.m be ca"1l~ ''cnfkd a~ £11J.I _ Q -

1:., \fl fl

+ f..·Hill WI

2.1II Thermoelectric Thermometer· It'" the 'llllpltficd arnwgemcnt lo mca,un.: the: t..:ntpcrature b) uJ<romg tht:nllOCOupl\! win.:--. 1l1e t.::omplCh: 1h.:-rmoch..."CinC thcnntlllll~h:r ml1 fit C.:OilSI~I'- of• Two clements l.'onsutuung n thcm1ocouplc. 2. Electrical insulo'ltion of the~c \\arc:~ rmd pruh.:cting luhc ... 3 Galvanometer c•r mtl livoltmetcr or potcntiomch!f for mcoburin~t the thermo c.m.f.. ~ Arrangem ent of controlling cold Junctl()ll tcmpcrnture.

Ht't{IW""f'"ll.lll.\filr l>iffi•,cm

Rm'K''' af1i•mpf'r1Wul': Pur low h.!rnpcrnlllrt.~' "I' 111

300"'C. lh!.! courlc ot h•'c mcml' 'uc:h :1' Fc·<.:•.1n~1:mt;m :mc.l Cu-con~umt:ul .1r.: ...au ... ruecul'}. J" they th:\·~IOJ' o.t lar~c c m r.tccnttgr.tt.lc Ft,r lll!!h tcmJX-ro~turc .... n........ ntdotb ..:anrlt11 he u,cJ ........ lhl')' ~CI "''d"ctt nnd melt Nr-Fe l':OUpl.: liMY I~ u'c(l up1t1 OfNl C. but .:~ltt\l' lhttl, piJtillulll ;uJd .lll\l)l' of piJtimnn mu!'-1 he uwt.l 0 Th~ u'dul rnnJ!c n t u lh,•rtml<Cicctnc thcm,nmctcr '" - 200 f() ltl4)(J C' h liMY g11 up lh 2 100.:t\ 'I he \.: hltk'i.' ul mctnl' ;md allny' forcon"itniCiin~ 1 h~ llu.:r-nH~~•upk tli!JlC.ntl' un llu.· t m,gc.: ol' tt•mpcnttuh: In be rncalt.ul'l.:cL \Vithin th.: r.m~c thl.' lhcrmu-cml •klt'l"i"'tl 'h11uld he lur~t. und 111 uvood lh< oclci•UI nl c m.l lh,· t tcutr:tltctu~r.tHIIl'

'huuhJ N.· l':tr r\.'IIU'Il' from the tcmp"·rutur~ H.,~ mc;:l~urcd

Cuu.'ltrucHmr iJf TlurrnoPiectric Tht'rmnmtt11r: Thcnnoclet.:tri.._ thc.:rmum~h:r cunMructum llt. 'hcJ\\ 11111 Fl!_! 2.71t 11 corl si,ts of two ciCfi)CJll' in the fonn 1ll a wtrc. Jnd nc~1r !he.: hm pn~tit1n I.;; in~uluted with firc ~ci~•Y· Tht~.:'-" \\ ir'-'' Hrl' l):. ..,t•tl through mica tli't.'' I•' J..l.'~r them in po~ition ·nu.~ Wh(\}1.' .trr.Hl~l.'llh.~IH i' !.'Ill h"t•tl in .J pnn:clam UJ llUiJI't/ tuhe. the tri.'C end' ur the \\'lr~s: •Ire CC11lUCUCd (l; l\\ n ~l'nninal" C 1 >Utl.l l. nt~,.•,e ccrmuMI!' nro.! conncl.!h!d m the cxtcnsh'll ll.:·.u.l ,, lt..-adin~ h1thc l!"tld jun.IH\11 Ch~. 27hl Circuli connection'' ~.:h~onl) t:\pl.tincd in Fig '!. 1.:. ~Ill~: cold jtiiH.:tioJl i, thu' mm,rcm:d It) u con\t:mclll di,tl1nt pl.n.·t·. '"her.: :.t l'On,L•.tnt l1u'' t~:.upt:-r-.uurc ...~, y 0.,(" "--:m be maint:•incd hcc:tu,L·m:tinuinin~ l'OILI h:mp~ratUrL" ..tl 1Jt1UII' (" I• C~ tl~t!! ].7a) \t~hich h. jll''l :th~\\ c IIll: hot julli.'IHin (\o3Y ut t~mpcnnun• 1tuKr·c, '' nPI pos,tble. In hccwecn the~ H\(l I!Sh!rhu•n \\ ir~'l. a C'otlihtnh·~l ~;.,h•mnnt:lcr '' UIIHh!t:lcd. fro m which.lur .1 parht:uloulhl.'nllll ,..m .t' t.'Pirc'ptmdmg ll"llll~r..ltuh.' ul the 'pccamcn a m he mc.,,urctl

UVrkiug Priuriph• Th\! hntl)' whc>'-'" II.'Ulfl\'f<Hun: 1' ''' ~~-·

m"·;,,urcd ' " .,roughI tn \.'OIH!I4;'f "llh th• wcld-.:d tmt IUn~tltlO ,~, 1h~ lh..:ml\11l1~h: r. When th.!Juncuon ~~umn ... lh" 1t:mp!!rdtllr• nl lht: hnd ~ llw th...lh.·L"Ih ln 11! l hl· ,g.ah;annmctcr 1 ~ noted. Th1"' rc;Hhnj: thrnll ~h-e"' the lcmpc:tolllll\.' nl the hrtlly. 'ml·-: lhc gnh•;:momctcr i' L.Jhhr.:th.·d h1r 1t:mpcr.uure. U~ l...'hn,""ing 'uuahlc mct~Jlhc wires. \\C can mea ...un.· tcmtwr~hm.: b<'l\\0<11 21)()( unJ lt>CHI 'C Mrrir., I. II ha~ ~~ \t••')' \\ttl\! upcratwn rnn,g.c. -200.,(' rn ~ 1 00('1 (' 2 Sm~.·l' lhl• \UfldlJ." .trt•a uf the hlll JU11Ction h smfilf and thcnn:.t1t·a p<Jt:lt~ tt( lht• .iunclu m 1' \m.tll. It c:m be tjukkly hC'~I11!d up l lcnl'.:. Linh: lotp 1..

viHually .tb"clll J. Rupidly \WY in~ tompcraturc• can be measured. 4 Jt b t:hC,Ifl :tnd CJ:.) IO C0115tntct 5. It can ml',...,un: tcmpcr:.~tut c at a poinL 6 A \'Cry htj.!h •~mpcmturc ('>:t). thllt of a furnace) cnn be m-:a,ur\!\.1 lnl~ llhkl

Dt>men'I.'f

I. A particul.tr thernuimctcr is not accur:ne over the "-id\! r.mg ..~.

uu,

Ct~l\lfuCiiun

•

of themM.~Io..rn.._ tbcrn)I"IICtl"r

( ":

Ih i

f.U

(<I

Fij#. 2..7 Thcnnudcdrit: llll'mwnwh•r

2 l'hCh."" 1111 th:orcucal fomlUia lfHu can be C"<lr.tpnl.ucd o'er·' \\HI1.· tang'-' For dlffcre111 1cmper:nure r;mgc tHf(ercol lonnul:t~o: .trc u'l'd 1 Dtnerem thcmlc:>couples :1rc rcqutrcd lor dtffctcnt r:angc-.:

2.11

Thco·noislor

The clt·c.:Lncal rc,hh.ml'l' or mo~t mctaJs cJr tlu:ir nlloy' ~cnl"rull) chJJIIt:~ wllh c::hungc 111 tc m pcnHmc lt.\ R, = Ru [I +a (T -7j1)1 R, = resistance ut temperature T

•c

12. 11ll

R0 = rc,i\t.Jnt.:c .11 O..,C t Rcr Temp.) u = tcmpc•--:u urc '-'clenn.:lcnt uf the rl'SI~tancc per <)C The

ICillflCl ,1\UI\:' t.:(l'l.'fl'i~ il'HI ~1( Hllhl lll\:L:.sl ...ul! llthiti\ c

Sn "ith tlw inc.·rc.l"l.' in the'"''''"' U) 1111hc lllCial mc-rCa"e' Rtn in Ihe c::I"C uf " &:1111 C4\1l(hU.'Hir tht! 0,.\"i'tl'll) ~t·nctall)'tlc"-·r~u't' \\ ttJ\ incrc..'l\.: rtf lem~rJt urc.t\ ,t!mH.:unlluL'It u U.\t!d In lhl! m:umc1 i>. L.alh.•d lhL•rml,hu whkh h:1:-. C~ICil!t~hc npplic:.atinu iu ICIUJl'Cr.Uun:

IIIC.nllllnlt'ICJ\, jn lhe n11.'U\UfCilli.!Ol t\( lllil.'I''I.\'!1\'C lrCtiiU:IlC)', fl')\\'l.'r, :1\. U lhi.!J 111.11

c.Jelay .uuJ rn \.'nrllrt-..1 t,~,., tees lunt.:IIOn\.'U by c h ange!<~ 1n rempcr.r.IUrc. Fur nh)\1 11h.'l.lh the n•. ,,,,,llllC ut..:l't'.t,co, .r.bt1u1 UA'?r'C "hen:: .... lor a '\t:llll conduc U)I '·'~ "' · Gt.•. ''-'''''·tncc dccn.:;l"'-'' tl 10 NC}/"C Su mct.1h h~l\'t' pn"titi H' L~,'K'flicil.--m ~,r n:'i't.ant.:L' m ...m.tllcr mosgnitutlc wh~rca~ "-':!mi~-:ondut lur 1h~:nm~l1 1r h:a' ncgtt11\' C cucffi;;rcrl ul rc~r ... t:mc~ uf h1gher maguuudt.·. ButlhC1CtHJ)C(;l1UI'C \.lPI.'ffi~o:h;nt ul thcnlll!oolfil' C:Ul :11:-.0 he: ('I();) III\ e.l11c 1hl!lllh'\hll' With JlO~tii \'C I\:'Hl(1CfatUrl.! !:iA:ilii.:JCIII ttrC gt:ner:.aiJy lt\ed in IC.:IHJ>c!fttl\II C IUI!•I\UIII1g_ anMn.uncm ... Thco rc:'''l:•u c~.· ,.r t1n.· ruw..mr" !!•ven hy

R, i~mpenUU~ l'HCJltt:tt.~nl

protx•rty

ufth~

=Ru x (IJiLI 111,.1

{J t.:UI he pn..:ili\'C! or

n~g_:J II \'l'

12 J7J depe.UI.JIIll-! Ufl"'O

tfll.'

mrm.·nullhg.2 ~ ). '01c tu:tJ\'C mntcn:al 0 11hcnmstor l'i tr:m~uwn

lllt l ltl HXhll• ur Uli,\ IIIH.' 111 HXIiJ,.-, (H"- It k , t1r llliln_g:Jilt;~i.!, nld.l.!l, l ' Uh.tll 'HJ'IJ)I.'I imn. 111.uuum1 h ,.., .t ly('M: 11f ..t ...C'uu ..c.:c.mdul.'lur Thermis11.1~ .arc m.suul ..t~o:luJcd 111 m:m)' t;h3J""!' .tnd ,;,c .. tx·.ul.....h~.... 1.\:tt>he~. rod\ :ltlt.l gl.l\~· ...c.alcd rn•hc,.

Mml.uur~ hco.~tls Jl\: \\dl "uncd tnr .lppllt.'.ttitlrb where fnM respon~c :anJ muumum thcmmlloading ar~ c.Jc,m:d In IJlr C::J.!ioe nr gla.s!\ Clll'llp!-oulalion the aim~: or rt:\fWlO\C

l"ig. 2.H

Vnrialion nf rc..o;i ~lnm:c in u tlu,•nni$ior with tcmi)Crnturc

fllrnuot!lt•('/l'fCIIY

(If lhC lhcnnt~lOf lO sudden lt:mpcrnturc:- \'tlfi;IIJOn inCn.~aSC~ !<II!:Oil!C:3IIll)'. rrom 1nitli"cconds

tO o ne ~t:cond.

t\J{~IIItlfOg('.\

1. The .li.lv;.ullti~C of using thcnm!<ltOr \\ilh high ~nsllt\ uy '' l<m co'l. prcci,.ion h!tnp!'rnturc mea~urcmen1 and conLrol. 1. Thernm.tors art!' U\':HI~1blc in a w1dc range of hagh n:sistanre v:1lues. Th•~ 1U11~c~ remote l\\0-\\'lrl.! me·•~un.:mtnh f'Xl~iblc wllhuut the •'ct.·~t fna lCIIlpCrtllUn,\ ntliipc':ih(ti!Ufi of the lt!.id\. bcl!oaUSc tl1c r¢M~lun(:l..' of lfll' lc::td.. beconh.:~ in'i!!niricant. Sinct! both th-:: 1'\!Si~li\'it) and h:mpt:r:IIUil' coeffic:H.:nl ol ·c:-.i,tJnec of copper \\ire ~·re Stl much low<.·r than thoM' ~:xbrb•tcJ h) lherm•.;hu~. there i~ \'inuully no limn to lht! lt:ngth ol thl' c<lblc 1htu m.ay be ' ''..:d between a scn~or and ;.L<;Sociutcd in.slnnncntation. 3 ThermtsiO~ arr ,n••u J.tblc in "null ~lt.c,~o nnd ftt~lcr re,~opon:-,c umc. 4. ·rney have lUng t~nn stability pro,·idi.!d they an.: not CApo!-CU 1u h1~h tculpi!wlurc Aho'llc .lOll~\. tht! \tuhility of mos1 thcnnbtar i ~ ~rc~ntdnl . Cllaracreri~·tlc c:u n·t! The ~i"iJ!UlCc \.:f'Si:'~ h•mpcrature t01 f)'ptc.tl thcrnlt:c:wrwtth ncgnii\'C ccmpN:HUtc coef11cicm i.s shown to 1~11!. 2.tJ. The reSts:Wocc decrcases non ltn~arl~ \\ nh

tcmpcr~tlurc t.:• ~eflincr,r rt a'

~(rl\ldOI ,

·'

For small runge of fcmpcr;uur<' hncar npproximn1ion i• vulid. The rung~ Ill tc.'mpcrnturc' O\'Cr whh:h lth:mli ..tol"\ ~an lx' u,cJ ;, ()to JOOOC. hi~h\!r lcmpcr;:ltun:'

f'i g. 2.9

Vur-irllinn o r rcsi~IDOl"t> in n lh\•rml<ltlr wllh ll!niiJCniiUrr

cnn he rncu'iurt.~t.l \\ i1h ~a me degree of .success. The rc~i!to l:tncc.- tlf 1hc lhcnni,lur tJc.~' nut jump iuunt:dialcl)' hi a new v:.ltu: when 1cmpcr.uurc Lhan~c' htu rl·quirc~ u "mull umuuru olwne to .!-f::tbilizc ntthe new

n•,istnn~c

\luluc _Ttu~ ... c~prt-.;..!-cd

in t!!Mn!o. ulth\! umc t:l'~nstoint of the thcmlbtor tn il mnnncr ~imilur h• the churg_•nl! u r [l C.:U(li.ll.ltur HI llC-c•n·uit. II the ch:mtcll.:rhlk or th..: thcnm ... wr j, known I I ., pil.....,lhlc tu rcl.ttc the current me~.;urcmcm tu the acumllcmp.:ruture. :and 11 l.!:tn be u-.:cd :ls ccmp.:ruturc mcu~uring: devlc(. For mca~uring Vt"l') IU\'- t\!mpcrJtllrc~ ncHr ,lh'\Uiuh.· /Cit~, , 'JlCCIOII lypc or thcrrnhWr ha.s been ~oh.'\' dopcd

I' ROBI, Ei\IS I. Fm h >l'u lhc nnuctltlpl~o: 11 h uh\c;ncd lh.lllhcmhtt• m I '"' 11•w when uur nlllh~ jun'l'!)n j, .at :!o~c. und the l)lhct j , ul ~orne luthe•· h.·mr~ rulut c. II lhc •tt:utrul

h:mpcr.tlut..: i ' 285 C. calcullttc Ihe ht~h..:-r lc:mpcrntu!T .uul h..·th.v linJ l •UI h:mpcr;aor - 2tJ (

lun: uf 111\ t'r,u11 .11 cuJi.J jurtCI!On h!lll(k:fllluh:

r :: 2lil ~~ c

\'ulllllm l

I = 211"C l ,, ::o. t f,-;.T.l/1

550'C.

1, :.: :!O"C

:\.•1"-

T,- = "itHf'('

I -:: 2 T~t

2. C.Jkulillc t.lh: r11.:utr..J t('mpctulUrc ..,f Fe· A~ thcrml.}\,;uupk l n~ '.1lu.:' cJ J.UJ ban: lh.65 .tml U095 fur Fe <mi.l2.8611nd 0.011 fur At:. rc.•.,pc.:~;lt \ cl )' C••h..-ul.llc .ahu, 1hc 1hm nn ... m l nf 1hc lhcrmocou1>h.~ when 11,.._~ JUill' IU•n., ltr,· 111 H"f. :'lnd II)(! ;It ' '''/1;111111 ~~~

I•

''tr

c flt -t'·rh •

=l rl

1.. ::.

.~.

b, - U OI .,

0 OQ5

n -

10 h:\ - !.HO = 1\ 1'i

1•,,, : 1. 1 ,

u,.,,. 2 _gh

16 (t~

.., • ~ 1

U.OlJ.S o/h

!:'

0 .01 1

= U.ll 2

7Qf(1.1 1:!

.=,

12'\ l '!"i...("

m+ u ~ bt:

I ' 7'l ~ lC)) +II~ ' 1- 0 II'!)" t W11f)fll

819

Thcuuudcclm: flUW('I t1l Fe " 17 J.a 4J<¢71 umJ Ihal u r ( u I I ~() .. H 11)1 iJ"v r l \\hen: r ::: H'mpc:r.u,•rc m Sho\4. 1hm c m I' nf lh4.' lh cnw"~I.HII(ll c. 1 h~.: Jum. uo n... Ul \4-')w.:h .He·'' .llld j()()~C j, O.IJ07 v.

<•c

p=(

':ff t-

(Fc·Pb): J 73-1

: II -t

J>t

~ 136 t 0 l)')J

<lf'<-C• :

17.\4 - 136:

1~9~

u (Cu l'h) • 13(•

b Ku-11l1 =- ().~5

£ tfc Cui=- •" -t 0.5/u~

15~~

• HOI Hl.5 x 1-H11 • 1IIHIOOJ

E !Fe ("uJ = IJ070U pV

= n n•J7 v QUESTIONS Oetiuc the tclllb nculful tcmpcr.uutc. IU\Cf'.ion tcrnpcrutuJc.thcnnockcuk c ttt f. E.\pli1i11 the imp<trtunu:. nf ncutml lcmrcrnturr ond ternpcnuure (J( im ~r.,1nn an the slUd) ol l hrnnoclct:lrt<' \'.Ill I 1. l~nr fc·f'"u lhcn·tocn-up1c-. ncutr.:tl tc:m~r.:Jiurc ,.... :!N~''C wht:.n ~l)ld JUP(:IIIlO lc.mpc.r-o.~turc ~~ U C. C;.~l\:ul.ttc: tem~roaturc ,,r 111\~'""'uu 11 t..ohJ Juncuu,, ,, .11 ;\0°C. 3

Wh:u 1 ~ ll~rmocl telrt c: c-ff<..-cl'! .Stutc and C.\ilhun lt~ Ia\\ Olln t enn,'l..h'u~ h.•mpcrntu~

:n'ld Ia."' ot imcnnelfmte rncwl .ol hlf Sccbcd. effect, f = at ... H. :'ihi "ihm\ lh:\1 n~·ut~1 tcmpei":\HifC r. ,... tl!h ~Nhcrc ., :md l1 me ~.:chcc~ codiidcnl .. 5 for Fc~Cu tl.u:n.t-.x.uuplc. ''·hr:n JODI.tiun "-'" .11 ~13 K. the dlCimUI.'Ietlnl em( L' found to be 0. "hen che uthcr junctinn j, ol 8.JJ"'f< On funhcr in<'hUIMnt; the tempcr::nurc of Jtnctton B. the (Urfcllt ~ ~ tound w be du.ll1glng II!It datt:ClJOn uf now. C"'nlculatc the tcmpcmtuw :)1 w hi~h ~ m I 1' ma"\lmnm :md the tcrnrcraturc ,,f UI\IC:r">t\ll1 uf .:uld !Ulll:hUil ,., !"iU 'K h l ·tnd Jn,er<ion tl'rnr~nnurt' ,._,, l-1!' Cu th<'mi'-"-''''J'Ik \\ h~n .:t•IJ tun'-·ul•ll j ....11 -2:-; '(" :111(1 2$~"'C 1\'cutr.&! tcmpcr~UUh! '"' 17i- <:. wh..:n ,-.~ Ill JUncunn 111 nl 2.5' Wme shon no101 on: Seebec.;L coc:Oiclelll rmd tl~rmr'M!!Iec t ru: themullllCh.•r I" E:\:plam thcnuolccttic po~l!r llu~ dOC'' 1t hdptu tkll!rnunc d and b'f

•l Stulc ;m,t C''(p1t~in

thcmmcl ccm~.

c mJ

fummt,,~,·

lim' nill )\JU iintl tltc neuH.tl

tt'tUJ)Craturt." frou1 iL

1U C"kulutc thr: thcmu>elccuic c.mJ m u Sb·Au tlwrmocouplc ~ ho~ Jll OCi t on~ :.rem 25°C" wul ltX.tC n.•spccnvdy rhc vuha· ond h "''-' .\5.5~ anJ ()_14(• lot Sh ""d 2.'Xlomd ()Jl)9 fur Au. rt'ifl'Cdl\1'1) \II C\lll ...tnnl' .arc m ltVIcC:

,,f"

:O,ulumm.

n SI>-Au

bsll

= )Cj 51\ 2 'IU ~ \2M

Au •

Thermo c.•n I

o_I .tO - lU)01J. 0 I u

= 1£:-.b-A.. = d(r1

11)

+ l /2b ( I:+ r1l

(11

- 11)

No..., r1 -=- 25''C. 11 =- IOU\ SuE~"":

1:. =

.H.6ll X 2~ 5 1

7~ ~

1/.2 XU 137 '(

12~..: 7~

+ <>12 1875; JU93 IS751JV

OI ..CliSS. ptopeny ur lhemliSlur.

12 .

n1e e.m.f. o( f-e.r"b t h CnTIOC(tllple, where unc junclt<)O IS ;tl 0"'C :mlf Olhe-r ;tt IOO"C is 1185 t-~V \lfhcn the .second junclic)u · ~ 111 3oocr. llw e.m ( t j 675 uV

'\1rt11lar rt';aiiiO)'' "11h Ag~Pil U'Ufllr .m: '71 11V dntJ lr•2 ' pV. h'"P.."'-11\d~ Cill!.:ui.IIC th1..• l h:utr•• l l1..'111JJ('I.tiUIC ltn J~c- A,; thcl111i)l..ti!J()It.• .\,,flttwJr.

~ 1'1

= II&.'\ =-tilt

;

II'~ 1>1\

uCIOOI ' ~ jlel0111 1

110, "

If• M

-I) O'lt•

'"'''

~/lPIKII'

u('tKI) +

l71

QOIIH •

!JJ:.tr•••'

'"~' 11(~1(11 ' ~ /Jt1001

""' =2J'(. /1, ~~~

.11

() Ul'

=- 16 t.~

!(~ a l_t (q

:-011'1h-UUI7=-Uil.\

,,,,,," = ~ = ~~~ ()1' (" lllt"tlll•I('IC\:Ifh. 1-'".._.' 111 Fe''" 17 ~ IJVf <. Jl U "C t1ml''"'''-'' (t-.(1 C th.11 ,,1 t •• f ("ill "I(" 11kJ ltfO .U ~0 ( f-lnJ lft~ \,\IU..: 1._1j C lid JUC f"'( ( U l_UUJ•k

1"- "\ 14\

"'h<'n ~o.·tdd 1""'".,1'1' ' ' ..11 O"'C" :and hot JUn(IM~ ~~ ncutul k"m('lt'r.atur.-

P•tl-+-{JI

= fl + /Jttll n u • (Jc ,,114,,

tP), • 17 '

l7 ~. #tr a -UU•II\t1

tt,

u·a. ... ~ c

,, ...

J.lt5th

n~a•Jlt<;tH at,.~

2 "'./it.=-- u.o<

fl~t.-u• 17 i

fJf"(

•

2.' =I' 11

u t).ISh (I

15:! p

Oi ,.

l"r..._.. -rl< l,.t+--..k-IJtT,.I'

fiiJI)'I;f'l

3 Thermionic Emission :u

In troduction

rhc pwc.c!'l~ ol c nw•.,ton e!nl~'inn.

IJ th1'

,,j L"lcclmn!'l h omo metal he ...urtacc '' l:all~:d cleurontc

~m t,,ion 1~

CiiU'icd due lo h c.ntin~ Lhc m~t~l. it 1' called a!\

t/wr,JI£11llf C'IUI\<UOIJ

3.2 Theoretical Explannl"ion for Thermionic Enti!>sion mct.1l1tl..c cor~r t~ r lun~"l en. tltcn: .1n· plenty of free l'IL'~:IrotP•. hut lht!} 1-:;t\c.:: the !01.' l;tllic wrf.n:c At room tempcr.tture, ordntal} nll.'tllh t.lu 111)1 In~ then dcctrnll'• Thi.. ll'u.·:m' th:11 ;' (un:e mu-;t cAi.,t "htd1 rm:ve.ont\ thl.! dct:"uv·. n, 1r.un I~.• a\ In)!. tht: metall11.: .\urrncc pcrmaotntl) Ftlr .tu e lnthtn tn ....,l.:-.tJll: In

~unnut

frnm thr mct,tllic 'urr;u..:c pc:mmnently. it must hn\'C sufficient ~1111:1k c.::nNgy w ,tvcn.:l.mlc 1hi' fun:c Thi' force i ... dt:M.Tibcd ,, .. .mrfac~ INHrirr ;·n~rg\' I (·'8 ) llH: ...uri.Jtt.· h:•rrll!ll' an~• l oguu .. lu lhc gntvii:Uio nal pull .,rlht.•t.::ulh .-\1mh•~ou ..

hi <--cu~ ' '<lucny. an ..·te~·uon cnn come out of the met:lllu: ..urlaL·~o:. HOI\ ah ' cl,"l:11~ 1tr K F ,.., more 1h11n •' particular ,,due . Mo\..lcm phh l!'' tell .. u ' that t.' \ t.:ll .u 111..: ,ah,ulutc b :wtcniP'!ItiiUrc. the \t.:ltxlt} ur KJ:. u t .dl l h(. t.:k "L-Lrnu tin~' nm 1t:duce lH lt!l '' Tht.! hig_hc~'-1 energy 1ha1 an u.lt:clron in .a mct.Jf ha.... 11 0 I\ ''~.:>.~lied F1•mu lrl't'l of ~'lft'r8\' f£,). F(1r cmi ~,io n of c i\!Clr\1U Hl t.t)...c phv;:~o.•. we h:w~ H> :-;uppl) :addlli<'nlll !nergy from outs1dc. The ouldlth.lllal .:ncrl!y nc\!d,•d f,~r \.'IIH''h 'O ut clc~,; tltlll i:o. c~•llcd ,,·or~ fimcrhm CEw = tQ• o f Lhc m~wl (Fa~ \

t•.

tiMt j,. /.:"11

=1:.'8 -

=eQ

rJ. I 1

Wurk lunt'IHm j, t:Xprc-:-....,t.'tl in 1crm:-. of energy unit dccrnm \'uh Ju,, a' c...,L.•IJ'h! \ciUCII)'. u 1:-. different fo1 different mc1:11!'1. There :u t! ll'l:tn) way~ w !o~Uppl y aJtlitional e nergy needed Jo1 :tn ~ JeclrOnlt: csm~..wn. For example.

\\':can :.oupply add11tonaJ \!1\Crf!Y &nan~ ot til\! totl\lwin~ \\'U)''i." hC.ll. C lt.~..::tru:.l l llt.•kl, light, lhnl~l l)l'tiCIUCCd by bo •nbanJm~ the "lll fucc \\Hh c lcctrum; AcconJing 10 lhl' way \\C chuosc the ~upply o f addith)nltl cn~rg)', lh c c leccronu:

e m1s$t011 ~~ c lnss:iliC'd a~ {I) thcnmooic ctnJsston. (2) h1~h hdd em ission. (:\)photo-electric i..'mis.sion nnd (..J) secondary .:mis~io1t. Ou1 ~,,r lht::M!. th~ fi~t (lOC l l'l rno~t common.

{ 1------1--

3.3

Richardson Dushman Equa tion

RJchu.n.hon

c19Uitl1Cn\'Cd

j.J

n:lillltll\ hct\\l!Cil lhL· numb~r

or ekclron... \.'11\IIICLI

tw '' unit an:a of the mcullh.:: '\Ill f:u.:c ell and the h:mpt:r~•tun; lT) ln 9 K ol th~o: emitting m:ltl~riaJ.- L.ltl'l oil, thi~o u·laliun \l~t' corrt•dt•tJ h} Dushman. Richan.h.on an h1' t'tnli~t .llh!H'I'H. dcri\'ccJ tlu:-. t"t.lu~Htol\ on<~ lhcmll1d~ nnnllc has1s. L:ttcr on. at \\'1.1' tl~ri\'l'd on the ba'i!> ~.,r Fcnni · Din1L Stulhuc' A. Thcm1odymuak l><•ri\'allon of t•Wclron\; from th~o.• '-UCfltL'C o l the IIIL'IJI•c,..:utbll!:-o the ptoccv•. uf

Th~ enti~si<m

Cl•IJltlf•llWit ffl,l1llf\l' MllfoiCC uf ,I litjllilJ o11H.J lhl.' i.'tii.:Jf~

Ull

-:Jectton

ffiU~I l't\:

gi\CI) for ir lt'J c~:spc.l':t)rt'c.;;pond, tu the l..ttl!nt he: at of L"l' .cpor.nion. of Lhc liquuJ. On 1hc b~•si.., nf lhcnnnd)·muui,~ ,t~ri\uuun, Rid1ard.:on d~ri\i.~d the cqu:.lion fm the t;UI'rcrU dtn:-.il)' (.0 nf dt•ctfHIIl'> Cll\lll~d rmm U hCtiiCd liJumcnt whil,:h J~pt:rld' nn 1h..: h:mpcn:uure of the ttlaml.'nl .mt.l w(lrl Inn~:t mn.

where A" i:'O the Bdtzm:.sn ~onstant /'the t cmpcr~tlu~ tn K. nnthc numhcr tll !!'leL.tron;; emmed per unu areo. j1C'r 't:'l lmm rtlaml•nt '' ath t,cJoclly u. A' and A .u.: some const:mts. whcl\' they :...:;.umcd th:'l \\c1r!.. fum.-lion IJ of the metal tP b~ mdcpcndc:ul of hiJm~.o:OI ICillJ)CI;ITUf\: f \Vhcn th1s rd:uion '''""' cxpclirm:mall) verifie-d. 11 (13\C rhc val ue~ A and Q. VL'I)' diffn~·nt lrvm CXJ>Cfllucntul 'illuc' ;uH.t rhtl' 11 wa .. lh,cardcd.

Luter on R1chard:;on ""d Dushmun shflwed that (.1 " a hmt·uon of IH:,mcnt h:m(J'l' nJiurc

I."' ~1"1.!11 by Q : (.!.,

whac

3/2 KT

•hl' work func tion ut lf'K. \Vith thb \'uluc uf (}. Rrchnnl::.on

.and

Du!<.hm:m got the: accurntc rchuiono,h1p U!rro (.1 Thi~

2hl

thcl'modyn:utlic derivution ht1~ ~m~ drawb~lck s. It is bused on the class1c;.l which is contrnry to U~e modem quantum cnn.!oith.!rtllllm Thus thes·mu<l)'ll:unic derivation h not udoplcc.l thc.'t t.luy~ tlk."Of)'

8. Quantum Ml·chunic& ll l)cri\'ution Thcnmonil- t:llliSl-JOll e:nunJSIOil IIi bc~t cx.pl;uncd by h:rnu-Diroc- Slah,Uc!-. m wluth the Ctmcc.:p1 or Fenm ("ncrg)' ontl h.:mll bund C>.plmn lhc (,'OIHlii iOO lor

th.;rrnion1c cmmi-.,.Jon nnn: dt!~ld) A~.:cun.hng 10 tlus onl) d1o"ic free ei~.X"unn' will C!\GipC hom th\! mcr~•l clu..:. to h~:.uing whu:h h:1ve ~ot energy :- 'turm.·c bJr'ricr ~n.,;f!;!~ ; EH or ~ r:utcr thnn En ;\ccon.hng co liii~HlHIIH cuthidentll<lll tht..• K E. uf 1he electron '' ncu 1cm ~~~ O"K Jlil{ll«"-'' t•m (~\ thai m; l'lntrmt m mt•llll luu at fr·K it f;f, 1lw Femu hTrl of tm•ry.:\·. St) lor crnl-.~l<'ll i U wkc pi;Jce ~h:ctron~; mu"'t po~~t!ss thi.· cncr:n rf ·a~. J.l ) 1l I I

£ 11 -= t•(! mtnunum cnerg}' net..e,,al) 10 hbcra1e electron:-. fmm mct:th So Rlchard\-C\n uu .. hmon equnuon (;l.2hl ~1\'CS the thcmliOilJCt.'urrcnt dt:n~lt'

tl'

I= t·l x1.1 15n,.,K1 )//rl x T1 r• rl,,llf.r (1 Jl When.•

CIIII~' IUII C.:UI'n:'l11 ~l'11'.tll)

A= f·l x1. 1 ~1.) mcK.:)/h 1 =- t.'nll't:»lon conl)l:ull I - Tcmpl'nuurc m K WnrJ.. tun~ll1111 ol mct.1J Ill a.:\ uhc minamum

CJ-:

t"SC-apl' cncr~)

11 lht.'

t.:ll."a.:'HUIII

Q = (£.- £,1/e, 1\ = Hollimon c"'"'"nt 1:.11 ~ ~uda'c barm:r ~o·n~o·rgy, Er = Fcnm energy.

t:. m: de:~.,:lmuh.: ~h: u !!~;.' unc.J n1a~~ If 1hc are:t •tf lhC' i."lllltl~l 'url'.tt.:l' " ~. 1hen Lhc tcltal cuH..;fOTon nnnm1

I>= ••tJIK

Equ:.Juon t :\A) i\ c-alled Ru.:b..mf,, m .. Qu\bm.tn l!l.fU;Jtion rnr thcmtinnic t'Tni,,IHil. A :tmJ b .1n.: the ((111,t.anl.., '-'f kkh.lh.hun-lJul'-hm:m ~:qumin n. Du-.hmun lu' ~lmwn th:tt A j.., cl•ll'-Hinl lt11 c.IIHcr~nl m\.•1:11 .. hut the \':1luc h, 1.1.'., wor.. functum \·an~.; from mctJI to

mct.JI.

1'111' cqu:JIIItn "U.!;.~L''h th.al l1w l'.t'l) cmio.;,ion of clcdmn'\ tht.:' mcl.th ,JauultJ

have high mclllng pmnl Jllt.l hm \\.\Irk runctinn. Dtlenmm~duu o)'thc cm1,·tcurf,\'

From (.l4) we !(CI

lo~. t11T~1 = lvg, !A x S! - IJ/1' Thi' ' ' Jhe equa11o11 of'' str;uslu hne. 1 = mx + r. Thus, il we plot the gruph between l /T antlll\g.. (IIT 2J lht!rl ~IOJ)C {Fig. 3.2) wj ll give the wor k run~thm h find intercept nlung Y~n.\is "ill ~ivc 1hc \·nluc of lo~ (A xS).

htf... Ill

liT

HJ:. 3 .2

3.-t

\~:.nulinn nt luJ.!, lilT:• 'lith ( l/TI

Therm ionic Valve

I'll~ RaL·han.bon. ou..hm;m cquminn n1k~ tlw ' hou.:t: o l •m•h.:n;1l' (or .:fiic.:icnt cnw.... um '"luch wa.. pul In us~ for dn·dnpm~ l'kl'trnn \'HI\.'c.• ll•e fin..1 \UI.'h

' aht: '':'·' dl!vclnfk."CC h) J.t\ Fkllllfll!• h) u"''"l= th\!rnllnnh; t:nl1sSIOO. II ha:-.. ~ mcl.al filamen t ;L' an e-lectron cmillcr, .an1l ,, plnlc n~ nn L'kccron ~.:nllcctor. f1Hcd 10 u gla., s bulb, whicll1s. lughly C\' O.L' UotcJ U rhe plate..,. £1Ven .1 po~tt• vc p<)f4!1111;tl, the ~lcclrons cm1t1eJ willl'h! aHrnctl.!d lo the plate and clectn..: \!'Um:nt will nuw I TOIII the lilumcnt h l the plulc I r m:g.allvc puh:nl!itl l!oi J!l \ CIIIV lh\' plale. cleclrt"llll'i \\Ill llnt tlO\\, whrch mea ns It WIJI Jlhm liOI) 4101'•\\';t)' f1ow ut dCt:lroll(,, Til:-U I' ,,.h )· 11 IJoo con..;1d~rcJ ~L" a valvl' Her~ ~mHh.•r '"' ••:aile-d c;& lhodt• :111tl t·ollecws i ~ ..,;,11..:&1 ;UH~h: . $111 ~~ H ha-.:1\I•U \.'h.·~ truJ, II I• \';lllt.•lt ,ft,.,ft-· •FH! 1 '\) ( .tthodc:-. nr cmitt~r'i :u\:: gcncrJII} ol

twH

type:.: (I) \II recti ~ h\!~H~d nr lilamcm

I) [le' '1:) tndm:ctl) he rued l)f hea ler IY[l\.' The I\\ •' 1) pc .. ul dul\k' <If~ ( J} 'at:uun•

d ioJc ;tnd (2) ga' r.llcd diode. V;1cuum dtodc ~c.·nsast::. of dtfC('Ciy (' f 1nd1rcctl) heated Gltlu"lh.' Twn fXJ'~Ihlc types of cll.-ctrodc arrangements arc: (11 p<mallclt.:h."CIJLK!e' .md (2} cyltndnc~11 dcclrodc:o.

3.5

Di ode Characteristics

In ;1 duldc, thrct"' lli(fercnt L lri:thh: .... .u.: mn1l\cd (:1) l: il:uucnt c un(!nt

~.:mn

1, I.e. the

L'UIT~Ill 1hut hc:.n.:o. the filtuuent tu enable ll

<l«lrons.

tO) Anc.xk or pln:c c urre nt 11,, the rniltiOIL cttrrcrll that nvw .. Ill the pl.atc~ (VI'). r;1thcr hi)!h .uuJ .tiW:t) ... pt.h itivc \~.r.t. fil~nncnl.

(t:) Anode or pl::u~ \'uh;\~c

t\ gr.1phic:al rd:tl on ut nn~ l\\'t1 ufth~:\~ (JU<Ullit ic~ c:un.;,tiluw.;. a charaL·teri,lic ~u rvc.

I The \';triation of plate current /1• wuh f'ilamcn t t.:urrent 11 for

\ olt.agc V1, i)l. called tlwrmirmh. r:lturw·t,~rhr;r,f.

fixed plate

Thf•tm;mur /Duu tiou

J. Th~: \'ariauon of phuc t:urrTrn lr with plate vo11ug.: \ 'r fnr " fi~ctl fiiHmcnr curr;;nl lr ict called mw(/t- rlmrttrttr;.r~i'-''· J.5. 1 1\ n ndt Chnra<leristics or V-1 Cha rntlcristks of Uiode In 11 \'tlt:curn dux.lc the fi lament or c:-.-lhi.x.k ., ~t)nncclctl tu t .T. lur f1l:ttuc.n1 hcnung a~l\\'een cathode ttntl plate ,) V~lriat'llc I')\ II T \tlhtlP,t! j... ..:unneclt!U (1=-i~ . 1.·h . \Vhen the fil:mu:m j.., hC':Ut·i.J up ~.·I(!Ciflln"" :m~ cnuuct.l frtlm 11 :1nd 1€ plntc , nltog< " kcJll "' t,cm (Fig. 1.} J, thc<e ek<trm" lonn un c lc,·tron cloud c;:~uhude. ~nown a.s space charge. Jntl lhat rcl;!Hln ' ' l'tlllcd .~fUICt! dm't:' r,.gum Oh\ io~ly the \p:U::c charg_~.: i' nt'g.UI\t.: and ;t' more: clcclron\ rue

arouod the

C"lllllh!d !rom tht.! nt:unenl they c:tpe11cncc: :a rewrdmg lnrn:. Bu1 ;L' the p l ~ll" \'OitaJ;:c h • nc:rcn~cd. n:orc und more clcctmn~ ar.: auractl!d w the- phttc. n llls thl' plntc c;urrcnl will he increased gru.dually The ,·annlaon uf plilh: curTcnt /1, With plutc vo1t:,p.c Vr i.s :iohown in 1-ig. 3.5. Th1' graph'" called\ ' / ch;u·;,ctcrhurs or .ulod¢ chamCIE'ri!-tic<i! d vacuum d iode. It t:an tx· '~en from lh~ J.!Pph lh:ll u1 lir:-.1 Pliitr

Fi)t. J.J

V(ll"uurn diode

,----i''~=-{

mA )-;---;

+ v

Ill

LT.

Fil!. J •.a

set up ror study the \'Qrin1ion Qf plulc curn•nl 1,. " 'ilh f)luh• ''ohuge V,. f. ~ptrlm cntnl

Auodt> c:har:u:h:risLics

/ ,.. .... -L

f"i)!. 3.$ \urbtiun

or pJall' t:Urn;· nt

/ r \\ilh pJute

\Uit;"tj.lt' \ •1'

:tl

Jl:.u·tJculur fil:um:nr h•mpcrnturc T the plate current / 1• 111~:1\:.t'L'' ro1p1dh w1th 1ncrcn-;c or \'1•• A ~l:.tgc •~ rc-aclli.'LI \\ Ju:n runhl.!t mc:rt:d'e m VI' th)C not r.:,uh in much incn::a~c in plntc currcm .'iuun, 1h~: pl:n.: turn:nt rc.tl"hc .. tb ' :uur:.tllon ntlue. The \'OIL:•g.~ hl'yuml \\'hlch cum:nt '-llln .. -.:uur:ttin~ i-. l'.tlk•J ./lttrrlti ml \'nlld.C:t' Upw ,,uur,ttmu ptunt ,\ m h!; .l5. :-,pu~.:c chutgc cxi~b around the cdtluxh: The ~urri!nt utthi, reg on " limjtcJ lluc t(1 rrcscnce ol .. pace charge 1 h~tt j, wh) the cun·L!m in Ihi' tcgi<m j .,. c.tlktl ''fWt 'f: drurgt' limitt'd C'tlrr(•lll \Vh~n th~ phth: \'Oihlt!\! i' mC'Ir.: thuntb\.' .. ,,tutoJtiott ' ·olt.•rc Jlmu.,t Jll the clcctmn_,. Me Ct•lh:ltl'd b) the phtll' I h\.· ro1h: ul nu ...,j~•n lxcorne-' muAiiHUIII anJ tht: t:ulh.'Uil•rJ oJ

ckumn' h: rh\.· pl.th: ..1 ' hu.nllh.. ... lhl· '-o.tlllt: Tltl.:'rdun.". th4.: 'J>.t~..~.. .. h4J J.!~o.: 1' t:\IJau .. t.:O. Jii.Ut: curr.:nt bc\.l\l11l'' t~lnln,tcnJl!>tant '"ltatt.'vl!r b.: thl• ''alut: ••l pl.ttc.: vuh:l~l' 11 '"c.: cun r..,·Juc~ lh\. t~mp~rJtur~ of tht: cathode by rcducin;; lll~ nt..•nt current. lh~H ttl ftthn;cd I\'IU J'~\' I oillll\", the ..·athod.; t~annut ~uppl) tht: l'kdrun" nt 1b hit:h r•l1'-' J' it w..... tluin~ ;u the ha~h tcmper:uure. Thcrd~m.:. the ..:uut~tth,ll current~ ~ til'"' 1•,,\.:t ·n111 .... thi' ... :uur.uJUn portiuu \1fthc VI ct'l""' (.h::pcn'l" nu lh\! t't~thrnJ ~ t~mpcrolltf\!, !'iu til•~ ...uur.ltif)ll ..:urrcnt J')Ortion h collct.llt'lltJit'Nllta • ltmilul' urrt•lfl. If thl' l~!mpcmtun: uf the ..:alhrxl..- i' further reduced. tht.: \UIUnilum t:urrcut ftutJ,..,.,,cJm:c" Nnh: tlwtt1il 'rm.:ct·hmgecxist:o, n•uum.ltll..:l'dljtudc.th..: pbtc L·urrl'lll i-.. <ll~,.-id.t.•d hy tJu, ..p;tt:\.'t:h.•rgc. It due.., nut mutter whal th~ lCmf':rouun· of thl.! ~.:atlllll.1c i~. Spucc t:hurgc llllllll'd t:urrem h. given by Ctuld-l.nngtnuH ·._ lhroe hnlf power low as

I 1' -- ",,I

,,'Nl I'

where /\ 1 ,.,. th~ C<llhltlnt ''' propor1H)O,lhl). S;aturalmn l'UITl'nl dcpcmh on Lhc tcmJl{.'.mhm: (If IJ1c c~ilhodc Cum:nl m the Lcmpcnuurc Iunited 1\'gton '' !!·.1\'cn b) Richurdson~Dushnum cqu:uiun 1.161

Thcrmitmir f;mis.,ion " ·here A = constant.

T =1cmperalurt.> in ° K (! = worl funct on

S = 3ren or cathode K = Bohzn>nn constant

r = e lec1ronic charge

The C:UI\'C: in Pi8-3.5 j, called ~t;llic ch;t rnclcri~tic t;tlrVC rl\r u diode !-incc no I~Hi d wa$ 1akcn 10 1hl' platt> circuil Tite Matic pl:ue rcsi~utnce r, and dynamic pl:.tt\! rc:~i swncc IJ

cun be obtainec.l rrom the M:11ic

SHIIu: pl:t1e re,l,..IJ.Jn\:t: =- Vpll r = r , D)ntlllliC piatc r<:$1Stancc li\11./Sf, =

ci1:WJCI<:ri~tic

turvc

:1\;

lultows:

("IMract~n .. liC' cur.•c wuh a ln:ld in the plnte carcuil L, c-.tllctl t.lynunm:- ~o..hur.Jclcri<.IIC cun.•c nf ~,lind.:.

3 ..5.2 Thermionic Characteristics \\hen otn<Xh.' voll:lge v,.,\ ~cpt t()Ol>t;,mt and 1cmpcr.1turc or ..:urrcmmthr:lil:nn..:nl 1' gradut~ll) Jnt.:l\!:l~<o¢d,lhCI1 the C:UI'\'C: helWCCO / p- J,. (lhl:&incd ror t£1ffcrtnl p lah.•

,·olluge: \- 1, i" -.hHwn in Fig. ~.6

Tht•.rmionic ehnrucferi'\lirs

I, •

Fie. 3.6

Vuiatinn ur l'l .. te cum·nt / 1, wi th rilarnenl curr&:nl 11 "ilh partitulur phut 'c.hagt V,.

1 he~~; UIIVC~ .tgoun Sill)\\ Ill\! ~:IIUNi\l()ll in /p for .1 !):ii11CUiilr \,tltJC ul \ 't•· Tiw~ hccUU'I! ur H1c fact lf';_l[ as Wt! incr~3SC 1hC: emission. LhC !\puce ch ..trgc j, nbo incrc:•~cd and ini1i:11ly /I' will incrca.sc with incrc:.!"c o r /pbur since v,. is constant so power uf aumc1ion by rhe plate is con!"tnnl. Thus only a limiled numOOr of electrons cnn rcuch lhe plate through the space charge. So plnte cu!Tent lr" ~tntunttccJ aflcrt.:crtain ' ·uJuc_Thu~ at the bend of U\c curve. fur 1.1 p:1r11cuL.r pl :tt~ vofl:,gl!. 1hc• s p3ce char~ is just s uffieicru 10 pre\'Cnl more clccu·on~ friltn gcuin~ throu~h lhc cloud of elecuons alrcndy nround lh(! li lament. ~l'hese 1"-'0 chnraeteristics omxf~ charactcrist;c and thermionk cluo·m·trn.)·Jic suggc.st lhtat 11 is not po:~si ble to obtnin unlimited currcnl from the pl:11~. only by incrca~in8 the: plate po1tnLlal or only hy incrca.~ing Lhc filament healin~ current I~

Space char,gc is .d\l::t}'" LhL•rc. play1ng ;m impnrtan1 ml~ for cnntroll ing llw plate currcm

3.6

C hild-Lan){muir La\\ for Space Charge Limited C urrent

A nMth..::mlujcal c.\prc,,iun fnr pl:u~ cu1 1em I,. undc1 'pm:e ch.1rgc limih;:d currcn1 cnndili<>n fnr pJr:&lld ch II<XIc "'"' liN J cri vc<l by Child ( I'HI). LMr. L.m~m01r II(H"\) 1:\ll·mJctJ ttn .. ;n1ah"i' ft•r ~;yhm.ln\.'ttl dt!L'lrcxlt''i. Fur p:mtllcl clt'ctn~r currcut dcn\11y ''

J-"•,··· ,. ,,~

\\here J ~ I..'IIITCHI tki1\Jt)'. undN 'pace c.:·h;1rge I united cund111011 1/ = <I1~HlllCI! h!l\\rCCI) c othtKlC .Uld pi:IIC c•. nl ;- cl..::cuon1c ch;~ rge Jnd ma!'.~ 4~ ,' ~.-~ m -=- snmc cnn,lnnt, th:u deJXnds o n 1he d1ock 1\. 1 -=- t; {f)= J'C011111\'II~

of h\.'1.' !-Jl:H'C

II .\' ,.., th~ ar~~~ ol 11h' L o .......,c~llun nl lh~ dct:unnu: hcam. then the cqu.allun lnJ the plnte cum:nt under 'P••c1." chotrgt' lnmh:d n:gion 1!'\;

LJt ..·r 4ll1 L:.n~muu Ill· ,111 t~\-1 ttw.. '''J1h.''"'nn h•r C) ln1t.lr u:alt"lc~.-trthll! lhc II•I,JI ~urrcnt fM:. ... m~ "'' u~·l~t ~mgJ,.• .. through .m tlnJJiennry cylinder ot hm~th I ;10~ rue,hu.., r ' ' 1,. =

4fu

~-,.ldm

l'pV!

x - "-, >< 21t I,.~" l'p fJ ·

So toal current rm.:."c" through unit length 1:. f,,IJ

=114.66 X 1111' • VP' lflrr/J 2 1

I ,,IJ = ( K, x 1' 1'/1 )/( r~{J 1 whcr..• K! = 2« ><

) amp.,unic lcntth llf axi>

-'ru · - T" 2.,-/m = 2JTK 1

jJ = t<>rr~cuun lac\Or = log •<r,Jr,), genor.olly cakcn •h I

=radius ur ;mode r t =radiu~ nr conhude.

r,,

tlr

pl~lte

bec~usc

r, >> r1

(J.R)

1'11rrmiollic Emi.t,'iim• 115 Equ~tion~ 3.7 and 3J{ nrc known ~•s Cluld-I.Amgnw;r cqumian" for parullel pial~ electrodes anti C) l•n<fcncal elect rod!.!!'. under ~pace: l'hargc ltmtted cut'rt.:nl regaon. fn'lm the C<lll:tti(tOIO 3.7 nod 3 K. we: c:m 'JY thm lorn g1vcn ch:ctrodc :o.y:'ilt"lll

tJ l/)

rhc: rdatwn IJ.tJI other c.:O•l"tant.

3.7

jjl; C~111Cd <:luh/1 cmgmwr lllfft lwlfpm'o'('f lmr :md AN ,, ....UI1h.'

Diode as Rectifier

Rcctillcr i, a de\ tee wh•ch con\·crh AC arHo DC. A'!J diod.::

nnw l'\U()' i n

Cll11.! cflrecti+IO SO II C~ln

tll:

U!»Cd ~tl- :l

olio\\~

half \\'3\rC or fuJI

lht' ..:um:nL h•

Wti\C rcUifi~l.

3.7.1

llnlr wH ve rcdiHcr :J circ uit tliagr.tltl of h;tlf w;wc rcclificr is shown. The Input AC' '' conn~.·c1cd ucro'' the prirn:lr}· 11f :.1 1nt11Sif1mu:r \\'hu:h ha..; 1wo .s~conduries S 1 nnU S2 . S1 i< of few tums thut prov.dcs lew vnlt< for hcaung of • lliumcnt. "I he tcnninal 8 of 5 1hlonnc~.:tt.-d ruth~ rlah:ill lbe d1oc.fr ::uuJ reno mal A 1'\tOnnct.:tccl to the fi lumcnt throuMl' u h1gh n:\l,l<•ncc N ~01c HlHpur l)C volltage I!'> r:"llcn In Fig. 3.7

;,lCfO~S

I[ ,\

) I'

'------'~ . ._,h!.___

-(Elt-

t':c 0."'"'

A' lht:' currcsu fU\.....C~lhrough thl! lil:unemn gc::t"" hemed up nnd stans emmmg electrons. The anput allemaun~ V<'ltagl! '"' :o:upphc<.l 10 'he plat.: . For''"'" h:alr cycle Ihe plme bctomc~ (h)stll\'~o.• :utJ Jm the :,ccond half it bt.'Comcs ncgnuvc. 1.e. when 8 is Jl<)SUIVC' the rJat~ bCCOilll"S poslti\'C :md the c Jcclron' CJOIIICd b) thC mamcnL nrc :m.ractcd by the pl:tlc a nd thu\ ll currcm now~ Ill the plmc cu..:utl through R. Now Ill che second halt cycle when 8 l!o ncg;tU\c the plate abn bccom..:s ncgauvc :md aMuclton tlf the electrOn\ lly tin: plate t~1kcs place m) more nnd ns :.• resuh thcr<: 1:-. ll\) no'\ of curn!tH Ill the plate cifcuitthmugh R. Agam .n t.hc next cycle the pl:1tc lx:.cvmc!'l po!»I1J\~ und a current Oows through N nw. process lS repeated fJ81UO 31ld agam Jn lhiSCifCUillhC' CUrTI.!nl now!<> ,11\\ays lfl Ihe s~mc direction, Fron1 ttbt:w c u is clcm that currcn1 llow:, through R for hnlfthc tunc only when plate IS posi1ivc nnd such n cu'Cull l'i called half wave rectifier. \VuvcJom1 ol the output DC is given in Fig. ~.9

01nput F'i~..l.S

1-'ull w:.,·e

n.'<'lifi~r

C'irc:uil C'onnt'Ction

3.7.2 Full wave rt.•clincr The urcuu i110 shown 1n Fi[: 3.S. Her.,:- we uSl' 1 dtodc!'. AC mpul '" upplu:J ncros~ tht: lmnl:U')' Of lhC lr:&llS(Ormer Which has 2 SC(;t)Od;tr·u;~ S1 4tnd S)• J'ht: 11HLIO secoudm} S1 •~ connected to the plaue of 1he d10dc:o-. t.c. the tcrn1mui/J ~~ ~.:unncctctl 10 1111.· ri•HC nl diode.: 1. and lcnninal A i~ connt."Clcd lU the pl:ttc vr diut.lc 2 SCN111d:if)

mmn

s1 '' tOilllt':le"d 10 lbe fil::trnent~ or the diode" The ('COiml poinl of the

.,~,~o ndary

l11c HUIJ'UI

C 1-l' ,•vnncc1cd lQ the fihmtent thrOUJ!.h the h1~h r!.!MM.tnce R. which iS dtrcct VOltage IS t)b t~uncd ;,u,;rt't,l,~ lhc IC!-i,to.n rc R

II\\. K

~------L-----~L-----~---ll ~lf

Uulput

Secondary S:. which h:ts few turns supplie-s. a low voltage to the filament for ~.'!mission

of clcc twn~. As the input volwgc is AC due to th• ~. when lennin:ll A i~

p<>siuvc then 8

negative for first holf cycle. Whereas In the nc.t half cycle tl

Thrrmionir• Emif,fiou

In ftna~hal( cycle. when A as (lOSill\'e the plate of .second diode as po~ilivc. and "current Oows through R due to second diode While in the second half cycle,\ ill ucgauvc nnd IJ as posilivc hence the plate or rirs~: d 1ode 1s posi11vc and a~ a ..,,ult the plntc. o current Oows thmuph R due to <>nly first diode and so on. tn thh wuy we ha•tc an output which JS darcct und llow~ tt~r the whole of Lhc C) de. such n rectifier i!'O called full w:avc rectifier. The output voh11gr i__" shown for half wove and full wavc in Fig 3.9. Though 1hc output ~~ DC but sull it " nuuuaung ror the rull w;,t\'f! l'cCiifier. So IO gel ~fll(M)th oc this llUif'IUI ·~ pra.....scJ throu~h f11Jcr cii'<:Uil l•htch ~ilo!S the lin:tl . ~,m,muJ dtrcclt'lllilUI

PROBU:MS 1. f•) Tunsstl!n lilamena Ctr 2 sq mm of :-.ull.tce urc,, I!> 11ue..t conccmnc~tlly w•t1i u cylindrical 1U1ode m \':u:uum diudc C"nkulluc ltH: ma:wnum obuunublc dcclfot'IIC cuti\!111011 t:un\!nt ott the nlilliiCIII ICIUJ'ICrmurc- ~f}f)(J"'K Ge\'cn dw: vuluc or C(tll\lantl'. ,\ nnd h '" Ridmrd'\on-ou ..hm:m c:qu:etum ror tun,g... tc:n wire l.b 60.2 x lO~ dmplm!°K. untl 5:!400 tCSJ)C\:tl\d)'.

S = 2 ~- mm-= l x ICr"' m!.

SolutiiJW

I =

I-= 1CMYK

x W' omplm 1· K h tt Ql~

(i() 2

~~~~ c--btt

~ ~24l~l

= t.0.2 x 10"' x ~ ~ IU -t· ><. t::!OOOI:

r- ~~.-.ur.Wvl

=20.145 x 10"' ;unp ~ ~0 1-l~ rruno nmp 11i) C.alcultuc

uuil area

cu!Ten' den~ny and Ollmbcr or ch<:clron(; seco.nd For the ubcwf! ph,h1em

"m1s~1on ~r

J = AT~t'../tiT = 60 2

Sl!luumt

x 10~

ftlt~)

emitted per

· (:2()()())!t.-"':""117rtr_,

-=- IU.f)725 Afm~ ,1

10·0725 - -c,2fl .. IH 1 "1m;~

;Jh:

1.6 X W 111

2. Fm certo.m \·m:uum d1odc 20 mA ur pi .tic wnml i;o. Jruy,. u 11l go 'o1t.-. ol pi,Lll!

\'Oitage. C'lliCui:Ue tht pltUc \'Oitl\gC In l1ht:tin ,,fl ftlA nr !"I.I!C curr..:nL tt<Suming thai the lil:.ment hcutm~ cuncnt i' COI)\tant.

StJiution; I,.

K\'j'

I~~ :. 2() = KU~U) V! .: A' \ r~ 1,! =JUs=K(V,.:o) "!

F1·o m ( I) aud (2) "e ge:1

K(80) "'

KW.,! "' Vr 2 •

(8Q)Jn

= W4.83 vnlls

(I)

QUESTIONS \VI'·'''' thcnnil'1111: c:nu,~ion·t Sun~.· diCCttu,auou oj thctmi~w ic "-uncut :md c\plJut lhH' 11 '' u-.ctul tnlk'l~mng "acuum Ju,Mlc.. Whtltl\ the rnlc- ''' \HUk func tion in lhCOllOI\101\ Cllll''llm 1

!. Dc ..~.·nht; the I.'·'P'!rirncnt uf 1>hUc ~urrcnt~ plate l:k1tcrttt;tl. ch;u~h:lcn~;ttL' \ll J •fllM.Ic. llltt.l h..:tiLI.! t=.\plain whether it is pO\)ihlc IH ,1h1.11n unlimttetl pl.ll~ ~:urrcnt b' lUI IIICH:.t 'lll~ fiJ1111lC01 t:Urn: nt 0111).

fhJ 11\Cf~U\InJ,!

rfllll!

fHI!enll:af 11nf)

t.'h.u);C lmutcd current m dcdnm ~ hut.lt: and llcm:t.' hotlf flt''•"-!f Ill\\' 1. tiJ \\'hut ,.. thcrmh'llh.' """".;.:um'' St:th,. tht R • ch.•rd~un-ll.- ..hm.tn ,•yt~.tlh•n ••an.t

.• 1!\pl.un

th~; h:rm .. ·,p.t~o.\!

t'\j~l.1 1 11 '1hfl't

httt,-c uhtaut cum,um t:ttnCul denMI'!I uml cmls.J::um current. (:, \ l'.tl tht' .;m, ..t~tnt\ . < , A .md I• lor Rit']Um.I'WII · Ou~hm.tn C(IUOUOn, .ue A: 60 X 1ft tiiiiJifrn-"K . /1: 'i.J ')I .f. 111 l in ltlch.lhhoJu·Du,.hman C<.JUitliUU thCJt' i<: u th,pnnly lnr ~.-o n ... liml A h\'1\\'"~"

w•

rhcmr:Uc;ll ~Hal

un~l c~penrnc nt.~l

'.1tuc. Gl\'c:

rea~ono.

ror lhh.

E\pl.titt til\' Lh.mtL'lcn..trc ttJl'~ h.•r \..tcuurn d !QI.Ic fur \11flatuu1 ul pLuc Lum·nt \\nil pit~ II.' '''h·•t!~· ,,, (i,.cd filamc::m current. What p.ut ollh..· lUUcHlnt ll•l"'k " l\.'lliJ~r.IIUf'c" lunll::tl UJUJ \\h.ll l):lTI 1:0. 'Jllll;e Ch :.Jftl(' hmiiCl l CI,IU'C.'nt

(hl E\phun lh(

\H.,r~mg

.. 111m llu: 1111tpul

t..IDI Fur

J '•h.'\IU11l

ol hn.lf W8.\C' rccufi ... r u!trng dmc.k:

"" ,J\'t'

J)(;J\\

ACOJII.h·•~·~ouu

otmt

htnll';,.

,hOOt.: th\! pl"lt.: cum:nt ohl::une\1 ~ ~ 2U 1111\ .tt ll!i.l \qll" ul pial\!' tht- rluh! f"U'It'nll;l1 10 ohtmn ~:; rnA pl.l!\' ·urrtnl. m ••ml.'ll!

~1h.'U11.11 Cll.:ul. h:

"'Uih::UI I~IIUUU ' ~IUIIC.

It'lL F••r .r v.u;uum tlh>Jc ~how grt1ph1Colll)' the regaun ol ~p.tc~ \:h.ug.o: lmutl!d o.: urr..-nt iln•l 11;1n ut h:mpmuun.• lnnued current 1 t\ tun~-..1rn c-nulhl u1~1:Ue.. al 2.~00"K. Whal L'h.:u1gc m..-.urL IIIIH.:IU111 c\rh.""''-ClJ m l' \ \\Ill ,,.u.,.._. 20'1 inl.'rC'a..···l.' mcmt,.,il'" current tJc-n,lt\ ·•

4 Ultrasonic Audin fn:qucn<) l'lln~c-20 Ht lO 20 kH>. RJcJin lrr4ucnty mn~c-550 kH>. 10 22 MH7 TV rrequcnC) ranj!C-17 MH1 lO 230 M H7. 1\ bovc aud1o rnngc-Uitrosonic !above 20 kHz}

Ucluw

~·utlio

4.1

In I rod uct ion

mngt..""-lnfru:,onu: (below 20 Uz)

U ltr:ls<uuc wa,..:s rcler., to sound wnvcs produceJ by an obJCCl ' 1\lmtmg at :• lrc<IUCill.') h1ghcr lh;m the humun l~ar can h~:ar (1 c , ;.1ho,·.: 20 kHt) Ry u'ulg modem h:dmiqm:" i1 ha."' bc:t:mnc p<~~•llle 10 pnxh•cc ultf:t'\OilJC '' :l\ " ' uf trnJucnq·

uplo 15 hdln111 Ht. whioh II>> a wavelength of 10 • m, compambl< wllh '1: "') wavclt.:n~Lh. An ultras(lniC wave as haghly cnergcuc :\nd h tt~ cx,rcmcl) ..tl0r1 wavch:::ng_lh bcC~IU)«! u( lh !ugh frequency and CllCfl.) · The U."oC ~1f Ult~a"'POU::~.

C!tpcc•a1l> 1111h..: fi\.·ld ~"'r o-.c.dtc•ne and in variou~ indus1nc~ bcctlmc 'Cl) llllf'klrt,tnl bcGJu~c ~·f '" ,.,,~,11 w:t\cl.::ngth and high cnerg}. ()uc h,l till;!. It hll' pn.'iltct (lrt.)llll'"''" 111

tuturc

means 1lso of very h1gh l'rc<(ucncy. btll ultr""'nu.: TllU'I tl..• dincrcntlal\'d Irum 'Uf'k:riOlliC, ~11\CC the fOmlCf ,1Udy of uff~c.l' pruJUC\'\1 h) ubjcch Ihal trdvd chrout;h u medaum at a faster speed 1hon Ihe \\ aVC:<i the) gcncr;uc, 'u!')CrM'IIIC "csscmi:tHy confined to ~\cropl a.ncs. mi;!.,llc'. "ht..·h II) through n~r 31 a ,peed ol 1he sound in air. Sound wave~ havmg fr~;q ucucy le~ than the audthle r.1n~c 1<20 l·tz1 nr\! called lnjru.mmc SuJ•c·r.wuk

4.2 'Prod uction of Ultrasonic Waves Ullr.,~nni..: w:tv~.:-. c11nnot be prnduc~d by u~ua l mclh,xts. hkc from J diJphr.a~m of n louthpc~t~cr. kd tu :llrcnuuing curTC.nt. Thi~ i\ due to Lhr fact lhal Jl \'Cf) high fr~Ut:IU.:)' lhCinduc.ch•c effectS ur Joudspcakc..r coil it; M) l.trgc th.ll pr.lctil.tll) no current p;•ss.c:; throtJGh h. Moreovu. the dinphn,gm ol n lt,ud...,llC4.lk~r coumt•l 'rbn11c al >uch high frc•ruencic>. Hence diffcrerll mcth<l<h .rro ;pcc1.tfl) u<cu for the produ..:tion o f uhrthOIHC waves. TI1e cwo import am method~. mo~tl) usct.J ttr"(' magnelo;ttrirllt, =tnd pjt':.Ot•lt~t.'trlc.. Magnclostriclion mclhod for fret~ucncy up10 100 ~H£ und p1czoelcc1m· method for frequencies :ibo"c 100 ~HI.

To undersHtnd nugnc.to~triction and pec/ttclcctrk o~cell:thlri, let us liN-t UlldCf$1.tnd the WOrl..ng prindple of nmrlilicr :u1d u,ciJI:Uor aurf then \Vl')U)d tll\t:u..;.;; the l•~C'HiatQr pnodplc.

4.3

Amplmer

Amplifier 1S no clectron•c de"u:·t:. whtc h crmhlc~ COII\' l'f'iiOn ol weak clcctncal unpul~c~ into ~trung irnpuJscs When uiode •~ u.,cd u' :m amphfler, the gnd IS no11nully m:untaineo!d :11 a nc~~urve potemial r.:lrut:d to cnthodc. Becnu$C of the ncg:llr~c potentwl of the gml. le~' nu111b~r 111 cl~ctron' ur~ ubk Itt rcuch the ploue ;h a rc.~uh •he pla1c current I\ rcduct.!d ·nw~ I he gnd poh.:nt miJ~ nblc to comrnl the number electron' n::tdung the p1atc. I .C:. the platl' l"Um!llL For a ~1\'l!n plmc volwge. a panicul:er ":~lui.' .,r gnU "'h~gt: :u \\ hrc.•h the pl:ttc ct1rrent

rs cut otf is en!led cue-off bi:.s (Fig. 4.1 ). The crn:uit of a vacuum tube amplifier H!'\111£ u tnndc is shown 10 Fig. 4.2. In the bU!\11.:' c1rcuit of :unpllricr. g rid becomes nl!gauvc w.r.t. cnlhode h} me.anns o l g_nd-hHh vo11:tge (1-:,.) The mpu1 AC signal

<'t to be ;tmp1iflcd is connected between the tennmt1l T1 :tnd T1 an 'lenes wtth E,.,. On the plate side IS IJC vollagc e1.,. en!led rlalc supply vullagc. wlh:t>c pvsiti,•c h:mmwJ 1:- connectt:d !O 1hc plutc lhrough lmtt.llmpcdancc Z1_. Tilt.~ lo~td impedt:mn~

mn) he pur¢ F., , i<;

rc~istancc.

fh!4!C-SS~IIY

F1g. o4. l

a compleA irupcdant·t.· fur a IUncd circuit. bia~ volwge to rnajmain the grid alw3)'" ncp~ttivc w.r.l. ~·arht~o~..l«! CFi!;. 4.2).

Vurlolion of plntc corn:nl (1,.) "llh urid

''ollage of the t:rid ror u particu1Br plate

vnJtn~c: (\'«) vo lt a~e

und cui·off

0 ' 1.)

In the ab~cnce of s.igmtl voltage (f"~ = OJ Tilt: ~rid Yl)llngc ic; conslnnt :11 6,.• . so th;ll constant platt.' currenl (/j.) nuw~ in the pliHc circuil. Due 10 lhi~ pl:ue current :1 vult age drop (I,. Z,J Is produt:cc.l ~ICI'U!'.S 1hl! tuatl Wl!'Cdance. i.e., 1he voltage drop depends upon the Jllate current, w hich in cum. i~ controll<d by grid \'Oilagc when ~, ~ 0. Th..: AC component of plate currcnl nowlng through lo:,d impcdnnc c develop~ the: umplificd output vohagc.

T, 71

t\Oit)hhcJ IIUfr'U

L----n-----'---------<loJ• Tt

f.,..

1!.. fig~

4.2 Cir't:uh dia~;ram for ampliner

4.4 Oscillator Any Clf'CUil that gencr.uc... an <.~h,:mati\'C: \'ltlln.~c i~ callell nn u~ill ntor. To gcnc:r.:u.:AC' vohnge. llt~ cin.;uil is \Upplicd cncrg) fmm DC ~ourcc: l.)c_pending upon bt.J\.1.' Oi>dllutuml> are prmluccd. thl" oscillator-.. .trc named ib (I! Tuned c~rcuil !l C. I "''clll:ll<>r< 121 R.C oh<ollal\ll' (3) Crysoal n<eillnlo" Here juM togh'c the iJc.:.a ho\" O'K:ill.th),.... wori.. the tunct..l circuit j.. Jc~:;cnhcd

4.5 Tuned Circuit An inductor ~L) and c:1p:•citor (C) <~rc conn«:tcd in parnlh:lto lom1 n Hmcd ,,r t;ml c ircuil. In Fig 4 'Ia) cncr.g_y h. imrc;duc-ed imo thi' circuit by connecting th\! c;tpacimr to a 0(' vnlt;sge hy thmw1ng S tn I llle capncitor gctc; dUJr"Sct.J :uu.J there i s U vollng~,• 3Crtl\4i H \Vhun :.wtt~h .S b thrown 10 2. current st:lrt1i Ouwm~

m the t.ircuit The ~•ifM(ihtl H1t\\ 'l;uh lh.-.~.h.ua;:ing 1hrough lh\! l ni.Ju~.hu Sml.\ Lhc mducwr hn-. 1hr rrupen)' w nppo'\C the l!m"'lh of current 'o the ... urrl!nt buildo; up ~lowly. ulttnwtcl)· th~ c.1pJcito1 j~,. full)' dischar~cd, Btu the m.tgnclic field energy arvund th( ind11:1or coil '' IIU1'<111lU111 nnd the t:lecaron fliOIIQn bcint: 1he greates1. I.e .. mliJ(. cum:n1 (Ftg. 4.Jb). Once Lhc c;1padwr i' fully di'\chnrgcd the mognecic fh:ld begin~ Hl collup~c . •tnd current in the ind uctor Ct1il h. going t(l dccre.t~. Bul lll(! ~clf-indw.:l;mcc: ur mduc1or coil Of1f'OSc!<. ·he dcc~y of cutTenl. So a buck e.m.f is developed in chc

inductor. whtch kecps the currcn1 Oowmg m1hc 8ame direction. Due 10 that bnc~

''"rl'

~ Ill r cap:ociiOr ug;lon 1hc chul",;on~. hulwilh <>Jlpol;ilo poJianly (Fig . 4.3C). As charge bui ld~ up ;u:ro~., the capncitor. the current decreases and m;1gncuc field decreases in the 1nducaor eoi1. Uhim:ncly once again all cncrg)' ~torcd in the c:aJ>aCilor i' in Ihe ronu o f po1crninl cnt.:rg.)!. The cap~1chor ngain begin~ co discharge through indJCIOr tLJ (Fig. 4.3d). bu1 lhis lime currcnl ilows in the vpposiu.::: dircc1ion This inh.:rchange ur o~dllution oJ l!'flC.J"S)' between L nnd (' j, repeated ag::& in ancJ ag;~in. Bu1 Lluc 10 the re!l.bUtnce (Jf tht- induc1or coil and ahe pacitor the nlllplitudc of oscill:uion decrca.~es conunuvusly leakage of lhc c'& (Fig. 4.3c). l'rcqucncy or oscillation on L.C. circuit is

F = 11 (211 LC)

~·

••

.~.

l_l

,. =

n (\ (\ u u

fdJ

h'l

••

1-it:. 4.3

Co m·er~ion

HJll u~e

rrom (.)(' tu A(_~ in :a fliOt"d drcuit

tn ord.:r w get undamped oscillation <tr SU!iol~tutcd thc•llntum l Fig. -1 3f). tJ1e of cntft!)' b to be supplied at the rittht tirnl!' 10 co1ch l:)'clc as lc:c~lh.u;k . 1110!'\

pul~c

llu; o~.;illator t:u-cuits which £ive ~uMa.incd ru.ct ll ution~ h:t\C 1hc following thrt:e feature:' in cmnrnon:

to -nacr.: mu~:~-1 be :tn ncuve devace Urunsi:nor or tube) that work~ as an nmplaficr. hll Then· onu>t be ( +vc) Iced bock m <he omphlier. 4m ) l'hc umoum of recdback must be sufficicna to u\<crcomc los'e~

4.6

Positive Feedback Amplifier as an Oscillator

11tc mam applicauon of J»Sitivc feedback i$ in an o-..;cill:nor. An oscilkuor generates AC output ~ignal without uny input AC stgnal. A pan of output is fed back 10 ulpul muJ dn!- rccdbat.~k Mgnal•s l he only mput Lcl us cons1dcr hg -IAa. which

o-.

--<>\ y

t i/Jrlt\(}lllt'

r-------1---~-o

1'(-0

"• t-r-t-o +

,, -

L---r-~r-;

·~ 0 +

AI'

'-----'-' t__j~

:--

oh •

v,.l

hll

fC)

·~·

,., J.'ig. J,4

Posith·c (c('dback amplifier

nn osdllul.or

!<~hOW~ the block drapn.m of a feedb;ICk Circuit \\.1here ..\ j.:; I he amplificaLion fac10r of Lhe nmpliticr :md prcprcscms the IC~).ko.lgC r:rCt(H', frorn the tuned CirCUli. The vollngc $Ource V denvcs from the mput tcrmmnl Y of the imemul :unplifior

( vol!ngc again II J 11te amplified signal AV drive' the reedbuck network tO prtl<fuce fecdb~~ck vuh~ge A{J\' utter pas~in¥ lhruugh rhc tuned -.:ircuit with lenkng~. fn<:IUr {3, A II htTflme> ti/)V 1 hi' vollugc ruturn\lo p<>11ll X. IT the ph:t<c ,Jttfl> due to the amplifier und the fcctlb:n;~ n..:h,urk I'~ Ct\m:~l . the .. ignal m po1n1 X wiJI hr cxactJy in phn"..: wath 1h: ,,g_nulthat Lln\ t:!'! lht: inpu1 tcrmllwl )' uf the inlemul amplifier.

Now 1f we Ct:mnect p4.HI11:-. X lind )' .and r~IIIO\'C- voltage. '\OurcL: V (Fatt 4.4b). Ihe rca::dhack ,jgnaJ rum driH!\ cJircrtl) tot he input tennin.:tl\ Y7.of the ;nnpliticr

Nu11 if A h 1h~ amplilka1inn faclltr aml fj1hc ic;l~ogc fltelor, !hen, lhr~cclt,c> arc po'"lhle.

!II If A(J< I, ,\fJI < 1'-uulput ''~nul witt dtc out (Fog. JA,·) (!) If A/) > I. A{JI > 11-ttutput slgnut woll butld up (Fig. 4.4d) (31 1f t\{3-= I. A/JV:: '1-oulput ''g_niJI ampli1udc will remain s-ame (Fig_. 4 4c) Herh.a,!. to !!1.!1 :.trshuncd undamJll.:d 0:\t:ill>~llon~. ca.'c (\) ~huuld be Ml.li,fied.

4.7

Magnetostriclion Oscillator

To produce uhr:llionu.: w .t Vt;~ nne of the wic.fcl)' U!~ol!t.l methods b nl.l,gncto~trh.:tion me1hod . Here! m:trn~.;lf1,11"icli(HI ~.·fft:.:l '' ulilitl'CL Accc.,rdint; to thi ~ dCcl't. 1j d 1'ud or rube of jt•rmma.~ltf!lic "IUKttctit· matc'Jial ;,, plucrd iuw u lllfli;m•ltr ftrltl parol/f!l tv it., Jenxtlr. tlun lt'llKih Jtt'H dumgcd J.tiJ:Irll'.. The change: of length p., tndcpcnlll!lll thr ''~n ,(the field but tlc)Jfo:nJing un the mugnitudt: of the fie ILl, n;nurc of rhc mi.ltcrial. it\ pre\ iom. ll't'.ttnlcnt. th~ tJcgrc..: of curlicr magn~:tiz~ltiun

,,f

and the cempcralure. It w~t..:; c)hscr\ cc.lthut out nf v:ui(tu~ fermnmgncti~ mnh.m:•b. nickel and ~orne a loy tlf niLkcl ~hu\\' ~implc and rcgulrtr tlccrca.;o.e ir1 lcn$th \\ uh the incrca.~o.c flf m:tj.'IICtit~UiOll :mtl 1'ur1her ffiOfL" lhC phenomcnnn i:o.. tC\'Cf"'ihJc. I.e.~ •• cnmpre<"un uf the wd nft,n!! IL·ngth lnl·rc!l\.C'O:.. m:lgnctit.:ttion l11u" if :a wd c.')r Ni I~ pln..:t!d JO~tdc." ".:~111 whl,-h ' " ~•trr~cnJ! an AC" ~urrcnt then it ::.utTe~ the 'tlnl\! chang~: in lcn:;Lh hiT c.tl h h~•ll l)'l k' \II -\C l.Um:nt t~nd !'ILUrh ''ibmung. An unmngnc:trt~d rOll \ 1hnHc\ .tl J Ir(!qucnc~ l"'-ltc thai ...,r Lhc AC licltl On the uthcr hand ifLhe roll'' prc\'i0\1'>1} m;1gnctitcU thl.!'n change in length folluw~ thc ~.mn~

frcoJucncy uf Ihe AC fie!<! The natural ff'ClJUt'nCy of lhC rl;tl

whl!re L i~ the length nllh~ rod. 1:. i... Ynung'~ modulu!', L> lhc d('n~ity of Ihe.! rod material!-- ttnd Pi~ th~,· h~Jnwmc modi!~ I. 2. :l, etc. Ordtnnrily tho amplitude o l vibrouon> or the rod is smull. I.Jut tf the rrcqwncy of the AC cum;:nl l::t :,.ami! a:.. tllc muural frl.!q u~ncy of th~ rod. Uh; n rcsonannc occur~ and the ~111lphtu~c of vibnttiOn a:. ..:on~1derably rncreascd. If 1he itpplh.:d rrcqucncy 1~ t•r th~o: urd..:r of uhr.t,Onic frcqul.'nCy 1hcn from 1hc CJtd,i.. tlf the fttd, u hrll.4iOhiC waves wi11 be crnhtcd. An expcrimcnrol arrangement for producing ultrasonic waves is shown in Fig. 4.5. 111crc is o short Ni rod which i.\ clamped nt the ct:ntrc. ~11lb rod h permanently magentizcd in the beginning by p:1.ssing n direct <.:urrcnt in the coil

U/traxonlr

O.C. Supply ~----------~

0-----------.

11rj

l Fi~•

..a_c;

J\lu~;:.nNoslrlrlion

I).'K.Uiutor-

(IJrilll.lr) emil \\hich •~ \Hupp..:d round the: rod. Thi!rc arc 1\\0 mhc1 CC)il..; /. 1 nnd / .l (secondary coil ) which arc w-rapped over primary co1las in Fig. 4.5 Coii/.J i~ connected 111 1hc plate cirrui1 of IJtc valve. while L 1 •~ connected 111 the grid circuil and L 1 and L.1 are mductivcty coupled. When 1hc pkuc c.,rrem p~..,"~inf! 1hrough n co11 1..2 1:-. ctmul!cd H c:~'U'c~ :a ~orrcstx~nd •nJ.! ~hnnA'"'" the ma~netiUltiOn of the rod (wh1ch 1~ Jlrcady m~a~netl/4-'d by .. lead~ current) wh1ch cau.;:e.\ OJ chongc in the lcn~th ut !he N1 md 11m. change in lcnt:.lh £1VC)o. rise to t•haiJgc of the nux l•nked Wllh the gnd ctul L, ;tnJ '-O ~~ change in the grid vol1:1~e. 11ti~ change of e.m.f :1crs on 1h..: grid. produ,·l's un amJ)Iifi<:d curttnl ..:hongc 111 the plate circuit. i.e.. m the emil.~. winch :lg:lm causes o change oflc~th of Ni rod. In this way oscillution of the rod is nuunuuncd. The osc•llauon lrcqucncy f of 1llc Ni rod IS controlled by the vnnnble cnpachor C and i" {!iven by

(4.2)

If th1s lr<qucncy ma~ehcs wnh 1ho naturul frequency

f = {L , I!ID of 1hc rod. ret-onuncc will occur. By ndJuMm~ Lhc length tl1c rod nnd the. capm:ll) of th~! condenser. h1gh frequency osci llauons or different fr..:qucnc.::1c..~ are obwmeU Frcrtucncies can be ex1ended up10 3 x 10' Hz. In order m secure maxamum arnnsfer of energy 1he tran~ducc r housmg 1'\

liucd close to the medium. so thai the !tunsducer clemem

111 cont:ICI wuh lh<

medium and trani-.Juccr ;, opcr::ttt:>d at rcwnanc~ frcqucnC)' of tht: dnving c lcmcrn.

The driving clcrn~111 arc Ni Thc ma;n (tc/\'(liiW.fl•1 .\

lli~"-

tlf'('

l or nmgncto!<.tri~tinn 111cthod.

Cl ) The pnnctp;tl al ,•:uuu~c'

llf m:t.gn~w:-.trict u\l't osc.tlla10r n.re simplicity o.lnc.l lo'' C0\1 u l t..:on,truc-tiun (2) At low ultr~~omc frcqucnc} I.U'~~ pow.:r c1u1put t'> po-.s1blc with(IUl rt!-.k,

or dn.magr tu tt1c

t)sclll.lltU

drcutt.

l''''-'11

untlcr temporary U''Crl<-~ad.

l J l The magne~o~uwtm ....-.m~lu(t'f' t,"'' l: <.'t:lhlin ,,cJvant;tgn n, ~.:rptcLnch;...:m~ h'Uustlut:c.~ rc~onum:c

Tltcy

pt,..,~,.,

l.tt'&c pm\l'f ll.mdhng cap.:.h:Hy and ">h:trp

CUf\(.

Th~ nwln tlwwluwJ. \

an·

( I) Difliculty in impc~">&nf! pcrrnruu.!nt pnlanll.llt~ mugnCII\.otlh'll of Ihe Nid..cl

md inatwll) 12) I ~umt:uwn ~,f I re(lu.:m:~ 111" OClt P'l'"'lhlc t~1 u...c fnr vay higher fre<.JUCncy r~tngl!

f ~) (irc~ncr dcpcmh.m:~ 1\l rrcqu-:nc) nn h!rnp~rmurc and bread1h ol te:ion:.ncc CUf VC, COU~C!\ ch.utp:c' 10 d:hiH.: niO">I;JI\1' uf rcrnmlilgOl.'(U; 'uh~lltnt'C'

\\ 1th dc~rcc nf mu~nt~ll,ntu•n

4.!1

Piezoelectri c EITccl

When m~:chanic:11 for~.-!., IJS..c t.:mnrnl! ..,Hm m l~n'm'' itn: applu:d lo u ~u1t.abl)' c ut piezoelectric t'f }'.">lnl lil..c t)II.Ul/, I'\ .Chelle MJIC. tourmaline in ·• ccnain tlirecti011 Lhen dec1rk c h arge..\ :uc 4kvch•I'JCd t,n the cnU~fOl'l.'\ uf I he pl:ue perpendicular co Lhesc di rection~. Th~ ~.u.,m.. ..:\p.:.rienccd hy the phttc make the molcc!tllc\ tlf Lhc"c nmtcnnb umlc:r;;u .a "·h;tn~~ U11lfl~ntataon \\ hil'h rc-.:ul1~o, in the.: "PilL::Itilnt'\' of ck..:lrk t.:hargc-:-. Tht· nloi~I1Hutl..: •11 th\.· potclll:~tl ,JIIT~renc-c dc.\doped .11.'to"' the £.tCC:, of the plate 1"' J>Wfl<1rlU10al IU lhc ~U11UUJll Of ftm:cl:l apphed_. 1.C., lhl' cxlcnt ol d~:funn:t11on pi\~<.Juc..•d ~1nd tts polotnty wa II be re'v~rse when the dii'C<'IIun Of I he di':fnrmahOII f~1r~\!" '"' h!\ I.!'I ~.;d 1-ur ~XiHI1J)IC. 11 the. \ olt;:IJ;Ii! pl"tKhaccd b) the cry!'t~11ss po~lti \I! wh~n ..:'~lUlph: ..,cd th.:n n \\ itllll: ucg:u 1ve \\hen !<.ln:tchetl Tlw~ phenomenon IS kn0\\11 tl"> thrtrl ptl';.tlf'lt•flm• t1fi'CI Tiu~ ,:O"ccl 1\ dln:ciWIHtl and hence lht! .:rystJI plul\! should he cut m pmpcr dtrccllon rclatl\'c to it!\ a;,c~ of ~ymm.:lry

Cnnvcrsc 1~ ;llso !rue. i.e. 11 the cry,tal plnle 1' ' uhjec!ed 111 clenrical '"c". nh;:ch:tnit.:;ll ...uo1in in ~~ part1cul.1r dm:cllon wiJI Jc, c lop. whic.:h me~m .. lh;tt 1f u dircctl!lcctrlc Oi.!ld "npphcd tk:twccn 1\Hl 1:\Ci,:l> <li the cty'-tO!l pl:uc, IIH:n 11 \\111 dther comr:tct or exti:ntl und tf AC held is gtve-n. Lhcn nll~rntui\'c e:<tCO!oJOn and conlr:.l~lt0111~ produced m I he ~ry:ilUI (i..nJ hcn1. t.: il slarl~ viln~tmg . n1b b..:a11c.d mrrnr pic-~orlt'C"Irw rffi•n F~c.tucrh;:y ol v1hruuun "ill depend un 1hc apphed AC frequency. I( the fr~.·-qu.:ncy ol lhC AC fich.l ·~or lhe C\tdl.!f of llltrn">\tlliC frequency and if II rnnl<hcs wnh 1hc nuturnl frequency oi l he crysmllhcn rcsonnnc. wiJ1 occur und cry:,tal wiiJ produce ullrn:<ionic \\ovc~. Quans crystul belong!'> to the Lngona.J system h bas a .shopc of h~xogonnl prism "\\Pilh pyr.amid ~itUched tu each end The 01.xi< joining 1wn end point~ of lhl! 4

pyramid is called tl(m'r• rJ.u\ (ZZ). Figure: 4.6(n} ~hown Ihe idl·al l(urtrtl c:ryo;tnl in

tiS muural ~taLe while Fig. 4.6(h) !r~how.s a M:t.:tion nf Lhc crystal at righ1 nnglc hi ax•s which i~ :a hcx:.gon Thrl!c line..' X1X1 , X1-'i!. X which pa!!Os through I he oppo>ito ~nrner or the cryst31 3rc C3llcd ele<ltiral , . X-u.~i; nod they nrc pcrpcndtcular to optic ax b. zz. lllc pic;.oclcclric crrl'ct ·~ mn:-.1 mur"cd along tlcctncal a:ds. Similarly, Lhrec line" which arc pc:rpmdiculnr w the side~ of the

,x,

,_ x,

••

X C'tll

,\ ·t'UI

f~f

\ll)

78 i£11J:IIIi!c'l'tn,ll

P/n'.flfl

hexagon foml the Y-fuh· u1 ,,.,.lrtJm'NII uxi.r. they are :•J•.::n pcrpcndicuhtr m the! nJ11u.: :Uci'- The mcclmn1ca1 U'<h Hrc at ris,ht angle..; to the rc!>pceuvc clct.:tric uxi .... Usu.~ly

tho qunnl plutc required to be cut has it< races pJrallclto the opuc nx"

and pcrpendtculotr In the dedrk oJ~"'i' or to th~ mechanical ..,.,.., Wht·n th lurge"'t ra..·c i\ ~f('lCOdicular (0 the X-axi\ it ·~called X-cut when l(j, largt'\ 1 h1l C Urc.l j, pcrpon<hcular to the Y-:t\i' it '' c:•lled f-ew platt (Fig. 4 6t>J l·or" pt,:l~lc~o:trn: ...,) ..,tnltr an clcctnc ~tress j.., nrrtlied m th..: chrt.:"-'lfi''' 11t \'a"' ''rclct:tm: ;.~At' TT1r.\.·h~II11Cdl !\lrmn \\illlfcvdop an Lhc tlhC'c.:ltnu uf lt' 'J"Cf..' U \l' 4

1'-:t\1\ nr mechamcotl illi' Suppo>e there is an X-cut .:rystal plate nf lhkkness 1 ancllcngth I f:liong copuc -...n .. ) Wh~n AC volt;}j;.C 1:0. ;applied :1Crt>~~ the f:.tce or I hi~ J)I.IIC ainu~ Ihi.! i:I.!CCfh,';tl nx1,, ithcm•ttmg ''r~'...c"' i1n~l \lrt~in ... arc ...et up hoth thid.nt:\'io and l..·ngth·\\ •~c II the frc<lll\!n<.:y of J\C \'nltag_c: happt:ll\ 10 be equa)1() the natur:t1 frctfUCilC} of the

\ 1llr.Un111 ol the pi:Hc, the.:n rc~vmmcc v.•ill occur. The freque-nt:) nf the tht~."-nc:<.s \\>ISC vihrruion tJ.c .• ~lnng ,\ ax1')" 4

·£

21 \! f)

IIJ .e

~imibrly .

the frc44ut:ncl' nl 1hc 1cnp.th 11

4 \\

i-.e vihration i.,

I' ( E D

= 2/ \

whctc P ~ J. .2. l, c:tc. !'o r tunJamcnwltlst ovenonc. 2nt.l c)\'(nunc ct~o ). E the Younl!·, modulu:-. .. hmi! the appropriah: (ltrccuon :1nd V the densil) of 1h..: cryslo.tl flldtC.

4.9

l'iezoelcctl'ic Osci llator

) 1 t~/HI.!I~ctfiL d fcct I'

UlihtctllurprocJuclli)n OlultrasOtUC IA1I\ l'S In the hlJI\)\\' 111~ u p i\ ~h0\\ 11 tu Ftg J "' ThL hi::~ l lru.JtJl.."lh:~ \'. \\•htl:h j.., applu:IJ h.! the c:ry.,.tJI i' Obl:tincd b)• itanlcv thc.:tlloHOf) ..:-m:-uu

\l...t~. TIK c\( ~fllh... nt~t ...... \ult:t~c

..............

K- t• l h ool,('

111

1-lt. 4.7

11iezoelectrie oSC'ill::ttor

llartlt!)' o~cill;ttot cun~ist!<. of a tuned oscillatory circUJt (inducttulce L unci •' \':tri;tblc. conc.hm!'cr Cin parallel). One end of the tuned circui[ i~ connected 10 the plme while th.: other end jJ; connected to tbc grid lnductnr coli L ts ta pped in

llltiU.\'rmit·

~uch u wny that the poninll L1 of Ihe! cot I i~ in plntl' c ircuu whlll' 1.1 is In Ihe gnd circuli Th•· omplilied energy in the plate circuu i< fed back w llw gdd circuli by 11\l'.lll' n f induclivc coupling. The tappinf! polnl 1-. connl"ctcd to the cothnt.k Thl" llUJfll en "' •~I Q h. conm·ccct.l parallel lll .1 variable ~o::.tp:.u.:itor C The Jlanlcy usclllul!ll carcuil s h!>" n an fig. ~.7" pJmlld lccliback <m:uia. cht: pl.uc cin:ull is l1ividcd inItt 2 p~1r.•lh:l hrun~hc\, u1W to Jlftl\ ide u P•llh fcrt dm..-cl L:urrcnl Jmd the mlu:r Cor nht"11l:uivc cul'tl!fll. RF ch() k~:. l,~cp' 1ht: ahc!ntlltint: currcnl out u(OC c iu:atil ~o.vhilt: the bloclins cap:.triwr lt~e(h lhe dircct l.:'um:nt uut o l the A(' t.'ir<.:uil. Thl~ pro(>er gwt hi!a~ ic; obtatnt:J hv nu:a11<oo. uj Rll until r ·ntc uumlcnt switch is clo~cd the valve :-,UlrtS run('tionmg us nn ••'<=ilhuor produdn~ ,l,UIIoa11UI1\ htl\'lng fn:qUI:!OCI!i!.._

r,,

f= 2tr -: LC 11t~:

frcqut•ncy of o~diiJ ti on ran be contwHctl bv

1h~

\:1ri.thlc

c-ap~• ciwr

L ) ol chc tuned wuh the n:.tur.LJ lrcqucnt.:) ( u, =- I' ,1 IJ 21 c ry ...rnl. Then re'ionnnce \1. 111 take pin~<: <Jnd ullra.-.onlt.: \\~t\l.!!i will he produce~ b) qu:m7 cry'\tnL Uhmsonic waves upto frcqucnq 5U. fKMJ ~H1 With a mod-=rnt~ ~i1c qu:tn7 Cf)~lal can he produced hy thi' mcLhoJ l lt.1\\C\L'r (n:qucncy upto I ,u,nnu kHz can he produced b)' tourmaline cry-.tal t\dvnnmgc:- of piczoel~ctnc. o'cilh.Hc'r un: n" f(liiO\\ ..:

111 \uch n way Lha1 11

•~

t I) F{it higher frequency rnn~c c-mc h1101 w u'c thc p1C/clCiccll'ic o"Cill;uor ( 2) 111C) :1rc small in <>;izc nnd t..-ctmomic:al t.'\) l'hc ..c nrc very scn,itivc when n~ctl in Uctt!llor 4..J ) Tht: \\::wi.! funn h good. n1c tli,,llh.lntllJ;t b i~s hw.· ptw.a h.mdlmt! ~-·•P>IO:l\'

.u 0

Dett.-clion of Ultr asonics

Ullra.sQnlc waves cannot he dctcct~d c.hrcctly. bul wm~o.· :uumrah lilc a b~H c::m' do )>.0. l lltm)o.OiliC wnves art detected in(hfL'CIIy hy the follcH\'I n~ w:tys: l I) Pitf:.orlt•t·tt•h• dr•trr·wr: When unc pnir uf Ihe f:u:l'~ (lf u 4uurt1. crystal 1~ !>ubJcctcd to ultrusonics, on the olh~r J>l!rpendiCular f:...ccs, varymg dcclnc c harge:-. arc produ'-~ed. though they :lTC very small but cun be :unphficU and dch.·\:tcd by ~omc

Mlilablt.: rn~an:-..

Ktmdt :'i wbt~ mt!tlwtl: \Vhcn ultrn.!>onic wavl'" \If rcl~1tivdy largt: wave length. is .Jimos1 comparable to audible ~o und . were pa~~cd throu~h Kum.Jc'~ f:})

tube. Lhe n lycopodium powder !!>priklcd in the cubc:. ~:ollrt=c~ in 1hc form ofh,WJ>S :mtinod~ll po ints trom which di.!H.~t: ti on h f>O<"hlc. (Jl Acr,ll.\lh tliffrm titm mt1 tllntl: \\'h('n ultra~o nk \\,l Vt:~ tu·c propagutc\1 111 a JiqUtd. lhe dCil!iiily varit.'S from Jnycr 10 layer dul'. to pt.~riodic variation t)( prcs~ure. If under this condition monuchromat1c Ji~ht is passed throuf!h Lhe liquitl !11 righ1 angles t(') the \\'fiVes. chen liquid hchavc~ as diffrocuon grnting. Thb grating behaves in the same wuy as a ruled ~ratint:.. He nrc lhc method c.;:an at nod:tl point-. and is hlown off at

he useti fur Uctcclint- and ft1r hndin~ Ihe W:t\ clcnglh and vclocit) ol uhr.t..\tnlc ''·"c .. in lu.Juid. Pn)pcrlic~ ()f Ullras()nics Ill 'I he) nrc h•~ 1ly t•ncrgcaic. ~ 2J rh~.-·u ..,"-!~~~ nf p1np~a.g~nion \lcpend"' up(m Hh:&r fr~qu~ni.:' ~. 1.c .. 11

4.11

mcr\!:h"'' '

Ill fr~~I UC-1\C) l 'hr.t.,untl"' \hnn 'Cr) m:~ hgJblc thllntc-uon due ht Iherr 'nl.lll ".;t\dcn)!1J1

Wllh lllCh':tM!

4~ J

l·len"· the) t

(!Ill 11111 d

'" cr lnng dh umce\

11 n hu HI ttn)'

I"" "' <ncrg)

lJ llH: llttnnllhrnul_!h \\ tuch ul tr.t~(.ml<.' wnve~ pa~!t. ~hav.:.: ih tt d1t1rncuou ~r.ttiOJ:"l undl!r n1nnnchrum:11k ll!:.ht

4. 12 Applications ()f Ullrasonics lHII.I'~llliL'

h.a'l' r,n,rh.l numcmu' app1icathlll' 10 the folio\\ mg lu.:lch (!, l ndu~ lry (3) s . ~icnu . llc world (~} Mcdtc-:tl \Vnfld. The\ .11'c ..,,l U'it!ful m.:un l ~ due Ut lhc follmvint rcnsorh;

' 1, ('ommumcatwn

( I t t\1 '\UIIich.'Ollv htgh frcqu\!nC)' niOlOSl (1:)

parallel

beam nl rlnnc \\'U\'~' \.'ttn

he pr••l),l~~ltCJ . A:-. rh~.: \\,1\C culttlh ..trc ' "'uJI , me.t'u rc111cnh can be mmk em ..a 'm.tll \:llllJlk \\ 11h0111 ;IIIClltrJ~ the rhys.ic.;U C()nditiurh like l ~ltljXI ..IlllrC. 1.h.:n'it) t.!IC

c~t

\\'ttv~h:n_!;1 h Jt ckc lrum~.: .t

\Cry hrgh frequency ts ol the onlcr ul nh•lcculur u.nd Jn.."l' pJLh SnIt i:,. u,cful for ~tuJ ying Lhc intt:rn.tl 'Lru1.·tun: vf

nur,·ri.LI

A. llhra'inni~,....., :u~ Mt•an~ of C ommunk:.uiun l•llr.t"'llll \\ ;l\ '-'~Me u...et.llnr ...nund sagnallllj;. Tht• hagh Jrcqucn<.') 't1UIIcl "''' "-'' m.a, I\ '"'·'•hi h•nn( J mtt• o1 h~.un and ..~, nllhc dc.!<-irec1 dit.:t.:w••l rth·1w.un .. l 'l'lllhl g.cl'i lllHI"C :..ntl nwr~..· lhtrnw. U!'\ the rudru~ ol Lhc pl:uc <•I th..: l!.~n...:r.:um I!\ 111\.rt::.t\\.'d an rd.ilann ''' the" ;IVckngth ui rnJmtt.:d !'lound Al6UO Kd'. ,, ptul" •• r l 5 ~.:m.li;mlClc!r t!'\ ~rtuu~h ttl confi nl!' tht: sound with :m o:m~ll" ol 5 t.lcprl!'l'' Such nnmm t)t~~un.;.: t:an never he tmamcd in lhc audible frcqucnc.) r:mgc and lfus lim power 'uurn~ can r.:tJi.Jte very h•gh intensity of ullmsnmc o;.nund ''a\ c,, wluch can ll':t\,cl many km in \\":u . . . r before being :lbsorbcd Suhmann~ uhra...:mir lt:.ul~Jll lll e rs have hcen dcve1nped rcu U.:!h::~:ung the prc~~ncc or ICeberJ;c; nr !<>Ubmorincs. A lypic:tl subtn:lrtnc ultrnsoruc lr:m.smttlcr u:-.cs fU C/0\·It.:CIIH l.!~urmiHr \\lm::h _g.;O~I'Hh.:!) P\WICr'fnl ulltOJ,UUIC \\~1\'C:> \If frcqucnq allflUI -10 LH£. Thc'c ... ubmarinc ultr.l\ontc transmiucr may be usc fo r the followmg: purpo,cs: frum ~htp~ro~shi p specially tn o;uhmL"rg~J 'uhmanoc~ d('t''" of tlw u'IJ, p<)Y..Itlon of :1 'h1p. po:-.Haon <1f wbmcrgcd submamh: etc. 1'/ris usts llrt• so~t'alll·~l c..·lw ptmc·tfl/t• l'iu:

tl) 1- ot

HI!IWilm~.:

(2J Ot·lt~llmlltlllou oJ tht•

worlong prin..-:1J)k 1'- 1hc

~· me (lS

Pulses of ultwson 1c st.gnals

thai o f :t C(tnvcnllonul pubcd

arc. scm

ouc n1 shon

electric trano;.miner which is lypic:,ll y energised

r{u.l~• r.

uncr\';1!~. rrvan n pji!JO ~~~ :1

frt!qucncy of ahmn

Lllrrnsmu,•

•.10 kc/s TJw rt:tumed echo · ~ rece1vcd 10 ihc uhra.,.on•c recc.vcr. \\ht.:h nl:..o U'\C~ pic£0 cry,wl followed by an amplifier and the 1ime imcrv:•l between 1h.: tn.r .. mtucd :md fi.!CCtved ~1p.•1nls ~~ n01cd h) umc- mc:hunng J c\ tt&::. U~ J..now1ng 1hc \•Ciocll }' of sound 10 w:ucr. the dbHulcc c:m be mc.,~ured

Tile vdl'W:il) C.)l sound in -..ca \\ uter IS

I'= l'n+ 1.14.f+4.2 1r-<l.Ul7r: \\hen: V = q;lnctty ol 'uund <~I r 'C 111 ~CJl wnlcr. {m/~c), \'11 - 'dnc.' ll) nl "''tllltl a1 O"C in "alc-r ~ mf,~d ( 15 J() m/~d. S = \alinll) (g_mllitcd. 1 - h.'lllJ)I;r.U un: of ~a w:1h:r in °C l hi" mcthntl for finding the dcp1h ~.. r '>\!•'· 1hc thn."\.tiun .nHI dt,IJ.nc\! of :1 'uhn1aruh· ur tc~N:rg j, called "Sound N~l\'i~:Utlln :nHI R:.IO!!IIlg !SONA~J .

lndu~t rial ,\ p pli c:tliun

Ci) f'liln' dr•tt't tot: In mu:,l cnt:.nccring nppl1cnuons. the. ;t;trcn£1h nf .c t.:omponcm piny:-. ;J ~~~mfic.:tnt rul~- l11c strcnj!th of the matcnal ~cts reduced ihcrc <~rc "lc(ccl!tl m the mlUt:li~ll' Thl" ddec1.; m:1y he ax large a:-. crad..s or :1s tiny :1s c nvuic:-. pmduct!d durm~· the process nt ca~tmj!. Thc.)C Ott'-" tcstmgs c~m be don~: \'l.!fY Clmvcmcntly ami ,tccur.,tcly hy ult• -.~una:.. 11w high frequency ultrilSOntc '''hrau u n~ f)mr:t~:th' in a hornogenou' :-.olld 111 a •ar.ushl lme. untl the wuves ~tre 1otall) rdlcctcd ;u thL· boundary of Lh~ solid wuh tnr Thi!- results llllht! reflectjon of w:l\ l!S b01h Irom the hole and the O:lck !t>llrH1CC nr lhc metal. nus tunc Interval bi:lwccn l\\(l 1Cf1CtltOib '" r~conlcd h) .ul o;-;.cilln:-;cnpe nnd 1S u1ihsed for loc:uin~ lh~ posnmn Of the nn\\ 111 lhC lnl'IJ d -' /tH\ JUHH'I upp/irtiiUIII

hi) i\on·lrouu1,&:0WIII•, I ·lh .c-,,mt< \\,t\1.!\r C>IU he u~~d lnr the :-,llhl~ nl non hmnul;cnc.:IIIC' mot m~f.lium ,uch a). nlc$tl or plrt,tic. For visual prc: ...;maunn \\ ". 4;;111 convcn th~: uht,l"'hiL \\ave' couuug rmm medium imn coiTcl\p,uuhu!! hF-111 WU\'t.:" Thwknr.~\ of th~ · t.:IIIH!c': lJitr:t.;.onic w:wc~ can be u"icd for mt.<:hu11ng tlw thicl..nc:-t.'\ o f boil~r. ntmm~ ptlt structure where nne ~•de Is nnt uc\!C~!'!Ible h~ the r roccc,, of n:llccLHln ul ullmsonic wu\c a!\ lt11\ power tt(Jplwatum

tiii)

tiv• ('u\'italuut: \Vhcll .tl\ uhr;hOIIIC 1fl.\llSdu~cr 1\ Jllaced 10 0 ltq uitJ 11 pnKhh.:\!'<. stnndint: wowe formauon ttnd 1hc~c rcs-uh 10 the dcvclopmcm and tmpln:;Jon Hf bu h blc~ . Prcs..;urc de\clups :n some pmnt..; inn liqu1d. when subJccrc.J t•) powerful ultr.t.wnic w:tve. .such lh:ll excc.;I\IVC ~arcs~:; breaks n p:tn o( thl" liquid :mcl pmt..lun!'

hollow buhhlcs. But til<.' " bubble' soon coll:opsc and :tt the i tm:tm of unplo,um. the pre... ..;ure otl'ltUild the buhhles becomes very htgh. nbmn ~cvcru l hundred .. of lHmosphcrcs. 'fhi~ hi1;h pressure rc!<'ult~ in cmulsificlHion The CU\'Hallon bubbli.'' fonncd b)' uhrn!'onk v1hr:uion hamper lhc propagation of uiLr:l:-iOIUC 1U) '"';•'e..' and produces no1sc. L1u1 1h1s has been succes!<:fully used in llldusm ul dc\'ICC' described bclo'' :,~ lli.l.!lt power ftpplirtwon uf U~ wa\-'tM.

( I) l'rt'l.lorarion unifOrm a lim·: 11tis pm..::css o1 cuvaloatJOn ~~ UM!c.l tor du.pcr~ion uf rUcl4tl' m molten ma11.·riub to obt.nm umform .tllo)IO£.. U) :.uio n t.:~f U·\V:\\'c;. i1 h.J' become pov·dbl.: to dispc~e Uiffcrcnl mct..d~ 'uch a.' N~a. K. llg. Pb. Zn. Cu, CIC, ~Uii..l tlll'Jr fu,ihlc :1110)'"' iu Ufcohol. OJ I. muJ \' tlft.' l

t2) SaMt•,itl.f: wul mt•tal Ctltt;,at: Th~ CJ' 1t.ttinn uction of ll·\\o~Vc..~ ~.an ~ u,e.:J for 'oltlcriug. mrlal cutting :uul dlillin~ JlhK.'C,.~o.t.'' in mct:.ak t.'\• lllllawmt• t /,·.min.~ dt•L'Il'l'. Cnnt:amtllalctl 1H1kl ~' L'an b~ cleaned hy u~o.~~Jhuln!! ultrn~nk'llly in sequen"'''"";-,.10 ...uu:.~blc ~\-,1\\'nl:-. \Ju\\<Jtby .... this h.."<'hnit.•u~: u~c

h•r \la>hin~ lc~lik~. In ullra>Pillc d~Uillll~ 1h~ J.org~ llllllllll'n 11facnu'l" on· the Ci'IUillllliii,IICtJ p:1n klc' fr\1/l l the \t.llf.tCC.

pn: ... ,urc JLIU.tiJ~· hrc.iJ., l·l)

:md

Puparmion oj ''t't"\' \Whit''"'""""' t\l

IWO 1tllf1Hc.t:Jhlc

lic.JUill,;;uch

~b eli I

Wltl\!r.

Photogwpllu t•mu.'·wm; U•W.I\1."\ UI\J''IIt\t' ch~ h•tiHII~t.'IU~I I~ and :-.l.ihlhly n r phoMgruphit. : t::..mulsion:--. 1l1c ir C\1luur ~11..,111\ II) lm:-. o~l-.n hccn II'IL:rea:-.ed b) lhc'lruugh ~li\pl!r,ion 11r the llyt.> m the crnul\iun umh.•t llu· innu.·ncc tlf U·W.l\C'

(tj

1i•J C<Jct!Witllitm mul a\'smlli.wuum~ The hr••ughl 4Uih.·

du'\4.! tn .:w:h f llhc•

pnnic!C'~

c,t

su ... rcn\.lcd hqu1d cnn he

"''"!! I IJtra,onu·, '0 I hou i. o.1gUIJIIUI1 may lnht.:

place "hu: h hdp:. m the mh: uf cry.. lalh ... atinn f tii) lllttchonu ·.\ m tlu~ Jllld\' rif.'itrurtuw r~imutl,,,- Th1!-. 1:. :1 t\'chniquc o l ullra.s.o mc:~ t.Ji,play111g ~nmllcrancl mlallcrinhonu,gcnclllt.!!l.lll ml:l.d A lim11 of1hc impm,cmcnl j, n·achcd when 1he \\I:JVelcnglh nf the li·W:t\..:. bccnnu.:~o compumbk 10

thc

~it.c

cH lh.: l'ry..r:~l}!r:ain of the 1e~1 m:tH.• riul~ fur lht.' lrcc.tmmcy 1angt! nf 1- 20 Ml'ls.•

l h!!n muJuplc r~O~!tdPn~ and lnti!rkrt:ncc' t1rc -:;u~-o;~d du~.· H' the 't:tuenng HI the l ''•'''c' nl th~ bc,um.lanc' ollht: \T)o~lt~l f-hUil 1h..:n Lb..: l.:l)'l<~lhn..: m.ll~tJ;ll 4

OCha,c;;.. hkc n .3 dimcn ... lonul dJOrucuon 1:!-r;almg whl.-"rc: the t.hfllnc-uun p;llh;lll ..<t ni:H~inc"l hy (J.wavl!:.. tc.:vc:illh ~ inh:tn:tl "')'tlllnctr~ \lf lh..: t.'r) .. l!tlline solid. like X ray ~ohffrociH\Il Jl:aucm 4

D. Mcdic:ol and Biologica l Applicntion.' hy l lhrnsonogmphy (~•l /)i\,.,t\1' ~tin t...

rn·mnwor 111c bctdy parh o.ffcctccJ tJ1ac tn neuralgic or rhcummjc nn hdng CJtp<N!tlto uhr":,o:onic~ j.!ct 1-!rc:n rchcl

Ib) IJctt·etiVII uf (J/mnmwf srowtJr: Cc::n:bl u1 fur lvc~uing ~· bnormal f!l'tmtlh in thl! hr.tin.

\'CIUrick~

me t.::Xplorcd hy U-wavcs

,l.!)c.,·cn c cuuing of ch..:.

\.luring an opcmlu:m .

Dl'""''

(d) t•uuiug: 1,.;'-wuvcs have t"lcl!n found very u~ctul for dcnud cutting l>ecnusc: Ill th.:y muk~ the cuning almos1pa inlc<s. iiilthcy cut ~lC hard material vny I.!OISil~. (iii) clu;y do nol r.:4uih: iHl) mcchanicul Ucvi~ for . .-uuing 1Uifp<')S4!.

Ulll'a.wni.· {C) IJ;o/IJ}:ll'll/ t;/ft!rt:

Smrall nnimuh h~c frog~. rat~. li.;;hc:o. CIC. r.an bl: killed or

tnJured by hi~h i111ema1y ultr.:tMmtts ilu~ may be the nnl) one dc!'ltrucu vc Jpplic;.~tton

uf U-waves s1ncc other :tpphc:.Hiun-.; descnbcd uhcwc :ln.• Hll

nundcstruchve ~tppl icutu)n!'o o l U-w:t\C~ .

4. 13

PZT <:cramics

B;mum tttonutc. lct~d ntrf:I-11H'h:th: k;ul 1tlaoate k:uJ tKruu:eh:. il' "dl ••' a number of m;u~,·nal' on h.·iu.l -tH.:rmlafC·ltt ~watc hase ( PZT) wh1ch 1C;\emblc: h;n nun

utanntt•. urc: ullocd a' 'iOfcrcd ,·cr:tnuc mutcrials hccau~e 11 i" om po;o:,ihh: tn produce l:lfJ;Cr 'tngh: cry~~'" It umtl'k.:tO.lllfN,: m:nt:nnJ ... are shm1. '"Spte,ctelccu IC' property. Milne of wlucb ur...• h!rr<'\:lectrn: ulso. In comrn:.t to qutlnz. hthium und oihcr ncutrul ptczodccanc cry,tals, ccrum1c~ a rc givm~ lhctr piezoelcclric propenie') by polari1:.t1iun

~ulphalC

Ccromic ptct.oelcctrt< crystals con be tonned in dtllcrcnl r<oqutrcd sh"P<''· The ground. ra"" matcnal1m:-.cll wtlh bmdcrl>. 1 ~ moulded us rec..Juircd by prc .....mt: <md simt:nng. above I (.)()()~C und I hen :.hnpcd :tccu•mel) by grmdmg: "' rct(Ufl\"t-1 P"I.T ccrcrnics an: while 10 y~.·llowi!-h matcri:,l~ nf 1,1wcr hardness and rc'i't:ln(.·(' lhnn <lunn.i', their dt.Jll '\ttlf:tce .. can he .. ehcr plrucd hy bakeng process.

PZT cc::romic :,ubsmnc( as ltri\t hc:ucd to cur1t.: tt!ll1(,..mnurc upm 350· C ' •mm: t~mpc:natun.: '2(J1C). nlli! materwl tl> Lhen penneucd lo cunl off. and o dtrcct \Ohugc ol fc " thous;mJ vohl-1 per cenu metcr lhu;kness '' ;tppltetl than BaTiOJ c.:unc then

du~

to lhi_:.. voltage. the

~m;all

t.'lcmcnt'-tr)' c•·y ...r::.f~ Ill the ceramic

rn~ncnal ,

which oncmcd rondomly cnrhcr. no11 ah~n along one UXIS and get frozen. So the PZT ccr.1mic materials become poluru~.o"t.J nltmg one .1X1s. pro,•idc\1 the tn~Hcrwl is n01rcheutcd dos-e lll the cunt: l~:mp.:nuure . I:SZT ccr.•mtc mttteri::•ls 1ln•' r.:nuun p1ct.odec1ric an the rrcven :o.t:•t~ due h-l the alignmcm a long one !l);i:o. CC1'Umic prciOCii:C11'u.:. u1a1cn:d-. ~ nn he u~cd tor nhlauung lntll!->duce-N. "nh cur\'Cd surf.,~·c!'l by S-IOh!rll\~ omd !_!flm.hn~. an wht.;-h pn:zoclec:tnc :t.\1"- tl> ~'fh.'llh:U ;nHornatit:all) ;u C\'Cry pmn1. normttl 10 the ~urrucc duung pola.ttl:•lil)n For qunnz cryMalln tmnMJuccr @round "tth ;1 cur\'e. 1:, nm ilOs:o.ible. II 1hc mm:.duccr ground e."-cc.~sivcly c(mc:wc or cunvex. t ht!~e face .. 110 Iunger comrihutc 10 lhL· radiation of lonj.titudlnal wave, _So the conMderablc concentrmions o t the sounU field a iOO!! Ihe ttXIS of the C) Iinder can b.; Udllt'\'Cd by U~IOg p Cf ~Cr'dlnu..: ptc£oclcctrk cryst;tl over ntuural tr)'~lotl. For nondcM•'UCII\'C •c...ung lead mcr:t niobate and lithitnn !-!Uiph:uc au: the he't

4.14

Ultrasonic Tr:msdurcr

Tmnsduccrs :m: ;u,.:tuallycncl!) convert~~,..... 1ha1 is. 1hey cunvc.n the cncrg) rrom on..: tran:..mi~iun syMt.'!lll. whcrt: it h. :1ctiv:ucd, m ~cond tran~mi"i'\ion \yMcm cilhcr in the: o.;am...: ron n ur 111 tHH•Iher form. An uhm~onu~ uansdul'.er c:111 he U~('d Y.ith clcclmntc amplifier tor dc\'clopmcnl of intense acou.s tic fi,ldo; m 'uluhOih and mmcrinL'Ii at frcqucm:y (rom kw thousand HL. to muny nlC~IJhCrl7~. Common (orm~ of ultr.:t.sonic trnnsduccr.. arc the nMgnctosui cliun bitr and the piezoelectric

crysw1. both lll't..:ful ror CQrwcning ck~·tric energy 10 rncch ~1nical :tcoustic ~nergy

PROBLEMS T\\o 'hirh an: rm~.·h•.l•cd :n 'omc th'l\tun« 1\\\oD)' ul tht." tktp "'·' All uhra.;on•c '':;u.d uf 5fl'-1It h -.cn111un1une ..tur It• .u1uthct h) 1\\umutc:... i I J tlunugh \I. <iter \\llh \"t"li)l"lt) I nv.. and (2) thfOO!!h •Ill wtth \'Chk..ll~ uaJ, C.th:UI!tte tilt" Ll•,•uw:c hc t \H~cn t l ~ '" o ..hip:... v. hen un.c tlini;n.:ncc 1•1 • e..:ci,·~ !\\u ' 'l!J.l .lb 1~ }

'·t1

.\oltriiPtr ,\ • \ 't hll .ut r, ;::- 34 \ 111:. ~ l·ur '14!J v..1t.:r \'_ = l.l72 m/~. S; \'~1~

s \'• '•

I;= 1: .')/\'1

'•

s mn - 3-13,

.I -

3H X 137l .

.\/\

,. _ 0

, 117 • - Ill.

2 ·\U ultra:.~JI\11. ,pul\:'t" ul U 07 ~' I ll ,c_mh Lhm n 11 (tuhc hm .u·th the 't'.il h.:d \\ tud1 rctum .. afl~r 0.65 we The ''clocH) ul \\lUnd m "M:o& ".J.tct '' 17tKIIul-...·~o. ( ·.,lc.:ulatc till'

t.lcpth ul

M:.l

.tmlthc w,,,•dcmt!lh nl puht•

I ,q

d = 552-;

Ill

=,.A_ A.:;; \'111:;; 1701)1().07 ..

thJ

U(' :- 1 J3-.. Ill - IIi

i. • u.U.!-n rn ~'

r-.• lt..ui.•IC o~turnl frc~ucnq (If •SU rmn lcn~th o l pun• ru·c.l

(il\'t'tt lh.: 1.hm~l\~

ptuc amn '' 7 25 " 10 lo:g/tn' um.J if the Y\tUII!' ._ mpdttlu' h II~ .: lO~ N/ut~ C:1n

yClu u"c n m mo}!Ctoo;tncuon oscrll:tLOr h." ttroduCl' uflm,om..: ,\ olttlum

., :

I' r£ I 1- ;: - , J../1) h,r I'=- I ll \ I J 21 •

f.: ..llJ 111111 = ..UJ > Ill ref• N/m41 • n = 7.2.'\

1-. : 11 ~ "

n :: .,.---'---..

!x.lOxl0 :

Jl) .7~

\\,IVe:.·'

w· 'l.glm'

II~ ,.. 10" :. 0 (J4'l 7 ~ 10' \ 10' \7.!Sxl0'

I..HL

Titt\.' lat!tiUI.'ttcy t!\. ntun: titan Ihe uutllhlc ran~\·. ~u t htl> t ~w.lt:an be u~d 111 m.tg~tO·

.. tri~UmJ u';r;JU:ll•tr lor prl)lll!ttion •" V ·"·"'C"

QUESTIONS \\'hul ... JucCI pactuclt<:{'l(l~ cffccl IU1ti HI\I.'l'o~ ru.!J..ueledfil' dll'll F'J>Intn u... 11Uf10M:.ll11 """'-' (~;>plu.::t.tmn and tnlJlortunc.c ,11 lc.bt unl.! t!:n•h». ~u What t'!lo uhrll~l"lni~.-,·! E.\ plain thl!' ulb£11CU>"lt11.:Uon mcdu.xJ niiHOlludnl! u11r.1~vOJ~ t•neq;y nml hcn~X de.-.crihe tls ;tdv-:mtagc' m·cr the: pac.toc:lt•c.lric.. UlCihnd lb. D•"lingut.<\h hcl'-"t."tn low power npplicmion ru1d hi¥h power ~lJJ1>Iicmmn ofuhrasonics nnd hence given nne cxounple of e.;ach '·' IJI'W'-'i the .uJ\'Uf.l.tt;C~ Urtd tJhad\ <Uil.a)!C:. of J1tC:tOCiet:l.rll.' anll lllol~llCto.o;mclinn

E:\pl~un 'h" prln\"tpt ~ .. t•t the followmg· ( 1J m~~nct•l"l l tc· mn cflcct. (2) pu~J.uclcc tn c effect -1h. D<..~.·nt~ tn bud the ~cicnunc app1ic:illiutb of ullQ-.onu; "-.J' co; 5 \Vh:d :m: du: :~ppl n;.tltOn uf ultm\OI\Il-.. Ot!\Cnh~ thl" nc ulth,: ..tru\.11\t.' h.' .. ltllJ! ·'I'PIIC~IIU;trl tn tkl:ul

.J.L

I I

t,1, WluT •~ m;.!!ncro.:aricrioo cfl'ce~'' Onm drcun dl.•tmm 111 nt.;l~net'"lfti.11HII t"ol tll:.tJCN. lhpl:un 1t:o. tAOd.iug:. l'h '\t;aiC'. the :tppllr..uinn nf uhm-.onic V.ll\'C""l u~inl! th\' I" int.1pll' ~~r (' f F.d111 'uuml.nl! 1,.,

,anti 111 ' (':n IIUihnl C:lft. uiJt~ the n;.nurnl fr~lllltncy

of ult.nhunl(' w:I\'C' lhiO~ li•llmt. m!! J.,ta pl~tle = 5.5 X IU 1 "' Yvung':-. tHV\.Iulu" uf qu~utl = 8 x 10111 N/m rtm·kuc'' ul

tJ Uitrtt.

II" ~<n ..n~r • Z &~ x lOt kg/m

1 Wh:tt .uul PZ'r

c~rtumc..:, :uul huw tlo they hdp in the: ~..~m~o,tmc;tum nl ullftl•'<mt.;.·

trun~;;duc.:('f'.

~.c.u l•\;pl:un f'll'-''(w.•lw•nr effect Oruw rm:u11 dl::t):ram fM rn~hi\.'Unn " •.1\:t'!lo U J..Itl~ (ll~.ltk!l~4.:1t-u.: cHe..:L 1:.\pluu; II.; \\·Hrlrr.tng:

•'f uhr;J.;:c,nk

fhl '\t;ttc the .1pj11tCilf1(111( ur ullr.mnnu: \.\,1\'e-. "''"!! lhc pnn~o.tph.• ttl'" C.a\lhiiiOft WJ Nuntk~mu:w:c tC)-ling. h. I tcul.uc n.tltlloll rn:'.JUCOC)' or lf\)11 ~tll.l UJ O.f)'l Ill h:ll{!-111. n~t• dt.'n~i l) Ol lfllll i.s 7 :!J x Ill' ~g/'111 1 and Young's mndului J J.h x W11 ' j'o;fln· 11 f\n nllrn~,m • .: hc;am oil em w;wclengrh ~~ 'i4!111 h) ., ,Jllp. (\'fUm' tu.tnllhc ...c.1 bed

r .•

.tth.'f 2 ~..:

uc•l)

~hnuy

Jil

If H at JO"C

..-t ullr-J:.vn•~ ~.un '" -.cJ ".Jtl.'l I\ Itt IH ml-<r. o~t H C. '" 29 J;nirrc, cakul.-t~o." the 4h:pth oJ the ,,.•.t h<d "'' \O'C .md

lll.'tfUI!IlC} ui ullc-:.b.umc bc:un V= \1u+ J. l.-.,+ .. 211

Snlutum

1t} ~nl

- ti,;m/lnrc • 1 a

TiiO(lC:-·c

10'C

\ ::: I.SIC)Y' IX('Ih ~~ rh.: <o<a • 1/ • -

t~rcqucnco.::.-. a \' •

hml

<"Chll

O.OJ7t'

umc of

e-m/~<:=

2IT •

l !'iiU'n mlwc;

15 W,t),, 1n

TI' • 15 1093 H'- :- 15t.lN' Ul1

uJJr.L'iOOIC"

pul.sc.

\\htdl

lr.l\·elhn)! wa!h 'clnl.'rty :\.~

x 101

u-.IM:..: an rruiJ ..hxl wh~c: correct 1h1d.nc ..'" mCol ..Uh~tl h) ~·"'tc ml.'tCI " I H mm

2tl ?d: r;T. T: -

T= 2x JK x 10 ~.9x 10' 1Jem:c,

c~ltu

tunc:

b. 1 X

1 :

6 , 1 )( ll) ,.

~"''-"

10~ o;c..:

1llt ultn.l~muc tloa~ det~tor as U)\!d wath ddcchvc :and non·d..::t«ta,·c .:il~d b:11 or 'lm:kne..\;~ 40 c:m" I( puh:e :arriv:d tunes ;m~ 30 11 ~ ;~nd ~0 JH. 10\.':ttc th~~:tam.'l' :tl

\\ tueh tlefec1 bao: Ol~urret.l '/

t I, -:Ja u1 a-,-. fl:: - . -

•

•1

:! ,_ 40

a: - - - - . : .

r, "' 111 a·/ w•- .;nI )( -)II .. a: T' •

Hcrkc, t,kl,·,"'t '"•;\:urrc.·.l

'J(

.al

I 0 ·•

ll\lm

lll,t.inu.• "' I~ 1:111

~:1\ '('l

5 Acoustics In tht: beginning of the 20th <.:cnw ry 1hc

t:c)nt:l!n h.1ll,. et.: I"CCCI\'l'LI very

nctHt~ lic

propc.ntef.

,,f hall~. thc:.tr.:s.

l htl~

or nfi cnn:.idc.ration :lt osll b) the.! un.:lutcch nt buildtng c:n£lni!Cr~. Vel) olll!n bui1dlng,. dt"signcd for ~uch puhh\: putP'-"C:.!oo \\ere butll 111 'm.:h il "-.S~ that they were fo und to bt-. un'iutt'\f:tct•H) fol' 1hc purpose fur ""'"" \\Cr< buill. There \<'<m.:d 1\1 be no planned <lfon cu t·n~ur\' th~ ~~ ... t r~.·pr~uLihlll clf 'J)CCch .uul mu~tc. Ultlnwtcl~ . ""' 1:1r.tm:h ul '4.:1\!U\.:C .tl•"l glH (lropcr allcntton ftlr il:. imprtl\'Cmcnt und rur hc.\1 p..:,fllnll.lllCL'.

''">'

5.1

IJasic Rettuircrnents for an AcouslicaUy Good Hall

ntc hr;ulch ol science wluch dc:•l'i widlthc pl:"tnnin{!: of a blll hJm~t 1'1f tl h;dl \\_Jth a vtc'' tu pro' tdc best uudtble ~\lund to the audience 1& called the flc'OU\IIn uJ bruldmJ.:S nr ml·lutntuml aomwn Prof \V.C. Sotbmc. Har"nrd Um,·cr.-.ll) t I'J II) wa\ the rir ... t t (l ~c•enutit:nlly Lncklc 1hc problem), of S(tll~facwr) lc:tum.:~ nl g(_~){) :tC\lU~lic,·

I 1 he :-.nund heard mu't he sutltctenLiy loud tn every pan ut lht.• h;•ll .md Ill' t.'..:hn..:" ..hPUhl tl\: Jlft!'S(OI 2, rhc t\ll;tl tJUotht} l'l lhC 'p4;t.~h :tnd lllli-,IC nlU~I bt: Ull\:hangcd I t: • Lhc

ol ~c,rrul componcms of n complex 'O(Wnd mu~t be tU!ttntntncd L For the .;;al e or cbril)'. the successive syllable,.~ ~pokcn mu~ro~ b.: cle:.tr ;md dosuncc. oe.. there muse he no con(u$oOn due 10 ovcrlnppin~ of syll:oblc' -& l<c\'erbtrutton !)lvuld be qt•Hc prOpt.":r rcl::tll\"c: tnLcn-.tty

There ,hould be no conccmrnuon of sound m uny pan of 1hc: hJII

(,_ The houndary <hould be <uflicicnoly sound proof co cx<ludc c.\lr:oncuu' OOl~

7. There should be no <Chclon effect. H. There: ~twuld he no ~~~onancc w•thm lhe bu.dding.

5.2

Reverberation and Time of Reverberation

RPl'rrb<•mtitm nu•mts tiU' JU'almrgt·d rrflt•clion nf .fOlWtlfrom u 11/J\, _(lnm--r. mul c·;,.i/m~ of11 mom. h als1' nh.'!lll:-. the.: gntdu:al 4Jytng out of sound. 7/u.r pmlm1~mum OJ' pcnti.flt'llc'c' t>f',Wund m r4 umm thw w rt'jlt•c·tion. t"\'t'll w lit'tl tltt• ,,amul :foUI'J.'t',, hm·r Mopru•J. is culled re\'rt·bcrm;cm. So il is also de lined as the pc'n'l (/t•nc.·c of awbblr .wmul oftt'r th~ snurct> hm•.fiUf1pt!d to emit tmy sounJ. Thu' timt· of

n·l·,•rht-rmian

t'Jf

u mun or h.tl l h de lined n' the tunr wJ.t•n h\ 1/w .wmul Ia fa/(

jmm tlf m•t•rgf! iiiiNI.\11\ to imnub'nbilll\. In 1911. $;thin~ firs t c.klincd the " Mtmtlarrl rt'l't'r/JC'rtlll(lll tlmt" by ~·vrhidcri l t g :ttl the fnchlf' !t'- "flw tiuw lll/..t•nln• llw .wwt11

to full ttl wu··tmllmm/; uj tl~ IIIINM'II\' JIIH 11/fc•r the .wun * '' cHI o.JJ.- S.ahulr: l nuntJ tluu tame of fC\I.:thcrulinn Jt:JlCIIJ , upon the ' llC Of tht: hull. loudnC!'t.'\ of the: 'uunU. und upun tht' tmd nl mu!'>il: or '-UUnd for'' hu:h Lh!! h~ll is tn be U!-.ed

In u hull If lhc rcvcmcrmion

lim~,, 11>11

Iorge. lhcn lhcrc "\IVCrlupping of

~u,·t·c~~~ "L' 'nun<.h '' llkh l.lll'c' ,·onlu'tl1m aml•c,ull' 1n h•'' ''' d:tnl) in tHmnnl! 'tl) "nall Ll1rn 1hr luudnr>~ will he umtlcqualc. 111U!-. the ltnh.! n l rc,ertwr.tltulllllr a hull -.twuiLI ncitlll'r bt.> too larg_c

On I he mhcr hand il Ll1r rcvrrhcrnunn h

nur 100 >mull. 11 """I hole u Jehnn~ ,,,lu,• "h•ch rn:.y b< '"''>f<~<IOI)' lor 1hc z:,pcukcn, 1lnd tbc .md tcnl:c ThL' pcrkl'lltllh' lnr f'\'\\'fb.:nthnn "Cltll(tt Ofllruumt rc'l' t•rbt·rution tim~. 11tl't.:xprc....~wn u l upunwnt n!\'crb\:rmitln IHilt: w.a~ given h)' Sahinc

5.3

DerivaUoo for Optimum Reve rberation Time ( R-Time)

Sabin~

d(rivcd the hll'lllul;_t lor C<tkuhallll!! OJ'IIImum rcvcrbcrfiUOn lime rur II

p.rrc•cular hall. •tlJtS il!l h.a ...ct.l on the ''''lllllf)ttun thut Ih~: .\flund l.!lh!f~Y tn the roont i" Ji~tribut cd uni(onn1) .all a ruuntl In ~lt:ll\'atiuu ,,(thtu (onnula. following s1cp~ me lU be t~onsidcrcd 1. Tn calcul:ue. in tc:m~s nf \!ncrgy d~.•n,n~ £. the rat.: ut whtch the eneri!!Y is incident upon lhc \o.ttlb und othe r 'ut (,,.._c:, .md h(ncc the nt t~ at wluch ll 1~ bcmg nb~orbc:d. 2. To <:~lcuJ~uc th~ f n:1l sh~ady \ :tlut: ''' 1: HI h:rm~ of the r'".JIC of cmbs.1un 01 power 1~ tlf lhe St)llnd cmittin,; 'ource. 1 Tu eu1cnli11C the ,, ,uulanl tc\'C'Ifwr.111nn 1une T '\ttp I. Jf t/\ j, .1 ' 111.111 t..• h.•llh.'lll 1t J' l:tth rc"'\!i\'ed from lhc ~our.c at tl~ '' fi' \.'11 b\ F \\ ht•re

tl\

\\ II II

\ H lhclt th~ l.tiC t)l encrg~

,.,~

tht vclodty o f -.ound. If an tilt' tn~~flith•nt oj t.thsmplion ()( the woll

Mllh'n Rule ( tl ..:ncrg)' ub·mrhcd h)' tiJ = l::r a

tl"/~

lienee, the total ~tbsorptHm of aU thl' o..~trrm.·l'' uf the w.tll where the sound "

f;•lllng w1ll be (5. 11

\\here Lmll =A= IOH~ ~•hsorpuon c"'l otlllhc 'urf:sc(!s on v~hu.::h sound f:sll~. Step 2. tr Pi" the power OUiput, 1.c the nne of cmi.sston of energy from tht: source and V' toull \'OJumc of 1hc room, 1hcn the total cncrg_y tn I hi.! room HI the mMunt wh~.:n e-ncrg.y 1~ t wtll b~ 1:. \ . :)(I.

R;uc ol growlh of energy

d(£1')

d£

= -- = 1!di til

At•tm\tU'\

But a1 nny insL.mt. Rate nf gmwlh of cn"gy .n srace = R.uc of <upply 11f cnor~y by <uurcc- Rate .til Lhl' ... urf••cc...

l'( ~,h\orpt~t.lH h)

\5.11

I~.

fltth.

when ~~c~•dy ~131~ i;o.. rta\:hcd. tJfldt 0. i~ lhc Mc.!:.tdy energy. 1hcn lmnt C(lll· 15.2)

t 111

15..1)

Nt''' cqn. r5.2)

m.~omr.!<-

tl£ <II

dt:_

= /'

t/1

:rf L

I -

+ 11./; =~I'

til (L

=rt\/J \J

Multaplymg. both ~u.lcs hy t.•u' and h) m tcgrntwn w.r.t 1. we ~t:l

[ Fr'" = ~~ ,-"' + w hc i'C K

= <.:on~H.uH

of n11CI);.ntlt<.."U'

G nm th ur Sound EntrJ!..''

De n~il~

in :t I-I all

lltc gL•nernl dtsLnbu11o1 uf M)Uild en~t;.!~

111 11

h;.tll ''

£.· '~~ _ o.lf ·"' +K ( - .~,\ c

whl'rl· P:::: power trrm~mhtc.:d., A = f\Jt.d ab~nrption b) the ha11 c- = vd~>eil)' uf sound 3-lll ml'<'· « = •·til-tI'. I'= wlumc of""" I -=- time, K = CLllh tan t Ul m iCJ:!.I.IIIun A

= I:a:t=summation ol the product o(dtl(erent nrents' :md the.ir respccUL-C absoi'J>IIon coefficient

{11)

In order to undcr;t:md the growth ut sou nd an a hall. whtch ts comrvllcd by

n11 thc:sc fnctors, we h:•ve to know lhc ,.,1luc or con:,ltuu K 1\1,

= 0 /; = 0

t.c. from l::q. (5.4)

K = -II'I<·A

So,

F.= ~PI<·II

1\l

(I -

<' "'t

I = -. F.= ~Pit-A=

t:.

1: = E,., !I - < •• l

(5.5)

I·

/,.

Ac:-.~urd111p

f_ a J:.ll -~ "'J

tn the cqn . (5.5) Fi~. 5. 1 ~h ows the exponcntl ;,l ~n.I\Yih ut cncr~:v re.tl'h(~' the \':tine £nr

\\llh lime t. \\'lw:h uhim:.td)

\Vhen ... uund tr11f1Mntt tetiJs l rnm the ~pcn kcr, 11 gctt; h ·Oct!lcd . uhsoJh\.'t.l und tran,mith~i.J

In lht: :-.UtTOl.mdtng~. II the nbsorption a.nd ttansmh. ... iun b

Jc~'·

thcu

IIHhl of lhl! ~\,UIH I ~lh!r~ \\ 1lllx rcncltcd back. Titcnlhi! lottlJ CllCf~Y in the hull

\\111 uh:-rcH-.c- lluc.ttly muJ .-uum the ulummc energy in u vcr~· ~hl•n umc But dur lh tht• )11'~,-.:"nt·~ uf .th,ufhing nuuerin1 in the hall ''-Jffiticnl ah .. nrptiun tu.k~:.

plnct: untl uhtnta'C" reJche, to the maximum ''uluc 1~,., ul

O~cuy

vr Sound Energy

If 1h1.~ 'tl\lh.-1." ' ' t.:ut ._,tf "h··n I ::. I .... lhcn P = 0 ~111 '\OUfh.l ~llt'll!~ will l :lh' pf1h.C

=...,

unt.t no'' the dec'' n!

P .;. U .n t -;:;. !) .tnd 1:. • £,., Su trum EI.J c~AJ. ~c ~;:c /:.'," = K I.C.

Hcrc

1 / ;:;C,.t:cu E<tu'H'I"' (.).b) shows 1hu1 docay of sound energy densll)' wnh umc IIIIU lh¢ :-.ource tS cut ufl . The cxponenti:•l t.lec.."Uy of ~ound energy b :.hown an Fit!. 5.2. Hcrt.! ~incc no 1runsmtssion powt!r ri.c.. I'= 0). :o.u the sound will cxponl~rniully decay with time rrom £"' 10 0

5.4

Snhine's FomJUia for O ptimum Reverberation Time T (R-Timc)

R c:vc.rhcrollh111111HC Thv d dinitiHH, .JI!~ordJn(! 10 Sahmc. ~~ I he hill\' l .t" Cll

r,u

llh·

c:nt:rg) dc:n"H) hJ falltu uht" millitlnlh tlf it:-. \'3luc .t (l cr Ihe 'uun:e i .. ju'l ~u1 ufl After dll' o.,uund

~tiUrcl' I '

cut nfl the decay of !I.OUnd encrg}' d.cn,uy (/·-) With

lime (I) iv

= 1:.'" e

''her~: £ ... = Mcm.lv t:nCr,l:!.' where :o.uurcc i:,. cut off (Fig. 5.2)

£=£,. ,. ...

----•1 FiJ!. :0:.2 Dtcay of sound "'ilh tilnr So when

1;;

T..;; reverberation umc. then uccnr<.lint:

hl S;,hlnl! 'd~.·fuut10n.

E =• "'=ruT = -1-->aT:<\Iog,.lll E..• 10" -

r= 6 x

2.3926 = ~ a

6 x 2.302(> x !_ = Q}~ II' MO A Em

I T =0.16 1V/1: I Cl.f

l.t.'

J'lln "

St~bmr \ t'tftWtwu

~l·ncr.d

in g~md

{or optimum rt'H'rbcrativn wu ..· Thl"' ~liU.sti("'fl ls in \o.ith experimental valu.: otHllinctl by Subint:.

a~rcc:rn.:nt

l.hnilutions or Sabine's Formulu l Snhulc's formu la. a!\ ,!educed above. b 1fl (:\Ct n "ipccaal case o f mnrc l[Cncral fon nul:, pul (orwatd hy C F. l!yring. S:thinc·~ rormub gives comr:-adktory rc~ulh 1n the cn.c:c o l' rs dead room. when a I, i.e.. an c~e nf c •>mplcle nb~orption rcvcrbcrttlion time 7' <hOilld be {l, but 3ccording to Sabine'< ronnuln 1 0.1(> 1 VI.< 2. Thu• r,)mluln. docs no1 give con-eel rc!'ult for nhsorplion ,,;ocfrictcnt mort:

lh:m U.2

.3. lt is ns~umcd in I~C derivation or Sttbinc's l'ommla thai the n~ l:r> umfonn energy dcn!'ity tlOd no too;.~ o( energy in air. hut that i~ nL,fl no1 pr:Ktical

5.5 Absorption Coefficient Codfint•nt nJ alnc,rpflw• of(llllrllrrinl i:r tlc-finrd fl.'i thr rmm of th~ .wwul t'ttcrgy ol1:wrh.tt/ h.\' thf J'ttrfua w that of th~ total lndtlent .rmuul (~llt'l7:\ nu lht' \urfat-·r, >.e Sound energy nbsorhed by ~urfncc: Ab,.orption coefficient (a) -- =-..,,------,--=~'-",.,---<--,---.,.-Tt\1:.1 c.t\lll'ltf ,.n,...rrov ;..,.,..; ,,,. ,~, ,..., ,..,.............._.

In t•rda hi complrc 1hc rl!lu1ivc efficiency of t.lin·cn:m ab'imbmg material' It c""cnu.t1 rn 111''1 <.tlccl o;;nml! ~aand.Jrd of Jbo;;orption. m tenn" nl \dm:h nil su0..-1~mc-c' "·m he 3!iM!'i,~d. Sahme selccu:d a unH :Jrt.!a ol Ofh!n '''IUdn\\, "' "'·IIH.I;ud. hcc,:au-.c .tlllht.: 'uunJ l.tlhlll:! Ull lhl! 01)\:11 \\ iuduw P•'~'~'~' uul .md nunc j, rtfh..·ciC\1, I knc.:\:. or~o·u \\indo\\ , .. om il.h.·.ti/J)C'tfcc;.·l ub..orhc:r uf '\IUUtl lhu' lht uh.wrptimr NWffit'H'm of" muff'I ml '' dt•/i,wil iH the' rc•('lfUYWul of tl\ urn: h'hlt h uh.wriM lltt! Mllllt' MtWtd t'ltt'lg\', tl\ ttli\mhr•d h) 1111 mlil tltt>d u{mt fiJit'll \I'IU(hm Suppt"c: l ..q m'tl~:crt.un t.:ll"f'CI .,h.,.un, the .,.un..: nmuun1ur rncr~). n" ah,Hrlll..'t1 j,

hy I '<)Ill nf tiJWil II i1\lll\1 11Jrnlhc wrrfi< knl llf Olh\Ofplinn l>f Cill'jl<:l j, 1/4 :: tl25 The :.h"''fJ''IHin Ct~·fl1~o.•u:m 1!- ntc~t,un..·cJ m open wuuJo''' unit (()_ \\ lJ • Pr S:thmc~.

5.6

Measurement of Absorption Coeffi cient

folluwin~

ar,• the rwn nlt'lhncl.,. uf rm·;~.. unng th.;. uho;;orrtinn l't>Ciiil'h.'IH

f I) SiugJt.. Stmr(t ;\.1tttlwd: nt.: .Jl'l\t!!l'Hinnc.:ucfiicicm ~nllx: UlC~i ..Urc:~.-1 illll.'(lllll. of n:vcrhcraunn wn~ 1R-lilill..") Fif -.t, the R-llmt.: ij;, nlca,urt:<l wh(·n Ihe oth-.nrhmg n\tllC'riaJ t~ 0\11 In the hlUI11. 1.~1 lh \oiiUI! he T,.

If/ I= A/1) It> II'= L{ISIO 161 I'

So.

"here a :: m cr'.s~l! .11't-.urpunn ~u~.~ftit.t~m

tlt R-chnmbt.!r {rcvcrhct.thon dhunh,•t)

LJ-= 111!-!dC' Mlrllh.:t JtCJ \ · - 'nltn1w () ..:humtx·r

Nm\ then: m.tv he h~l l difl'cn:nt Wtl \'' or mca.\uring Lhc Ub<iorptinn coclhdc:nt an ~tb,ori.'.:r j, rrc,-:nt h1,iUL· the n ..Hlffi. Thc~c ~Lrc ghcn a~ foiJo\''

"h~n

Ia • \h.fc,rher \u(pn,d.>d Jmidt tht> H.twm: '\Jnw ('('IO~Id\•r .m a('o.-.nrhin;::

like '101~1.' 'l"rl;.'~ll. \\ hH IJ I' ...u~pt"thlnllll'ld~ lh~ l'll1"liU, Untl ~-(lfll~·

nMt~, 1..

f-:_ 1' 111\'o-I'UI\

n~mn, Tll.:u

=- ;th\1)1 plion t:neffiCI\!111 of Ihe m;uerial or . . rea S:,. \\ h!Ch 1\ 'U'IJ4:0dctl

wheh::

111~1de

Ill\' rnmn

S1ncc 1he nhs\)rhln~ m;uc.:nal ~~ :,.u ...pcndcd mside the room. so absorp11on '" 111 uccur trom hnlh thl· s dL''· Sn tnful ah,.orplton due lo lhulnmtcnul t ) '2112-..,

:-.l''"'

~Uh:O.U1tt:tlllg lTI(.'"ifH.'Il1lt

So.

(5.H)

hum(~ f.J). Wl' ~el

" 1

0.161 V ( I 1S:: T: -

I )

c' IIll

by knOWIIl)! all other ~ulml tlu.:.. the ub:-.Urplit.ln coerticicnl tl~ of ;th~orhin~ 111:\lcrial cau he m<:;l\urcd. '' h1ch '' ,U.,J:k:mkd in~ ide 1he n.10m

i\cnti\IU'\

9_,

(h) Absorber Sprc(ll/tm lite Flflor tir Spread ou tht n¥~11: Ntm' it the ;;tbsorbing rn:Hl'tial b. -.;prcild nn lhc o f R·cha mher like carpet 0 1' if il j, fixed on lhl' \\'~111 m.e wim.low gkt\' Ul' c:un.ain elm h. I he n rnr I hal 'YPI.! ~~r Ul;:th:rial. ;,b~m-pl ion cn(!ftiCI..-nt wi II he dciCIII'IIIh!d Hl lht: follmvi ng way. Ir R·111UC = ., ' v.. ith that m;UL'ri;al, WhOSC :lr~.t j-. Sl and 3hSOtption COCrficicnt U) lhcn

n.w'll'

1 _ Las+ "-'S" T, -

aS,

t5 II 1

!J. I 61V

Her~. aS) '' ..;ublrach:d bl·t·;tusc now su1 fa<.:c areaS.\ of Ihe rtonr or w:111 dc)C!'I no! cnmribul..: tu ~lbM.Ifj)11UI1 whu:h '' mc.:lud~~d in L(l.f, the lot;d :.tbsorpuon by the chamher. :and he-re 1l is ti tS\ not twtce oflh:tl. smcc absorption 1ak.,;!'1 pl •.u;e Irom

one s1de o nly.

So by <ubLracung F.q. t5.HI from (5. 11), we get 111

= U.lf1IV

(j_r, _j_) +u r,

by knowlnp OIIK~r qu:tiiiHiC!'. :~hsorplion cocfficicn1u, of <::tl"))l.!l <n \\ nuhm t;l~"' cnn b~ fnund uut.

(2) Double Sm~r<·t- 1\fethMI: ., has tn\!thod requlfcs two sound so ur~c~. of r\)wcr:-. 1-' .und P' AChMI fW'"t:rs tl~l·ll onl oeci!S:S~rily to known so long "" LhL~ir rutio ,, kUliWil.

The Slc:nl)

!1-fltiiHI

cut::• ttY 'h;u:,iay.

F.~ : -IP Sf1 for

I W~ ~oun:~' ~•:aU)'

. . ou111J cnc!]:y Ocn~uy" .uu.l

Lei dunn~ thl.! 11011.! ol dcl..l). 1h1.~)

rca~.:h

E,,, - - I

"''' '

n v:.lluc of ban.:: ul:mdhtblllly l-.11 1n aunt:'

T and T'. wh1ch '"' ~p·.·cn h) . F.n

P' _ .,utr p - <

i.e .. ,S0

-II' = -c•

<'A X 1'1' 7fV

1 ''

w here

a =4 \'

'T'\ • IllJ;,. p P'

Sn :wcl'll!!C ubsorpuon cociTic1cnt oi the hull i~

" =r

4 V log (I'' II' )

··sci- T'J

where S os the tOI<d ontcrnal surface area of the hall.

IS. I~\

Eu~mt'''' in.~.t P/1.\'Mc",\

ll) ~nuwin~ all <he <luanutic' o n the R.II.S. uf&1 (5 I J) a•cr.tgc .tb;orpuo~ \:c'H.:nicic nl A c:nn he find ~)Ul.

Fuct ors A ffecti nJ~ Arch itectural Acoustics a nd their Remedy

5.7

B)' om ucuu~llcotll) :;n•~ hJit we mcnn u h:dl 111 \\.hich l.'\'CI) 'i)'IIHhlc l..lf nHl"iiC31 nu1c rc~tc. he' :m .tudiblc I!.! vel nf h;luJnc..;~. :11 C\Cf) puinl of th~ lull, :md th~n qu11.. ld} du.•.., .tV.1;.tY to m.tlc nlOm lor chc nc\l '} ll.thh.· l•r gwup ot 11PU:' I "h.'par1ur..fwm thl' m:tk~~ lht huli det'CCII\IC aC,)U~Itcall\. rhc fo lhl\\ IU~ l.iCiur... ~tftCd archiiCllUr.tl .tCOU'>IIC)> I flc•.,.rbcraliou; In a hall ''hen rc'~rbcn.tiHIIl '' lar~c.th~.:.rc j, ,,,~rldpping uf 't.lt'cc'''"c 'ount.l'. which r(•,ult:-. in lo's of cltmly m hcunng. 011 thl· •'Lha hand if 1h~· ··~\!..-rlx'r;nion i' very small. the JouLine" j, i•1ackttu.11c Thu'. lht• time w r\!'\'<'rh\!r.tlilUl for u hulll'!huuld neither be tc)O l.tr~l! th~t h)t~ ~m.tll \ fl•lmul .. fur 't.utd.trU tunc for rc:vtrberation W'-1' given h)' S;Jhlne whil h j,

/' =fl.H> I I'/II =Cl I hI \ '/~"' \\here A. l" the 101:11 ub.'it'l'l)lion of the h.a11. \ the' oluml~ ~~~ the li\\!(.1~~ Jh\.ClfJ~Imn t.:od1i~.. l cl'll ~mJ .\ the tntcrnul surface area of the hall Expcmncnlldl) 11 1'i ob)\Cf"\•cd tJuu rcvcrbcr:Hiun lime dcpcntJ~ upon the ,j,e uf IJ1c ball. luudOC!<o~ uC 'ound. and l.10d of mu,ic fl'f "Juch hall 1'- U,f!c( J•or U Jh.'ttucnc.v pf 512 c/s.thc bc~t fi!\'Crhcrruion 1111h· s:-. umtmlft.•d 1w lht: h1lh"l\\ 111g iliLitlfS

•~a) Prundn1g w1ndow~ arld j

h.•J

hll tel I fJ

t,g.J

vcnti1:•10r!- lh,tl com l~ u~nct.l 1hc 'nluc: of re,•t.~rbemuon tunc opumum 0Ct.:Hral inp th~ W~IJI, with pit.'lUfC' .t.nd map'l 'mg hca\) c:urt:lins with rnldl,!. Wull~ .ul! lined wath nbwrbent nuh::ri.tl:ro. ...u~h ,,, r.::lt. Hu,·ing full c~pud ty of audience. Ct.trpt.'tlll£. the noor!\. Pnwu..hng acou~lil'~ llk~.

~'r (h"h~ll t(a ntotkc

fi~r

bn.trJ. ct~.

::!. \rlcqnof<' IAJmf11ess.· Rc\'crbcttHion cinn.~c:mlx•IJimk '-tnalh:r hy m.in!-luh"'4.lft111tt;. IIH.Il\!rt.,IS, hut thc r~ IS ll Ch:t.n<:c thtH the intcn:otty nf -..ound I:roo WC~k \'II Cd und muy ~o OCiuw the lc,·cl of mtcllig1b1h ly t1f hcanng Suffictcnl lnudncso;; m ,.,.c.ry portmn o l lh~: hall 11r1 ;10 1mponun1 l';tctor lor .''itltl.\f.anor~ hc.mnll: . l.uudnc!-1'1 nmy t-"1~ uu.:rca.,.ctl hy f•1flo" iug ways: (u) Tu gcc gc,.nd I01•dne....,, ll"•<~Xt n)um f\:n~..-cunn PI -.nund llnm 1hc qage r•rea '' de:t1rah!e !-iO th:u th er~ lb no los~ of ~ound cnerg) lnm1 hpcn~cr,o,. llm• c.-tn he done by uMn~ large ~ou ndt ng boar..t~ hduud lht: i'pcotkc~ l~u..:lllt! the ;uulicuce L;ugc puli"hcll wooden rcflccwlg surl';JC:c" innncUiatcl) :1bo,·t: 1hc :o;pc~lkcr~ tlre al~O helpful U~e ur goOI.i yuaJily Joud~pca"Crs J\ ;ll su C'$111tal. (h) Low ccihngs ar~ also helpfu l for rcnccuon of sound from ~IU{:c 1oword~ the a uthcncc.

At·ou.'flics

1. Effect Due to Slwpeand Size oftlre//a/1: Refection> from the plunc >urfac"'' nrc quhe helpful in inc-rea.c;;:ing the loudnc~s of 111.: !->Oum.l .&nt.J f«>r diMri buling i1

uniformly. whereas the curved surft1t'C!- c:m be Lwuhlcsonu:.

Rcncclitll l~

fm111

...:urvcd :-urfuc:"'s can h~ hamtful &mi.;$.~ dcMgnerl properly. Curved surface-S ~)11 \1..':\Jis, ceilings. or nooJ prt1d11C~ COOCt.::nlr;Hion of '\Cmnd 1010 particular region, while in ~omc otlu.:r pam. nv t'Ound tt!.uciii!S a1 :til (r igs. !i...'l:l, h) If I he centre of curvature of the ceil in!_! lS made IWICC the height oi the r<)Om. lin; had foc using as removed ~Fig. 5J.;•. Large "il l~ of u hall ~ult~ m 1111: ancrc.a.sc in rcvcrbcmticn time. Un~nc:ct:,~ary larg4: ' at.: nf hull ~huuld thctt.:fon: he :Jvoidecl

-L Absent·e of Behoes: .:\n echo i.:; he.Lrd. when J m:ct nnd renee ted sound Wtt\'~:o. C:\lnling frvm tlu.• ~anlt' ::;ourcc rc:tl'h to 1he liMcner, with a time inten,ul "'

I I I

_ ,I' \

1 \

I I

1 1

I I

I I I

(tl

Fl~. 5.3 Focussine of Sound du..- to s haoe nf I he hall

117 sec. If lhc reflected ~ound L'i arrivtng curlier lhan Llmt. 11 help~ m ansmg Lite loudnCS!Io. whtlc Lhnsc irrt \110£ larcr produce echoes . a nd CUU'\C conrusion These ,;hould he :tvOJdt>d by ~uuable arr.mgcrnen1o f :.tb~orbtn~ nuuennl for lon,g diSinnt W~\ll' lllltl h1gh CCihll};

i Echcrlnu Effecr: A set or milings or suurc:-a~e or any re,gul:;u ">pacing of rcll\!(lcd produce :1 mu~ical n01c due to regular ~ tt CCcs:-ton nf echoes of the ,mgmul ~ound to hMcntr tFi£. 5.4 ). 11ltS makes origm:ll ~oun d w dppc~~r .;,>nltt~cd ' urfac.·c~ lll~ty

nr un1ntdh~1bl~ So the<e I}P<! of mrfaccs shvuld be nVt>IJcJ t•l pr<>perl} coverrJ \\ ith he a\)' t::ttpcl-..

Fi)!.. S.J

Echdon l'fl't.'t"l

t•. J::~tri.mf'UIU' Nqisr: F~tr:\ noiS\.' frnm out...iUc or 11\'tdc. o11u:r Ihan mu,,c and 'Pet•ch. '' c:llh::d t.:~l ran~~•u~ U()isc. (1\J ..\rr·how,. ""'" · 1\o•~c..~ which arc c.:.onung I rom Huhulc lhmugh open \\ 1miuw!.. de Jun.•• \ entiiJtor..:.. are knc)Wil 3~ mr-home OCII\l'.' .tllllc.•otn he conln•llt!tl toy: fa) 11'111~ duuh1c •n lr..:hh: wtm.low' Ju~m~ "11h '~p;H.th: 1r01n11;-.; :111d h:l\ lUi! 111\Uf;lh.·~l OMICrl;lh ht•f\\C:CO th~m .

fht

U'-ln!--

h, .H ~ ~l,t~'-.:' in

1\'t ntnkint! pcrh.•t.l

t.lt"Klr' .

WHit.IU\\''· .tnd \\'llhb •r th~ ilnnr, ,,n,l ,qncht\h.

;lrnmg-.:mcnt nf ' lnnin~

1/Jt .'w m"ftfh' h••1 nf· 1u1t:H': The nnt~cs w hich .u-c ~'"'~"' cycJ lhmu!!h th~ 'tructur,• ul tht"'" htuldinc: ;m.~ c.:ill'cd -.tructurc-bomc nol"iC,. l'hl')' fi tn h.: ~tmltnll ..:(l h) (n) m1mducing di-.cnntinuity in the. puth fll the ~''und . h~c n,u..,c lwm w;•tcr pip~: c:m b(' comrnll~\1 be u.sing rubbe-r at JUm.'IHln,. !h) "'1111! douhlc \\ltlls. \\lth an ;.ur space hctwecn thrm In wit• nm.l't•. fn~•dc OfnS("' 10 a hlg office frorn IYflC\\rtle!"'. m::u:htnt:r}. elC .• c:1u'c~ tliMUI'O~IOC~ 1h~11 can he controlled b)' wkin~ pmpcr care

rc•

7. R<Jsouauce lV1'tJtin a IJuilding: Strocwrnl resonnncc c~m-...: \tnt•vcn n.;~oop(m..,c til fret]U•mcy ;tod hence c:tn lead ro unplca')nnt ciTcct. Re.,nnunl fr~qucnq of i.l big hall L~ nonna11y well helm\ lhcaudiblc runge: hccau.sc 111, ptt;l[l'II"I1Utl.ll hl 1/ ~ vol. J<IO\\'C\Cr. somct t mc~ rcsonanct! can be usclul . Some hnll~ \\hlrh arc fumou' hn Ihen lh:OUl'>lll' propcrht!'> have.~ a Jorge nrc:' ol re:.nnam fn~lh!fl.d m the lnnn ol wuoO pt.\nclhng m order to tmprovc the loudness of the hall

Ac..,mtt'-'.f

CJ1

P ROBLEMS l..cl lilt rc\Crher.llion umc be l.:'i ~for ;m CffiJll}' haii.IOd I \.4."&: \\hen ol\.UOlllll do1h t1! 20 \LJ.m 1!. ~u1-pcmiL~ at tht' centre uf tht> hall. J[ the lfuneu, tun.\. ol the !mil : ttl.! I0 rn x 8 m :x 6 m. t:ll1cutue the ~>e(fident of ;tb.,orpl•on <,f 1hc cun.un clo1h. Sullltffm

hn \!111(>1) h:tll R·tJmc = 1 1 =- IS sc.: With ,.;unum ~;.·imh "-·lime = T1 ::: I o,ec ..\rcrt uf .tll\t)rbcr: 10 sq.m

Voh.noc ()( thr hall == 10 X)(

AtKorpuon cocff~~;u::nt

~''

= .:SK() c.:u m

or the curtum doth

cr .: () 6.l Sabine.\

Fur :m

t'.U\f11) Ob.:lt'lllbly

h;:tll

or ~1/.C.

20 )( 1.5

10 cu m the R time ,.. _l 5

r ••kul.lte the ol'rc:r.t~C ahwrpehm coc-fficl<:nt nf the h111l 'hvuttJ tx: t..u\\!rd b)' c-urtJin:. i'O :&~'-Orptiun

~co redu~c IJI\'

Wlt.11 .trr;! Hf thr w.tll R·hnh: to 2 ~ ..c ... G t,·cn th..:

(;()efficient of cunnin cloth is 0.5. T1 ~0. 1 61\f/A

I ll

uu • 0.1611.~x.l!KXI "

I'X

.S =-Total insadc surfne-e orca • 2f2U ~ e:

x 15 •

I ~R/1100

l f (}

:<.IU

'* :!:U "

I 'HIJ ..~

1Ci6 ,, w u

Cbl B~ u~om~ cun.1in cl!Jth of surface arc;~. .51 whv-.c .1IN1rptiun ~o:ud lu:icm '" = n :il ~'n the \\:1ll. revcrl)Cr:tth)n Lnnc bccmntii. I:_ whn.•_h '" cqu.t111'

rmm

~ ..

c ll

all~

(2) we gel

u..,

I.e.

Q,IM_\1( I

I )

-7r

= ~Ji

•tl

a - a~ 0.1611' ( _!__ _ _!__)

•

0.16 1V ~ (u"' -u)

Om=

I )

r;-- T,

0.$. d = ~ll = 0.106.

·r, =2.5. r, =3.5.

11..,

V: 3000 I:U Ill

s,;

"'where S

14().10 15 "'1-"'

1 is the '-urfucc ur('A ul' thl.' curt.un cl11th loflreul1 un thl.' \I. :tit due In whh.h R·IUnc i~ reductl.llrom 3.5 to 2 .5 :-ec So thi.!' llf~O of the "·'ll CO\Cr(..'(l by cuJt:ltn

cloth'"'

1 40.101~

!-4-

111

;\ C:lh;ultllc the h:vcrO~oU~IIIOll 1111h." f~u . (0 cutpl)" hull tii) " 'llh 60 JJen.on) (iii) whh rull t::tp.n:-ity nl .uu,hen'c ln\tde lht< h>lll lmm the (n11n"'tn& d:ua·

· (Volum~: ofth~: b.tll = 1~50 cu

1111

Surfact

,\fc.a

I. PltaSICh:\1 Wdl 2 Wo\X.Jen flour Plill'ih:rcd CC'thn~ -l WcxxJen ()Q(lr 5 Sei.tt O •s.hi<•nct.J

t~tml

Absorpltvn cocflita cnt tl

112

0.03

IJU

0.~

1711

U.iJ.l

.::n

II.~

1.00/o:c{tl

lOll No.;

.1 70/p.:rson

Pcr~n.'\

Sulwum

Vol. of 1~ u all ::=- t.aso cu.m AbMlrpuun Llu ~ lu plttMerccrcd wotll c 112 x 1~ ~ 1\U X tlll(o ; 7 H Ah~''flllnln due ro ''oodcn ""''r Ah:\tlrphun t.luc In pJa.,rd &:r l lm~ - 170•011.1 ;hR Ahsoq11ion dm•tu WOOlkU Oum ; 2Ux0()(J;J2 Ab!\Mpliun due h• (;U,hiuncd -.:h.tif' • ICMI x UXI s ltMI

cun:'

TtliUI .lb'tlrphtW in :t emrl\ h.tll

Om! I· For emrt\ h.tll Jj•'V (

"'"

II11

f _ !L!J!.!.!._ _ () J()1 X J45fl I !.u lltfltt

, _

-1 «J:W't!t:

C'1u,. II: H;,U "llh 00 otudlcnn: m'>ule

Rev ume . T.

Ir, CiiJ<'

. 0. 16 1\' ~ O.ll•l x 1·150 L<<+60x47 11'11~• 2M2

o '82 "'" I

Ill• I Iiiii wuh ruu cr.p:.lo'h)'

Re\ lime

I _

U 1611' 0.161 x 1450 100 X 4.7 - 119 16 o .170

' - I:a.o+

r, ; 0.497 .,.,c 1

Actm.wr.~

CJl)

QUESTIONS 1. (31 J;numcwte Ill~ rrquu·cmenl or reverbemuon ch,•mllcr Ho" will r(lu l.!'pcnmcntQ I) dch!rmJne 1hc ..:peff ol '-Quod .,h..orpLiun (11 'omc ..h"'"whang m:ut:.n;•l h~c "int.lt'" gl.,,~ Detluc:c the formu la u~~.r~ (b) Denne the term fC\ '! :thcrnlion moe. Descnbe any one olth~ mcthuds (or the deu:rmtnauro 01 the rc\'erberntiun ttmr? :!. (;1l Wnte Jo"n Sabine'!\ fl1nnula E'<plain the terms iovohcd in it and dc'iCril).;

lhe unil~ or ear;h n( them St:ti.C the lnnimh on~ or the (unnulu I '\ (,,) E.'pl<t.in ho" h:\'c.tlX'ttuiun uf hall h uffected by (ilu' \ll.c (ul nauuc ut '"

".LII "'Urfatc:<t (iii} <llllhence Chl Rc.,.erbcl;.tll\ n hrnc ,, fuund to he 3 sec for 3Jl empt)' rcverbcmtJon ~;h;unber

;uld "" ~coustic sh«t of 15 sq_m IS ~u~pended ntthe centre ofthf' n:vcrber.uiQn

4. C.t.

(b)

) _ {o) tb)

hall Call"ulliu• the Cll('ff, \l( smmd ahsorptiun uf acuushc ~hci.'t tl tht! \'Oiumc (lj the chrun~T 600 cum,. Define th«: IC-rm ('udf a( 5~mnd o&b,orpUon ,md hcnc;e .Jc.,cnhc any une ••I the mi!thuth, m tk-z:tiltu llct.cuuinc tlu.~ coefT. of sound :lbS1>1pHOJl rl,Jmula u.M!d for it'! hxpl.un lhc:': l~ml!> (I) Ktllecuon, (It ' RevcrbcrJlion. and (u1, Echo o( \OumJ energy nnl.l 1hcn 'how tl.mphicnlly only the n11turc of ~rowt h tmd dcc;a~ nl <oound encllCJ· m a hull due 10 tevethet3ttl1n. l::.1pl:un h) Abwrpllcm cocff, (li) Echelnn dTec:t, (iii) J~trancou' nut~"· A dos..ruom h;lt.liu nen~ion 20 X 15 x S cu.m. The Rev. tun-:~ ~ 3.S ~~. C;:.Jculah: tl): wtotl ab:.orpuon of ns surfact :md the ~wtrnge ~~~~nqnum

coeJr '' 6. Exphun In ckt.-lllhc ~<lU\ Ii C denuand'¢ of:. h~ll'' 1. (11) SUitt: nnd C).pJnan Snhme·:- formu la fo t reverberation timl''1 (b) Stule t.hc .u:wstic requa rcment~> of a gOOIJ uuditonurn l!xpl:un how t;tn tht.'~ n:quurmc::nu ht- acht:.l\'ed1

8 E),pl!)jn the ,,·nn C'"tlCfficicm nr -..nund ilh:oorption and rc\c.rbcr.tllon 9

KcverhcrutnlO IIIII<." h•r ol ~:ubti,'OII c;hamhcr HI wide j.., ~.t)X '<~ Cal\ ltl th• ,, U\'Crtl~e oll,nqrtwn t:ncff. 1£ one t,f the wttllb> i!t 1:0\'C-fcd WJtb O.COU!t1u. hk~ the rt\crbcralu')n tun..: Wlllt\c: .!.U -.cc:. CGkulat~ the sound :.bsorpuon C('eff of ~c~·"•"u~o.· tH~!>.

10. 1\ <'lnCOl:.a hJII has. a vulmnc ~11'7500 m 1 II is requncd tu h.a\~ tcH~rbemtimltimt:

or 1.5 >4:4' Whllt wnuhJ be the l~l~l aj,M>rpdon or the h:tll? Wh<~l \\Ill N 11'14: .:rr.......

,r )'O\t inc~11"'e t~.e total ub,orptiun uf the haU'.t

6 Semiconductors 6.1 Band-Theory and Formation of Energy Gap in Different Materials 2 X-my and o1her suuJie.' sho\\. 1ha1 mo.. t mt:t.al~ nnd !<.cmil.onductors arc cryMalline '"structure. A crystal consist ol space arrays <>f uwms or molecules or ions It IS buth UJ'I by n;~u)ur rC:jXhhOII n l :,om.: rundam~rltal-.ti'Ut.:lUfill Hrlllill lhr-cct.hruCfiSIUII Nuu· f'l£•cfromc e1wrgy lt!t't•l.\ w/udr ar~ wdll..mnru }or smxlc Jn·•· atom,'i, wlll no lrmger apphcflblt- m tht. samr war ltJ t1 f'ITSifll ln l·rystal ~tru clUr~ Ihe: dwngc an cncrJ,J.y levels vfthc 1nncrc lcctrvns w11 1he ~•null. ' I nee thc•r~IO!,l~d shell clcclruns (are nOI .~ffccu:d very much by the prt:scncc of nct~hhounng atoms. But tltt' lrn~IJ of owrr ~·aI~nee drccroJJ.'i tift' J:,.ttmh· affi~rtrtl nm·~ tht.•s~ llfr' 1ht! dectr(ms whirIt ore punidfWiillg ln clwm;cal bond.t The new energy lc\'cll\ of I he outer clcclron.s <an he dcternnned by me-•nsof quomum mechanics. oJid 111~ found thattll~<:ollplifrg ll('hn•c·u thr outrr shc·/1 t•ult'nf(! electmn5 uj tlij}C'rrut tJinmt '"a crv.,·wl wlucll arr luumk uluw$1 wmrr em Yg)~ _form tl hmrd td • fnutl rpacrd t"u~rgy ttlllt'.t , mstrad of1/w wftll'l)' .otep(lrutrtl tm:rg'' lt!rt'f,, oj tllf" i.w fntnl tii(Jm,, "' shown in Fig. 6.1 • l luul'

c t ..,.._.._.

l.-.l.

l · Do~oo: .;upw:d

~-.

"1.11(' pn alnm l~thll!'d f~ t':afhrm :Ut>m

iJ.~A-

I I I

Ji------~~,-------------~ • oooo2p

K-

_!.-----7-~'--------------t' •II : !

•

---!--+---+-----------+-----------------~

;?..

•n ~ I h

111L---------------L--L~t~.~~orn~oo:..~,u~<~J~,~:,:,.:K~<~~====-----------: l'i~.

b. 1 •·ormation of \'alen t'e band an d conduction ba nd. Region A-Melt•l. R-SemicOI~duc::·tor, C-ltt.~uiMur

SemicomluciOr.f

I 01

The width of the energy band depend.< upon the coupling between the outer e lccm..m~ or tl1e atoms, I.e upon the dl\tnncc: belween atoms in crystal. If lhe 1ntemtomic dis1ancc dcc,:rcusc, lhe cvupling wall mercnse and b:md width will ulso tnerease (Fig. 6.11. lt i> a thcorettoill eur\'c, becau~e it is not po~sihle to vary conunuou~ ly the mtcratoml( dhlnncc m n cryslal. as il is ~h(1wn in rig. 6. 1. r(lnnation of Lite bancb io different matt:::rial:.. cun be explained more clc:1rly in the f<•llowing way. lo free cMbun llOm fl 6 _. li, 2~ 2 . 2p1) 101\C"nuost ~hell Is i~ complete ly lill<d up. In 11 = 2 shell . out ofSclectronk states 4 are tilled up and 4 ttrt; vnc:ml (\s inlcrntomi..: Ji ...111nce tlccrt~ lhe...c two O\ll~r di~~r~h: syb ~h~ ll~ (2.<, 2p) of 11 = 2. get brundenrd out and ultinmtely overlup with cnch othc'r (region A. Ftg. 6.1). 1n cuseof>ilicoo (Sil(Z= I~ ~ 1>'. :z.'.2p0.3>2• 3p1)u. interatomic tlhl:JJ'Ite decreases n = I nnd, 2 ...hel l will tx· unarrccrcd as Lhey compJetcly filletl

=3 shell between 3s and 3p. ln 11 = 3 s he ll , out of 8 electron~<' strttes 4 tilled up and 4 voc:\nl. Similarly for germanium tGc)(Z = 32 ~ Is!. ~s!. 2p0• 3>.1. 3p6, 3dtn. 4>.l, 4p1l up btn overlc.pping ukrs pi.ICl' m nutennosiiJ

= I. 11 = 2." = 3 !~.hells will be una1Tcc1cd bul the ovt'rlnpping will occur in 11

= 4 shell between 4s :md 4p. Now in" = 4 shell. out of 8 electronic s tates 4 filled up nnct 4 vacam~ So ohvnys ovcrl ~ppmg tnkes plncc in rhe ornemlOSl sub-shells where as mner shell!<: arc un:tffccted in crystalline moueri:t1S when mter:nomic distance is very s mall. Now 1f the inter :uomk dJ~tancc rs 1urthcr decreased. a split occu~ !xlw~X!n 1be upper fo ur \'il<'.ant swtes and lower four fi lled up su:tte~ m oul ermo~t shell (for

11 =- 2 in carbon. n J for Sr. 11 = 4 level for G'-· crysml and so o n). Tire ltpj>f'r pan witiJ /cmr ''actm t ,tul/rs /Qrmt•d C<Jm.lurtimr Band (C.8.). 1hi!> C. B. IS gcncrully empty for Insulator and paninlly filled up for Conductor. 'nrc lower pan will• fuur filled up .rltllt:J ft1mwtl \t,le11cr Hcuul (V.IJ.)_Th1s V.B. IS band IS C1ther completely filled up or p:utinlly filled up. Tltr gap orrises in b<-Meen C. B. and V.IJ. wlwr~ rro elrctrmic etr('rgy lrrrl orr prrmillctl {.<r cnlkd Fnrhiddrn r11rrg.r ll"fif £,11 Fi8. 6.1 ,w/6 "'

C'4lndut'1it)l'l

,.,1

b;utd

J"Uf1)t(k"=rl pp(t't)

.," 0

l1a..uu-c<~1~.

6.2

V..ltnc:t hand (V.B.) and t'ondut.·tiun baud (C..U.) with r •._..h ; AA... n

.,.,. n ~

fn.- " a.nlil-onrlnrl nr

Now ;1' the mter ahnnic d1!-.1uncc dccrc:.J~C.'\ l'uriher. the forhidLii!n ~nergy g:tJl wtll £r:tdu:•lly in:.-reL'-C \Vhcn the forbidden l!ncrgy g:1p (I:~ -=- Ch. winch ~oohu,..., the u\cri.Jppin!! rcsion Am Pi£ (6 I). •.md rcpn!\t:lll\ ml:tdl (t."g. Cu. AI, Sh eli; I nu: fCl!IIIJ1 n in F•g (6 I •• whcl'l,." the fHI'hlt.hh:n Cll\.!1~~ !:!:.tl' ,, 'lnilll (li p .lfi'H IIld I\!\') rt!prc~~nt Scmtctmductor (cg. Si. G~. GaA~ <lt:.), The rc~ton C u1 1·•8 Cf1 l }. ''her~ th~ l01bidd.:n cncrg~ ~·•J) " \c1y b•g lht: oar•mrHI (, cvt rcrrc~cru tb~ ln~ul:llor (cg. diamond). f•flUf ciCl' lfOO:o. fmlll 2.~.;, 2p Ul' 3~. Jp tlf ..1 ....Jpln lhC \' UfC.OCC b;.tnd dl.!ll.'fllliiU: tht• v;tlcm:) ,,f c.:t!rlmn. Si ur Gc rcspccu'·"•ly ;md they are pomu:tp:um~ 1n C0\.11c.nt ht11klo.,. In J1:unnnll cryMalthc f\)lU \'tdCn\."C \!1~-ct run .. bcm~ 'h"re~l \\ tlh m.•ighhounn~ illnm\, un: dn\cl) hound w 1hc nuclei und ·M 1hrn cnc.:rt:> lc:H·Iw \1 B '" h.m cr 1111nrc nc~uti\.' C1Lhan the energy lc\'cl uf ahc t:nnc.\pttuding ~.;t.uc,,)f f1cl! t.:arhon .uum•. 1ri!! (, I). -..imi' .lrly for Sl Jnll tie Nuv. ll it'' l"""''ih1c w renH.wc on~ ..:kcHun 1rom thC(..'H\'alcoii""Hid m valem.·c hancl '"1 ,twmnnd t:ry.;tal or m S1 or Gt then h nmy Olcqulr.: '11111~&-:nt cnctJ!}' tu ffiO\C llllll tU11.!tiC.f8.Y St::UC of lhC CUildULIIOO h~tncJ f1~Utl.! b.~ 'hnw'l. I he (')01''-0l~C ''' .111 ch:llron from Lh.: vulcncc band w l:Onduclion band 1'hl' minimum cnl'rgy d1.11 nm'l h.: unp:1ncd tuthc clcctrun h, rcmuvt it from lhl' CU\ ull'nl hond.. '' Ihe I.'Jh~lg) thlfcrcncc IN:twccn 10p t1f I he ' 'ulcncc b;md 1u h ..mom Hf the cundut;Uon h~tnd. 1111' b I hi! wtdlh of the forbi~Jdcn ~JP 6 cV IL1r dmm,mU. \\htch ,.., \fU&h: laq;l' omd hnmlm~ 1:o- n!Sti very strong. Stlal j, nol Jlt':.~•hk tu n: mnvc om ch:t:lrun frum V.B tl) C.R for diamond. tim~ 10 whu:h 1t ll.:h a.' an lmululm. Rllt II 1hc. t:let:"uon t'JJI n::.tt:h 10 the conduction band. ~s il hJppen' for Si ~m.l Gc. it 6 fn:c :•nd <::Ill rmwe wtllun 1he malerial from Jtom lu tHorn. bt.•c.J.u~c lhe cnmJuclion band is <rnpty. Th~ electrical und thcnnal propente> ol o m>LcrluJ ore due 10 llh)\'l!lllcrn o f the l!lcctron in the coot.lucllou h::mtl. so in C\t'\1.! ~,1 moatcrii.lh like Si cr:l; 1.1 ~V}, G..: (f;:1 -=: 0.76 cVl. by bt'C:tki ng the cov1.1lcm hond in V.B 111 room temperature MHlll' electrons can rcal·h 10 1ht C.B otnd ).!.1\' c n ...c to t:dnJucuvity llue Itt dlitl th.:\ Jrc t:Jllcd as. St1mic"tJiltluum. (I!,_)

6.2

Mctuls. Insulators and Semicondu<·tur·s

A \CI) l"\n~llcnl umductor of clcclricity 1S called mc1al P<•Pf cnndttctor 1:-. rtn m ..ulator o~nd ta 'ub.slllncc who~c condu..:uvily lies in hctu.ccn in~ulator-. nnd IHCI!IIt. 1'- .:tilled '-CIIIII:onduCIOr. A malcnul lllU)' he placed Ill .my tmc of llu:n: chr!!c da~:-cs. di.:'pcndmg upon i1s c!Otrgy·band ~tnH."Iurc.

Mctills· A II mcl:ll< Aic gencl'nlly vet·y 1\<'><ltl cMduclnr of dwlncil) l>ecau'e b~mtl "'tfU\'tun.· uf :1 meml crystal contntn:, na forb1ddon gap (E~ :. Ol. (unducnt'n ul'ltl \,1lcncc h.ulth QHrl:lp with each other (Fig. (l.,,(.t), Rc~tl1r'l A U'i F•!!· 6. 1l Sn under the lnflul·ncc of nn external dcctric riciU. dt."Clfons arc COL)ily mu\'cd (u)l)l \ otlcnc~ b~tnd ro cu ud~•ctnm ham.J iUid they ;uc ttl.!c tv •nm·c ubuut in the cry,t:l1 rrom atom to :nom and 1hh con\tinne~ 1hc condt1ction current (Jcl Wilh nu:n:3~ of temperature. "'1ndm:tl\h)· nf m~:tah w1ll ~h.:-~,.·rc:.'c tluc to 1nncusc ol rc:'t~t;m.;:c.

Seuucomht£'/tJrJ ln~ul.ators:

··r hc

n..•qut rcment~

I 03

for a cry~talline s ubSt3ncc to be an in'iul:nor

:t1

tempcrmun.! ~tre. 1he vnlencc band mu.sr be full and the conducJjon band nHt\l be rHmually empty and conduc1ion b:md should be scparmcd from vulcncc t'l.tnJ h) .t 1a~c forbidden energy g.1p u;t = f• cV) m room h!mpcr:nurc (Fag. h.J(t,,, Rc:~1011 C 1n Ft~ 6.1) In diumond.. the CO\'alcnt bondtng I' !\O ~trong. 1h~11 lhc l:lh!I'£Y whi~h can be supplied to a.n elct.:LrOo from an cxtcmal appheY field 0 1(._1111

hcconu:~ \'Cry

small than thut n:qutred Ul fr~c the electrons horn "~lienee b;md A' 1hcn.: ur~ 1W lr'l!c clecLrons avo.ilnble in C.B. soconducuun cannm 1:\e po~:-.Jblc. Hut :a' 1h~.• t~mpcrJturt! mereasc~ !.Utne cleclfUit~ llltl} gel (!flOugh Cl1\!rg} tn

..-rol'-' thl! h•rr.c lurbtddc;tl gnp nnd wke pan m conducunn So cunJuclJ\'ily of gc.,ml '"'ul:uor like di:tmcnd may increase wilh 1cmpcn11urc. hut lhc cham.:e-!\ un: \'~t'Y

r:m:

•

W~Z@~B ;; /y /0.

h:l

f.lJ:. 6 ..1

f:nt·rlO lt\el diagrum ror. faj mt"tul; (b ) im.ulatur. (('\ ~cmkondut"lO.r

Semiconductor: Semiconduclo~ hnvc lhc sumc l)'f"'! nf ~nergy band struciUr~

a.' an insuhuur. But an insultuor has a (orbiddcn ~up wluch ·~ ~u wu.fc (Kcgton C. h£ 6 . 1), that v~ry few clcctruns <;;m <.:n•s.' it ~11 room tempcr:lturc, where:.~ a S.C-micom.tucwr 1)\)St-cssc~ a narrow energy gap (F1g. Cl.3c. Reg ion B in P1g 6. 1). whu:h oil ow~ n conside.r.1blc nmounl of <.~onductit,n al roPm tl!lllf.Cr.ttui'C-. Grt•ph•te• • cry<tnlhnc ronn or corl>on but h•win~ u <rystolline symmetry whoth i- dilfcrcnl rrom dmmnnd. h<'i' such ~~ srnull volluc uf 1:-.11 , l h<~l 11 ~~ alnw~t ;.t !<.emkonductor. G~rmmuum otnd !-.lhcon (fig. 6.3c) :m: chc two mo'' widely u~cd l'>~mic~tnductmg ch::rncnt;, hnvm! the rorbiddcn gnp ll) 0.76 ami I I cV respective!) .tt mom tempcr.uurc 27DC C• JOO" K) nu~ condUL:li\'C ,,ropcny or 'emicontluctor. he h<!tween a <'Onductor (like copper) •nd >n onsulotor (like dmmon~ 1. Tlw mmluun·itJ vf w•micmuluctorJ mc.·lt'aJ,~J' wilh im't'r'tl~'r oft,'mJH"rtmm• IJuJ tiiiJ~K .ftmkom/u,.:·wr.f un u...- tJif ituulmur. 8CC"'.s.u.sc covalent honds arc very !~lrong ond lhc v:tl\:ncc: electron' of \Cmlcom.luctors (Fig. 6•.Sa) cannot brCll~ away Lhe co\•aJcnl OOnd without m:civing tht! c.xtcm:tl energy. :and ,incc no rrcc electron~ un: fl\•ttilnhlc

In C. U ut 0°K. so t bc-huvc' U!" an in~ulutur. IJUI us U'mp('/'aturt im l't.'t'-'''' m<'rt' anti m ort• bomll w.'/1 b,- bro/..f-'11 llml t•ondilctldt.\ "ill increase with lt'm[nnmw -r

fnr .Jt•n ,;t•cmtbtt·tor.

(,.3 l nt rinsil' Semiconductor When the condu~tl\ uy In Cr)'l'taJhnc ..,cn\h.:nn\.IU~o"tors is only due to breaking of \!<w••Jc::nt hnnt.h. nl 1111..• dc~.:1tm1' 111 the vulcm;c h•nu.l. then thol ~ub~t ancc 1!\ "•ud to he un uurm w '' mu omhu ltlf ( h~; (, k

(>.4

h ~l

Electrons :a nd Positive Boles in a Semiconductor

\Vhenc:vcr a cova h.~nt h'md of Si ur Gt' cry,h•l a, hruken, t h~n:. fret dcctrun f,) nlll\C\ from the \',Mun: b.mJ ht lht: umc.ludion band of u .sC'mjconJuctor. umln lt!t~ve' hchind tu' uofi1h:U dcctronic ,t,Jle m the v.tluuce bun<.l CFh~~ 6.2. 6 3r .md Cl..Sbt Thr ah.\,.tWr- u( .m l'lr• tmu m \•a/,•m·, Jmwl i.\ •·ulh·tl tl 1'"-'ifh•r lwfl! (f1J, The wc\rd "hole~ '" t1 $Crntconductm. 11tcrdor~ rclcrs tu the empty cner~y lcvd ..

o·

0=0=0-0

0=0=0

II I 0II 0II II II 1] II o - o o-o II II II II o =-o-o-o

II0 - 0II 0II 0II II 1· II II 0=0 0=0 II II .o=o II II o=o

0=0

II II o=o II II II II II II 0=0=0=0 o-o

g=g=(b=g l'"ig. 6..t

'" Jo'onmuion of boles in Y.U. a nd

; • \'O:l huk'

"bleb ght rl<it to h olt o<tJ !"NIU

n10V~Oil'OI

or hole,< in V.U.,

in an utherwiM:- f1ll~c.l 'ulc:nce hand So whenc\'er there" ~n c'<Lra elec1ron lllJ 10 th~ cnnducllt'n h:md 1hcrc i~ a simuhancous produnion ol a hole (p) m lhc \',llt:nce h:md a •tg. 6 2. b .kl fh e number of cltxlron" Inc ll ~lml ... nnuh~m~ou"l~· number nt hulc' 1n \'B. w1ll IO Crc."l..,~ \\llh •ncrcao,;c ttl lellli)Cnllutl,' IJm jm '"'',. w .H·mu·r,mlttc'lt~r mtmbcr fJ[ dectron1· m C. B. (II} mttl na. of l1olf'., m \ ~8. {pJ m·,. ""'"'' wm,.. Su m:llhcnmllcully, we ..:an ~llY

L'· =

= "·

,, ,,

.... hen! 11 11.1 tltt mwJbatl{dwr;;,· rt~rn'tt'S ill uurinsi(' semtromlut tor. The p..1!)111\(' lll•lt:. rc~;.u lied u' the ;~.;.Uvc ~Jatuclc tn the vulcncc band, ullhc .,,,me ".ay thut th~: clt:t.:tron , ... \'OihldCI('d 1t1 bC' :.u.:uvc panicle m conduc11on b:mJ l lu~ lc.ld' II> tho,: ~..mu.:cpt thai ,·,mdllc ,;, II,\ i11semicmrducwr .l IJ n rusc•tl ntJI on/\ hv tlu mminn ") t•lc•t llmJ.\ m ,;,,. 1 amlucllmt IRmd wlm·h gn·~·'· ru'e 10 Jlrt: (·fmtlm rum r lll'l f'nt Ill

C./1/)ttt u/_w IH tiH tlu· nunion of til~ po.r itit•t hole wfm·h 4:1\t'l nsc. tn lwJ. unrnt m tin \' If The 111ovcment of Lhe hole 111 Ihe ' 'nlc.nce h;,~nd I' unckr,lvnJ 1rom Ftg:.. 6 .Jh .mtl 0 ·k II ole ros•uons c:ln lx changed Irom une plac(,' 10 other

h>• uucrch:llll!llli1 1hctr po,iuon will1clct:Crons (J-i gs. 6 .40 und 6 ·k, Thu' puMII\'C holes ;1rc also ph)').JC:.J e nuuc..... whose movt:mcnt con.MIIutc " fluw ..:urn:m. \\htch ,... culh:d ''Holt' Curr(•ll(' SIIICC lll(W('I))(.'_Jll or hqJc I ' n p J)IJ ... IIe hi lhal ul l!l ~.!,;tron. M• the \hl\'~o·uun ()f hole cumot IS :,arne as dtrcction "tt cl•rrcnl tlvw

s,.

m \fm•cumlm-rw·,,, that•

twc1 dw11.1~t' f'tlt'(u! f'S,

elec:trmu Gtld Jt,JJt>.1. /Jill m mt'lllh t'lt·tHntl.~ arr llrt.· rmh rllars:~ earner hecmtfe then: n "~'~ tJttr.tJin, of hrrukml: 1hr hmu(.i, multht•n-h• fonllfll/.' tlrl' lwle:r.

6.5

tlr('

Fer mi Level and Effect of Temperatu re on l nlriiL~k Semiconductor

h.I\C \c."t'n c:.trht"r lhnt nl uh,nlutt" i"~IO nil 1hc dct.ll llllll' '1u1c' lH the b.anJ ..th: Jull .uu.J thu~c uf the conduction band Jr..· t:mpt) .... u 01 ...~rnh:ondUl.' ll\f LlC1.'t101l'' lln msulJ.tor Ul 0°K But 1.lS tht: ICm!X-'r.llun; incn!a'c' ..u nlc c:l..:caron' ftum the v:lkucc band gN sufficiem energy ~.~ nJ ht.:Lumc I h.'~ The') J1lOVC hl thl! ~t'lnJucuon band and tuke pan in conduction ~•nd give m;~ to .;c11H.htClJV II~ 111 tlw ...cnucunduetm (Fig. 6.3c). N1m we v.~\111 m cli)I.LU~' the phenomenon With n 4uamum rnc~.:hanu:u l pomL J\,

\\C

\.t l en~~

o f ' ' ICW. C la...~• c"JII) .dl (kclron!- h~t\'C zero cn\!rgy at OOK. bu1 qudnluJU •u~chnnit.."":tll) a ll

dc~ tnJ Jh

.lrc not ha\ ing /.CI'tl energy at O""K.

Tif t!

ma.umum enl't)!\ 1/mt

elc•c·irotM' men pos.wssal 0°K is lht 1:crmi <'"l'tgy £,.. So <tu:mlUmnh:dnms~~~lly the ~lc('tmn ...u:u~o~ll y have cncrt,lc~ cxtcndrng from U 10 1:.1 ;u ab.\olu t~ tcr(l tcmpcmturc (Ftg. 65) Now m order 10 know how mnny of the clcctromc energy sun~ an the vo.lcncc band .and conduc:tmn b:.nd wtll be occupu:.d al (.h(fer.:.nl h::n1(X:nl(lll\:'· Wl' 11\11 oduce a 1-t'mu~fiwtor. f ( fJ, • ·lm:Jr r.f 1hr uumh('r tllm exptf.f:ft'-~ tht• 'Prohabllit) slra1 n Stfllt' oj a go·c•n ,.,,erg_\''/:.') IS f.K;tuptcd by an c.~ltrttrm mrdc-r ,.011dltum oj themwl Nfmllhnum 'Tiu\· mmtlwr /I(J:} «t mlm: lu:llntetl tt'fU and umf,\ ' mt,J tJ tl ftuh lion of t'llt:r 8'' rutd lt.' IUJU' t'tllllr-t' (TI as' .

F(/i) ;

1 I+ cxp Itt. - £,. )IKTI

(6.2)

I Oh

En~meermx

Pln•rir·\

( olfldU~.-'tiHtl hund

1'.1 - - - - - - - - - - -

------- -------t, "[------===Fi~.

6.5 lnlrin'"h: '-t!Uiicunduclur wilh ft!rmi lt!''t-1

where K .:: Bolt:tmln CtlO'\IUfll, 1';:;: temperature m K :md EJ. = fcrma level <>f cn"r~y 10 cV. maximum po.sc' J l U K

fl,_

cnc r~y

= 11,12

that elccuon Ill:\)'

The Fcm1i f~ctor 1:-. wdcpcndenl nt th\! cnerg) Uen~lly of '\late.:.. If •~ llw probability lhnl the :;;tate' ,x~ur11cd al thai level. arrcspecuvc of 1he number of st,IIC..-<i :.u.:IUally prc~nl TI101 •~ Jl h Lhc I ruchonaJ ~-w::cuptmcy of po.-;siblc ~tnt~:..

'l11c

\~lriJUon

fll h;.rm• l.h.h•r 1-.f.') \\lth .:-nc~) .11 thffcn:nl tcmpca.uur.: lm 1·. ''" •h •l\\ 11 m Fi}! t1 h \\her..· (ullline curve ...hm\ \ F( F 1

inlrin\i ~~ ...~nu cont.hl("lnl

:u W'K .snd ..tuned

hn~

cur\ c .u I "

Prvh:1Nh t~

·•I ,.,:..·ul'l"'~ cn..-.fP.)'

k~cl

fil:.-1 fii'.J

( H

i"i~.

6.6

\'nrllllion of fermi fnC'tor F(£) with h·mperutun-

\Vh~n

r =()°K N ,.,, ~nn l .t~e IW(l \.due.. £>1::,

lll

"!I· J -

r••

)

- L =- u. '~···,tu'c ,.- :::: o.oJ + exp (oo) "''"

F. <F.,

(2)

/.'tJ:.'

l~Xp

t- w)

= I thc:G\u ...e c'l:p (- ':O"J) =n

Thu"" T= o•K. F(£1 =I. ~<-hon < E, "hidtutt•.ul\ !ill the lc•cl' below£, I.e. VB l:ig. (6.5. 6.6, urc l tll~d up by l'l~cm1n .tm.t hE.,= 0. when 1:. >- 1£1 l.l'. all lev~l all(l\'C E1 1c C B F1g th f\ {l t)) m~ cmpl)' Sccau"c. ut O"'K nn hcut Cll\!(~} i:o. prcSl.!nt. SO n,, '()\ ollcr\1 bnl\d~ at~ bl:ing hn\J.:t.:n und the \COUCOOdUCl<'>r

bc.ha\'C:> ·'' an in~ulntcr

=1:1 , I c1-. 1 become:, (·: •·" =I)

But when 1 = I ' K I hen ;u I

wh11.:h mcano, thai owhtn lhc lcmpc:r.stun: i .. nol H K hut ..orne higher \ttluc 'a) I ~ 10()0 K. Ihen iiOmc ('0\ .11~111 Ntndco v. all be hrnl..cu and ...omc cl~c1mn ... v. 111 be a\':ulnble in C.B. v.hcrca., ~nmc ch!ttrvu va(:~tncj. l.c huh:. w1ll he 1\\'\lilnblc ul V.B. Thi~ is shown by 1hc doucd line tn Pig. (,.(,,

6.6

Fermi Lc,•cl in an Intrinsic Semiconductor

l'ht:. JXl'illon Fcrn\llcvcl 111 OUl 11111111:0.1\.: ..c.:micundul'tof 1.!".:111 he t:alculmcd in 1hc following way: h ~hou l d bt· noted Lh;u the Fcnni level will be- :-.omc.whcrr m tht rorPiddcn g~tp . \i nC~: nc::trh ,til tht v:tlance h~u t iJ ,I;UC\ .\1'1,' OtCU!'iell ••anc.J \1Cry few ci~~Lr,mc; Will be iounll 111 LhL' L'HIIliULTtum h.tnd, Jl rnum lcmpcrniU re Nov. th~ ltll:tl numh..:1 41! t••.:uph:i.l "'"I'-'"' [A0·.11 h) ..:kl!ln.tn .. , Y.llh cnt.:t{!) between E und (E + elf. J "equalro th~ pl'<>duct n1 1he ·'''Otluble number ol ,1:11<$ ISII>II ,tnd lhc prnh<thilil) uccurancy 1111>11. lhOII ;,,

\If '''""

Nl1: !.IF. : .)(f' JF(/i 1.!£

1fi..')

where N(f:..); toml number oi occupied !>IJtcs 10 C B by c l cctn.ln~ . that i:-. the: density of deer run in C B St £)=Numb('( of nvntlrablc ~uues nnd r<F.l = Prob~t~ility or OC'l:upancy or tho<c S l 3 lOS.

Simtlurly the numhcr nf hole-~ m the VB. wtthm the energy E nnd (E +liEl•" P!l:.l dE= S(/:.) I I - f '( /:.)1 dl:

toA)

Con~idc-r ~11 \lr};Y lt::\lt:l £ 1m C R. ami C1 rn V.8 wJm;h .-rc "'ymm<:trically pluced nhm11 1hc t.'t"fllr~ of 1hc l'ner~} ~ ar (£'('• (Fi~. 6.7) For nn CJil'rg) ranged£. lhc number of electron!. in the n is

N(t:.1J JL

=S(t:, ) F(c1J ,JH

Si milarly. 1hc nurnl>l'r ur hole~ in V.B.

•~

P(E,l d£ = S(E,) I I - F\£,!1d£

C'o:nto:-1

,.rEr

t=~~+-

£,

V.B

SW! Fi ~.

6. 7

\ I.Lri:diun of Unlil::thlc· number s tales ISU:.'l l "Hh \'n·•r,t) IF) in ' ~•lcn cc omd COildudi0 11 b:ultJ.

,\,~unuu ~ lw !'ouupl~t,·ll)' .\'(/:." 1) = SH:.'J). the number o l' avaibhll"' and VJ3. are ~ ~~liU\1 \:um:. I kntt:.

'\I,HCS

in C.B

((>

lluJ~·1 \.'.;IHnn \.Pild:non. 1hL lollmnng t:tpproxun~monto tht: h he m:1dc.: A''umn•r 11a1 :11 111(1111 h~mpar~tlurc tmergy le\'f'l t. 1 ahfl\'e the FemH h:\CI 0!1 ), ,;·•y :u lf)()''K, 1hcn flu: f;·tcwr

11111 l.u.h•1 ~,.,n, 1n

C H IS tar

~ilmilarly

aso;u111ing £.lew! in V.B. which

- / :, t

far be hl\\ from Ferm• lcvt'!l. the n

1 +- rli.~ 1:', .,.,.. , 1 >> KI' ut morn 1cmp. so the :1bove ~xpr.:sston bc..:on1cs Fr 1. 1 1-= I -

wltel'c £ 1

.Y(£1)

CXI>[U::,

Etl/1>.71

Pie: I= oxp(le~ -£1 i/AT(

£ 1 - J::p ;>> KT nm.l EF- E: >> KT at room ll'm~r.t tur~.:. t:=or intnru.t"-' 'emiconduclOr ihc: nu•ubt.:r hf cle<:trun' l' cqu.tJ h~ number ol hole' I E'l" (>I! io

tl) ,,_.. \unlin~

So. Hen~<

1rom 1!\Jn. H1.8l

L"'

- -~-l

111

whc11: 1:.1 anc.l f.., were t:u:cn '\ymmeJricotll) .tbnut cht: ccuth: nt che tmh1ddl'.11 ~ap ( E•. l. A/ml'i' t'tJtmtitm ~lu. w\ tlmt tlrr /·'( •n,; ft·~·,•llu·"i 1111lu- , 1 .,,,,. t~/ tlt1' {tu-hiddt'll ,I!II}J fr" wnunit \rmh·uwhwtm (Fi_q.\ r'i 5 mul 11_7, mtd It n Wlh'tkmfc•ut a} th, · ,,•mpertllllf'tl

6.7

Extrinsic Semi conductor

The electnc-al Cflnductivhy or mtnnsaC' s.cmeconduccor '' \'N) "nlull

T(l

muen~~

the nmducta\'11~ u l 1ntnn~i c sem•cooductw a s m;tll pc• ~o.-L'Ill.l~l' 11t 111\:llcut ''' pt.·ntJ\Cknl .uum ... nn: added hl lhl' pure ..~mtt.:HnJudur m tho: ph•\.c .., 111 Ct) 'l:thiJ-:;.IImn wlm:h 1'1 calll.!~ol Jupmg omd n.: ...ull'lt 1h.: unpun: '~nu~omht~,-lnr. bcrnJ:l t::all~,;d u~ c\ lrins ic ~cmiconduc10r. The ~o.'fHh.lu~llnl~ of t:.u riu'i'-· ~o,cml comJu,co r ~~ muci high~r. !oa)' for t.:xamplc. I:!. l llnL' '- than 1ntrin:-.IL' scm,conduclor whon an impumy Is ~dded I part in III'. The mlllUrll) .uum h:t' .1 !.llC whil,;h ,, ~llnm51 lhe :tame order or the hn~t I,IHICC S1m:c pcn.:cnt:lgl.: o l

lmJ'UJMI)' t'li OUh j~ \'Cty Smilll \0 C\'CI')' llllJ'IUnl)' a iCUUI"-; 'ltUI'ft'llllilt!d h) •1 Ul"'~llllill

lattil-t" 'he. Sn ha~ic Structure or the cry~l.tl "iJI Ollt gc:l .lhl'r~J ufh.:r Llnping. Tit.:rc .tre tWO I) (X:' of CJiitrin.,ic ti.Ctnicnnduc iO". (I J IHY''IC 'cmiCOIIiJuc1nr and ( 2) /Hype

~m1coru.lucwr.

11111-typr srnlioonductor If IJ t>en1uvalclll nwu' is Introduced in the iutrin'lil.~ ~~llHCtnHiucll ,,. '"'>' ~c nn.HlilUH, the ,ituauon "ill be a.\ \hown in Fig. 6.8(al. Thl'n impumy rxmnvalt.: nt utom-... '•Y .mtimony 1Z =5 1I or phospurou' (2 = 15) or '"""n" tL = 331. '"ill tfi,plae< some of !hi! gcnn{lnlum {•toms ln 1hc originul

c ryo,;t ~lJ

laulcc :.uu.l fuur of 1hc ti\'C

VlliCilCC Cle<:tr~n Of the impurity 310m WiJIN:CUpy fOUr CtiVaJ~nt bond< and lhC fifth nne" ill be ulmnst free.. :1~ II dOt:s 11\11 find n pla~.:c 111 the CO\Uienl bond.

11 0

lill}lillt't'rim: P/1\ w·.,

~o - ~ o-,o

•0

II - ·0II II" ()II=-- II II•0 - · II.. ' II

II II •0 II •0

•

·o~,o-~u

1 1._)

...

I I

t,: I I I

J(~l

(

•U

t·tcc ck~ntlft

•

'"' t"U

•

V.Jl

,,, fi~.

tt.l't n-l\ JW '"'mkonrlud or "ilh donnr impuril) and thllhlf ·~·\1.'1

~vel)

unpur11y :.wm th\l<i

;l hnk, o111t.l llm:-L:

ftl.'l.'

il,tl

,·t\ntri~Uh!"

une

almt'!'t trc"• i!lectron \\Hhout ~h~<itlnl!

ch,·1.:lmn' :td " ' t.:otrri.:r of t.'lll'rtll l. A Vt-!1)' ~ulilll .tnhH111l ~•I

cnn~)

'' rcqum:d llllrcc the: fith dct.•t ron from the atom, of 1l1c un.Jcr ~•I ()_()I"·\ rur (k .mll o.ns cV ICII Si Sllll.'l' thPM! pclll:t\'~knl impuriliC\ tiOJMIC C:\4.\!... \ c lct:tnnl c~trrh.·r. ...nthc~ :.tc cullcU ~onor ur n-typc 1mpuruy. untl rhL· ~ ··~,t; l l l..lut~'' "11h dom.1r 1n1pur1ty" c:11lcd tHype scmu:c.mduct<.>r. E;u:h ltlnl£ec.l \JPnnr

;uom IU~> ~

net chaJt:c ol l+rl .111d h hound or inunohilc (Fig. 6.8hl. \Vhen I he- dun+~r mrunltc .. ·If'--. Jnpl."d to nn m l nn ..ic bcmi cundu~;ttlr Cit" \II S1

lhcn .&Jllllu'lno•lth-.crctc h.~~·ch .•rc JOifl •ducccJ ju't helm\ the t:r.mdu..:tmn h.uhJ '" lhc fc•rhtddcn g.tp (Fit tdkJ. Thc-\4.' new ndditit1nal h!\'cl:\ will hl! Ji..crch.: .nul k nm \'11 :1.., th.ml)r h.•wl £,1 ~Pig b.Xc) hcc:IUM:. the :uJdiliOnal impunl) alUm' .u~ <;.i1Ulllcd

rm 3J')=Ut Hl lhl! Cl V~l:tl ~lt'lh.'IUrC a nd hCI\l"C th t:!il

intct"'.tCliOII j.,. '111Utl

HI uncrt:) lCl.O I .:V ful Gt: and o.os cV ftll Sd i• rc4uirl"tl to free tht.• t.•lc("tn•n from t.louor lc\d hi conduction band. thl'fdon:

.Sin~C' H'l')' ..1'11.111 ollliPIIIII

ulmo'' all the fifth c:lccuun vi the donor mclenul urc m.i:,.cd tu tbc condu&..linn b~tnd .tl mom tcntJXr<.tturt;, 1c:n•il)g po~itin~l)' ionhoed donal' ''tom~ t)ll th!.! tluntar 1 ~\'d,

St•mit't'lldm·tur.\

I ll

(21 p·I)PC $Cmieonduclor

Wht:n n triv.. Jcnt impurit) (blnon Z = 6:i. ~nlllutn 7. =- 31. or Indium Z = .JU) b tddccl LO Lhc intrin'il "<'lllk••nduclnr. iml_:.· three tlf Lhc CO'uJcnt humJ, ~.:un he: ltllt:d up JJU.I the ,-.u;u H.:~ lhllt t.:'< ,,,, 111 the fourth bo ntt c:un,i uurc' t1 hole u::-1)1. ()_9:a) \V IIhOIII fn:-~ing :Ill CICCIMI1 frt:C. 111C~ holes C;lll :JCCCp l ciC.."Cll1lO'io from VB und thu~ m:.kt tl' rulable (l(~ " t ll\'.: <.·amt.'rs hole m Lht! vale net.' b:tnt! Sn 1hc~ Lrivl.lli.!lll iulpuritrt•.arc Lull\!tl !.u.:ccptnr bccu u~c every lri,•:t l l~ur ~\h1111UCCCJ)I t:>lc<.:Lron. in1111B.ic scmiCIIIlductllr wllh ucccplor unpurily b c.ll lcd fH)'fX" .;t~.nlc:ondudor. Each a~:C~Jlh.lr .t(mn h,,, a lit: I c harge l-t!~ nnd iS: bouml Ollllllt iUhilt: tFi~. 6.0b)_ \\'hen Jt"t;t.•plm impurit) j , tr~,ped wan intrl1llr.ic ...cmi~.:cu\tlu'-' or (j(' or Si. 1h~n lhe ndc.Lillun:JI Uh..:rele' cncorgy lev~!ls art! introduced JW•1 ;JbuH• the? \nlcn~e b~tnd hg {6.9i.) 111 1h~o: turhiddcn ~ap. which 1~ calkd a~•xrHnr h:\cl a;,), S111Cc a \'t:I'Y !'\Ol.tiJ .)ll\~o)um nf cncrp) is necl.!~sary (or nn el c~non to fcOtH! the \'Uicncc ha.nJ .md ~x,up~ the ol(\"Cflhlf ll!llCI~)' IC\'CI, so alm~t allthe .~:;Jn\."11'\ of tht: .1(."CCptor lll<llCI i.tl ,tf(' t'tllcd UJ'I b)' cle..:tnm;, rrnm v B. and fonn~d ll-Cl!~tll,'d) l(lt11"Cd ncccrmr ~umn I IIHI\ Crt.•at' ll l:trger nurnhcl' of hole.~ 10 the \'~llt:n-.·..• h.mJ whl(h t:Cti\SUtutc \hi! l.u!!l.!'-1 numtwr ol hole c:1rr1N m lh~ \'JII.!nl.·,· h:uul tn th1..·

C.\lriO'IC.' 'CIIIII.:IIIldth.'l,tJ

Thu' h)

d~o•rmg

th.·

.mpuru~

;unmo., m

th~.·

mlfln!itC .\l'mtcolu.luu''' nul unl)

cnndm:h\ 11~ '' llh,·t,·iJ'-t'tl hut 11 :al ..n ''-'rvn ro prnduc;c 11 'cuucundut.·tot 111 "hh h

II II !I

1 ()

c. a.

,,,...

II"

II I

I(')

I\,. - - _ ,

1\.J

__ ..II

0 V,B

()

''"

I hi

L\trJ.Iwk-

h:)

Fix. 6.9 p-1YJW Stmkt•ndudur with fi<'t"t.•ptur imJmrity nnd uC<'eptur kH· l th·.~

lht.! d u rgt.! t..tn icr....1rc mmnly ck~ll\m' or hnlc.. I:.'II', mm \ tm• lllliJnnt\' ,·m 111·r.\ lwh•\ ttn• mmu61\• •·mrifln 111 u~I\'JII' \ f'mf('tnlt!ru lm w fu·ri 'IH m J'·l\'pr w•mwo1tr/w. 101 Ilk ltiOj(ltftv ''iltrtt·r ar~ lwlr,\ aml lntlfttfll\ c urrtt'l',, uu ,.(,•, tnm,

11111/

C\.8

Ft:r mi Ll'' eJ in an Extrinsic Semiconductor

intnnsk '-l'rnic:onductor th~ number CIL"CtWil' j, cqu:al lt..l nunaht.·r hole' t n, I'•' llu1 in H•lYIX: extrins ic: semiconducwr numbl·r uf ..-h!clron .. >~rc

<IJl

!llt.!fCII!>.Cd

due

til !he

dc.•ping of J>Ciltftvl·lcnl atom ttr, :> n,J untl numh.:r uf lu.l h:,

CO>IIdU.."'tii'ICI bltlll

- -- - h:nni 1\."\•d ·I

- -

•+

e.-- h"TJIII k\ d un~ h;an,:<'tl fflr \loo1!h ll'nli'CI":UtltC

llllflfl'l< ~I!Uo..lJnt~Ulll +f

VHktll,'l"h;,vlt.l

•••

-·

,,,

Cm~~twn

I ·1 :,~1 I • "'IJ ( "

""DIJ

e, 111 f ; HIO'C ----~-

+ r

-a

I r + +

-- -·' 0 E>· r ..

VaJ~<'l" h:uwl

,,.,,·pt•lf /

\ l .lll'\

Di.si.WII."t' - --

Fig. 6.l0

l'u~ilion

nf fc·rmi level (1-:f., for fu} inlrinsic; fh) n-t yp~ and difl'erenl I CIH~~Cralu r~

{4-'J p·IYJW s~mi ronduc l or a1

un: t.h:crca~to!d tp, <p. I thtln whll:h would he UViulublc l<tr anuinsrc s~m1~ondu"tor. fht> llUIIlhCT hnJ.:, Jr~ d\,.'Crc;a:.~d ht.:..:Olll\i! tlf IJu: Jat;;t: rtuJI\I'k:r til el~ctron' pre..~n1 which rncrca.\c Ih.: rr11c ol rct.~mnhinauon ,lf dectrons \\ ith lull\!~o;, \Vith ., 11 nllrtr a~umcOI it c~l!1 he \ hown 111111 m (H)pt: C\lrln'n.: \cnucondui."WT 1hc number 01 huh:' ;U'f: irtcrC:t\l.!d due II' the lhtpmg uf Ui\'alcnl illlpllnl)' oiiU111 If•, .,. p,l ond number of clcctnn< dcm:a<c<l (II, <II,) th.ut whtch would be ;1\'rti Iable rur lllfnnsic ...~lniCOr1tluchlr. Nmc. .,IIH.! t• lh1.' h:nna level (I:., , is tl ntt'U''II't: Hl the pmbilh1h1y of oo.: upan~.:) nl1h.: .tllttwl.'d cucl',t;} ''·IIC:' hy Ih.: ch:~.·tr\111, '~)

IN tnLnn'ic scmiconlioclor 11 hen 111•11,, Fcnni lc1cl tf.11 i' 1111hc ccmcr nl" thc

IMllithJcn g;sp (Fig 6.7). But fnr ll·l_)'p c '~mi comhu.:tur. ~.!Jh.:C n 1 > p,.. 11 jJ.l'lctar th:lt 1;. 1_ 11111'-' m<n·c upwnrlJ c..' h i\l.'f If• c.!uncJucuun humJ ( ft)! h.lf)b ). w rndi c~t c that many \lf the encr-~~ 'late-. tn th.lt hanJ ;'~ li lll.!d 1\y the donor cl!!ctr,,n:-. ••uuJ •' fey. hole... CA lM 1n lh~ vnl~ lh:l!' h~ui\J S111111.1rl~, lur /'''}'~ !'ll! nliccmclm~tur -.inc,·. (~" > 11. «t £1 tnlL\1 ffifi\C df'l\\-11\\iiHI Itt rh~ '-alenct.• b:rnd lFig C..t(k.· •

6.9

frmn the t:~nll'r uf th!: rnrhidd.cn

Variation of Fermi Level

11 ith

~ap dth~r

Tl'mJ>Cnllurl' in

Extrinsic Semiconductor

l•or olll llllfil~'\it" o;cmicundurwr 11 1 : : f'1 .111d ''' h,::napt;f~llurc im;ft!~l'to!~ huth .tntJ I'; Will tncre:tse. ·nm ... Ihe lcnm lr\cl ( e,) \\Ill fCilli.1111 dJ'J>hlXim::ttl~· nt the centct of the forbtddc n gap. Thv:o. for nHnu-.tc !\.('!llll'<mduCh'l' h.:nm lcvcl1' independent l)f 'cmpe ratur~

(Fig. O.IUn) Uut H\ ~u1 cx:trin.Mc :;cnurclll\lut.:hu H '' c.hlicrcm. ~.t)' lf'lr tl·l)'pc: 11\~h!.fl:ll Ihe electrons arc corning from t\\ c> dtlf~.·rc:m o;our"·c,. Somcclcc Lwn~ come fmm donor ~l.i.IIC whkh ;.m; t:a~ i Jy '\Cparah:..J j I'Unllh..:1r pan.• III ;IIUIII .Hill Th~)' do flOI \<~ary lllUC.:h ~" th4"" I.Cfll(k!r31UfC ~~ I T>Crea,cd Tile ntht'l dcciH IU' ao the conduCUI'In hund nrc rr¢sent """"""'of the hrcakrnj!OI 0 «Walcot hand Such ontnn>t< efteet h) br<aktn~ thl.' hf•rHb "ill ln~l\'.l't.: 1n numt'l.:r ,. h.·rnp.;r.ttur~.· '' r.,, ..~J. S\1 wuh m~.r~.~~c nl h::mper~iltlft' propnrhun u l th~ lnl.11 numhl.·r ''' ~.-undut:hnn t:k\.':lr\10 lrnrn 'ukn\."t: h.tnd b} breakmg tOC hcJOd\ \\all in~.h.~olM' ThU'.\fl.\ '"" lt·mprrdlttn' fUt',\ 111 .. mult'rrul (lt'fmm'J morr cmJ morr rmrifl.\if om( 1-".•nm lt.·t ,,/ more.l down rfnH·r ro tllr illlrlll.\k poutinn, Ll'., ltllh( Cl'lllft' , , rhr• fmhultlt'IJ ~tlf' tFi~;: (dOh).

Sumlarly .fur p-t.\'f>c. SPml'"cuuil;o,w m tt!IIIJit'f(ltrtr't' lllt,'l'c.'(l<t'S the• mtai•ritll uf ~n IH't'tmtt'.\' UWrt'U\'in .~1 \· wtr uu,,· mul tht• Fr•t'ru i lt·a•t•f ri 'W\ uttttl il fl(l(11lNU'ht··' t/1~ Ct•mrr of tltt! J:llf' ru Ur tfw UtiHtr.w· u·mu.mtdtu rm ( FJ ~. ft ff)d l11U'l hotb It·

"I'

IYJX: and (Hype: matcn :LI hc:cn1nc murc unci murc m.~: intnn .. ic nmtcri:1l olt ln!Jh

h!lllfK!I'3l11re. Thi'> plac.;' a hmit tlll chc OJlCr.llin}1

1i."II1J"'C'r.li UfC

or :m C:\lrln-.ic

'~.:mic.:om.lutlor <.l~vicc

6. 10

Electrical C•>nduclil'il) in Metalic Conductor

r\11 conductof'\. contaimng

~• pt!nt'lfJtc 1hrc-~ dmlen\ ann~tl array

u1 heac. ~ ugtlt l>

bound (+\"!.!) 100!<> SUff (lUJld ~d h) d~~lwn clt.nub, \\h1~h C3t\ Ulfl\1! :JhHUI C.IUHC

freely duL' to thcnnal u~itnciun Bul the a\1.-rJgc \<..:Juett) 1~1 the dcctron cluuth tluc 10 thcmhtl ogitutmn \\ill!'~\! 1cm in Ihe- nb.~cn,.;t• ~1 1 the cxtc n~al E-hcld .

No\\ a,ccording 10 Coulomh', l!.lw in thc electron~ will experience nn uniform fon:c

J)fl.'~C ilCC

F -:; t•f

u f .10 exte rnal E·l'icld Newto n. m the direction

,,r

''Jlro~u..: tn thl: cllrc"' iu11 1he f·lic ld \\ hic h ac&::ch;l :llc' 1hc cln:lron' l.lut :11 the''11111.! 1i me due Ill 1he l:OIIb.ion nf lhe eleclron!i.A\cr~tp l' Jnll \duc,.'lly 1 ~ directly rclo.tct.l 10 1hc bfich.l ~~' I I•

lllo

whl'fl' Jl, '' colf~d tbl! mob1l1l}' of 1hc cltctron in u gi' en m::ttl.!ti.ll "Ju,.,c unu " 111 "t\•ull"' \l'l. A\ C:l oJ!;C dufl \ .;h.)(tl}' <ii,, > of clc<: lrun ;, in u llircCll\)11 upptl\ill! ru tlh.: JnLTtinn of E fidd ££}. 'n ( \'C) M!_!ll h~,.., t'-nnc: rn Eyu ill.)Oi (Jt, )_, 1 ll.OU I ). ~ji_.J(·11 .:: 0.()032 nt:/voli li.CC. 'fhc d 1ift nf ihc clt!ClHtn' Ill <I ClllltfUllllr Lluc lL•

~\tcm.tl

E-ltt-ld

..:-:tu~c

~lectmn

llml

~'·htch

I' C':llh.•d -1' \or\t.Jul·Unn

l'urr'-·nt Cum.ltH.'IIi'n L'urr~nt \Jcns1ty ( i, lor dnH cummt den. . It) 1J (hl lf~t·U t..'li:t:lrtJU!'o C;ln h.: \\ IlliCit .IS

) \•1 ncUJh't•.-'l) II>. II J

''here''· 1:;. n.: '''',h..• dc~.tron dt::n'itl)') t !.\ a ln~c-ciL":clmn ch;u~'-· t.h-11'11.\ ol nc~;tll\ t: ':till!.! =-:m, h) \Ub;o.tttuting the ''aluc (If ~ fiJ > fmm ;thO\(' Ctlll lh HJ) L"lllhlu~untt -:urrcn1 Jcn ... h) hccnme.'

1,,, =- J, • + p,.p.,lf ;

r\mp

\\ ht'lt' C1 1,.).1, '' l.aJktf Ihe t.'tUll..hll"II\' IIY Ol dh.' l~t.llt:n.al \\ hu.._, 111111 p. 111h11fm "lm.:h 1.... ts.:! ._ 10 for llluminum and 5.go x lU tor ~uppc1 (\h11\.,: ~~u.uwn 16.111 '" .,;.JIIcd thl! "•'1111 loll Ul Hf O hm"" L.w., \\ ludt ~t .1W"' 111.11 \. tur~nl lkll'>ll\ 1J, J \\all I'"' tun,tom! w lon~ E-fidd t 1:. ' i-. cuthlllnl The L'umtucti \' li'JI' il tuucliun or ternpt:r::ttun: Rc:-.hlt\ It\' \\.IUdl I\ '"''l!.I'\C nl l'llndufll\ H) lnl'fl':l.(l.'"-llnearly with tempcn1tutc :md dcc-n.:u\l!' ~t...n hn~;trly '' Hh ICIUtll'r~tlo~t.• But fur,unh.: m~ttcrhal f\'~i:Hiv·tty drl"p~ ...uddcnJ~ 14-l h.:ro •• t o.1 p~anl.,;ul.tt h:llll'<'•llur~ H( fc"' Kchin. \\hi'-h .arc..:-o.~H~tl :.-.. '"l'J1tr ,,,,,, to1 \lumnunn h.-,, llh" 'lotlf'1'11:nndtl.l•1r hL·hl\\ 1. 1-'° Kdvm I It lll'r h utJ""-"'·'tult \ .tu-...· ~ry,t<.~Jh.Ut" l..a.Hh.r: \ ihr..tllon lu~1h.'t 1 _ .. .1u .. ~.. thl· htfhl'l ..-ollt •ttlll 1.Ut: tJIIht• ~.·h·t.:LrOn'- with i01h Oalli.:l..'"t tlul.' tu "lurh tJuh '\'lout~

llltb.IL',I\1,.' So hll" .I !!IH•n E-ll ..~ld !<.lrcnglh-lowcr ~,.hill \.Cindt\ r ~ l m~l'l 1111\I'I IH\ fJl. •· rc,uiL" Ihi.' ~:cmduct i V H)' (0) lm\•cr ;u htghcr t~mpcr.tw.n: Frnm the point h.um of Ohm\ L:l\\ cqun lfl 12) the well ~um\ n (Hun·.., IJ"' 111 ,·t n,:ull Lht:Ol) c-an be.: Jl.'n,·cd tn th(' fu llmt. ing \~.tty. LA!t' ctm ... nkt .1 ~tmdut.:Hif ... , tu Fip. W II:•}. v.i1h ~~~~;• ,, .md lcnl!th L The ·•Pplicd \'Oit.a~~.· bl.'t\\t."i.'n t\\O

I.'IIJ, ol 1hc conJucmr '"' \

= I:.."L J,

= o£ = oV/1 N1m

/.·

rD. j._--11 _ I_

1hc L:ondu.:-untt ~urh·nt

thh cuntlultur

•

_.>,.(~

j_J

f.:.-11 _ _

I.e

1h111U_g .h

=J.JI = <TI•V/ \=-1(/!(i \

I~~

where m. wdlluown Ohm·, Luw 'late-. lhtll

Fl~ . h. I In

Current fl(IW In •• t:linductor

II= I, R

(6. 15)

I 15

St•,llnmdm_-rnn

Hy ~(•lnpannp nhnv4.• t"~' C((U~Ition' ((l l.t) ;md .6. 1))

\\ I.!

I;!CI

Kc:o.t!-.1omc..- ({()::I./erA t•luu ..

6.1 I

Rclaxal iun Time

Swady

S ~nt c

In the pre\i~nc\· t.1l ~\lcm:ll D.C source cll-ctnm\ 111 a t•ondt.l \hH \\JII ~x pcricn~... •n ...wl~mllnn, ,hr~ll~~ "P(lO'II~ 10 I he itpplictl t •fldtl. "lud1 '' CXJlrc,~cd "' II= d :lm. Sc) th~o: r:th.' ur 111 C ft:~ll-C ur \'Ciudty with lime I I: :u..:~.·.:lc rallnn tim: Ill olJlphc(l l:."-11dd t I:; • can be wriucn a~

r!!_ u ] (/1

J.ciJ

= - e£/m

lli. l11

l\hcn.· r· thl· ~dudty ,,fthl!cl~l.·tron under £.ncld t E •· Du.:1u ttu .; .u.:~.:d~rauon t'Hrltluc::li.Jn c urr-entdcrl\hy \lt =- n~u) will ~1lt.tt incrca.'c '"·' p.trih:ular l,llul' HI L llt:ld f E ~. whtl·h i' (Ontrallicb the Stt!ody :.t:llt! condition ur till' f'\)lllt lorm ot 1he Ohnl ·, Ltw E4n ((1 1) ( J l = o £). l\ hu:h !\UIIt.:' 1h:u ~urrcnl drn,ll' U, 1 r.:UMIIh lOfl'ii,Ull i1\ long ,1\ /~-lldt.J ( [) n:OHIIIl\ tnn,loUH

lh.: .thtH'I.' t.:ftn1r.•t.lir..:tit•n will gt·• in the r,•llm\'in{! "'·'} Tits.-> t.•lc\.tmu .h..:..:dt.·r .tlhlu an lh~ prc...;.cnce Clf I!XIl'.m,tl /!'-fi!!ld t.f J \\ill countt.•r b:tlam:e h\· lhl· 4.:t•llt~oum ut lh\! '"h:ctrnn v. ith the 1,1\lli.:'C (+vc) iun t:\1r.: ;tnd ulum.th.•l) dec1r1ons will ill:(IIIIIC ,tn 11\'CI"'.I~C tJnft h~lOCily <IJj> ,,, u. e h:tt'c Uidt:u,,eJ earlier The ;tlt·r.ag~ cJJo,t.lm:c tr.&\cla.l b~ the electron h''''""'~n 1'"~• culll..,iun \\ uh lttH i tc cure i• .tlkJ lh'l. ,\/, •lit ft'l 1'1cllll tA.l, QOlf tln.'llllh: t.OJt..en bci\\Ct.:J1 ,,.,. ... collision i ~ l·J.IlcJ Hdt.uiutum "/imr 1t'J Nell\ m the ulh.;rll:c of rhc c)l.h.:rnal J~~ftdtl t L 1 the vdod 1~ 11t Ihe t•lectron ~11 (I == ())"'a)' (l'u). ""' tlt~.: tunc p~~~~C') tluc tn th\.• ~t, l h~w n '' tth (+\\~t ion core vcloctty uf 111c lo!lcctrou \ll'Ch.":'l...e with

,,,u

um-.!. So at any llbtBnt ,,r ttme vl!locity vf 1). or the ¢1t:etr,m \:om be \\ nu.:n ns 11>.1 s)

nhu:h IS loihown !:'f:.!phlCJIIy m Pig. (6.llb) Tht: r..tte ul t.lecn.'oN.:: u( H.'locit)' with lime due

II ] [ -r/t u Sn t'mm ahovc

1\\0

I()

collis.ion 1\

I = - -u \"((lh· ""

Eqns. f6. 17 and 6.J9) in ~Hcudy <C'J> an~· conductor Wl' g.c1

Mute

Cllfn.'lll nc.m

\\Hh

'1\·cr:•g~ dn ll vcloc uy

l j -tl U

t/1

l•r-1•1

+ [d - U dl

~..dlo'fM

d < U.J> ==0 t/r

{1>.20)

!r < FJ >

t•l- lm = -

=- 0 1 c < l'J

-=>

(,·r)/ =

Jl,

Ill

16.2 11

c.:.: ) I" lh.: lnllbllil~ nJ lh~ dcctron. ~, .... H ".t' ~h·c-n iu Eqn ((1.1 1J Ill ' II 'C" Nm\ IH .. u h . . liiUiiul! the '.Jiuc: o l <llJ> Jll t.h&: ~.Lbu\c \\ hu\t.: una I I\ m·l\'t \\hac [ Ji r -

f"..(JU. Ch. ll ), wo; gcaalu.•

t.:"~;pn: .. -.wn

curr~nt ~l cn..:ity

u t l'lHu.lucuc'n

J., 111 meL;.al

,1., W lltiW\ -

-=-- ne < V 1 > =

\onduch\ 11) ot

6.12

•r

ru~'"

F = m• JJ F =- rrl- Amp/m"'

111ctul t t1 =-

1/sll .::- ~ =

'"'Jl,

Ill

mholm

Conductivity in Intrinsic-Semiconductor

In ..cmu;cmdtacaur :-.mcc the!'\' :uc •wl) dt:lrt~~ t:urnc~ clccmm :tnd holt:. :-.o m -:\! m1 ..:ondu~:wr conduc1tvity JllJ mub1ht) th!pc:nth u1xHl acmpcroturc. punt) of lhc m.llcll;tl .md un 1hc I:.J\'l \\11\"lht>r clc..:twn m hlllt: llltUICln take!) pla..:c For "'CI111("llfldunor (.u,.J •~ the nm~ihl\ •~I clcdrun 10 t:••lh.fn~..-uun h.utd. where a.' (Jir) ' ' th.: nwhifily of hoi..~ m ,,.;&LliKt.. hand For \CilH(OnliUclnr mobilly o( dccmm (Ji 11 l1' !!-TC;\ICI th;mmob11! 1y nllwlc \JI ,I bt•t:;na ...~ ~lcclrCllh m the C.H. ''more Iret.• Ihan the

hole ~

nl 1hc V H

L~·h c-onstdcr 'he s~nw.:undu\:htl hJ\ mg un de\ twn dcn:-.11y 10 C.B. ts tnlll\'r una I Htlurnc and 1hccha1~e~ \\ hu.:h ;u c '" :u bhle lon:unchu.:lum t"' f111'), ;and 1hc~c ~hargc-.,

"ill mm c whh :l\ cr~agt.: J.ri ft 'cluca1y < tr,1 > under Tht £.field (/:", ,, Su unth:r thi .. ~r,i tuati on condui.:IH•n ' urr.:nt dt.•n,ll) wall he J, = nr <. v,1 :> 1'\n\1. II lhi! ~.·cmducll\' 11 ) •'' tht.• au;m·n.11 c.lu~ In ct..·~.· trnn u1 \ R 1\ lO,.), then

I •'IT1 Ohm'

~''

LtW r:ondU~o.'U1'11

"''"'rl Jn1

II\ \\JII

th.

fmm ahO\•c ..::4n. (6.2.3) .ul\f h> u~ul!= ~.·qn (h ..:! It we ~c1 0'11

~'here m" j,

Lhc

JJ£, ;

IW .

mre.~ a~-.ociut ct.l

\1.

t' J

">ff ::; /J(' ,Un ;;

ith

ck~.:tron

rtt'! t,/111,.

(6.24tH

in C U. ami r" is the rcluxatiun

UlliC fur clc.."t:II'OI1 111 C.B Smulotrh ..._mHJu~tn it} 1•f hult-· 111 V 0 will be 11> .2~h)

where "'r•t:o.lhe mru.1:- ._,"O('I:I t~d \\Ill'\ hnh: 111 V.ll .mt( ;I',.., lh..: n:l:t:\:JIHJIIIuuc lor h<'k 111 V.U. Sin<:e m s~rnh.:untl\11.:10 1 both cl~~.lft1n .md hulc ur.: t.tking Jl.lrl 1n t::l)nducuon tu C B. :and VB h!-.pc~r,;h\cly....u lh.: tot;al t.:onducl&vtty will be

'("r• pr,)

u= a .. + u,, ~ ··~ "''" + l't' ,.J = ,..

, ,h

For intrin:-.ic :-.cmu:ooducwr number o i c..~h!t:lroo tn C U = I' ::!:: n,

hnlc m V. B. 1.c 11

t:!o

+ mI'

l'<JU:l1 to the number ~~r

Semic:andtt~'ltlrf

So com.Jucllvity for mrrinlir ~,.,mcmuluuor UJ,)

11 7

will be

Effect of Ttmperawrt on Conductivity for Intrinsic semlconductor aud ca/culatiorr of Etwrgy /Jtmtl Gap (Eg): For ullrin!\ic !-lemicom:uctnr 11umher or cll!ctron and numhcr of ho1cs ur~ very !rrocn~uivc to lh..: lcmpcr.llurl! Rcc.tU!iC a.'> h:mpcraturc increases more numher~ of co\· alent bond~ w1ll be bn1'-.Cn .mJ proJUcliun nf frccdtclrOn and hole p:u~ \\ill also inctc:t'iC, '' hil:h will itn.. IC~tM" 1he conducti\'ity of the imriusic senlicondm:hlt h can be shown lhlll lor my antnns.K senucnnductor the mmns1c carrier conccnwunn ( " ' . tlflll hcncl: C~llldUCU\ II) ( CT) lll~lC~t~l.'\ \\ llh IC111J>Ct1't1UfC (f) ;1!.\ flliiO\\.'"!

where

A ;- [ 2rrm~ /1-

Krl'': [-m,.-m,. , - J''~ • m = ma,\S or clccuonm lrcc

sp~I CC.

= Bohnn.111 con-.t~HII. I:; lcnlf'>CHtlurc 1n K .tnd f..1 ;;; PorbidJ cn cnt:-t;?\

~ap

111

intnnstc ~m 1t:onduct<rr

The: c.:cmdu~;u' II) of tnltu\\n; ~t:nlu.:onduc.:tor Cic. S1 I!> fl'lund IU h< ma=rl':t,('' approxtm.ntely 6 to NCR per dt!gree mcrea ..e o' 1emper.nure sn Lhe lollowmg \\a} 01

-= ~,f' t-.tUt.l

lb "7a•

whcrcas rc~l~hvit) wtll dccrca-'c wi1h Ihe lcmpcratun: as

p-, "

p,..-' r "

(6.!7h)

Thb property ~~ U!<>Cd 10 T/rc.~,mutor. u:. 11 was alre-ady lliM;u~setl 111 'ccllnn l'.m I \\hu;h h&.L.. C:\h!U!'-1\ c upplkation 1n t.hcrmome1c~. in t11e 11\l"d:-.un:mem t~l mKrt..,\\•1\1.: lu·qu..:u~_. ,, ·''~ lh~~nn;d rdJ) ,md 111 con1rol dc' t'-"l'" ·'' 1u.unl ~.II 111

chan~"'-'

m tcnlpt:r:flun..·

Resl:-.rancc ol the .SCillll'OildUi.'lOr (thcnnl'l(lr J al

und (:! 17) frum l'ur1 I \.':tn

""-'

Rr: Rro"' .nA where Nt,, ::: Rcsi'it:m:c .u T()"'K and

Now

r<>K from abo\'t! t:.qn I fl. ~7h,

wnth.·n ""

0'(1·

l~- ;o) ro nrc

~umc: conManl.

1 lnR; :ln /11• + E,/211[-:1.

which 1'\ u cqun110n ol n 'lruighl hnc (fig. 6.12) lmving !!.hlJX' 1:,111\. Su mt~ t'aJJ ca/cu/au Ent'fX)' Bund Gap (Et) ior un iruriu,ic ~cnUc.;tJnlluuor li'e Sl or Ge from the slllf>c u l tho strai gh• lith! <t:o. d rmvn bCh\' l:t~n In R 1 :n)tl 117', in Fig. 6.12.

l(l2Ks)

~' O J

j. Fit:. 6. 12 Variation or In R1 " ith

6.13

Conductil•ity in Extrinsic Semiconductor

For I!~II HI~h..: 'cnu..,;muJuctur u<.'Cnrdmg "' tb<.' llupi11¥- one: c:.urh:J pn:Jumin:uc.., IIH~ • ocher .11 H'M)m rcrnpcr.uurc :tm.l thJI will become lhl' m.ljOnt~ d urgc t.:auacr. Cli11Ci.ldl'r ;1 Sl!mtc~uh luc iOr \thidt i.;, du1wd ln tri,:alcru '" ''~.!ll ·'' pcnla\'nfcau .thllll 1 ht.• <h.'lhHY uf trh·ah.•nt :uom is. tN,1 J anJ th~u o l Jli:Oid'•'-kllt ~.~tom j, (N4J \\~hl'ft.' .... lhc llcn ..it) t1f elcclmn 111 ( ' B , .. , .u ol lld dt.; !htl ~ (1( lwlc Ill V.B j, (()I \;.tH\ ,all~ • Uunah! t:\lt,l e leclron to lht" C. R.l'.1d1 pcnt;t\.llctll .ttcun ht.::lomc t+vl•) tJou.1r i11n whee..: a .. t-.) :u~~.:crlin~ ckt:lll.m fn •111 v U c.ll' h 111\.tll-m ·''~•m hccc,mo: 1 \C) .h.cl'ptur rtln lhu ;,.;. n " hole c.·rv..t;tl lll\''' be clc<.·lncall) n-.•tural. Sn tr()n) lh~ ch.tr~c ncumtht) cond111011 it c!ln he wrmcn '""

u + V : IJ + .V,

(1>.2'))

I I.'.

...,u for p

~~pc

\CDJtconducwr

aboH~

cqn rfl

~'U

hl!'t:on11!.. ....!-+,\',,.:::I' + N., I'

N • +,r'f ,\ 1

/\'1 •l f ·Ill,!

In lhc ;thovc ttvudr.atu; t."qlHII1on (- \d

,j~n

hu,n't 1.1kt:n

ht.·c.~au'"' 11

und 1' 'houtd

tx- t+\t.'' Btll ''hen «if ol c.l,lpm£ nf do11a1 :tHIIII "tiiPIC: 1 ~· Nd ·•••••

:va ;mol f \ (/

No 1>>

1lw11

u ... N,1 - N.. um.l I' = w;/(V,1 1\,,• 'inHi ilrl) wh~n

rN,.

't uf Jnping nr .u:c-eprm ;Unm , ..

llhHi: l.\.'

'··

>> Vd .unJ

N,1) >> 211, then (631 J

'uch moucnah u~o~jurit\ r·om't'lllrmhw ·•rrm;\jnl.th,·)v t;qt•J.J t• I Nil N~ I, \\hu.:h i' lt•mp,•ratw1' im1t•pt'fltll•m. "her~ .t, mitWitl\ ··mw,•utrOiilllt wn rt'\ wall (nd und duut}(('\ t'UI'•(/f-.· "'"" tc•mprrmu~. \\ h.:n Nt~-=- l\d, th~n lh~ nwu:nal "'II Ill

l"~rorn~ t.tl;:\111 an tnn~k.

For n·t)'pc ..cnuconduc wr N~ 0 nne.! N,, >"> 1tr1 then n N,1 •.tncJ p = u'f/NJ I ur /H}pc 'lltm icondul'tor Nd 0 tand /IJ,, >> J: "• I hen p - N, ;lnd 11 t: n;11N~

So lh"· ~t•lhluctt\it\ ~''' n-lYJ'C' t:\tnn-.k ~nm:onductur ''Ill h.:

cr,, = nr Jl,l -t f't' ~~,. N11 ~·Jt,. 11:1

=m• ' r .. m~~

(1>.32)

Simil.trl) 1hc ~unducti\H) for 1Hypc cxmn•m: scm•conduc1ur w1tl b..· Up ; IW Jl,1

6.1_.

+ pr )J1,

N,,

, ,,l rJ'

,~Jt1, =- - - -

m ,,

llall Elfccl

In ..,t•uucondu...·tor phy:H·:' it IS olt~n

nec~~.;ary tn knm'

v,·Ju:lh.:r

J SCIUICtl m.luc ltlr

nMh.:.rml ..., w1YI~ or n·l)JlC'I Mclt'IUfCI1h"lll HI I.:I)IHim;ta,·it)· l\mn,,l .gi' c I he .mswcr IICCilli'C

LUll nlll Jl!l~'ihk 10 ui,llll~ll"h 1'<:11\C(Il

t.:• mducuon.

h,,, hulc .mu 1-H"I clctiJtJn

/lw llt'fl t'/Jn•t hi!lp "·' tu th•h·wmlr "/t,•tht·t

n-1\PI II rtm th.ttln,l(uuh J,,.lll'i't'll /ll'rJ l\/'1'' ii/1-,Jrnrl ,/,·tt•rmuu• tit~ tlt•Jtlll\' t{/1\'0 tlrffi'Jt'IU dwrxr t'UII'It'TI.

"'l'n ;,,.u 1\ /Hvp,• or ttlwlp'' to

U\ llt•// , ,

tlisem•ercd th;tt \\hen .t •.:urr\'nt ti l wa..., p:t~'--~:d thmu~h ;s ~lu h uf matcri:tl in the prc:-.cncc or IJ'tii\,VI!f"'l' tl\~l~lll:li L fl~:hl, 01/!llflilll putt:llll.tJ thffcrcncc was e~tttblishcd In u Llirc:t:tion papc:mlkul.lf tu the c.litc-critllt Ht 1.UITCIII nt)\\ rt\ weU .t\ 10 lhe Jn~lf:!lh.!tit.: ficfcJ

ln 1897

l l~tiJ

!I "i~Uiiconduclin~

1-..i~. 6. 1.1Cn l

I lull r1Tc."l"t in P-typr s~mirnnductor

Fig.. 6. 1.\(b t

llaU d'ft-tt iu

"\'-t~ Vt" M"mi·

~.·u udut"lur-

I .c:l u .. \.Vn ..hll!r;J/'·t~rpc ..cmH.ullJUt...hlr ·'' ... lut"llllllh.: 1-tg h. I -~\-'1- S ancc 111 r type 'cmrn)rufuctm C!ll:ugc ,·arru.·r ' " l+H'' h\,k -..t• th,• \lart:(lhlO of hoi,• tlow ... ;,;am,• :t'- dir<!Cl on of cum.·nt den-.it~ lj 1. \\hkh I!- Jltt,du~t!d in t..h~ ,cmiconductor bJr due Ill the! Eh:c.::tril field f £. l No\\ th~ Tmn ..vc:l'\c f\·1 o.~f!,nctk likd nf llu~ c.Jcn,ity (B ) npplietl ~lt,n~ Z-axi' (papcndicutur to lhi! pl:·rn,! ui th~o: p.tpcr 1mt.l in .t t.fu•..:rtion out n( lhc p.tpc:rJ Since: hulc_•, .trc- J1n"'ing under thC' E· licld ( /:., ). so they will move v.:ith n drifl \'duchy Cu"'", • ~u•l1 tllldc.r Llu.~ inOucnL:e ul lrnn..;wrsc M~ficld ( ii.) lhey wJII cxperiCI1CC 3 Lorentz tOre.: as

the

F - t:'t'"-• R. Uul' hl thi~ Lurcnt.L force ht))l'S wm he dl!llCCICtl duwrm·urd Thr ...

C(>.l~J

l..;m:nu fore<.·

c.:nd ltlthi\'C I he llulcl'o cow:ml!o the tronl ~urlacc ut the block us shown an the Fig. (l.l 'tn). So thi.·re IS nn c~ccss ()f hull: m the hom 'urf:i~.:c. )i(l rl ~huw~ C+vc) p.1lnrrt). \\ hc1c a_.. tlh·r~ \\Ill ht: 11 ~ldH.:: u.:m:~ nl tulle autorn.rtlc.tll~ m the bad-" \Uft:h.'C, dut• It) which that ~hows the t-\CI r~)l;tJII>·· Stl an f:-li~·td f £\ J will be

foamed .rlt,"'l n~ C+vc) Uircc1it11l o f )'.. aAi,. Ill\' ct•rrcspondmg voltuge •~ ettlll'd H:JII \Oituge ( V11r). Thi~ £-field <if\) prochu:c' .1 force on thl: cleclron in the upw;.ml dtrecLivn i.e ulong (+"<) Y-ruus u< (ci:,J. which will be cnun1er bal ance by 1he dnwnw,krd L«lrcntt. foro.:. So II\ c!.t(tulrh11um

(6.35)

I he currcn1 Jcn\11\ due hl h'1h: m p·IY~ ''"•mit:t'lnLiuctur front F...qn. (6_11) \\ill he

), =JU. t',Jt I.C

..lt>)

;\c.:On.l mg lu thL' Fij!. tlll(,ll lhC' 1/a/li·o/111!-:t' \ -'11,.lft'\'l'fiiJU•d llt'IYH'\ lilt from rmd hm:4 wrjan'\ r1 rJ,,. H'minuulu1 tnt ..,Jah t)f \I. idth (u) io;,

Where the f:u:uufRm,•/\ u1l/i'd 1llr• ll11ll t'~t'fficie nt {nr 11 ·1rp1' \'l'nm ·nmllu·tor. I Iilii CtH,'I hCitr:nt \'olll ,ahu h.: \Ht11L'.II Ill UOlllhC.r form h) .:onside:rlng Ihe H'IIJI curn!lll Om\ fll lhrrul!h ,, '\t.:ntinmUm·wr har FiJ;t 6 .11(11) \lfllm:~ncv~ lJ) mnl WJLILh fw • I t' u l

Su 1111:11

olll.."·l

t..: UIICill

\t\

=. U

dt•n,u~ ).' An~.,

•~·(lt,rJ,-1/Iwl

f-=.J,

i.e.

NO\\

t/1

I : t 'uucm

h~ "'llh~utuhn~

lht ,,,ht,· nf .I in

lh~

FAIIt (6

"~H

\ uri uH, 11>.-.1

=/8

ror Rup• we

"'It C~ tiot

{H)'JX ... ~rnu;nndU("tn~

/lull co-eflirit•m

/{111•

\'uptl

c&. ll)

nntt 111111 Vultag '' ~imllarlr

ror

ll·t~pc

\('11\U.:nnducUJr ;!\ "ih(m•n Ill lhc

Will h.: Jlong. 4 \~)) ., .... : Nail \lrJftage

6 1)(h). Hall \UIIotl=C:

, lnr '' ~Hll' wnn"'c >ndu~IOt

11, : -

L '' -

H11, / H, l d

flail CIJ·c:fficii'nl

k,,,. =

1::, V11,.1w V11~d lim·= - - - =-- - - =- - R J,

R /fwd

I B,

C(>.J31

eq,,., 6 ..JH ~tnd (,.43) I he Olua....u•..;n\Cnl of c urrent Ul. the mta~nuutk tlr H.tll \ uh u~~ f\ 'H). ror .an) M· nux tll!nsily (8: ) glvt~ I he :<oJ~Il ul lht" chargt.• c.amt'r 1.c. wht.·lh.:r 11 1<-.. p·lYfk! nrn ·l)J)I.; u.; well as !.he hole d~n~uy 1/H or ckt:cron Cul ..:~m ~~l ...o be l"'.akubtcd ln CaS<! Of 'C"nltl.:'ondui.'I\Jf Ihe r~ v.dl b\! SUint! ntod l riC~ttiou Jn th¢ dnll \ t.'IIH..-Il) (t141 ) o l lh~ chur,ge c..1rr1cr under .6· f1cld. ~mcc thC)' ore not fr4..'"e ch[lrge c~mcr :t) 11 wft.\ :lssumcJ. Sa) the nl<Kfificd ex pre::.:.. JOn for I loll co·eOicJcm Will he

Now from lhc i"'IHJ ... 1~11

Hur ~ ~!f/h !1/pd

and H11, =

31!/8 1 1/,,..)

<1• .•1.11

l111ll an~:lt·: t--·r,>m Fag, l(,. 11otl irl:. dear that lt11! net £-Held in the S(mkt.lntluctor E, .JnU £y. lllt.' .mglc ( 6) bctwc~n the r\!~ultant £ ftciJ I'£)

I) H1c veL' tor :-;um of

wich

( +\'C) x--~1,

;, ~nuwn J> 11 :.11 Uflj;)C. s~ fn> lll Fig. (6.13u) W< ~,;c c

:wmlnnultu'ltll \

l.-n (:)=-C,If,-:; fl

~.'

I :21

ro ..t'lJ

Jlf'r..,

Ntm cum::nt Jcn,n\· lrom Eqn. (fl. l2) for wtypc nuucnat J,-.;- a,J ,; prpf 1-., :-.JH\\ hy l'Omhunnt; the ahovc I.."<IU'IImn ft ) l" ;,· with cyn f(l-4~). wt: !!Cl 1.1n

n a,, /J: f-)=---=- a,,= p 1, IJ

,,..

,,,.

lip•· • Rnr •1trlar or llul' •llr; a,.Ru,

l.l

lh -171

11w.. }1 111 • ''nnw GtU:c.l a.\ Hal1 mobtiH) tor fJ-t)'pc 't!'nu.:tmdu..:tm !\uw when lhc -.crmconductor doped w1th triv:tl~m a" w.:ll ,, ... penl~\Otlcm unpurH) "1mu~ of ~o..hflcrcnt percentage then both the type'' o' ''ell ..... rH) pc ''til he prc'lt.."nl 111 1tn: ~mll""unUuc lor mutcnal uml 1t w1ll he m:arl ~ 'iJIIIC i.l' uHnn,u.·

m:&tl'fi>tl In

lholl "-"•'~~

llall <.:V·Cffit.:ttlll Will be

£,

311 1

Rn= - - : 1~8.

Ce~mpa.n,uo

,,j the

fill~ - nJI ;

l.'(pJI,.+11Ji 01 1.:

allmc cquatio n (f,.48) \\ith l::qm (b-lO.

t1~l

A. h l.!. h.4'l)

;;;hm\' 1111.11 llnll c,,.ctfi~o.·lcnt t Ru) und Hall vohngc tVut arc 'mnll f"nr nt:11r 101nnsk m.ttcriod .t-"- .ihU\t: m ~,.,llup;~ t i'on tu Ihi! material whi,·h 1~ high I~ Jo(ll.·'.l ,l, C:\lnn!l>ic ITI...Ih!n.t.J

P roblems Related Conductivity, Current Dcm-ity, Hall ll:ffcct, For Metal and Semicon ductor:' · An dcctrun Inn l.'.lthnde r::l)' tube foll11> thruugb :1 Jllllenlmt Jtflcl\!llt.'-.o nl hKMI ~ ul t ' II thr cJI).;tmn mitially 'tatted fmrn re.o.t. what i~ 11-. hn.tl \·t h~uy"!

/2•1'

' "'

r \ - - miJ: or v = '" -

10 •• ,, - \ ~ > I 9.6 1 xl0

.!.. hn\1 the /;·h..:IJ

I()(XI

= I ~K X Ill

h.'<.~uirt\1 hJ tM.abii,IJ llliUrrenl d-:n:~tt) I,Vm ,,, {tJp~· t tlhlll.'

" ho"~ I..""QnJm•t 'at~

a: S.k X

L' :

10~ mhttfcrn

S.S~ IO'

=0.1724x 10

V/on

J.. J-!ind tit~ llllll'flllUJc ur the E.fic:Jtl intcm .ity in •• !toUmple ufSii\Cf" h.I\ mr lff h.l7

M Uf mht.Vmtllnd t/1,. • 0.0056 mltv.s), il (Ill) dtlfl \'Ch~ll} '" I mnll-.c._ lb, ~~~ ~uncttt dcno.tl} •~ J0 1 Alm: (cl tJn.• '>..ttnple '"a. culx' 3 mm em .a ~H.k•. c:.urymtt G

l'Jt."tl current ul ~tt ..tmp (d) -.ample'' cuhe ·'nun on .t o;u.lr. h;n In)! mV bc!tYo cen ~"?PP''~ite f3CC.'i.

Stllmirm l:t) 1-rom l-.A"In'. Ch ll, b II ) we g<:t

J 1 : al::' = - p,.JI,. E = - I'' ul wlwre ''J: I mmfo,ec. = I x IW1 rn/~ec Stl from llh<•\·e t'iiU.nion we: gtl u£: - p,. p,£

p ..t tl1 U '\

I.e

1. =

, ••..J

IC• 17 .: HfMJ>I)'i()) ~H•

f-ltdJ

1 Jtl X W .-\ lm

.::

U I1Xt1 \ 'lm

z ldrr::

J,"" Ill =-hl7·~ IU'xC

Ch)

hd1t

F..

'" hh h-fidd 11·1

n:, =-II 1621

lll'ltJ tEl

,,,

ltla- 0 l4-l Wm

'C>

\'Jd n tt "' 1u 'n IH u 166 \'lm "'· An itJI.IHhiiiUIII ..:••1thu:htt \\ tlh \."1111dUdl \ II} t.~2 .... I07 tnhWnl . ... ll)l") It IVIl!! h.h dr,ul••r Ctf,.,., ~..t"-ll'"'" ''llh '"·''n~h·r o ;oc tn~.:h. II th••re ''at) t \'Oiflli!'' (,f I.::!\ ll(ll1hcd ht-1\h~Cil ht.' end, lhc ~JikUJ:Ih.• l:tllhC CUI"f\"111 tlc11:..1ly tht hJI:tl CU!rt'r\1

:!Hd ((')

pl'\\it'f tfl~.;,tp.111Hfl

\'nluwm Lt·n~th Ill

tot~() II

R111.hu-.. (r) .-:- ll J

111~.:h

UkiU-.. 11 "~ )--'

=- H J • ~ ~

o..

'I(

IU ~-:- li)J :otll m

Ill : = I.U It-1 X Ill

111

\.$2 101 .-.12 ~ .. -lo..; SO s. I."'10J X IU Aim

Ltl rurrrm tl\!n,il\ f_f. I.:: C1l ~:. rJ\'1/ :

th) Tot:al (.'tllr~ntl/,·1 1!! Ji • \ .... I "H~ 1 til'"" 1 14 :v (I.UIC\;.; In ·•· v: -Ht ~ t\UlJI (c) l'fmer cJ ' '"'P~•on 11'1: I· \ = IKN .. I~.:: 5~ S6 ¥.all 5. ,-\ n~ ,,( JI•I\('C lk h nuu lun 1 I 11110 \\i~l~:. unJ U.Smm lllll.~ h.:t~ om l"leclm.:.tl IC~~Wll\.:\: nJ ( ~(J 1IUU '~1\\ {,11 "fWI i'J'"'l~pt: Hllpllril) lOOI.\."fllr'J(MU. b~ MCJc!kt:IJJI~ tn murit) ~.:.t.rncr n>flc.:mntttnu ~ 1hl \\'lnu punum oi the t."'n.ductn•tt) '' dul· tu hole.; and d c:,·twrl,'' (itn·n th,tl tJ 1

.;.__'\

lll''',,n' u -~~~·•m'l1t,1J,..:tJl 1Jm~f,,

.\'p/ifiHH, lotllt"k ~o.••n~..:hll.thurl ..- / 1

l~h w here p i<: lhc

t.c. lor t:qn

rt-<h-lt VII~'

il_

\',,

o~n..J

Oi' =- /'o'.,eJJ,,

IO ~· :: IOH tHbt,fm

Hhm/m

th.~~t

~1:11\llll) 1,.'\Uh;('IU"IUil'R I.e llt\fl: Ct}Ol.:ntr.lth\n a #J. n~ )( IU11'1m' th2..,)

~hn~m•v

,·tm·t:t•ntrntlflf1::"

•

t::.h,IU"l' .,

=- tl"IN,. =

12X x IH 1

l'omun .:.1 nunnr«v ,,mt.Ju~,.t,,.,,, <T., =- ''"JJ.,-=- O.U l'>x 101~ x 1.0 '< IU ,v )(' tl : UCH IX m111lltn ·' · II~ ..0 I I k! ptUf)l'fHun n I ll!lluUlll\

I.C.

a,, a.

= II MI/tltll l ~ =~H I ~

1,,,,,•. clc•lt<lll ~.._

. l

N,,,.~ '' ll~Jl

a,, a.

\C)

SemicunducwrJ

123

6 . C:•lcul:tle the curr~o·tu P' L'i.loced in~~ smull ( ic pl.th! Hf :m.!a I ern: ani.! of llud.Jtr"""' 0.3 mm. \l.hi!n . t p.d of 2V ' ' OJ>phcd :acros,. the facc'i Given the cunccntrauun 111 uf (rt::c el«:non i\ 2 x l(l /m'\ t: ,,) ancl rnubthl) of dec1mn o:tnd hnlc 1U\' tt.. ::;: 0 1{1 iUUJ Jlr ;- 0 17 f/1!/\' \ ('urrent I : J '.<A:: a/:. X A

I. :: \ 'M .tnd a;

when: 1

fl 1((Jit

+ Jl,.t

_a.dti,+JI •.-. \ '.!'; \

•I !x

101''x l.f1'<

10 111 (0,17 0,_1

CU(\)X2X 10

-I

I = I llOh Arnp.

1 7. Tilt resistt\'tl)' o S1 to: e:d x ltl' ulnn·m :1t 30CVK Ct~kultuc the imriMi1.· 4'iiJTicr den'''> Oi\en tlnll Jt11 = 0.1--1 .•nd Pr = UUS m:IV.S ."inlutum

'::: PdP~ .._lirl- flJx IU1 x I ft.-.;

,,, -= I lll"i

10 111 ,..U.I'J

111 1./m'

tl. A rnht~m~c: hcM..:-cn Ul'' f'lhtk hu:c ul o~ I 111111 ..:ul•~o· ol ,, scnutundu~:htr 1.. t 'i ulun. A Uotll ltciJ ul 0.6 \ 'lm •k' l~ltlpl'~l \\hen a (.;Um:nl 120 n\A 1..'> c-arrie~ lx!'t\~C~tt uppus-ih: l'occ~ untl 0.05 \\him~ M-flcld tnductiun j-. npplle\1 pe:rpct)dic,llorl) U' 11 CaJcul,ltC Jl.•fl "''It·'~~ f l.•llt:~""~·cfll~t~m I lull m•'hthty, Hall :mgh.·.mu.l Jcu\lt, 111 ch:1~~ L'nmc-r h~ :1:-'>-unun~ •<~ IIJ.' l;.• 1:amcr .:mKcn1.Jtinn

Solultmt

-= _f_ = HA

1 IO

I~;.. IU "

(:.1 1-w•u f:-1.l t(JJ71 lhdl \oh:,j!.:

-=- tl6t1 "

/U Ill

\'1~~o = F 1t.J= on x 10 '\ott

Vu"'d U.bX IU'xl0 tll)bum&J (h..IHIII.Ill1.lH~fl= Rur -;~; "'0 Q.

1..

(\.'l f--tom Eq. (~.~?• H.1ll mull1ltty = p 11,, • (\1}

From Eq. (6J6) H~tll

oo- =to ____,, m h· )(' . '

a,.R111 a (HXm m 31VS.

~ ll = lan -1(flur IJ_.) -=- O.t9 "

Jll!!IC

fcl From Eq. Cb 'ft) O(,·n ...it\' ul t:han·e ;.:amrr •

•

s- I'-=

~ R IIJ•(t

: C.2S x

10~1fm'

9. Wh,tl i-. 'um.·..·m·atllut ,.,( thth•' 1n Si "h1~h •~ h.t, 1111; a \Ju1wr ~o:\m.:c-ntrot•<m I I >< J07'1m, .Ulcl &.Ol'J(IJIIO: (\U\I.!Cnlr!III\UI I -1 X I o•~,,.l C'onddcr C(JI\\!c!tttr:ll1U11 HI clc.;tmn = flunl)' cnru:entr.Uu)n l-u1t.l aho lhc t;llJO of ele<:lfon \:on.;;emr.u1un 10

the hole conccnJr:uion Safmum

II ::: J\,1 :o

I.J

n.-=- lA )(

•

lfl~ 1

w'''

tJ; !!.:.._ = !!!_-= l AX t0 11 /m 1 n

N;t

IH. r\ 'f'<I.'Hn\.'n ''' ,:.l' ll1h.'('ndu<:lt'f hilS .:•l lnll C<h'fl 1'1 J 66 ~ IU Jm 1·· and r.: ...1...th·ll) 1

t'l g~)l X Ill '~lhiiHII. tn.Jihlll dfccl C...'P' ·' M·0UI( dcu .. il) HI u; wh/m~ ,.._ 11'-l.'it Hml I he lt.tll .mgle, mnhihty .1mf d en"IY uf c h;tl'};t" c-.1mef ~' '"''un1111e !.In)! I~ ~.: h .lf~('

r·''

c.1mcr .. ooccnu:tiiOil

,,, ciMr~~ c.\tmcr =- t• e

Dl.•n~o~ty

fhJ lluU muhtln) =-JJ 111, = oR111':

,,,,.,.

-;;-- ~ Ru~·

.,,

171 x I,,. /m ..,

=- O.fl.ll nr/V.S

rl·tl l.lll A n!'ll'; O:;;~nn 1U.t11, IJ.:) ;- I 17 ll . (;~ h:l-, :1 .tontt ~~ fk' nnpurity oddetl to 'he cxtc:nlll"lf Ctllt' 111• om rcr l(r" ( lt" otlLllll Wh.u cll\!t:l th.ll.'' lhl .. hnvc (Ill the t:onductl\ IIY uf I he mnh:n;~t oil '"U .... whcu }t,. =- .~t)(IIU .,;m:/u... p,, = l'i()IJ cm·Vu••. 1\o. ul .\h\Jll ol Gd\'\. =- I 1~ " ..... ~ olll\l

n , .: lo .~5 x 111'''/l(<:)~

l nnm,lr ('(lndu~U\IIY = Cfu1 = t11~JI,. + }t11 l I

fJ,..

;-.!"

IOH

1,(_,

W 1 ''!5~H)()); 0.0:!31/U ~111

"m' 1 dunt•t a.hull fl\.'1 tO~:~ Gc .11uru dHJ)pt'J Sul.tmhll I.:Hit;.,•nlf.IIUJ!l ~ N 1 ~

~ ··" x,10 '' ICi

e J.J2 '<. JU 1 ~"v

<;,, C\lrin,il u'mhtc-ti,,ity = cr~, • N,1 t'J'" 1c

= I \1

(11

I1U~o'

c.h'IIIIIJ:!

IH1.. X J.b X

Jl) l<.t X \ 1K)t)

L"OIIdUCih'll) IOtrC:lt.:Cd

h) lO

= 0.'26()/H \"Ill

lllllC.~.,

12. \ \ 'lui ,., lht• rn,l"lah•lll) Llf an d('«:lnm hem~ 111cnn.all~ prmnu1nl w tht: l B m JL.uuond !J\ rc.om tcmpcnuorc 27"(' Thco hand )t:tp cnc:rl!\. j., ~.(, C\ m dumuuul ,,,~ A. : UH ' Ill '' JI"K.

Soluu•'" Fm111 FtJn F!F.,

I •

({l ~l.

' •.T. -;rn; 1:.•

Nil\\

Jlmb.lhilil)' tlf dl!ctrun lu hem C.B... Fc•uul;a~'hl l I! t., l

£,

= 5.6 t"V i.e. 1:.1 ::

1~·, = 2.1'\ rV :md KT = L'\S x Ill )1(27 + 27\) J A I :: 4 1-1

10-J: 1 ,/ : 2.h x IWl' rV

,-t:. tpll >> 1

I.e. FCE,) • I ttl'!)( 10_.1 - t h s ''ery ne,ghg_•ble tor :sn in~ulntnr lilc t.la:uunnl.l, "" cooduclicm.

c.liumoml can m•t 1:.tk~ part iu

Scwucmulur·mn· 125 IJ. A bm of n•TYJ>C Cit of ~11.c 10 mm ~<" I uun x I nun" mnurntd in a M·lidd 0.~ 1 11Je tl.;ctrnn dcn.:;IT)' Ill Ihe bolr I\. 7 X 1Ct!1/m' II I m \ ... otpphc\1 ih.;m-.-.thc Inn~ e!IU.l ul lhe bJr. then dclcrminc The current lhmut:.h the b.1r, the H.sll ul·dL .mt.l H:)ll vohugc beTW(CI1 Boll clc-:trodc~ rl~C'd .-.~ro-.... lhc '.llurl ...:mJ u llh~: b.u. v. hrn p .. = O.JIJ m:l\',:o..

Solwum c.1l 1\y u\in~ cttu:uion t6 ll .md b l.!l (\ancnl -: I = J < <\ :: rrl "' o\ ~

= nrp, f.; x

I'll

·..:".:...::'~:..'_'.:.x:..:.. l ;:b_~...::•o:-''.,'.,'..:"<''-''.:.'....:'.::u_x;;_:l;;U_' I= -7

tn . to •

I::. 4 _\7

'Amp.

.< lt1

JH-'" m 1 /;· I CJ 111111 \'Ohl.l~<" • \'N., • t

c . V 11... e

R. 11.. Ill ld

~ CJ X H!-J X ..1 ,\7 >t In

\'H, ; 7 7"t

(>. 15

" n :!IICl ' X

lit

\'lh

p-11 Junction without Applied Field

S~tl llcontfucaor junctions arc commonly rl,rtn\!J l'k!twc..:•t d I' Jnd ,, -tyrl! tn!lh!tiul . J..' )l.J:tt.l \\1llll Fi~ 6. 1Jtu) But the JUili,;liOn.~ 1..Jnnc11 be n•uJc by pht,mg l\\·0 picc.:c' of ,c.nicnnduLIHlft m:ucrinl.\ ~ide b}' sid~:. ht!c:tu,.: ,,.r(;,cc fil111 :Hld olhcr

·nlC

IITcgulnriHi!S would produre mnJOrchSCOniiOUIUe~ 10 the Cr).-.1JI structure. r~ 11 junctiun can be mndc hy difru.;:inJ.! thl! tf~)nm •mpuritic' uuo one ,icfc und Llc.:~ptor 1mpun1ies into thl! other s1dc ol .t \ Ingle crvstal ol n ~c miC{mduclOr. '-'llhcr h) ullt'))•itlg f'Jf!'k."'\:'S..,OI' .g_fO\\ IIl!! oJ ..:l:~.,l•ll \\ llh Jn llllf)tJIII) Jcn:o.ll"/ Which '"'a tuncuon of distnncc Stu:h a s)·sh:m ~'I r-u runrllun ~~ "'hm\ n en ~'-~!! · 0 l4(b) JU,I fJCrCr fHJ jUilCIIOO I~ fOI'IllCc.l clcClft! ll' \Hl IJ ·l'oldl.' (I( lh~ JUIH; ll011 WOUld

h.t\'c an average energy higher than tho'c on }t4 'itd~: ru~ <iih<m•n •n Ftg. 6.14(:1) . ... mcc fermi le'vcl b,.,. fortr·Sidc IS h1ghcr than Fcuru level 1.1 r for p ·Sidc. So there Would be trttnSfl'f Of ene-rgy anc.J dCC!f()JlS Wtll nnv. fr()JU IJ· .;;ldC 10 fi•Side. unul the Fcnm level in the two srdc~ doc~ hne up O\ !ihown 111 F1~ . 6. 1.J(c) Elec:tron~

difru.' (. from n h) I' side which lc;nc ( +VC)I} kuu..;cd a1om on n-siJe

nnd proouce (- vd)ly torused mom on p-<td~ near f>-11 JUne IiM dut m dtfluston •~ shuwn IR Fig. 6. 14(h). Similarly when huh:~<' \.hiTu'-C fHHH fJ In 11 "'d\! 1heu lhC) leave t-ve)ly oonos.:d atom on p sode nnd prf>duce 1+ve Hy oon><ed tmmobtlc n~om uo n Mde ncar p•u JUnctiol. 77IO.H" 1muxnl uttmu nn· mmwbrlt· .n11n· tlrry urr hound in tl1~ cl)·stal/am ct' clo:;e to the JNJ )wJctun~. thot.fare thr•te art! rery fe\\ mobilr rlwrgt! rnrrirrf nw1ilaf11f' near fNJ pmrt;nfl So thi f n·ginn it rr/rrred rn tlrr chnrgl! detplt!titm rc~thm or spncl' charJ:l' rcgi'tm Dur tn rlu \ \fH11.'l' r·lmf'8r rr~um ttl tltl' mmtcclime ndg!JimurlromJ ,,f tht jm"·tirm. tl rt'.'ttnring Jon:(' t,(*. u r Ollltlct f)tJit!llliul dt]}ert:m't' is :tt!l "I'· w/udr i.l( c'tJIJnJ barr{er pntelllial (Vn). The phy~ic-JI d1stancc frnm one side of lhc barrit<r1o 1hc olhcr side. 1.c .. the width of rhe depletion fC!I IOO h rdcrnx.t tel 11, Ihi! witltll dfllu· lmrri~r The di rr~rcncc Hf

lit

12(1 E11uim•t•ru1g Pin-,,;,.,, I'

c II

R..'D Neumtl ·o "o

C' ll

UWILICfll

btlli::

47 •

c.:

•.s! vc..·

-o

• 8 ~ 0 0 0 ,., ,., )

'0 "0

~Q·-'

·il~ i ~

'0 "0

.thWU "-tlh "Q

r,..

I' 088

"$'**Cit.' : li> ;

_. Sp.-..'" \h.11 ~.: • Ncuu••l llll'rtloo~

\ll

, -alcJII ..ll••rn '1'1 11:

IIIII

Hr,t. fd4(u)

I' ('

~h = ' \ II

II I·

1 -•-

\ II

'"*'-." ~.h;ary:~ re~pl)n ~1~- ~.1~(<1

...if!. fl I-I

tu) 1-: nci'R' ll·,eJ.; fur "'ep:;1rn1e p :md n sid~: (bt ..-unn::ttitln uf ..p:tt't' dmq..<t• nr d~ph•hun n·~hm in p-11 juucliou; (l"i Eu tq!,' lt,el dlu~l"anl ••fp• 11 jutk'tiun und.·r u1••:u circui1 rondilit>n wilh lmrritr ,,.,h:utiul •·urf"l!' l:r. \,

"'''X"' of tltr Pottntifll R11rri"r (Tin= E',., -£'"" t'V1J :ts ~how" in Fi~. 6. 1-Jtc)_()ul' h1lh•' putcnual t'I,Lrri~t. no furt.h~r .:lcctron dtO'usion is swss1bh.' l rorn n ln u.: '"ell ·b nu hole Utffu..,u)u I' pm.,thle fmm Jl It) u-~tdc F'onn.lll\11' ol fhlh'nll.tl b.•rna ,;,m h~ t•xplt~inctJ tihH'!: ckurly wilh cne:~) lc\l'1 dia~rarn 11s h•lltl\\ '· In 1-'t~ (l IJCc) the cncat) level diut;rutn ror llpcn CKT ,,., jun~;;llon h1" he!~ II ..,flown. A' 'urm a.' P'"" juut:tiou is formed 1h~ P'l!rmi lt!l't!llu.•cmne\ cuiP\tallt tltrOUf:IHIIll /h{! !.'flt!dm('/1 Ul t•quifibrium, 1\ ftcrth:1l OU turth~l l'lt.!l..'lfOU ,111d lit til' diflll,ll11l , .., po.... tblc B\11 Ill tHype regton Fcnnt level u~,. J \\'Ill h.: ~ru..~ Ill ..:uuflld f)IJh: niHd ~l weco 1\\ u ~u.lcl'. of tht: bru·r•~• •~ rch:rn:d H• a'

com)ul'ltun

h.tllll t•tlt.!t: "am~

,,_,,dl•..

han,J l!dl!c £, ... \\ht.:rca..o;. in (Hype ( Ef,) \\ill be close w \,tk•ncc S<)(" 0 ~n<J

IIf f' •I)IJ)C fCl:\i l)ll in,,.,, Jllll&.:linn L-:tlllhll he .tithe

il•\cl"' u"' 11Cl"C ultH.YJ'~ r.:gwn ns it wos before tn Ftl;.. 6. 1-HaJ I knl'\! thl'

~nt:t,S) k\d thu~r.ut' of 11-u JUilLiit'ln will ht! chtJngcd 1h ~lhJ\\11 111 r. ~. 6 . 14(.:), where a ,},(t m t'Ut'fl:\' lt•l't'l £~ will t~PP'-'ar Wi barner fJOlL' trlial cut I J:\ . u hit It I ,\

(•qual to

St•mu·multwlnn

127

Tbi' l'J1&:rl!y J!~1p En= c\'a r~ 0.5 .:.V ot mom tCmJ>crorurc) l'epr\~~cnb thr pott:'nli.tl c ncrg) of the e lectron ill the fl"" junclion. R!!causl! nr 1hi' contact p11t~n1iul ditlt!rcru...:~ \lit :l!,;ro~~ ~t junctu.m .•m electron til Lhe boltom nl C R. in lht: p ty~· r\!g111n '' h~tving hi_ghc.r f'Oirnual c rll'll!) EH = cl', than the cle\:tron Jt th~ buuom of(' B. uf rHypc re~ron . rlris pntttufialllllrric•r rc:,is t.s tltt! flo w of r l t!<'lrmt.\ frmtr u top .\ ill~. So 111 an upcn circuited t"'"n jun~;lin u. i c . \!.llhtiUt c\lcmul

voiHIJ!C. net

6,J(,

no,, of curr~nt i~ urn.

Se miconduct or .lunclion wilh Applied Volt age

Whcu ;tn c\h,mwl \Uir:tgc i' ;tpplu.•d w :11N1 jun~.:tu' n it i\ fuund thntlhC \ull.;a~~ f.:U~fl1 ~h;Jr.h.:Ccl'l . . uc is '"m-hn~ou (Fi.(!. 6. 15-e). It pc.nnu~ the Col"") lhm uf curr~nl In llllt' du~\;tlttn ''-h\"tC:oJ... Llu: llow ul current in uppo,lli! lhfcdum ,.., ~'llltl(~l lh1' I'TC1Ill.:.rl~· '' u'cd tn con,ider lltt'f'~l1 jmrc:tim1 tl\ \t'mu·multwlm tlimh- mulu\ ,.., ll{irt

6.HJ.I

t•un Hird llius: Ttc

tmpun~tnl

cffecb due{() lurwurd b1a., 'IIUnlhm

.111.'

:•.... rollcm• .. ·

(I) II JHYJlC" nuu~ri .11 is m.u.lc f\'t ollld il type \'~ h) .lfl C\h.~fllltl \ tJ!I.t•'t' \U('Iph lllfh,:lmn. th('H tt h ~~ lie-d htrward biH.S(d (foi}!. 6.15u). In tht' 'ttlt,!lhlll d11.: resbmncc.· of th~ c..IL"\ ic~ '' ref) low .am.l currcnl lluw.. c;.t\11~ Cht; (t 15~. J t:!) In tfln\ ..ud baa~ corduc1inn the ~... idrh of 1he ~pace cl t arg~ repiun .... til Jcc.·r,~ ......\." hl!. (f'l 15:•• du~ 111 Ih..: rcpub.itm t'lf lu.Jit:..; 01nd clcctrnlh lrnm •.. ,1nU \ e rnlaruy f\1 lhC l"t:lltCr) mw~1rds lhC JH1 JUnCttOn. t.\l In lht"' prC<o;cncc nl r,·rwnrd " ''" \'(ll!agc ' '·deerron.. rmm II h', "ILl.:·""' 11l0\"ill!! tn Ihe dm.:chun nr the UJ)phl·d C:<tcm al fidd. SCl banicl' JXtiC"ntiUJ \11 \\Ill be.- Jt:c.hu:nl ht \ 1 - f \ 11 - \ ') ;unit h.: c.· U tlml VB t)l the t•~ .. Jd.: fm\ '". h1."1.·n 1ll'•1 lnwt:rl."l.l h) .u-. .unnum \. c cumo \'O il' (Fig_ (, 16:t). Tht' Ft:t fill lc\ d ltl tla· I' IY[k." m.th'n.•l I I \\ hh.-h Cll10~ itl ..... \\ Jlh Fcmli '"' l'l rnr ll-typc mrtll'n.alll· .l..

o.,

Ill H g h l ~tt.) ... lln\1 ul~ou l•n\et.:J h~· \ 'clcCtn.lll \'Uh \\ t I . IL.. .:uunt~r- p~l I 111 lh\.'

, 1yp..· nmu.·rr:rll/: 1,,p I h~~o lot\ nUl' d1t.• ~:onditlt'n ol \·a~y lleow t•f .:Jc~·tttl•l lr•,m tHYJ)..: IH tH~ pc :-.~de 'F•!!· h. I ;"i~·t (-1) In lht: lnrwun.l hiu,L"d ct,nduclinn. mojonl) charge c:.rrncr... 1 L. l~tl}:.: nmnlx-t 11f dc'"lnm' will cllffu~o,~ from U · 10 p·~id..: J'- ''-l'll a' l.•rgc numhcr 111 holc..~o, wall dll lu ..c from f' tu 11 \ldl! The t..l~fictcncy ur ~ l cctr fln., 10 tr-,nlt: \\ dlllo,• CPinJ'''n\i.IIL'd h~ Chl' t:h.'<.'trtln 'IIJ'pl)' from(-\'~) ll.'nmnol HI the 1:\ICnlill 't•Ur\.·~.

Sinulurl) In lhc !H) ill: lliJII:nal ,, n~" hole I~ crcmcd ond cump~"''''c' hor lhc '""' nl hulc..... \\ h..:n .111 ct~:'-=lnm ,., \.:Uming out h) hn:.aldng the cm-o~knl t"lom.l in ;, cry~lltl olnd crw:r' 1hc (+H~} h.'lllltnnl of1hc cAtcnutl ~uurcc Tim .. in1h~ l urw:ml bi1" (.nmhunn thac i' tt .;,1ntmunu' current now in the drcwt lf fc.•rn.1r..t htih \'Oh!lgc ( l ') inl:l"t!a ..c\. tnnt'l! diJTu-.,iun uccu r' sn mnrc l.."ttn cnl f I~" ill P·" " thruugh thl' JUlll!liun 0:1!! 6 .1.!k). (!it Th~: flo " uf minnrit) t'olftf''l.. remain .. unint1ucm'Ctl Ouc h• fnn\uul ht.t"t. which ,!!I'C' ri.)c tl' a VCI) 'mall LUrrcnt in the d irection oprositc lo thai ul the cur~nl clue 10

forward

bi~

128

Engmerriny Physics

If 1Hype mahmul 1s made posahvc ,~.r.c. p-.IYJh! m:ncn:tl. the 1uncuun ~~ ,;ud w be rcvase hi~L"icd (Fig. 6 15b) und liS rt">l~lancc I!\ very luA:h whach :tllow:::t very fee ble c uiTI!m. ~l111ost zl!ro. lhmugh 1hc junction tfsg . 6 . 1~d

o·

o• <I

•

o·

"..

<I <I

"cr

.. :.. "

o· o·

o•

.. .,.. •

•"

- ltR-

.. .. 0

• "

-/IN

: 1r

• .. .:a,, 1 - • " ••

,I ~------------4"~--------kC'\eN: Oms

,,.,

Fi,::. 6.15

I,U.-1 !

'" Cn) p·n juncliun under ror"' :trd bil•Si (b) p--n junc:lion under re,•tr~ hi:.s; (e} Current ''oltuge (/· \') relnlion In p·ll junedon under forward and ~\ t'rSt

hi:L'"

2. When rcvcr;c htn.> •~ applicLI. &he free clcr·tmn' in 1hc tt•rcgion :md hull!' 1n ahe p-rt•g1on :m: •• ur:u.tcd ;1\\,t) lrt•m the j unctjon und1.•r ;1c11on of lht> revef\c \'OIIa~c V c,luc 11, whrch I hi! \\1dth () f 1hc c.h:plclmn rcgwn mcrc:•'c" (Fig. 6.1~hJ. l. Due In the prr:-,.ct~ cc ul r~\\,'r...C \'Oll3gc \' th.: j)Otcnllal bJ.rric:r \ln \\Ill 1ncn:a.M!

lo \ '1

= \111 + \

lF1!! 0 l tih) Bcc:m•"c m the rc\·c.r"\c b1ascd condllmu

...____

'·•

" <' R

, , 1

______ j _

F.,,.

('\' ForwarU t•1;:as

c,.

v.u

ll•

.-\·u- •., '"

,, I

..,

--- . - --

H.c\ «W Nn;. -----~-·--------- F.t..

VII

)

Fig. 6. 16

Ent'lt\' lt'\'t'l dtus:rum ror JHI junction under rorward bias \'OhUii!C ( V). wllh d ecrel..;cd bHrrier putcntl:d ent•rg~., (EJt)• (£11 : ,. Vr::: t'(V, - VII: (hJ [Ut'r~,, lcvtl di;a~r.un rur p-11 j uncdOn under r~WI'M' hla.\ vOIIaj.:e I\ .•• with lncn:uscd hnr rier pQit:Olial c:m•rJt>· ([;,) .(£~ ~ ,.\IT = r(Vn + \ 'il

(U)

\\hen \!lcctmns are m1wing fi'Om 1t

I' tcgion thC)' nr..: n\C)\ inp. '" :1 dtrc,.::hun

di~ccu on nf electric field So harrie r 11otcntml '' ill rncn:a:~ot.' hy an amoulll \'vult (Fij?. C.. l 6h). I ncrcascd h~uTic r poh!othtl rc~i!l.t :-; tlu.: flU\\ ul di.XII on,

t•pJl(,.,ilc to the

.tnd hole:-;

.tnn~~ the JIHU:t ton \uluch l'\tabh,he._ a IH£h rl'!ot!ol<~nc-.~ Th(• llll'rC:ts(•d hmTh.'r pOicnualmakcs u dtffkult for the m~t jum~ can 1cts Lo tlrl lu~ .h:m!'l' the junc-tinn. But thi:-; h.~nit.'r pt:J!~lllittl ftu O:\Cf'!ol' hm'\ \:lmJilu'n help~ t il~: mmorlly ~arn~" tn cmJto~ing the tuncthm ~•nd gl\c~ n'e lO " ,m,•ll l'urrcut Thi' cumnt ~ ~ n.·~· small m comp:m4ion to lt!I'W>Hd bi.t~ ..::un'l!nl hct·~t U'\c th\.' number ot muwrlty '-'UrTh.'~ 1~ \\.'f)' ~mull Sinn· the f:!.t.'lll'fnlii.IO ul nunonty

(,lrnt.'r~ tl~J>Ct1tls tin h!lllJ'tCr'illurt: only.""" lh~ 1.Uth~tU

Ouw '"fue hl min~mty c.amcr;.

r ..·mJHI' \illllc, u doc~ rh'l Jcpcnd on rc\'t.:r!'ic hj,,, \Oihtf!C ,., tim. .:urrcnt '' LoiiiCJ rc\'CO:c xmur.ttton cuncnl (I.,) (fit;:. 6. I .5c). It i' \l'f) ... m.lll. tlf lh.: ordrr '-,I nanu .tmpcrc!'o for ~ 1 hcon =tnd l)t tht! order l'f m h.:ro .tmpcr.:., tur gcrm;mnun diode.

5_ Thtt fl'n111lc \•tll for p·type mntcr1al (£11,) '" ahtt wi't~tl \\' 1 I II\ cuurucrpan, l.i , 111 tH~pc Uli!ICri" l hy ~Ul .m1uunt \'·d~l"lrun \ulb. whkh \\ill H!"'l 'l' Uw t·onduwn of 11t)w of dcctron fmm n 10 p "'d~: U·tg. O.l6h) l·mn1 I hi.* .tPow th,.lUS!-JClll Itt!'- ~.~~~:ar lh:.tl Ulh.h.·r lht.: t\n·,l.tn.l Vi.to. ,jltJ.IIiun pha... !I luw r.;~t ... f:tncl" :lrld :tHt.m'' ~.·urrcnl In nm~. aero'' lhC IUU(Iion hut II\ h!\~r~ hmscd situntion 11 hns h•!!h jun..:ti,m rc:..t,tal\1:'~ "hieh will ntH .slhw.

" IUOl'Uill ll

Ihe ~o:urn.•lll hl Ouw tl~fll '!lo Lhc juncllon. Ihi~ bc:h.tnuur 1."1 '1m1l.tr to So , •. II JIUWiiml

(>.

1\ ojft'Jt

c·alletl (1\

,\'t'llltC'OIUhtc'lr!( dlt'dt"

\':t\' 1111111 ~ltvd..:.

trlrtt~t· ,\Tutholn

V-1 Characteristics of JI-ll .l uncliun/SI'mkunducw r-

l.)iodc

!'he \·.om•uwn c urrcn1 :1!:tu n$l voll:t~c acm..-. p " JUnction 1s called Lhc \l'lllk·onductcu ~i1<lc ch:u:tctcri,lk. 111c \'·I "h;tr~tt IL'r1\tic.s :1cros-... p~n JIIOCIiun "'r l•lt"-\.lrd h1a' o.nd r<'ver'e hi!L~ are n<: o;;hm,n. m thl· c tr..;1111 ..:omiL"Ciron

"'"'"'fl

und {bt. rcs),e<."U\'cl~ o\l ,~,,, tiJlpltcd voltage 1hc;: J'lQICnl l~ll barn~r \\Ill 11111 .llhm ~n) current hl nnw ih--rH" 1ht: tuncUOI\. A;;. forward bm," V 1\ npplu:d .u.·n''' 1hc 11-11 Jum:lhln_ curr\.'nt uKrcoLl')l., cxponcnJi:llly with 'ol t~1 gt: cxccpl l'or d 'nwlln.:gn111111 the nc1ghh\1U1huud <ll till· ungm c;1lh.'d "Cmm or I "'1'.clrold \1(1/lilgt" C\' .J (0 2 fm Gc. ;mJ <\6 V for ~~~ h..:hm whtch the current is very :ot~null . otlmosl uro. bec:Ju~ th,· :tppll ~d vnllaJ!C '' h:-4\, lho•n lhc b;u·na pulcnlm1 ullhc: JUU>hi!U Wh~;nlh(" :·tpplictl HtiHI!!C:: n.~ccth the harnu po1c-nual 1.t:., he yond the lUtm \-Oltllt:!C'. cum:nt n-..,;.., 't•ry

u h\!:-. (•.1

(Jf

r:1p1dl) \\ Hh apphcd vollagc. The penni frmn "h~rr 1ht• (Uncnl j, .;JIIrtl '"''(' 'oiUif:C'.

;-\fiCI

'Pll:l!-!c. h~I \'IU,\; u ~ mall

~n~e

I II(!CJ\C\ rap1dly

vohaJ.!l!. t.:utrcm im:r~:"c' ~tfntt"')l.t liru:.Lrl: with

con!-.HLnt re!-.i~mncc

R1 1H~ h 17q

l'hc r.lll[!C t,f forw:u'd t•urrcnt twa wh1d1 a \Cnltcondm:mr Ueudc I\ upcmtctl '' man) order'\ or mngmtudc larger th:m the re,•cr~e stt.tur:11ion currcn1. c,;n an

turw:ml .tnd rt•\cr...t: t.:h:ll;~t:tt'll\11~~ lu~cllh.'f \\I! 11\o!c\1 3 A .. xht •wn in Fig. ft 17ill 1hc CUrtl'l11 \COtl~: lm fun\.lftl hm.. h nnllt;unp!-. ...• IIC.I\m.~> for rc_vcno.c bia;; i11' mk-mall\ 1)~.1\1 .1 p:mit:ul.u reverse vnll:•gc c.nlled IHtul.thJwn ,·ullttJ;I' ::t l:argc revef!'i.C CUITcnl flo' v", t..hi.s r..:giun u( 1he

urtlcr Itt al"pl.l) lhe

t.hff('l\.'01 L"Urr~nl ~cnlc

reverse duaructeristies i.; culled brenkdown region

In lhl' fonv.trd bi:a.. condiliOII lhc I':Hi,, or vnh.a~c lO ~u rrr.::m is called \UIU\' u il,:.. v. illdv :1' t1pct:al ivn puul« u11 the chawc1c1 i'li\.·~.

r~~i~lan..:l! (r,). 11 \ fh)

/)wuuuit· O 'H\Ioll/('c' 1,1 ~

81'/6/ "hrn

In fur'''tlrl.l Pia ... C•11U,h lu:m Ihe r~'t.'lprn\.'UI t1llhc ~lt~J)I.! ollho: JUnction <.'har.tetcri...hc-... 1\ called dyn:unu: r,•..,i\t;nl~,;c (r,t) II j, nul \.-on,l,ull . rnlht:r tl dc(1\!nd~ nn lhc ~lp..:roJUon pui111 .tml J~~r..:Jl"tc~ a' l ul\\'iiBI \ult.&~l: m~r~il'l\;:,. For lorwunJ Oi:h ~.:.·ondili11n, r .uul , .t LTIIlh."' •lUI 10 he \111.111. nf 1h..: nnJc1 nl h.'.\I. ohm... Out m fl"\i."('c bm' nmdilhln '.I.:Ui\.: rc..,,q,m..:c '' \'cry haAh. of 1hc or,lcr nl

h'"''

mcgll uhm~. DynumJc rc.!ss~tancr.:: '' mu.:h high~r.

6.18

Semkunductor [)iode as Rectifier

J\lmo:-.1 fill t'ICCIIOOH: t.:nlllpllll\!llh m.~..·,ID (' )>0\\l'l :-.upply fkc;11ficr i!!> ._ d!.:\'lt.';.• wilh CliR\Cn:-. A.l 1\1 o.c .md alltm' llu· cur'u.:nl ((I now onl) illt~I)C t..lirc'-=1100

'J11U:-. a device \\Inch o ltcr-. :'1 Jn" fl!'l'tnocc 10 the cut-rem to nne dtrCC:TI ~•n l>tn high rc"i"t~nc\" 111 Ill\.' orro:o:nc thre~.·ufln '' cnlltod a rt!('tili.:r. The rcruiymg d~\'I~C b usunll) a ..cnuconduclm dwdc"' \ acuum duxlc. SitlC'C M!llliC(tndu..:lur dioJc or p-u junctwn ho-. inlinuc rc:"t'i.sncc tn rc' cnoc hin' condi1ion hm a .Mn:1ll ilnl.l cc.m-.I;I!H rc'''lillnl.'l~ H: m thl" tnf\\,lrJ hii:L' ..:ondllion. :-on it t:an be used ns :t ree l ifh:r h (::ui h..· u~iJ ~" h;tll ";n ~ , 1r 1ull w;l\ ~,.• rtcli licr a"- follow~.

6.18.1 Hall' \\';ln J< cctifh~r Th.: .:unncclinn fnr lmlf \\aH: ln·llll.:f '" 'hCl\\11 m Pi_g (d X( OJ• and inpm, ou1pu1 wn\t" funn.:.. .arc 'hown 10 hg_ fl. I X(l'l The inpUI A.( t'>l'Uillll'Ctcd h.1 lhc pnlll.ll). on~.: t:nd o l ~ccombry S I!- conncltcd In {J ..,Hil~ ur fHI JU!h'linn tttlh'l \.'IJrll' ~ •'IHI\.'.;,'11.:4.1 W iHoJdt.• uf fl 11 ftlllCIItm lhH1Ug_h 11 luJd rc:-.t:-.1unc.:~· R1 hll P''""'"'-' ho1lt .. ~"'· 1..- t'l lh'"· \ C tnpu1111~ !')O:'!IIh c \\,r.l n. Lh~n (Ht junctmn '' 111 the fnr\\.:mJ hia,nt ~.:nnduio n wbil'h ~tllow' the .:uncnl h1 flow through 1ht• JliOi.'tinn But f'nr n.:gaci\c half cydc nf thl' A.C inpulp j.., ucgathc w.r.1 u. th:11 the jum.:tiun will he in Ih.: n:vcr:-.-..· hi:t)l.ct-1 cnmJition whsch will not ulluw lht: -:urren1 ''' tiC'w thr<\U)!Il th"~ junction n~ well n.s Lhruu~h H1 He nce dindc:: dnc.:. unt ~undue! .111d thch' i:.. 1m currenl tn the ~~~~~uil. Thth tlu:n.• h Oli."Urn:nt /throuJ!h Rt for the po,Hi\ ... half cydc n fini>UI A C. \•o ltal!C" V; \\hich ~ 1\'C:-. nutpul voha:;c V11 -= I N1 lhu fur lll:t!:tl i\'C hulf t.:ycle o l v. 1 h ~ rt! t:-. 1111 t.· urrctH thruugh RL ~\) t.tutpUt \'UhJg~o: ..~cro~~ Rt i~ lCro. \V:J\'c form for input \'ult.tt;;L' ( V,) and uutpul \Uit"~'-· ~ \. 11 J ;trl•gi\'cn 111 Fig ft. JS(c). A.; the drcuil ght!' uotdircclit)llfll currcrtl onl) fur po\iii\'C half cy~,.·lc ~n ill~ c::tl1~:d twtr W:t\'i.' reel iller. Oulput c~m be ""'~"hcn..:d whh the help ~,)r filter circuit. h. I S.Z

F'ull \Vuvt: Rcdi_fil·r Full \\'tl\'c rcctif'icr con.;;l,;; r ~o. awo di,,dc!<o. Tht• circuil cl i :.~ram is shc, ,~· n In Pi~ . 6. 18{b). and irpul and tHnpul \V3\I(' forms arc shown in F'tg. 6. 1M(c).

Full wave circu1t comprise!' two lm lr ~v:wc circui1s. They are co nnectt.~d a~ shown in Fi,g. 6.JSrbl. The two ('nd~ oft hi! ~ccondnry S 1 nnd Sl ohhe trnnsfotmcr

•

,., ,.

'•

1 ,. r

,, )

"'"

+ ·

-,)

[)t-

u \\H..

,.L 'I

IJ,

\IUtpUJ

f\\

(<)

FiJ,!. t,.Jg Stntlconductor diode as half wa,•e r«tirtr. full ,, on t output \\Q~t (orru ror l>olb

~ctifi~r

uud

arc connected to the /J..~idcs o l two ~c:tn i condu c t or ctiodc w herc3s ccnm.: point C of ahe secon<.k1ry i~ connc(·tcd to the tr-s•des of two diode through lo~ld R1 '" such :o way chac conduclion ukcs plo~o chrough one diode D 1during one holf cycle <>f

EugiJu•t·rmx Pln·.\i( .\'

Il t

'he A.C. powcrcydc \\hl!n S1 1~ p,tsili\ 1! .Htd lhruo!!-h !he othcr dwtlc D~ l.lurint! llu; ~ccund half cycle of u.c pm\Cf 'UJ'pl). when S.! "p<t'-lti\'C Th¢ <.lucCIJ•In of ~.·um;nt now in l\\0 htllj"' j, ·" l<o htl\\ l l in Fig h IR(h,. ftnlli ,, hk h ll i~ dC~I f lh;u 1t1.: Uircttltln ul L:UIIcnt lltm fhli1U!!h load R 1 1-. , ;IIIW tnr hull! the lchll'\ Thu,, CllflCUI (0 thl" Jttad '" lhl! 'Urn Ol lht>SC I\\ U t:Urf1.'nt'

uulput \'(llt:t!!C ~ll.m~' I<Md A', IS V11 ~ I X Ui ;h th~ <:ircuu tJI'\'' urudth.'CIJOnal .:ur r\!nt l or hmh the ~)'dC!t. M) u ~,.'ot llcd full

Wl.l\'1! rectifier. Outpl.lt IMill Iull \\ ,,\c f\'Litfi.,•r 1s it' ,fu 1\\ H 111 F1g. (•. Ok. whh. h c jm ~ :trnooth.:ncd with the help uf !titer t:lll.!llll

6. 1\1

Flo'\ uf <.:u rrcnt Across 11-N .Junc tion: The Rcclilit1r E(Jua tion

lhc currcm nm, aan" /)-11 JUiu,:uon tlu.mtll.tl l ' d} c:m he dll<oCUl<o'Cc.l ul thl' fnllo'"'IU~ "''ay. Ftg. 0 ft.Jl:•• 'htlW\ 1hc t•nc: rl_!~ h;uu.l' nl u JI-lt JUncruln unch:r lun" ;ut,l h1as ( +- VJ t.'•tiU.h iiU11, when I he .:l h:CII \'1! h;nTI.:r Jl4 H~ntmt hc1ght rs ( V1 .: \ If- VJ, h nb,<J ~ h()WS th~ (Urrcnt nnw h) Ih.: lll:IJtmty .lnd mmonty e:h.1rg\! \:om ICJ a..:n:~ thl' JUil\'llou 111 (' B. ;tntl VB "llh.·n.· urc lht• lnllnwing lour tlO~S i hlh11c' ul c.:urn.:nl 11m\ ~•C•l''-' rlu- JUIIt'ltun ;111J .nrr"''' !!''''' 1h.,.. dm:cuon oJ Ihe purucu lar L UITl':IH

now.

I. ) 1 : L' Ut'relll d t•tt,il\ due.• II' fl >i<l" in C.B.

ntl\\

J ?. =current J l'O'ill) due w ''"" , ,de m C.B

\II nUjllrrl\' ttf

ch:1r_g~

t.:<tml!r (II) fru m

II t ~ 1

muwut) ch.trgl!' c:~rner {1\J fl'm n fJ w

J 1' o c urr..:nl \ll.'n'lt~ thr.: tu II'm t•l llUJHfll ~ ~o.·hur{!C carr1cr tp) fromp

" "u~ '" v.u I.

J; = C'urt~l' llh:lhll~ w p , jtJc in V ll /'

L>H~

...:::::::

- J:

1.~,.

!~~1-

du~ h•

n,,,, u l llilllOCII) L' h.Jt~c e.trri\!1 {I>J rwm II

.I= J;/' ,..,

, _-- r

.,. -.._

1\'iJ:. 6.19ta) t>irrrrtnl currrnl Oo\\"' ucms.~ ror\\nrd hiu:oo r. ~ jum:-linn

...

J, ' -J ,..i~.

6. 19tbt

J. \ ' l'h:.tnu:le-ri~lics fur\\ltni and n;\'t:Oicd

untJcr rorwurd bias(+ \') net \.' UITL'Ill nnw lhmugh fl It JUilCliOil tmW II't/\ C .B. oas well u~ in V.B. ~·ccording hJ the Fig. 6.19(a ) will be

$()

IIi

•I

·' J, I '•

fi)l/tt

J =(JI-J,l+!JI'- Jjl=(JI +11')-!li+J,) wh~r~ t J 1

IHlle... 4

+ J ,· ) b the !!oUrn uf the mujorit)

~.:urrcnl LIL·n,i tl~~

(f>.4'll

ft.)r c ll!clron unc.f

J! ) h. the 'tun of the nunnnt} ..:urrem c.ten,ute' lnr rlct.•tnm tultl hok

=J,, NO\\' 0\ lhc barricl I)Oic llll jtl llll.fCa-.c .. UlrfCI\I nn\\ lhrt•ugh p-11 junclion J.zt,;t t:a,.C\. Su lhc maJOril)' CUO'Cnl t.lcthil) it~ c fot the ll\1\\ ul ch:uron ~u:ro.!. ... the JUnction towunb, right CJII be! LL·riucn m.tthl'mutiL:.tll~ :t«

(6.50)

Simil.trly majOrity c um· at dCn.'t tly 10 v

n. fur the now uf hole :Jcro..;s lht: junC.IiOn (6.5 1J

Now mlhc open t:Hl.~ua t. 1.c.. when no c~1crn.al hta\ \oil age'' gi\•cn. the n ( \ 1 = IH and ( V 1 = V8 ) ;md there wtll not be ;Uly l:Urrt•m now nrmss the,,_,, juneunn

fmLun.h. tigtu cnhct m (' 8 or 111 V. IJ So tmm the :~bovt! cqn. (0.49) we- get I=!JI - J , l=cJj 1

Clr

.. uni brl)

C:!t'

<;u in geuer;ll "Ju.:n

l'lif t A.I

J: = II

rl~t iAT

rlltW;ard

c, =I:. t:'~Nt A•1

u u.·

tna.S volt,lg_C'

\.tlue rtl the corl.SHtnh C1 :md ('! iu the

J:l =0

(

it"'''"ll\f

(6 521 (f> 'l.l)

~ \ 'I I' g .l\ 1tn

C(JII"'..

then hy 'Ub"'tituting the t 650ittrHJ (h ~ I J. w.: get (6.5~ )

Sunilarly I

.• • n

\, lo.T

Thu110 the furwarJ b ras eurr..:nt I rom b-in. f(,..-19) olCros....;, lht.! p·n 1unction towurd:;

flj!hl Will be

Nnw l'n =

Bnm~r poLCII!iiLI. and

l'r= l l'n 111= Reduced barncr fl<llcll!ialundcr

H>N·;u\J bia~ tV). ''hich g_r,·c~ f\'"- Vr-= VI So Ihe nho\'C ClJU.tliJn no ,.. lJCl'tllllC"> ((1 )(>)

'"" here .I -: = ( J i + J :. J :; Kevcn)e ..;:mrr.tiHlll cuncnt

( 65 7)

C a,;;e-1 f."'o rward-Rins

Now in the /01'\t 'll l'd lm1S, 3J)pliC'd V(Jil,t!t;.' ( \fJ HICI CU.S~ t+vc)/y, Ml t!\'/A-r >> J, Ml we can ncglccllhe In<~ ICI'Tll in lhe eqn. (6.5(>). So Lhc eqn. (6.5(>) becomes under forward billS condition as rollows:

II> 58!

Sua-; the lorword bt.L' vohugc t r1 mcrcn.....:~. currcnr denstly (J) wwardc; right ,,,JJ llll..r~d't" ,, Juch 1~ th..: n."Ch ficr C(illdlhm 16 O l111 forwitnl h i1h mul l \ ' ~..ltdt .tLict 1\ltc.; f\tr lnrwurd hm~ i~ " ' shtt\\ n in the: Fi!! 6 19ih}

.u•.m:-.' I he JHI tunclmn

Cn.se- 1 Rl'\'\'rs\·· Hi<'~ Fur tht: u'lc't.u.. bw, .tJlJllt~d \~tll.tg~:

en increase:-. (

\Clh. ~,, r_· ..-\'1\l << I Su

Ettn fh.5()) l'~Coll ll''

1;;- h th5')J the n,:\l' I :O.~ ,,tiUr,ttion LUrTclll Juc tO l'lliiiHrlt }' Carm.·r only n\}\\lllt luwarJ\ kit .tt..:W" ,,..,, !U11CIIull. tl j~~, Vl'fY nc£ligihk .1~ :-.hti\\n in thl' I \' char:tCil'fl:o-lll H,g b. I'Jth f l nr r..:n~n.l! bHLS. \\hil'h

PROBLEM REl.,\

n::o REC IU'lER EQ UATION

II JtHiliiiiO oll 111U K ,, 0 ! nncnt .amp" hl!n •' l:ugc fC\'('r~ "'·" (llfn:fll 11u\\ nhl"TT l't'I"\\,Lrtl hi:.' 111 ( I I \Hh h "'~"""'"·I fit'H'U th;tl 1i ; I 1X • Ill Jr t; 11 Sulutiun 1 Rl'\t.'~'"i! -..~.uur..llllll l."uncnl a: 0.:! X W .amp Fur·.\.IJll t•t;l~ \UII~II l oh.\I.'~IIUIII;: h) lhc b.(n. f(;.~b)

I . {'urrcnt llnw UIJI

,, ••rrli~·.J

llfld

u.:: ",,

J .- l:,tc J~•J!" 111 .. •

~l)Jli., I U".uur•::9 J9nucru-:tmp

6.20 Transi.,tor ,\ Jlnlt'l mn trun ..t ..lnr ., l,.'~ln:-lllh.h:od

hy phu.·ing 'wo p ·n jum.·th•n '"'' ''h~··'n nr {:Crm:UHIII1\ ll)"'·'l t'1 .1d tu h..~ ~ Jl~;~l ts. C1thcr tJ 1H)'pc :.llkon '" !'!o.lnd\\·1d1l- Jan hci\\C('Il I\\U 1..1)1.'"£' nl (H) pc "11111.,)0, I c .. cnllcd ('•tf•(l tmn:-.l,tiiT II( .J I -1~ r·· 'it icon h pi.L~cd In hcl\' c~·n I \\ (I rHypc materials whidt h called n•p•n lrtlll'l'h'f ·1he 10\C'IllhlO ,lt th~ lhln!'!l,lnr 4.."nmpl.:rcly t'h;mgt.'d th.: indu ..1ria1 dec,;Lmnl...-, ficM il-!:tuu"'~ 11 1(0 , .... r-y hunrl~. d t.:up t'lm he (.tpcr:uctl :u very low \'(lflugc ti,,~,., not r..-tjtlln: oUl) ht:o_.t.:r ,,r hlilmt:nl. ha-. ;t lung life. ~hnl: "- pr'"'r l"'ll' In llJ-t1 lht• tr..tn''"'"'r "''' Ul\'cntcJ m Hcll l.thnr.twry hy John Bard~tcr. \\'other Br:uraiu ouuJ Willmm Sh,._kk) Figure.. 6 ~0 (tt) ..utd r h 1 r~o'JU\!"L'nl II~JHt .lnd p·n~p 1r:m"i"""· three p:u ' ' , 11 .a lr..t.OM\Wr c.tllcU cunner. h.l!-1! .uuJ t:oll«to r. J\l lhc Hr11L' .,1 m ;mul m:tunng. .1 lrim"-I"H,r 1hc ''""~ r~gtun '"' m:uJc h~lu l ~

doped wh«<•.< omlucr" hco\11) doi>Cd •nd the collector i~ doped m btt"«n tht: t:mlltt:l .tnd ha:-.~. lu ~,rJc r h• t.f i~'>'iJ.Mic mor~ hc.1t. ~ olkc1111 rcgmn '' m.hk· lnr~er th;:ut th~ l'I1Uih!f h!~IUI\ Tit..:fl.! .m! l\\iU fJ·II JUill'ltnn:-. m tht! tr.m..;i,lnr. One i ~ bl·twccn l'mith.•r anliiM,c. cnhcr '' hl·twt.'l!lll'ttlh:c.:tul ~uul b~"l'. Bcc:tU.,e ofthi' tran .. h.tor j., c:lllcd " h i-Jli.J);u·

junction tr:tn$'t~tor" or nrr. 1111.:" ttrrow on the emitter leull ~hows the dlrt:C.'llon t.ll oonvc ntion;ol cmiuor ourrooll llo" t /1 ). Figures 6.21(a) and 6.21(b) >ho " th< 'Ymbuh of both tt·p·n unJ JHl p trunsbton.. In n p-u lm~Dtur the"-"'"' '"' 4

S<'lfrinmdtntan

137

It I

/ 1-:.m.ll'-'f

' ( ._,lk~ 1nr

U:.~

I hi

t~\H\\ itrJ.

"'-:(all'!'

h~.·rc

c:kclron.!> nrc the mnJont) -..: hougc:

~1amcr

hut hlr p~n~p

tr•tn'l'h'r th ..• hnh: ... ln: majoril)' t·h~tr!!~ c:arri~r. lht:n:f,lt~ th~o• ;1rrm1. h.;1" thrcl.'Uon It'"" ~Ut1\'c111Cnl Lo a......ume ~.·un~.·nt

both type!:'<.

'ht. anJ "'t1lh:c;ur c:urrcnt (/()wall

th~: ~millet uutt!l11

'"''-'n..l

tl,-1.

h.1~

llt'""''..: \\IH.'II th1.• ..·un.·nt flu,,., tnh' lhi.' tr;m<ta,H•r Jnd ncgauvc when the curr~m h ~umln!! uut ol th..: tr.1n''"hH 1 he ") ltthtih \'u•· Vr 11 oand \ 11 1 clc.not~ emaiiL't-l:la'l'' ,~,.nlll.!i..lur h."\! ••ml n 'lll'~:tur l'm1ttl'l \ ••lt.1p,L'. n:,pecu 'd) .

(IIJ

Fix. 6.l I

lht

l b u~•l

nututiun r1)r

uptr and pn11 lnm:.i~ofur.

6.21 Work ing Principle of Transis tor (Under C.R.

Conl1~uralion) For ncth·r opr!mlhut tJ,(Ifmtsiuor thl! f'lllill~r-ha.u~ ''nlltJN" V1.11 ;.~ mmlt

f,,, ..,,d

' ro /wgr v,.lf iJ mmlt· rt' \ 't'r.\'(' Ju'tU , Th~ magnirut.J... tJI l orw urd hm-. l 'tlr \~ I J be m ade 'mall i n compolriSOil ll) the m:tgnituLI~ fl"\Cn-.1.!

/Jul\ w h rN'It\ n JI/t•t l'lf·hm f'

bith HIJtdl!C l'n~ Sm \:c JHr-plr.llh!"'lur' .1r~ u~cd llhlr\! thouln-r- fl tronsbturJt ~l.'au:-.c tlh,' ) u1..: the \\ urk m,g pnm.:iph! PI flwfl·f l tr.ms a~tur J'i.l!Xpl;uncd .., uh c ncrg~ ll·\rlln h g-. 6 ~~1.1J :md h-~~ Chi Smulor{\, 1/w 11 I' 'llrt lll '1 \lOT l'tm " ' " ' bt•,. ' f'l"uwd" ith tlu• lwlp uf J t.~-\ () ! Jlu 1 mul (),23 (h} h'h ''" ' 11rl n tt l't'UI mul ••tdlft~,- ,.,,Juruwt un: tilt< rt' l't' " 't' otJIW\4 ' " m co~,icr 111 111tlnurauur:.

tlu rmr ot a f'·lf -1' tnm.o,r,tw /'

II I

htll)

'•

.\,>-----1 ,_ '" "

l II

T RO:''I."t~ '-lil\liW11~ln ~urren l

\lf hnk\ \ .8

1 '~-., I U\t' hnlt< ft.w. !k;tO"-\ Jh.llllll

Hote Om~ b; \hfi \W UO

l bl

ttig. 6.22 Wurking ,,mcedure for hole c-urrrnl Onw in V.U. for pn11 lrnns1stor a nd t ntr-ey 1('\('l "i...;t: ib r.:~plunuliun

Since lht.' tr.snl\btn- ha-. lwt) j unctu-m ' l)f tmiucr and cnllet.:t(lr wtth ho&:-t:. "" cherc arc fnur pns-~ihk \\:ly:> of hia,ing of Lhosc two junctinn'i. . Condit inn

Emmc1

CoUec&or

Re~ton nl

Junt:ucm

Juuc1jou

Opct:tltun

EH.

fOrA'nf\1 f'llltM'd

U,,:ven;~

F.F

hn·,\:uJ

Fucwarll Rc\'E:rsc f'!'orwurd

" R.R.

Kt.'\CI"\1..:

Rc\l.""'c

1 .

R I'

hmsed

Salut:tlmn

nu nil In\ Cited

1\C-ll\'l'

lt._Jt_,

'• y~.}--;:

(.'H\.

11 1

c fJ.

LIN:IIi.lfltlov.

k)' tlllru~on

~J Forwll.u.l ~\\ F £

"nftll

c~ c

blil!o

f - - ~- - -- f

~\'('f'<oc! ,:\IUf'llll\,\1'1

CtHrem uf dt'ctro•l~

L ____ Pcmult',e1

vu th)

Fig. 6.2.\ (a). (bl WorkillJ! prot"edure for ~ l ectron current now in C.B. for npu fraus:b.tor und tnc.rf:~' Jt ,'el '' i.se its explanation

I JO

l:.itRittt'('tm.~

J'h\'Mr,,

O ut ur dw~ rnur hia\lng npcr.llion:,.. aftin· oprnoimt uf ,,,. Jrtm.H~Wr iJ' '"'' IJJI}\IIIIIJHmtmt ll'ltt'IP nnm;•r.Jmst')Wicthm ;\ u/w,,·,fnnl'lltrl hill \I'll mu/ ct,Jh•(·Jnr

lmw lltlll'ttnn 11 nltwn r"''fl'.'tt• Jnns(•tl . f·tgur~

6.!1fu t "'""''\.., ,.,.,, lnt.n"ii:stnr und\!'r uch' ~ (')peraHIJn \\.hen thl! ...\\'1lrh\·,

S1 o.~nll S:- ;arc upcn h111h JHI JUnchuns ul'l.' unlm.t\\:tl Su uu f.:Unl'lll \\tllllm\ ~tt\\ .t\ 'L"PII ·''" S 1 .uul ~.an· un. cmhh:'r b:t-...C will bt: rurwarJ hia' .mJ L'tlllt'~.:h•r h;"l! wtll he tl•\·t.·r-...t.• h•~•" Smn· cmhh!t h:l5.t.'! i!- (or\\JIJ b1$ ,,. UtJt·ll*fl trdu,i ... tur hvl~.·.... the m:tt~lnt) ~o:Jrri~r. wtll t.htfuse from p ton, 1 i..' fwm ..:uHth.'l IL• l"':h\! ~t•H'11t u!t~ 11w c.·1mllll L·urr\'ut/r. l 'uJI.:t..~or -h•N: JUIII.. tttm I'\ nuck rcwf:'oc bi~t"d '' hiLh ••[lc,..... ''"'~ lu~h r.:"i'tilllt.:c r~..r tJtL' lll;tj~,,il~ L.lrril!l .. but it j, hclpl'ul fo r min\•rit) ..:.a.rrtl'....... In ,,...,.~pll~tn-.i ... tur uw.:L" hPIL'" Ln'"' the ~:tll t th."l Jllllt.:H(H) thus become ntin•.ml) t.:~u·nL'f"- m Ilk h:..._,.

Thus. ,lu~ hi th~ t..Hffu$ion o l hole$ under rorwnnl hta .. ~o·on~itit'n tr.)m tu h;,,,.. lht.: nunonl) cmricr th::nsit)' has. hct•n incr..~o.~,cd in lh\! h;\\1! rcgtou Sut~.·c 1ilc l,,N. n•t;ion h. \t::r} lightly dop.:LI . ..,,, .1 \l'f~ ...m~tll JX:f'-."~o'HI"t!'' ut lh.tlL'" ;.&u.: h.'~.·, unbtul·tl '' lth C'lccLron.s. and rcm..munp lwk ... •re uo" .Ltlrtldl•d h\ l ilt..' ,,,\ L'r"e hta" ( l', rd \ l)ltttgc a_,. :. ~ni nnrily c:u ril!r. mwa1'tl\ ~~~ I h•t'tlu '''t!inn ~UIJ ~,.nu .. tllutc.; collcchu'.:urrent 1r {Fig. 6 .22'a). In th~_· h .• , ... ll.!~inn I'm p--11-11 lntn'i~ tm :l small pt"tn' lthi~t· ,;t thttust·d hole, f\!l!t tm

,~111111~·•

lhllll lnuth,·r ht b.•,.: n:crunhuit: \\tlh ~lcclmn,. St•lhen: , .. a ""''n"~~ ''' dl'l.'lnlll' In thl· h,,,t" h.:!!ulll 11! IJ·n·p tr:m'i'tor. T his lt>hnn.tg~ nt .:In IWth \\ 1ll l'lt' flllt'd•IIJ' h~ the 'Upf' l ~ t1l cll•t."'lnllo;. fm tn (-\'CI polarit)l oft"nllttt'r i:M.'ol' I\", NJ \'Uit;H.!~ n11 \ '-'nmul,utt.:.; thl! ba'~ current 111 .

rhl· .....u\!l:Mr L'IJrfCilt /( I.. :llW:.t}'~ IC$\

ha ..\· .:11rrcn1

than Clllllh:l

(UITC:I11 ,,

lly

.m .Hihllllll

1 !1. ll'\~'1 "-' ht;t'l .I~H"' lh~ ~,.lf,•~tOr jUilCth•ll lhll!

.1111~1 I' lhl' 11\lll•'rtll~"'

com •~·r l~t•k

tnuu h.l\C' r~~um 111 p·11 ~p Lrn~J.O.lPr. A.' 111 h;! n .!~!•II nun~llll) 1.:~1rn~.:r lh)lc ''ill dif(u\~ from b:L\C tn collector t.:nn,tuul~ l.'nlk... wr cuH~ III I h) ' ''" wh~n \! lntiiL'r ' ' C'l pl!n cm:-uu. then /1 0. in 1h" ...nuatinn h.N: :1ntl ~tlltCctur

\\tl l l1\: U~l fl'

i.l

I'C\CI1oC ln:t' diOtiC. l h Cil the: C'OIIe<.:H..lr I.'UITCIII (, \\til

be C(J U~IIIO

IC;.tf..••g~ c:um.:OI Hr n,':\·cr~t: ~atul'flhOil ~um::.l\1 lrRO• due tn nt)\\ ,ol 11llll01 11\' t.'Mfl~r fwm cnlkcuw 10 h.,...e lum means 1hc cum.·nt bct,,ccn the cnlknCir nml Oa'ot' when 1:1111111.:r j, tljX'l.

lhc cu11c111 g:uu o,1, 111 CB

conli~umLion

c:m be "nttcn '"

a,,; ''"'· lc = \\ hl!ll"

a,.,

!6.1>11

l r;:. 0. II :. It ,,

fhl.'lt:tore m ~cn~ml. t:qu.uiun tn 62l &:.Ill ht: \\tin.:n ... ,

Under \'lllllh:r~ba-c Jorward hi:l.fi cc)nt.litic'>n in fi--Jt~f> trtmSi:,U>r. h(')II!S will diffu.M:

Semrnmtlucmrs

14 1

fro111 emitter If' h:ase re:;ion. So tlh.:rc i~ a shona,gc or ho le~ ill the cmincr n:gion. New IH1le ~ c:m be cr~ated ;md t•umpcn~:u~: fnr lhc hJ'-' of holt>:, m eminer region when clectronl'l arc cmn111g out by hn:aking lhc c:ov:tlcnt l,ond m the cry~t~tl :md

cota 1hc +\'e tcnnilml ol cmincr bMc voll:t!J.C sourc~. Thu:. m the ~•ctivc region '' lwn Vnr h lurwllnl b~'' i111tl \ 1c11 j, rc\'t:£'Cc.l bin.... lh'-•rr h" cunlmlll'U' c urrent no\\ 1:1 y IWic\ in,.,., lr':UI\i\1(11' Tht~ J ircctiun ...r huh.· fk~\\ and i t\ cncr~y k\•cl wh..: ..:\pl:umtio n I~ gl\cn In Fig_. 6.22(h) Thu< rrorn 1he t11rec:uun <11\'lmventionnl cu~nt tlnw :s~ shown in Pi~. 6.22t:t) for p-n-p .Ultl Fig. 6 .:?1l.t) fu1 n -11 n 1J an'•'~h11' ;u h l fm tn "'l!-fl t:PII\'t:nliun uf

tmn,io;tnr 11 i.s clear thrt. ft•r JIIIJ>•If :: (+VCJ I c. /8 " ( - ve)

Fnr fl{m-1,. = f-ve• lc./11 ::. I+H'~

I coo" (- ,•c) (+vc) I' e-n= (-,·c)

lc110 ~ f+\'C)

v,."

Vr.~: I \'C)

Fen= (+\c)

6.22 Transistor Charactt>ristics In Fig~ . Cl.22(a) and 6.~,(~1) !JIIJI :uld nrm lf;ttl'i'hll'•. ft''l'lCt•li\'d}. :u'c! l;tHIIl C&:'t~d m t'twmum b<rse (CllJ cunfigur..tllon. tl'llt'lt' htHc i\ rlu: nmumm for inpm and output. In the s~unc w:t) by ma~111~ ('IIHtlt'l ''' collt 1CWr c·rmmum, we ctm g..:t ·ammon rmiurr (CI;!) ('If rommtm .... u,•aor (CC) 0:('nflgur:.luon. rcspccuvcly. ns

' hown tn Pig. 6..24 for J»tJt 1rano;.1s1or Hut m :'II cHnfigurahons-thc cmtHcr ;unction 1~ alwU)'S rorward biuit.·d und collcct()r JUncuun I'\ ulway!l n:\'Cf:\C bmscd in •klll'(f R<>gimt or the: t.r:msiswr. lien:: Wt' willlii-.<:U ...) Ill detail-- only co anti CE configurntion~. which are mo~t l y u11cd tr~r ptachcal purpo~~~~.

·~·

r·c_·__ ~

Fi ~.

J...

6 .24 Thtte Jln J' lrunsi.stur c unntdicm.:": h•l C U m cMJe (h ) C E mode- ld (.;(.; mod"'

The relation bel\~ ecn 'Jrinu' cum:nt~ usu.l ,.,,hu~c' in ;1 transi!\tor c;m he n:pn: ...cnLcrJ hy cun..:. .. \\hid I .m.: lnown a~ ~talic ch~u-:to.:h.:ri'-liL"~ cur,·e,. Tht.• 1wu rn~-•M illlf'\oOI'HHH ~ h.u .h.:tcn,th.' cun·c~ rur uny Ct1Hiif! ur:ttiuu un: the mptu :tnd outj'Wt \ h.mu.:lt:ll'lh.' tilt\ c ... luput ~ hm 111 ll'l';,'fll• ·,,, ,.,,.n tdcllt' tilt· inptu t 111'1''"' n ttll itr1m1 ~'tlltll;:r {.n t1 c:mntmu umpm rollfiJ:t'. flu· mHfWI ,}Ulrm tt•rt.\tu· • un ,., 14'/att· till Oltlf'IU OIIT4'IJI With 0Uif1Ul tnllfiMt" (ur nm,\'IUIII IIIJWI I Wlt'Jil

Comnwn Ba<c lCUI C'onfil(uration ;t /l!tfl llot!l'l't'lt -tit: u.... ,Jh\\\ 11 in Ft~ t(, .t-;.u .tm.llur llJ U• llllll'lhllll' 'hm,•n 1n Fi~. t6.:!5b) Euuu~:t bli.'l' 'ultugc {\ ,u, .111d the outpul '~,,hut;c t \ 1,, .uc CfliHWII~tl hy v~ri:Jhk rc-.!'.:lllr. \uHn..hn!!- tn th..· rulnnt) l'Ufl\'Cnllun tiMI :til I,.'Um~n1 lh:ll flt)Wj;; inttt lhC lr~l\'l'tur j\. lo.tlcn til (1\.' ~t\ th\t' .utd th.at \\hH.:h C\lnlC:>. out tlf th~ tmnsi'itor i11 tJkc.•u a;.,. llL'_l:~lli\'1..'. Sn fllr filii' lftHhi'\hlr !Fig 6 .25.t. (l_~{m. 6 27aJ.I, j.., pt)\th\.;. lr .md IH ~.trt nc~ull\l' I Un\,tfd ht:Jo., \ fl'll' flt''tii\C .md rc\cr\C: bi.t~ l'rR i\ UCJ!.tlhl.' r111 tr.m'i"t••t tltg 6-~~b. 6 2M\ h .!7hJ ulll'urrcnt ilnd \'Ohagc pol.lntH.'" .Jfl' j\1'\l n:\.:r..c 11

(..22 .1

Tit~ L.II"L.UII \.0110\:CII\lll tnt (.'JI mt'\1~ uf

''f'"

tho-:c U'-}!1\'l!'n tnr P"l' trunshtnr. i.l'.. 11 i" nct:-~llivc , If, In .ll'l' p•t)o.iU\l'. \', 11 " nq;:t1t\t' .uul \', n l~ pn:-.iti\t

l"i~. h.l:O

~I .

(Ill\'

( 'irruil t·umH•ctiun fur pnJ' and "fl'i undt:r C' l< \1,N\r

In\'

' "' \ t

Ill

" :a ••

•v,

~..,~...,. ~..._'

II II

.,., ,.

.....___.__.___ IU \'u..d•

'"' F"i~.

6.26

lnJHtt charuclcrl..-lks rur pnp and

II/1N tmn~l'itor

under f'. U, nuu.h.'

St"rttU'tmtlur·tnn

I ..I1

/nJIIII ClwroclltriMi n

input chur:•c•cri..,tic' t•urvcc.. for J)llp t rn n~ istnr ure plotted between I, n.mt V1 H for d1rfL!rcn1 \!Diu.:'- uf v, 1 (Fig. 6.26a). For Vnr 0. tt j$ IU'-t like JUlll..'tion tht.xl~

Th~

~.:hrtnu:lcri ... til'

111 the fof'NIIrtl bia-: dirc~tinn. Th~:rc j, iillt>o cutin or thrt,Jinl~.t \. c•ll.sgl' \' ht-IO\'- "- hiLh the emitter current ~ \'CI) !>mall When \', n I'- O\lt L'iJU.tl tt' zen', 1hcn 1hc l'miW.'r rurrcnt j~ highe r (or a given \•utuc o f t'rH· than the cu~~.· "h~n Fe 11 >:i fl. llCl'au-..c 1m" c,;nllcclol nllt ac.1s the 111innnty ~~rric r mun: f10111 b:.~-.~.·

,uu.l hPlu' hu ..c 1.:o~n .mru~t more holes: lrom the emmcr. FMm th\! :,h.lf>l! ,,f 1uput

c.:h.mu.:h.'fl">t k ' we ;.."ltn c,•kulah: l.lyn;un ic t llfWl r..:'-l:o.l.tnc•· i N1) ul the trun'i~tur a..,

I Itt\ c.l~ numu.: 1nput rl'-si ...tunC\" R1 b ''cry snwll . he I'' cc-u :!0 ,md I U() 11 h~'" .ul"'-' lmt•ar.t\ ... vl:l, mcn::n ..c~ vnluc or H, dt..'CrC-thl"' \\ uh tht: tl(l'Ci.lttn~ pc•tnt. /J•J'UI dmm("ll'ri.,tk n( HJm trmuL~ror will }J,. ,lmtlm to FiR. fJ.1{;(tJi tl \ .~11011'/1 11J ri.t.: II. )OibJ IJJ,f\ both /F.um.J Vt.l:l \l'i/1 bf lft'gtlti\t· Ulld l ttf 1\"'fl bt·

I he CUI'\"C ,, 1\111

flt1'iltO't'.

Output ('harru:tcri\licJ The uutput <.'h.tlul.lcristics for ~nmc JutfJ transistor t:o. sh0\\11 111 l'i~ b.:!7tolJ anti for npn J·a~. u 27(h). llcr: It· ~~ pluucU ug1u n~l Vrn r"r con~1 .u1t ' .1lucs '-'J I 1 fhi;! U i fl~ ll.'lll t n i ('CUl!Ull

roims of OUIPUI ch amcteristic!'. nr~: I. l•rotn th.: U.:scriptl<.m ol the work.ing principk of the tr.•n'•'tvr It ' ' ~11o" n thai It •~ ~llghtl} lt·,, lhM ft ·nw~ is: tn1c in at:ti\'t' tt;.:irm ''h~n crnattcr h~ts..:" tmwnn.i biol' .tntl coUcctc•r b.tsc rc\'CriC b1as This 1\ ~ l sc1 .,...-en from th«: nutpul c hMotl.'l t'll\ lt<.:' ·1 ht."'tliflcn:m:c: 1-.cl \\ ecn I 1 and /(· ru On) p~ount '' th\.' h•.t~ l'Un~tu 111 :!. Th...- 1mtp111 CUI'\'('" n·~ nearly ht1TILOntal hncs pnnfCkJ \ 1 ' ' n:,·\.·rw hJ;" !:w 11 l"k'l"" ..: .. ol'- ;1 c.: un~t:1 n 1 c.:um.:nl soun.:c wlm:h m..:;ul' tit~: lr;m'l,h.lr h;,,·c 'cr) lh~h

I)IHJ'IIII

fC...,I'il:l t)l.l' (Rl)• \\herea~ tlltlUt

dynamu:

fe'\a't.Uu\&:C f }(1) 1\ \c.'JY

\nlodl

"l. Sulltrulilm N,•s.:ion I I' Vnt hecornc' rurwnrd bia~ed. hhh:Jtl ot n!\ l'f"'C hiu..•.cd . colli.!CWr t'tlrT<IH /(' ~hurpl)' cJccrcase~ I() 7CrQ ror ull vnhiC'- "f I, . 1111,.. n·~HIII when cm m~r .tnd cntlccteor (F.F.) both forward binse-d is call~~ 'oturlltion rcci(ln

here I, tfoc, nut Ucpcnd 1m I r· -L When 11 = o. th.:n lr " not 1.ero. and very smoll rt-\''-'f"e JcNIJ CXI!'.l~ I J~a g. 6.27), d ttc to the llllllOrily C:trner n ow. ~. ('m

orr /(;•J,•trm

Th~~

tcgio n hciQW and I() the right

~•nur..111 0n

ilf If ~

curr"m

0 l.'h:U :.I Ch~ l l\ti C\.,

lor" hkh coni ncr un~ collector ;uncuons (R.R.) ore both r<vcr<c bou,cd h callco.l cu1 ufl rcg:&on Dynumk output rc~io.;tancc of the trnnsbtor i~ obt.dn~d from th10: outpul chamclcrisllcs t Fig. 6.27) a~

1u.M I

/,•tnAJ

,---• - :! ~

·-

t\ Ciu e ~£ tOn ~ F.R •

-'·

-l.U

...

~ -\Ill\

/1 .;.1 Utu ~\

- 1.5

S;tlm.alm

n:;:1•1Tt cl fl

lr ..: I \ ru.\

·-···· ..... ············--., IU

...

I( u

··~.·

• I<\'

f'ut nil

.... ,,--=I limA ····~·

fl 'li ll)A,

Ill!

It • U

" _ jI

t•

'""

"R~

•••

.•, ff~.

t..27

Output chara(tcrlsllc:, rnr P"P otlld upu lttUl.slstor

Ufldtt

CB anodt

.,uH.:e Die<< c5VUI so the \'Oiuc of fllllpul r~i"t.:mcc if;: ''~ry IU)!h In CR mudl" lh rurrcru gam <>I (he tr:ml'tswr IS defined a~ aJ.. where

(6.1>1\) I~ rom the oulput chntactcristks we ~J.n S(c ill any point 1,

>If hut the d1ffe.rcnt:c nnd lc i~ \l.!ty ...m:tiJ ..;o (),1, il\ lc'' than hul ' 'CI) ~;. lu!'I<C to tmity W.98). Outtmt dwm.·ur'rtiL' (lfu·p ·n ll'lmu\ltil ;, 'lwwu i11 Pix. 6.27(hJ. smm· 11\ flltf' tnui.Hnrmtly It· mrrl Vcs Hill b~ pusitiw.· tmtf l e nH/ bt' negmil f . b~t wct.!n/1

Semlcomluctnn

145

6.2Z.2 Common Emitter (CF~) Confi~nrati on In ('E configur~ tion l h-: em mer lb the C('llflmon for input nnd OU1pul. Tile. Cl tCIIII ~onncct.ou lor pnp m:an:-~tMor 1~ u$

:.-ho\' n

'·

F•t-:.· 6.28.

.... Fig. tlo.lK

l'irt'l.l h tunntcliun fur pnp uudl'r CE mntlr

'111-: bn'c emitter \"l lhJ~" ~ '1It Jnd cuJI~l lllf cmiuer 't'lh:ag.e ( \ u 1j , l'\.'1f.UI.IIcd h~ 1c'i'1or' At:curJII\}!. to pnl.tnl)' t.:lll1\ c.'lllh1U m C£ mode fl•r fJ/11' lr~Uil»I\IHr In .tnt.l/1 i~ ~ -\'C) :md t, (,H,·cl. V11F.Ir.. t- \'c t and Vcr i" tal~<t ( - ... ~;) TIH•.,r or~· JIHt OfiJHMilt" jnr 11/111 lrti/I\1 .\IOr . lnp m C llllrarruistic,\

Input chant(.'lC'(IStu: / 8 IS rloucd ugntn~il " HI lOr ~ivcn value oft', I :l~ :.lwwn Ill Ftt:. (6.29-a). Tile.\«.· ..:un r ':'l .trc almo~• 'lnlllor- 11'1 lhose 111 C/1 configumuon The t.•h;mgc- 111 uulpul '• thii!--'C ' , 1 d<lC' nor have much cffec1 on .:un~nt /11 fh r 'l)'n:JilliC '"f' ul ' ""'*'1UU(,"f t...l ll be uhunn~·~J lr-1m Ihe. im·crsc nl the 'l~lpC" t•l th.: mput ..:hrs.r.tLtcri:<~tu::-. t.'ur. n a~ (1>.67)

Since lW,,, << tHn "'U lh~ tnl1lll llynanm: n:~i~lnncc value b ' 't•ry ''"all Input of , lr.ullii,lur w1ll he \ tUUI! n' Fig. 6.29(.1). ~m ly t, .mtl \' ell will ~ pcl\lUive .anti V0 \dll al~o be po~hive

~.:harm.:.tcris1ic..\

, ,

Outpul Cltaracteri.stie''i In ourpul clmrJclcn,;lfc'" of Cl:. mode for pnp trnn.sistor, vanauon ollc· whh Vn I\. !.lUtlled (or gi\'CI~ \ 'ltllll! ~tf /11 (Fig. 6 ,lCJtlJ l"hc different impor1ant r~OIIll' ()( lhl' mnput chal':lctcristl\:,.: :u.: · I ForCE motlc lr ancrcasc;;; ~l uwl > a.\ \'n mcrc~!W!!'o. The . . loJ>c uf Jlu, curve t.c che outpul r-::,1\HinCo: ()( (.'£ mode circuli i~ much lowcr than CB mode circuit In C£ mode curretu gnin is dclini!U :1$ (11.11!\J

HI\

1u •

•""

'"'' - 1.. ~·

.... •• :u Ill II

•

••

c.t\ .._,,

'~"·-

•

'·.

S..lhll•lll•••l h'll'''" I

...

'•

'·

•u Uutpul

\llll \

--. (':..,,•.,,, n/0_....,.1oft w~-

thRI'llfltrl~lif\ for pup lrNml\lnr

\'uf'-·)

undrr ( 'f: modr

No\\ lur "'al.'h •'Uif'UI chur;u.:h.:n,tlt" ~o:ur\~ lh ,.,, ,,,,~1111 hu1 1, llll'IC:I,C\ wuh \ t 1 c jJ,L- IOCrC'.I"t\"\ .. 111\ \'c 1• .:! \\ ht·n \ '11 ''\('f)' do"-C lo 1crn. '..&) lvh'" h'" h'Hth' ''' \llh'. It decrc-."c"' r.rp1JI) ;1' \'1 I tit-C.Tfo.",a\C' 1111\ tle:CUI.._ f-.ct..tU\t.' \ ( i dUifl' hdO\o\ lhC' \ dJU;; Ul \Ill "'ha..:h Rh:.Jn, lh.!t both It~ JUlk:Uon' ul th< lr.m'''"'' .&h lu; ·.• .ard hi.t.'-l."tt llu regu.m '' «.:;lllcd \iluroncd rc~wn Her..: 1r- '' I"Hi'l tlc:(k:rkkm ''" / 8. I

llk.· collc\,:ltrr cumnl / 1-

rcH::n<

~~;,,~r.,,,~c- ~ -.rrcnt

''not lCfO t.A~n 11

- U

It hoh

\';due

lcr,. lh..:

1..17

Semkmuluctnn -S, FrtH1\ hulpul

charnc te:nsttc~

\\'C erm dcrcrlllinc tlu.: foiiOWIIll! teml:-i:

( 1) ,HII pm tlonumk ft!'l'.l l\t..:uu:~..:

, IJ,j,_o-- !.£1 /1 \'t I

{Ja.:- _\1 ll, l.,oll lol

ff lt L

HI!L•I

(,.23 Current Relation in C.E. .VIutle ('.ll. c:onfigurntiun h ll\ th~ enput curtt:!nl and I; l it~.• 11u1put relallun hl!lwccn inpul ami uuti')UI cum:nl 1!-1 "' curlil:r

htl

,. ="

t ,,,

ttlffl'nl .

rht;.·

(().()())

(6 li I l

Nu\\ '" t l~. ~unligurJuon In is tltt.· 1npu1 ~UNt'OI .un.l/, IIH• nutrut curTcnl Nu\\ m nrd\!1 h'l lind out the n:hlhr)n belwcl"n /k .md I, \\I! l:&tlt pnk:~cd ''' h•lltm' In C.E mnfi~ur.tuon. currem

!!·"" ;,

/1.,. = ,, ""

161>1\)

I, = fJ.s. Is

l ien: ;,1,(1

YCV!.!~c

from collccwr

ti.2-l

o:.ruunlllon current lct.o i' t.lue-

mlnorhy L.u ncr wuh llm\

w (!miner when h!t,,.,; 111. " I,Cil i c . I u = 0.

Relation Between a.,< and {Jd<

t'urrt::nt g~li n of lr.tn~i .. HII Ill CEtonflgu r.uiun I\ fJ.x. u.c· i.Ufr\!nt guul uf lrau ... i..,tnr 111 CB configumuon i~ ~h.· Th~ rt!l:uHm h..· Iween 1hcm I" :t.) fc,1ft'w .. ;

rltl.' D (_'"

l..;rum

L'(jUaltulb (().6~) ~unl ~6.60)

J,.(I -

\\'C ge-l

1.- =""'! I, '" '•) .. ''"" =a,. lu + l uu;

liJ,}

.-= l a.,,t.r1r.:

!6.70)

r"wlli'M inng (().69) and t6.70). Wl" gc:i

{J.. = -1 a,. . a.. = p..,{J . l ,.m = 1 + ..J.. - u~

((1 7 11

When tmn. .istor if. used <.~S :m 3mplifil·r th~:n input \viii be .t\ .C. ~i~nnl ln:>tcad ol

ll to!. Then

Thus.

11>.7~)

or in t;l'nrraJ

I'RilllLEMS ll LhC' r.-.rwo~-J cum..'l11 111 1h..: c.t.'r: ol a junclhm diode j_,., 6f) mA wbcllth~ \ uh.J~tc .lCO.l"'' h i" I -l V .tt1\J X'\ mt\ then lht:. \'ohagr is I S V, flind \1.ltic ami d\'namk f(')J,{.U\1.'('

- I 5/CSS X In '1: 17 o U

lt'.J : r/Vtt/1: II 2

I 4\/(l:i~

60) )(

w I:

(I fl

For <~ltnn..,J•t!lf ""'''' 111 C. B O)t'\cle: 1he \!mllh:r tun ·enl h I IUA <IHlllhl." 1-oJ'L't.:llllt'Ut "U U1 mA t-uuJ u .uu.J {J

Soluu''"*

I, .:: lr +

IR;

I 0.0:!; 0.9g mA

1J : 11 II•: 0 4Ml U2; 49

" : /II< I + /JI = -1'1/~1 J, lit = H l,Mfl

J hl Slh•\1. Jl\.1 / 1 , , ~ u) 111e a b.dur ul Snlullfl/1

IJ-=-

lou

l/1 I .t

(l_lJ~

tt) lum

u..tn'l'tur j, 0 Q1) t=ind

u/r I - t tl

1111

'=='

U, 1}9/j I

ll9~

fJ, lf l nu• = 0 5 11A. limi t, 1 , 1

0.99) ~ 99

td 11 " ' ; ~ (1 /11

0.99))

x O.!i =SO JU\

lto.a ..s mA v.ht.'.l1 pA. keeping cnlle.;lor.emiurr 'nha.v-e

4 . FM !llrun\1111ltl.'l' 1n (.~ 1!- 1110de. cull eLtlll \iUITem ch~mgc:. rmm

~l«' ~.: urrt-lll 11,

r.h:sni•t.'d hum ·10

ru j\(1

c.·nn,mlll C'"JI\ ul.11c u ;md {J

I.= -10 \

Jl.. = .JI, t.JI, =()2.5 nu ;: fj,,/(1 -t

/J.,d • 0_9M'

In lhc C O lll1Mk !h~o-• ~mluer .;urrent '' l mA and lhc- outpul umcnt j, O.OJ mA ~ ~~!> J~i n\J CUII('III ~:tin

It-=

Sulttlirm

I ffiJ\.

lr = I - O.I)J = 0.')6 mA C,."ur~nt

r•:tm

(:l.tt

1,.11, = 0.96

InC B mudc .,urrrnl ~am j,() 96 l'lte \ Oit&L~cll.rupat..rl1\' I Kll'-\1\lunLec:unni.''-IC,J ln the cullct:h.n cin.ui1 i~ LS V. find lhe baM! c-urrent

Snlutmn

V:l,

. I{

lr =VIR = 1.511 x 1()-'

lrfrr ~ 1.510 '!6-

= 1.5 mt\. I.SI>l.~

/1 = lr· + '•

'• = it- lr = 1.56 !5 - 1.5

QUESTIONS Wholl "poh:ntu.l b.tmer • llu\\ J,.: 11 tornu.."tl m p ·IJ JU11 (;1UII1' p,"",:u..,_ (ol"\\otn. hin" ~md rcvef"c hia.. chamClcrhlh:' ,,f "4:'ffil••tOt.hll.h•r 1.h•"k \\l1111 1-. lhC 1.Jilku:ncc bCI\., CCII .t IHCiaJ. imui:1Htr ,lnll .....lllh lfulu~o: hlf hlllllllu· Clh.'l);) lt:\'CI pi._IIJU of \'iCw':' UIM'U:o.)' """ otn'-- Jl'lf' l~.~&lllli:nor "'orkmg Jmth.IJ>k 111 h:rm" "' ~.uuct mH\\:fllt..'ul· ncm-... JUnJ."Ilon" Why it ,~ c:~IIC'd rur• ~ Dt~Ul-\ C" 8 01114 C. E. mocJe llonfigurmion for Jmplr-.an'"'l•r. \\ uh ~o: Jrcuttllilt~uuu 6. Sho'-k dt.tt Lwurucd.atlon in C.B. mode i~ ~

1,·~ rt..t.lr+ l rbO

l noo

l uo ;- - - - 1

-a,.

15 Uc\4..r lbe the JonnoiU\)11 o l cnCI!!)' b~u1ds m Cf)'!oolalluH.: "'-'I hi 01.'1uu: ,.,.Jcnl.:C b.ul~. ('ondu,tn>n b:.ud. und lorb•d<lcn g,:1p an cnet~y h.•.nll '''u~,;lua: . ~-'J'Iu111 holt .. . pusnh c .;;h:1rg\· : :anier ·~ E\pl.lun lww IJL•pleln)n luyer 1\ fon!led tnp-nJUilCi~tn .;tl'ld \"\pl.uu thffcrcniiYfX"' o( CUrl CUI Ou" irag :tCI'C.».~ p•n j UilCl!Oil. W OeM:nb...· h11.11 l'!J.t~tu@ condJttOn~ ul ~~ tr.tnM\lOt II . E:\plam how eD!lJ) b<~nd .. arc form~d in ::~ ~-nlid, ·" i ..~lbtl!d ••tom... .u-e bmurhr IIJg~Jthc_r hi rorm che :.ohd. Cl:w•if) solid~ into condur..IOI"\ '""'ul;;tl'' "· ;aml'-llml· .. undu,tor~ an tetm!-1 ot' lhrur energy band and he1lCC e.~pla1n ho~' thcar .:ondu<:h\JlY d~pcnd~

on leJw,.ermure.

11. Dcm·e lh~ .:qu;UHHl f01 \.-l'tOdU(II\'11~ IN mctnl ;,, well

1-"'pl:nn hn'' 11;111 dfcct \.hu"'" "hclht•r hul..-,

o.Lio

lur ..cnu cundlw l ~lr

+~1

dccunn .. predt.nnm.ttt' UJ ol "Cllln::undudul .tnd ~. t ,•n\l." lht! ('=-;pre .. -.tun h1r 11 ..11 n,..ctliul'nl. H .tll UJl~lt• an1t llall "ult.•~_!c lnr 1'-t)pc ;.c.. "ell .... (ur N·l~ JX' :r.cmiconlluuur '"' txrivc R«llli.:r l."t{!,l.lhlln hll lllni.IIHII \\lth jii'Upt'l t.IJ~hllll IS (';lkulatc lhc tlcn.. ll) ul Junm atulll \\ hu:h h:b hi lX" adJ(•(I Io mtnn~l\ c , ~ In produ~c n·l) pt· m.dL'flltl nl \.ltn,tuLII\ II) U l'J nhm em II I'I g_t\l!ti lll.ll lh~ Uhil ,th l ~ ul elccLtUO' 10 n ~~ ri'C ~lllll'lll'IUl'UII 1\ '\25U l rn~/\ llll \ct 16 An n-typ.• CJch.t~ 11 dumu ~oku"h ul IU1\ JX'I c ..... It I~ u(l".ln~Cil tll a 11.111 Clll:i,.l I'

cxpc:nnlen\ " lt.:r.: 13 - f) " "'''m .md currl!nt d(-'1'\foU)' J : ~tKl .:miJlfrn~ \\ h:u 1 the 11:111 '''11:-t~l~ tl the "I"-'~ 1mcn •~ \ nun l lml.' 17

T he tt.'lol\Ultl)' ul lnUhl..h: fil' .11 'till' t\ '"' U J\ nhm e-m. C:tlt:ul:ttc 1hc clc\ uun .llld h11lc l"l•nn•ntullun \\ h~·n ~ : II '8 .1JUJ J.lr:. 0_ l l) 111:0./\Ldl .,¢(

7 Magnetic Materials 7.1

Atomic Model und l\lagneli7.ation nt ':tnf~u~ 1ype" •Jf materi:tl in •• mut;,nctic field cnn

OiiTen::•lce 1n hdt;H 10111

~tCCUf:lld) :111~1) )'/Cd "llh l h~ help

uf QU~IOIUnl lllCCh.ulk~. whtch 1~ t llll fll lhl! ..cope oft h~~o Le:u llu1 :o.~mJllc :.uomu: modf"l wh~eh ;,.;.,umc:- th:u lht!rc ''a ccnuul pu~ooiii\'C: mu.:l~l' "' 'urrouukd hy dct·Lmn!' HI '':mous nrt1ns £1\'CS rcu-.onn"h· qur&llla11vc rc'uhs. An ckdn111 111tallng m ,, 11rb11 aruunJ nUl·Jcu, l~t!· 17 I ». as. .uMh•t:."u" In •1 :.n1ull t:UII cnl ltwp " IHC'I' ''til C\fll.:m·ncc u um.JUl' HI nn l'XIcrnal M· fidd uu.Juuuu1 {il,,• 1'h~n hlr<JUe 1rw' 10 .Jh~n I he mugnc11c OIJ'kJic mumcnll m) produced h> 1hl' orbmn~ ch.•c•wn. ulnng th, ~'\t~rn.Ll "'-1-l•eld uuluc1um tB.,). nw~ tilt MJidd nulucttuu ciil. ·a mn f'Ollll m tJw mUir-rwl mmld ht xn·utt'l tlum tt \nmld hr ut tllar {Jtmtr r/tlw mtlft•riot lW'fC' 1101 f'll'\'t'm An nrhitins ch!'clron ;.rllllntJ thr noclcu~ 11, 'hown rn the riA- (7 1-. hdm\'C' " 'a 111.1¥nctu.- dlflille h:m ng .1 magnetic nH.mli.:nl ( tTH, dm:ctcd 11'1 u Ihe phmc of the p;aper :\hd perpendtculur h' the phm~

J''"''''"nt

o f lh~ P"l~' · bl!!t:lhln~ .u~ 11111 ~m ly

mUlling a.rnund tht

nmku~.

lhcy .lfC

""') ~opinnin!!, .,lmut tlll.'lll,clvc\ In addilion to the clc.;mn .. OhWCIIll!nl.

nucfcu' it'-d ( t1l~1 hn\ u 'Pin muunn 3SSOCIOI.h:J Wllh II. Ahl'hll!;th lhl:-. UUI!fe::tr

Fi.:. 7. 1 Orbilal mot inn uf t'lt~t'lro n

'Pin hW) a 'crv m:gli}!.lhlc clh:c1 on the ovcrullma~ncla:- prupcn~ uf the m;llcrMI. l'hu' c.1ch alUm can be ch:mt..:lcriJcJ h) the \UpcfllC),iliml tlrll~ uM~•.:r•c: Jip ;lc m<mll.!nl .. con..:..pondin~ 10 1h.: clc:c:trnn' orbital mt.ll hm. dec:tmn "Jllll mmion and nuclcur ~pin mminn. So the l·ffcc-11\L' magllCllC dipo le fHl!IUCJ11 C.'; lll h(.• \\'rllh,!O lh

iii ; I Aii amp. m1 (7 I \ Where I currcn1 in 11>: lt>op. A uroa of lh< ckctron orbiUII loop. ,; = UIUI nomtaJ \'CCtor. nnrmJI ln the.! pi one of Ihe; hKI('l On nm~o:ru~cuptc 'calc thl' \'Cclor tV i~ t.leiinetl a~ llu- mo~snc:Li1.u.tiun \ICClllr. = m:lgm!lic dipole OllJnlt!nl !~o. ~r unit \'Oiumc

I.C.

M = Nm

!l015)./Jn

152

1-..n.~'"''l'l'in~ Plr\·,,if' '

where N =Number nl mokculc~ p~r unil \ OJunH:

iii= 1 ..-,i ~ '''crage d iJ)()IC momem per mokculc ump. m.:

and

I huMl'I.IJ:!IlC'tlt.lh,,n,cc-tvt ( \i) h:" e 1hc '"me lanai amp/m ....... ~f . ftdd mt~n.:-.11) Ill t So re:oult:uH f\1 fidtl1nduc1n1n •li) 1n 1hc pre~CilCC of a magncuc matcmLI \\ill be

17 ]) In mn'i nl the nC\n fe rro nm2ncuc matcriul, ma.gncu£ntwn Yl..'l:lnr rhlpilfSWOill tn til'- /l.f ti\!ld 101CI1S11} ( f{) ;Uh.J Ill the ...~11111..' o.l in:t' lU'Il

( .\1) 1). l lf

(If

Thu~ ''c t:.ut "" ' ''~ !7.4 1

''hen: ((IO(j II!- the ~·~n~t.ull ol pro ron 10nal uy ~ailed as "'"K"ew 'UH "t'f Wiulm nt tht"' m:ucrial Thi' rdauon :1pplied for l:u'£e d:L~s ot' paramag.ncuc ;md d~::unug nclic f1lJICrtiil'\. So lh.: ~\\.' cqn n.~) n()W bc<.'UI111!"

-H

~- - x

Jl,.

l 75t

"' v. here thL" coelltuem

\lJ 1a... culled the mtlJ:IIt'IU llrtmt·ahtflfl,, \\ lm.: h , .. \\ nucn .1\

Ji = ~l,\ 1 +X,. I 1!._ = ~l, =\I + X~l " ' Xm = \Jl,- I t !J, \\ h-=rl~ duncu,um J~,.:;. quunwy (J.L,) 1!\ C'JIIcd tl.' tdaltl't! p~mualnlul.

••r

7.2

171•1

Molecula r Field Inside a Magnetic Materiul

\lufn uLu fie-ld ~mrck 01 lthl~.llCiu.: nmh:mtiHw)' 1~ '-'.Jkuhtl~tl HI 1hc fv lh.1wintt •\ .1\ Ld' u>tbnlcl .t m.~,t:ncti c materi:&l oi tubitrdf) 'h ~'l"-' \\ liLh I' umf••nnl}" ma_gHL'tl/..cd wuh rugnL'tiLJtion vecror t M1. Now l-.!ts ' 'm'iLh."r an irnJp:tn~\

..ph.:n~o:;tl c~~o·ny In th\! rnugnetie material. at the centre: nt \\hl ... h l h'-' nutll!C:ubr hdJ i:o. h.l he '-':1lculi!h:J. The nhth~rial outside tluit ca,•ity 1:. tr~.ut.:U .a~ \!Ontinuum ftum the nutcro:o.Cl1piL point o f view. \lhcrt' u' in,idr the ul\ ih the: dipole' 11r~ tn.o.att!J lb Lndtvidu1.1 lhpolc:s or dipole group!-. nut ..u. cnrumuum Tol:tl inlcrn:tl ntoh,:c,lhll field :tl th ~ Cclllfe Oi the CR\' 11~ c..' UU he \'-'fi iiCO ttS.

Fim = Fit ;:;, + ;:;, "here

(7 7)

~ E\: tl·m~t l

mucro:ot;opic M-ficld mte ns11y uppllcd to lhc. !o p~c.: uncu . 10 1he M·field 1nten~i1 y a1 aht.< ce111re u l the C:1\ ny du..-cu ~ ul f,ll"C pole den!oH)' (a,= A/11 ) on the.! ca\ U) ~u rra cc. \\hcJ\• M, I:!» lh\! norrn:ll compon<.'lll or IIHtgnetu~IJOil ' '-'~tor M .

F/1 = Ct)lllrlhiUi\ln

fi .. :;;

ltH~rihution

to 1hc M~ rield intcn~it y d ue to vnrtnu!-1 dipo l~~ tiH-.H.Ie

the t..a\'lty. Nth\ if 1hcre :.~r( b rgc number of dipole~ in~idc. the c:l\·il} . "luch nrc oriented bul mndt>mly dlt:ilrlhuted in (X'I!'Illon. tht..•n fmm .:ub1C:11 ~}' nnn c lr)'

p~u·:~ ll c l y

C(m,uJ c r~UI(Hl

11 "J :. 0, in gene ral.

Mnl!lft"th· Matc.·rillls

153

The surface contnbutmn will come out os. (7.K I

So Irom

Ctlll

(7.7) Ihe mtcln:tlmnlcculw·fictd '"'u.h: u nm~n~(l(.' matcnal can be

wntten as

Hm = ii f 1J/J

(7.'))

.uuJ lnLCm.al mc>lcculnr nux dcn•HI) Bm

Jl 1/m

C71UI

hlu;uions (7.9 muJ i. lm gc\c 1hc un("tn:tl molcncbr llclc.J iw.. iLic !.1 magnetic rn:ucrial in tcml'\ of applied lll.l+.:lt)~I.:,~Jlic M·lidd irut"n!'til}' (Fi) Jnd thl" magnetization vector (M" )· four mm: 11} diama,~tlt'lit ond JNil·amagm·tit• m::atcrial'\: thr ~ennui 1rnn (i.e .. Ml'\ = X,,./113) ;, nrglixlM.'· '111011 h.c.• fim i/).

o,,.

hill for,,.,.,'t), UISIIPiit• ml.llt•no/\ I hal 4.'\1HI:-.:"ItilU l"i \ t.'f) imj'l~lri;IIH, m,. II Will 'h0\\

'ponwncou< mugneu:a1ion even in lhc ah,ence of lh.: ex1cmal upphed M -fi<ld, (a< .. Hm = M /3, even lhmagla Ti ~ UJ

7.3

Various Magnclic

l\·luH•riu l~

b1ch otom contains diffcrcnl CllfllptJOcnt!>. of ma~ncllc t.hpnlf' IOOIIlt:niS c:lue 1u \.'!I.."\:II'On orhltid motion. clt..-ctron 'pm mufcnn .tnd nw.~lcJr 'pin motion ::t..~ di.M:"U,!>.el1 :1buvc In section c7. ll. and 1hnr Wlotl dfct:t dch:rmin~' lhl! ovcntll m;•gne1ic dMrnC:tcriMiCs. o( lhC m;llcnal ;cntl prcntdi! II' !!i!ller.d rtmgneLic claMoilicutmn

rollowcng :are the diiTercm

l}'pe ~

nl~l).!llCtiC nl3t~riJ I !ot.

7.3.1 Diama~netic Material In tlinlmlgnctic mntt:rial.s the or/Jiwl mutiuu of th~ dauuu wul .\flitl

motiwt nf tl••rtmu {'rtJtlun• ·hr M .p,.ld llf'P"Htl' to t'tlt /1 ollwr. ji~ lit'I mngn~tif thtmlt• i/1011/l'ltf ofrm·lt mum, i\ :t'm tmtlm•l \1-jit Jd utt/ttl I/O, ( iiI imule (/ltmUIJ.'Itl'lll' mmrrials ;.,. (t/so :.('IYJ, in thr ftiHt'nn• of lltr •'·''lf.•mul M·{itld. rhus on cxtcmol

tilt*

M-licld cannot produce uny torqu~ ~m th~.: .atnm. nnd n1l rettl•gnanl!.nlt:tkc., plu\:c. But in th!! prc.scncc t)f cxtcrnnl M· hcld tmluUifJO (lio) U\ .\hown m Fi1;. f7.1) the orbitin£ e lectron rithc.r spcc-1.h up or ''l~""' down i1l ll' L'rhit t.lt!J>Cnding upun wh..,:llh;:r Ihe orbitaJ m;~gnclic murncnt h unli p;liUikl or p.trullcl tu the uppHeJ M fic ld tnducliOI1 ( iio). bu1 in ritltt>r ('(nt- till' dllut,t.:t' 1n orbiwl mugnrlk IIUUIWIII t.t m a dir~crion oppMittt to t/1 ( applktl ;\1-fidc/ htdut·t;o, f lio) So the Vl't'l'd/1 tiW)llldit im/u~ lt'tm { Ji~ U'('tiJ..('IICc/ Jl\ t/tr pr..:\ttltC(' tJ.f t/t~ Jifmt(lJ)IIt'lic m(llcrfa/ For a diamagnetic substnncc cnntountn~ N dipoles ~r unil volume. 1hc magncu.anion vector c:nn be wnucn u.'

where

ii~"* ~ JJ, Ti,.. N no of thpoh:~ per unu \'OI .. R a r-Jdlu~ ul the ~le<:tron t.trl'H loc•p. For dmmagnctcc material //~"~ = 1-1 . so Di:Jm:tgne1ic Suscep1ibility <XJ,..)

will he

Nr'! ' z,,,. =Miff =- -:r;;;'" R-p.,

17 .11!

Nr-: ' 17 Ill =Mill = - - fi • I' • < I 1-ICI ..f m '11111'- dtiltno•gnctll. ,iJl!oiJJill' h~w•ng C1. rm < I). (-\l'J, and lt'llll~ faturl! 111depe.ndl'OI 4

St' tlw uial!ncli\.· \ ~·,:hn l V J is olb u (-v-.::) 111 &1n 17 'h whidt fliU\\!., thHI mni[ur·u, uultw11o11( 1/ 1 ' -' lt-nll.rml In tlrt' flfl' H•IJr' o( clwmmtrlt'tt( nu,rrml ()hun.t!!llt"li'm i"" ah,: n-,uJt '" l.c n7."' l:.m opcrming on an ;Jtomk ..,-;til: Ottl" In

the :tpphGIIH111 111 a M 11dtl

1 h~

dcctronk cutrctll m ".1d1ilhlln urr m•llltfl<~ 111

'lH.:h u \\ot) tlml lh\.') h:m.l t>' wc:ll...c n lhc cffl"CI uf du' :l jJph~U hdtl Stnc\."111" a .._,·u t:-..cqu.:n~'-" ''' nt;&~n~lt.. nmmcnt ind u~cd in the .Hom~) the c~t~.:rn.tl M~l fdd, ...u m the., 'l'n'c niJ nl(tlt'fUII mr tlumw~m·tir. II b parlkul.lrl) prc!ol"l1l111 m:Hcn;\1-. that -.:on"'l'h t·nllrd;. ul atom~ ur 1011~ " ilh clo:-.cd dcctrumc 'hclh. Out: tu tiM I p.&r.-uu;~J,:nct i-.· I.:Pntrihulit11t ~t't)to. ca nn~ ll cd out In ('It her mntl'riat .. •li.nn;1~11l'll\m i:-lrc<lUI.!ntl~ m.a~~.~" b}' "'Lrt'ln~cr p.u·nmagnctic or lcrrunt>tt!U\!HC bch;)vtnur. When om L" \t•·rnal M-hdd " applied t o the ---• t.houn.I}!Jit'lh. 'llh\l,&m:c' 11 L''<pch l h \." / . ..- --,..__ tu:.l!IIL'lll. hni!, ul l itre..... Juc tu l..c.nt·, / LJ\\ ,•.., .. hn\\11 111 tht Ftg f7 !1

H :0,

...

IPnh;miJgn..:hc .. uh•,talll:l.!" Co)n ii : Jl,, t fl + If l = U o.<.l.J,., = ,11/1/ = t-vc) E\.unpJc.., n l d t.mm~ncu-.: ' ub:.-lance.\ "'" Cu ·\~.Ln. Ill_ Au. C. C~. l lg_ I'll,

r,,7~~ \.:

\1, i.'h;

7.J.2

f•:l rl11 11 U~IIt'( ic:

i\ltt ll•r ia l

IIIJIUJ tiUlll,t;W'Irt' "ltlli'TIIII\ 1/w orl1itul 111(1,1.:111'/W ftllmtrnl mu/ \'J mr nm,o,;twfw mmm•m

~~~ tlw do

·tnm filL' nlll r·,mn•llm.:; l'trr:ll mho: tlltn dlom tl\ u wllo/c" 1,,,\ o mao.:,wtu

"''"'"'"' r m1 1 l•ul mmlom rrru•nlulum oj tlw almn' m 11 nmtn ml maAc•., tlu on·ru/1 01 nu~:t· uml'flt'lt t mumem :c.·rn Due In lhnt 1n the- .•t."'nu· '•l th'-· l'\lcm•.l M~hd.. lthu ..( mo1h:no.b "Ill nnt ~ ho'' ;my mag.ncllc prnpcr1~ Bur m tiH· prc,cnn: 'll !:\h:rn.ll M lidd 1 Wrt.~th.· \' Ill :tprly w l.!ach ;uuruic m~t_gn!:li\: moment ;mJ tr) In Hlip.n lhl'Ul :IIC..'IIl "ilh ap,'l lil!d ~f·lit: l d . Sn lfw 11111}-:IU'IW hultu•Jrtm r HI I\ 'ffrl' ll l!lllt·nnl h\ fltt prrJt'llCt' of thn~ rvp~ aj ma,rrinl:r, wh~~.:h an: ...-aJkd a' par.mm~•n~uc nl uh;ml' Smcc th-c: dumm~nl.!lic eU..:c.:l '"" \UIIth~.!rc \\ hu.:h Jt:cl'!aw-!> M~mtlllrliHIII tit \u l lll· nt.' l m-.:rc;L\ c in ( 8) i)to. ,.:mall ~u in1hi' c~L'..: J•:u.un:&guctk '11'"-'-'Piihirit) ti(,.m, 1\ \UI,tl l l'lut pu .. hhc . Wilh lnl;fCOI\C ur 11u: t hcmt.~l Cll\' 1~)

mndum ••nCnlllltnu t•lthc .,w nuc d tpoh.~' will tncrc.t..-.t:. So u•u h tltt' "'' '''Uw tl/ tnnJn·r,tiMt ••t•,•roU M IIHIUt'l iPn ( /i) will tlrrrt>tiW", t r, U',,,"t rc mwtH'''

en.

Ge:ncrnlly when the Irt:l! .ll~lnlO: or i(\U\ h••,c ll••r1 1} llllcd inner ' lu:ll' or ud\1 num~• ,,f l'h.:-\:lrntb. thcu tile) rt"~" panuuugncl tt. hdm,·iour F'ur ;tfl pt a~t icul P~!JlU~C~ CXCCfll fo r CL'Ini)Cf{UUr\! tll"!Jr ah.,ithlle ICrH. magn~.·lll:ttwn ' 'CCH•r t M 1 lc.Jr p;mun:tgnl.':t rn:th:riul '"'1111ll"~um..-

J!ltiJ'OfiiPitOIIu u/H(I/Uh· lt'ftiJU•rururr

,,u,, H ,. :w=NmH'T 1

(7. 1ll

I )5

Mugnetit Mult't'ml.\

Ft)r Ptlranm~nclic.· mt~tc'i~tls l,.ftl.

Hm e H " hicll give\ the p~rnlllrtt:-1\Clic ...U'(;~rt:ptibtli'Y

= Mill = Nm~)l,,

r7 14\

JK/

\\hcr!o! ( fi11, 'FiJ I' th\" M-fi.:ld nUensity w~iclc I h.; par~un>~gncl l~ mah.:u:tl Of inu.•rn:tl molccuhtr fi.::ld. (;V) h. thl! nunthcr of nto nh or molecules pl!r unu \'l)IUI!ll!. lml') is lh~.! :nrnnk or nlolecul:.r dipole mt.HIHmt. v.,tuch 1~ 111 thl! rang~ t'l tl'W Bohr m~1~ncton ( 1 13uhr m;tgn.::lon dd:tTtm, It -= Planck '' \"UI\'I~H\0, IK) "the Boh!.tr\ann \, Cc.m ...htnl. IS Ihe tsbS{)hnr IC!klpt.'rmurc In d~~l'('~ Kt'l\ Ill ,\lw' ~ c<111 £7 J I) c.1n nlso wriucn :ts

x,,,.. = Cll where lhc con ... tanl C

' = NmpJliJ JK

is known ;1s Clrr;r crm.\ltml, ;uhllht: cc.tn (7. I;\)

,.., lliU\\!fl J ... Cw~t·! l..tl·'. whJch "!>hOW.) tlwtthc pdn mwgn(."IIC ...IJ,t,;f!pltl:uiH~ '' in,~..·r!-el) prop11rtlonal to the 3bsohue h;IHI)I.!r:tuue c.TI. Ex~unpi C"\

7.3.3 Itt

of p~u:)m:•gnc li C

m:1 1 eti !l l ~

nrc Pt, Mg. AI. Cr.

~ln.

ex,...,)

Su. V \V. t.'IC.

l:erromu::ntOf Material

,,.,·mum,~m·tir

mtJit•tinl t•ach a/om

(lr

mofnftlt! litHo

.\lt"OJH:

thpalt

Jllrlmall

( m1,j ,{w to mh omtU'JJ.\'ntr•J t•lt'clmJI ~pin mamt1Jil. ~~·hich mr n·n- m·orly uUI(nt'cl

t•t·.:·n m t/lt• ab~'f'lll..(' td 011 <~Xl(•nml M-fh•ld, flu ni.H• lut~•ing (HUll,\ (tlll'tl imit'l l'lt•Umnh" .~lh'/1. The c::u~ ol'lhis alignmclllt:-. lh1..~ un~..·m;tlmolc~:ul.'r lic.•h.l (lim) '''h11.:h. :u.:~ordtn_g LOCtJG. t7.9), does nm vantsh when lll = U). unl~s:- fi vun1sh<;":.S

Mmultancous ly. 'l11.: ~cne;:ral lt,cd

\'c;:ISton

nf tnicrnal lllolcrulnr field {1/m ). cqn. (7.Y) can

he \\ rmcn as

17 I hi when."'

y:::

1/J. \IC(I.lH.hng 10 I he ::ample

l ll~c•r)

IJut fur

t., . . ha\ Ill); .a large nluc of lhc order orr - IH'•

r~fllll1t.lJ,:0~11( tn;ltc.rwJ.;,

So lor rcrromagnt.·uc: rmucrial~ when f ii = (h. 1 c .. 111 th ..· .tlN:m:c ul the M. licld, lht' il!lcru:\1 fnol ~:tulat field \\rill \l1ll llC' 1hcrc \Vhu.:h ''..:.tiled .l."i

cxh:rn~l

vumtcm<•cms maJ:_nl'll:...1rion. m that case nbo\'~· c~111 (7. 1~) rmxltll..·d a'

17 17)

·1'111! 11tlllccu1ru li~ld H~.~n:-. g.•Yen 111 c.qn. (i .I 7) i~ ~lhl\\ll .&::. \Vt:: ....... ~ lol~~w.ulur Fi~IJ. Wt'J.\.\ · Ht'i.H•IIhr·r~

Jl!eon predict!~- how nw~n~;tiznLion ch.m:;~ m tt.·rrnmat!nc::hc

mdwrial with tcmt>CrJturc, The theory shu'' c:d that fcrrc.unagncu~rn ....... the lumung c~tsf.! of JXtt:unagnctism in an extcrmcly l:argc- 1\o/~liled. A lcmpcr~uurc '' h1d1 is c:dh:d :1s C11rie tt•mpuaJUre (Tc). :tbovc wb~eh s pontaneous magnctiolh'l\ ';.t nl\he~ and fcrromagucuc ma1enal bccorncs ordulory JXtrnmngncuc mmcnal. Now when T >> Tc m;:tgncLisolllon v~eciDI' ( M) for lcrrt~mu~ni!IIC m;ttcn:JI c:ln be wnucn as 2NJI,.m~ _ Npflm,, Hm 17.18) - 3KT (N+yM) 3 KT

- ( _ yNp,m{. ) _ (Np,.m{. ) _

M I

1.e.

'KT

1KT

_ Np.,m;. / [

XJ,.- Mill-

11\T

I -

\NP .. mr1.1 A l

( yNp,.m;. 1A7

X •~ =T y(N!1,mr13K 1=7-e

J .C.

Where C-= NJI,,m;l:tK ParOJmt~gncw.:

tcmpcrnture

Cunl'

17. 191

=Curil' Con..a;mt. anJ A= "(N)I.,m~/1K

1empcnnur~. \\h~o.:h" 'll ~hll) hl~hcr

tJw

thl11'1 (e > 'IC·) Curie

rn·t ;,.; ;,hown In 1hc Fig

(7 J) though thcorclk:ally the) ~m; ~nne 1l1..: atbm c ctan t7, llJ) t !\ culled ~, ... Cttrit! \Vi•·~" Luu \\ohich i)\ \:tlitl ;a~ •\,. \uric h:mpcratun.- tTt ), when fcnn mugncuc m::ncn:tl t'ch:1vc lt!-. p:.ram:ag

.•

-'-

netic m:neriul . ~: tntpl.;..;, ~lf f~rrumagnCit..: llluh:n ~l'

ar.:- Fe. Na.

1.\

C ll

' -r ~

etc

t<IJ:. 7_\ P:tmnu•gnctic Curie

h~m1u~r:t •

ture 7.J.i.J ;.\nli ~FcrronHignctic ~tutcrinl In :anu-terrom.agnem.· nunea·anl, torce... ~t" een adJUCL'tn atOms cause the momK dtpo1c naumcnt~ W lm\: up 111 ttn tulll p .• mlh:l way n~ shown HI lhc hg (7,--ll:t). which c ause lhc net ma~ncuc nmn~~..·m t.l.'m and lhi!-y ;m: i,ricc1cd s ll ~ht l y by th~ J"II'C'~lec ~·f e\ll'lnal AI 1·1 dd t\l11. Cr ... ,,,,..,,, :11UIInn•<~ l;"II\' II'IT1 ;,1 n~enr'l h:lnpcr: •h•r~· Mn~. Cr~O_.. MnO ur..: c~runr!c HI .tllliiC:I\IIIl,tt=,nclu.: HJOI C comp!.lullCL ,\ott fcrromagnctil' m.llcri.t l ~ ,(on't have.: n~•li.h tcchnic:J.Itrnporl:.ncc.

I •••I I Fh:. 7A

7.3.5

lbl

h.: I

(ul J\•rrunw.:nct : thl t-\nli rrrrnmSIJ!Ocl :md (\')

~"errim:tl,!nt'l

F'errimagnttic Mnteriul

Fcrrima,gnctic "uub-.t:mc~ h:wc

mo..;1

general ordered ..;pin structure. contnim.

bolh spm up nnd !Opm down dipole mumcn1 componcm~. but of uncqunl m;~niwde m, shown 10 the Fi~ . (7..lc). dul! 10 wh1ch ahere 1S ::. nc1 non-zero m3!lncuc momcn1 111 one o l the,sc d•rccuom.. rhcy nrc ca11ct.l fcrrnnagnel or fernie~ Fcrnnm~ncuc m:ucnnls arc ccrnmrc nuucnnl$. arc ~ood clccmcal insulators Pcrriccs nmlllly COihl~b or FclO' comhmll-d wilh Orll! or more OXIde~ nr diva kilt

me1ah. gcneJ'<•IIy repre...enrcd :ls t\1 Ft;-:!04 or M.O Fe10 , e.g.

FeO~ Fc~O\.

zno .Fc~O \ etc Com[Kl~ilc ferritn which nrc ~olid ~oluli on tlf une ferrh"'· ln anolhN. h'-c Ni-Zn 'lUI\\"' heM nmgnetit.: pmpcrtie!!.. Gaml!h Jikl! Y ,f'~.,0 1 1 Yllrlllm mom garrh.'t ~V I G) l'lt.' \.'lUl'•Uiutc :mwhcr group uffctnma,.:nellt'matcn•'l" 11>e) h."'" <OO>ideruhlc lcchn~tal•mponancc because m add1110n 10 the rclumd) lorgl.' m:lgnclltl.ltwn. lhC) itf c \f.!r) ('H)nr comluctnr of clcctncil) • ..C\(tJ.II nrdcr-.. of magniwdc lc'" tlmn \Cmkondm:IOrs. have VCf) high r~'ist.uu:c. J)uc w lh>ll the)' c:an ht• u...cd h1r high Crcquenq applications. when" the rcduci.!J s:.urcnl" teddy ~:urrcn1--1 lt:HIJ w the lov.:cr t'hmlt' lo~l\'i in tlu: trJn.,fnnncr.

7.4

F" r romagnelic Domain and Magn etiza tion Cun e

No'' ru;Ct)rthng tu the abov\! !iCC l i on (7.~.3) fc rromngnctsc nuHcnal:. ' '"'"l,llle mngnctut:d nl.'urly -..~lhnatmn al h.·mpc.ruh.l~ below Cum! h:rnpcnature (7r) But .;,ay for cx;·uur)fe (/·d. which" a fcff~unitgnetic mntennl .;::xis• ~ hmh Hl lllt~ncttt.nl ur urunugllclilcd u•ndid<"n 11le rea~on ror Lhis i:;. tbaLa ferromngne tiL' matcrbl brea"~ up into number a1f dnmam~. l>umain~ may have d im.·n:nl .:-i1~' :mcl~>h:1pc' r.m(:llll! fwm atnc nucromclcr to several ccntlmch:r. EM'h ~k•m.am (fllll~un .. pcmwncnt JJpolc-. and mta ni01111L torcc~ cause th ese momcnb tn hnc up m p.ll'llllcl m cr ~~ rcgmn whKh .:~mluin, n large! numlxr u l ntom., 'l h~-..c r..:~lfllb .lrC' callt:d a.. rlunwm , .t-.. .,)lown in 1h.: I.; I~ (7 .Sa). Th~i: pr(~t!IU,:t: u( domilhh ",, .. Jir,l J>O"'wlutcd hv Wc.1'' m 1')07 Ahlll'u~h c:1ch domain I!, magnetll'ed I<' '-tllllt:tllllll uccordmJ; IHlh{' :ll~wc "-I.'C:IU\11 ,, ~.,),hut the dln'{'ti(H1 urthe lll"f:n~IU:H~tm 111 varinu11 domoun, •arc raDd~'mly oncmcd as sho" n an the Fig. f7 .Si}. Th~ rt.:}!tnn bch\cc=tl l\\11 dtmhun-.. '" t:.tiiCJ lh~ J(1m.1in wall So du~ th mcrnll c.uii.:L'II;•Ium

oca

n1.1~nctiutiun

f'ig. 7.!0

i' 1cm, in tlH." .tb\Cncc of :my external M·fidd

\\1th incrcost' t~f applied ,\f• O t~ld diiTc>r"('nt dom11in..._

~ H ),

Ch3ngt of djn:cliou.s of lltOnwn Lt. In

Nm' due m the prco:cnt:c u l' the CXIC nl~ll M-field. there ls .ul iru:rc.t.;c in Ihi! \fl1lunw ol the d'>mnm .. who'c moments are favuurubly on e nled rei aU\ c hi lh..~Kl\"rnal Af.lih"d mt~n~il) I fl J, ;11 the expense ndghtxmring d\111HII11' whCIW mon\cnt~ ar.: unfavnurnhl} oriented as shnwn in tht! Fi,g. f7.5b). by the prw<'C.\O'i of dnm.un w.tll rnotum N()\'. tf the extern:.! M-filc1.l 1:. ~nmll e-n<mgh th"'·n tlu~ proccs~ uf domain wall moth:m i:" reversible with 1hc removal uf the cxlcnutl l'ie h.l Bul u' the t\f.ficld intcn-.il) ( jj) becomes stronger domain wnll motton

C1llltinuc hu1 in .1 irrt.~vc"ihle munnt!r D uring 1hi:. Mage: Hh )\' t n l\!nh nf1cn l.tl.c' plact.! 10 I.J.rgc JUillp. which IS known as IJarklrauun jump. due w whtch !<;Urn"''

irregularity moy t.lkt! pb ce in the m(lgnctization curve. \Vith funhcr 1 0~It::..1~t: o f external field. domain \o'Olll mution b o1ccomp;micd by domnin rotahon. 1c.• the ohgnment o l tna~nc:uruuon m du: md1"idual dOill<)ln, nlong the duecuon of ahe cxacmuJ field ( ii) 1nkcs phtcc as shown in Fig. (7.5c) und thereby magnctm: the

Et~~uu!t'l'inJ:

15S

Pln·.w·.,

'"hulc mutcrial to .J ln1tmu hln '~11m: ( U m). Jlun ~ the thrcctinn ul the ..:xtcmal M -

tldtl iniCII\11)' ({j) Oiffl!r~n1 ~t,pct'llit•llflfiWil\.

uf clw whnk rnlt'C\'- ;ll\' 'hown til thl.' Fig. n.(M} the cur. c (0,\), whtd\ i:- ~.:.1lkd ~.~.., mt~)!tWII:'trlum 'iu't {. where M-hcli.l mdul'ltnn (8) \'Ci'S!!I> M-ltcld mLCn\il) ~ 1-H '' lllil\\ n am.J It ' ' c.tllcd m, (/J/1) \.'ur.e Nu" :tftc.r rc,u:hing the ,,uur.tuun ,uJuc (Jim; .11 CA). '~hen the e).tcrnu1 fidtl (/I), .. rcmo,·c..·d gnufu.tll\' 11 c., JJ -i- th. <~ nunpkh.' ~:~mJl1111 dnrnatn alignm~nt 1:-- nPt uo;.uull}' uuo.~incd. ;, r~ . . iJu.al ''r r~m.Jn.u"'t d11~•h.· fidd ...ull rcnMin ... tn the lll·lll'nul 111111 "II' \11)' IIJ.OIIhc lllll~llrlrr 111111 o/t/11 t•hll<'llill 1111 {tlllrtillll t•/ ill ;alvn~

lllriJ.liWIII /u.\lm \' \\ bid1

'' t: .1ll"cl

il\. /t\'\1('1-,. \1 '•

• [lill(rUitn RtiJtl(lfl

II II

btt\t'l'lilflk di!IIUUI \1'!111 lntl(ltll\

1•1

Nm\ con_\tdc-r the Fig. (7.6hl •• tlct r..•::u.:tuul! the ....tUI.al lt.Hl P'llnl (r\) wh~nl Ti flm). al M-fidd 1111cn~H~ r fn rcdut:m)!. then dfccL' ol by.,ten.-"i" ..Losrh. ·''II i"t '-IW\Hilh llll' l:;l!! (7.flhl rlll!ll II \\ I ll IIIII l l'lroi\:C lh ung11111lt;llr\ C' l t .C,

't""'

't • when l /i =01. 1hc.u ( Ti -=-

't) 1but dccrca~t:' .dong .1 l'·uh ~ ·\C1 AI 1hc

otllltt

li' ~ OUI /\!fO. \thidl l"t t...Jih:U J~ if"IUIIIh"ll•,

to"/1 nit •!\ uJ

lt•urJua/JilL\ Jt·lt.\11\' t il :OJ, lcdu~e the mngnt.!tl( lndUo..IHU\ ( ii = 0} . I I the P~lllll In •. II 11\- (Cf.JIIIred I hill ;) rcvcr:-ocd nr (-\'C) \'!llut: l H••, ... hould ~ llpplil'J. wluch b knt1wn ns t'Ot'lt U't' /on1· liy rhanging 1/11 "' 1 1/mt .Jinng (/)/_'I thl! \,tlut: t1f (. lim) re!'u1l' J l the Jhlllll t£). Ry rciUoung to \II :: 0) ;II lit\! pv1111 (G~ \\h~n (/J eFannlly hy th~ p nX\.'!'!!. o(completang the cyc-k frt'IOl t tf = U! to til= iJmlalong the ~urvc n.~· pmrl1 ('; (8.\-) ..lum .. dh.' \j)I.IIIHIIII!\'U' lllll~f1l'III<IIIUO \tht•n

-r.,

Urt.

tt;IIAJ. fom1 a ci0111!d 10(')1' l·~·sit·trsi s loop

J:o.

,IJtH\n ul lhc Fi~

t'1 6h), ·whi~h..., ktH''~ " .....

QUESTI ONS Ocfl\'t:

1h~.:

lcl:ttuml)CI\\ct·u H , IJ . amt M

2 Perhc th.: C'Apre ....,t.,n HI molt•-.:ular fidd '"'ulc .1 m••gnt.· ll~ nultt'rml 3 Oiflc:rentiotte tltt\\ttn lll!lt•rent maylli!tl~'nMional .. l1'-c Dtanu~nctlt: , 1':\r.tm.t~nl!.lll und Fern• mtiJ.netk m;ttcrh1l -1 hx.pl:un SpOnG.IIlt"VliS nltiJ_!nCtlfOII0 11, rcrnltu<&gn..:IIC donuun ~IRJ ma~ n CIII.OhOil CUI"\'(" (ot (crrom.l?,nChl~ m att.1ml

PART-2

1 Interference, Diffraction and Polarisation lA 1.1

Thin Film Interference of Light

Wa,•e Nature of Light

The phcnomcott of 1 ntc•fetcnce~ diffr:1crion, pol ~n~ation cnn be explained by the "a\le 1nn1ilm nr lif:'Ju. 1l1is mo1ion is periodic in mature. AI lhc end of dcrinitc inh.:rv~tl

uf urnc,the p:aruclcs find thl!msel f in the same posuion nnd havin~ :.arne \'Ciocaty. 11lcsc muvcmcntz.; arc h~ndcd on from one jXlniclc to th¢ rh.!).t in :1

definite ph~•c rcln~ionship. This type of periodic mo"emcnt or particles ts en lied s imple lmnunnu: nu)tiun (Sl-iM ). t\t 311)' IOSLant of tlmc I the diSplacement Of the panicle in II iS f!IVCU hy y

II Sill (l)l

2trf

= (J Sin T

( 1.1 )

whcsl' ru i:-. the :u1gular frequency c·= 2n/T) and T the time period. Ob\·i\IU:-1) the disploccmcnt vuri~ with time Cc.ID~Idcr jJ partic ll! f-1 o=-it I ' I } .it .t ..Ji,I.UKC 'f101u ~1ur1in¥ poull 0 II u be the vci<JCI!) ofrhc panicle, chen lhL· panidc I' S1.1rl!<o \'ihr:tting some lime 13tcr th:tn 0. gi\'cn by /1 = ..:!v tmd its <.hsplacemcnt :.11 any ins".:lnt o f lime 1 '''ould be Lhc :-.:une: :n 1ha1nf0.1 1 o;.f.!L' CMiicl·.

:md

11 j, r~.·pr~sc mcd

fig. 1. 1 WA\'C"

propa~:otio n

of li~ ht

\-a ..:m :!; p

11 •

~ tl 'In 21r( ~· - u;.)

Now r.t F= A= ,,,nckn!;lh

' =a''" lmtlf

rJ}.l

l'hu~ th~pl~u.:l!mt.!nlut parttdc 1~ ut .any tn\l.llll (II time ' ''

L\-=-,,''" 'II/

,'Sl

ol ''

8- "21tr!A. • phil\1.' Jtflt:r.:m.L b.:l\\..:1!11 the p..midc' :u U until'. /' 1.-t:' ll~·hintl 0

()HI Jlhii'C

1.2 l nterferenc~ \Vhvn lt~IH '' a \c' JHHn I \\ u ctlhcrcnr \llltrc:c' mix up nnd cro~s each ntlh.:r·, path 1hcn ,, mc~.hti "·•nt1tnu l iml·n,tt:· o(h~ht ,qll orcur 10 Lhe regaon 01 cro..sinf! Tin, llhKfl lic111100 Hl lht" ih'l I thUI11)11 flf h!!hl COCfJ,!}' obtnincd by the -:upcrpn~;umn t1f twp

1.3

nr mnr~

\l.J,.~, '';.:.tiled lllfc•r(c•rt·n,·t.

t\nalyticnl Discussion and Conditions for Constructh·e und Destructh·e Interference

Le t S 1 ;:uut .\ · h< •~~~ ('H•IIll \uurcc' ot h!!.ht ~cpanw.:d b)' u dJ,t.mcc d. 1he lll(lnochromatic "';p t:' o f \\ :l\'dCnAth ). ar( ..cot by thl.!lll (Pig J .2 t Let us ossum~.· th.u \\,1\('' urc s:wnmg from S 1 nnd S1• coherent 1n n.uur~. t.\! ., l.hcy otrc, 111 0\:l.mt.~ pl1.~'e -,.:~me :.unrluud~ same sutte of l)l'llan">atiOn ;md truvdhn:! m·arly ulunl! thl' '-i1Rll: t.hrccuon S\' they can produce an 1nterkrcnce p:.au.:m Let lh~ Hl'l~lllf.HJ:~'u ' cl''l'lan:lm'll1'- ,r1 ;and -"l al I' '"hkh •~ rtt a d1~tan cc ' from S 1 ~•nd l : frnur '- dul' 111 '''o \\:1\t:\, he J!I VCn hy \

:rJ\HJ:!,"fltl/'

, 1/,.t)

1>-----------·

lntt!Jft·l't'nn:, D{(frm:tiott and Pofun'mflan ''l

=a ~in 2.JC(t11'- x 21A.)

The "ph.,t-.~ thffcli!nc~.:" h::rwccrllhc'c \\J\CS "hen th.;y

From lhe

pnne~plt:

163

l.liTi\'C

al 1' l '

or ~upcrpos111011 of W.J\'t!S

; ,,[,in 2rtlt/T-

1 1/Al

+ , ;n 2rr(t/T -

t~.l.lf

.v:!a~Ul~ lf[ttr - f,, .,.i.'Jl]cos2Jt[l~ ).r 1 1

1 = 2o C1•' {i(~ 'ill [2KH//'- t1/J.)- c'f/21

( 1.111

Hence displacement a1 /'IS nl<o S.II.M ol Ulc same anguiM lrcqu~n"y but 1.11 nmphtude lr1 cu-. 6/'2 .u1tl ph:t~c l~tt![:iug i511 lntcns-ily 111 ·' ptHnl Is propontuntJI h, the ~quaft nf lhi.! ~unph1o1.k Su. lntcn-.it) :;-I~ 1211 t'()~ 8/2)1

- I

-Ia~ cos~ 8/l

( 1.71

Cttu 1:

lln'~:hr Jo'rmgt!s

~.;o' 6 = 1 I

\Vhen

i.\!.. the com.ltllon It" phase Uiffcrenct• ''

= 1..,..,.

.:on-.tn•~h' c tnl~rf~rcncc M

6: o. where n = 0. I . 2 In rerms t.')f path difference tht.!

bnghl fnn~~-- 111 tenn' ul

~tr.'.' 211/t

~undtllon

f()r bri.tthl fr•nge.\ ,,

?Jr

l:'': - ,,, =211/r l'atlt difference= ..1 = (,,, - -' 1) =

" 'hen n =- 0. I. 2. Cast II: /)ark Fringe> When 5() lhi! CnndtlUIU fnr t.filrk

~th

0: where"= 0. I. 2 .

0 ;:- - I. I= 11m11 :

[ringc~

in (CnD!t of phru.o difference IS

II. )/I, ... (211

l)K

!I .8)

Sn n1 lTIII!!C'

lt'nn~

ul JXilh

~hl t ..:n:no; ~.:unclcho ll

fnr

dc~lrm.ti\.c

cnh:rkr..:n...t.! m thu~

whrm 11 ... U. I.

p4.11h dil ll'rCIIl'l': .J =(X:? _ ,, • = (~~

±,

,;.,u

.l.~J.

INTEltFEtU:NCE BY THI N I'lL:\ I N ~W I IJII

;tnd r hiOkl' uhM.'(\'Ctl anJ tit;:\ I!Jnp~d

:til Wh!tf~.·rcncc phrmtm~nun lhl('

ntnlhrk '"'11\!tttttn" thun th\." ...urtucc of 1hin tr.an~p:trcm rn:u-:rmh. In ,l:ul) hrc. \\ c ML" luuuliar with th~: l.'OIOuJ' produced b) the lhut film ul uti un tlw 'Utl.u;c ul ~' .lh't h\ th~.: lhin ftlm ul ,. ,u.1p bubble und oth:n mthnt 111m' u l nuc.1 'nun~ \\,,, ;thk lo l.'xpl:am thb phl'l1111111.!'11llrl illllhl! hur.." uJ tnl.:!ff\!fcllt:(! lll:t\\ecn h}lhl

r-:n.•.,. k.,.lti,liH th~.· M (' .tnd th..: tmuom surfac~ of:. lhm rHm. It hus f:\\.'"cn oll«r\"..:d th.11 lhl'

rntcrf.:rcntl~

11 ~111, .tuJ

1.-1

111 lhl' (liW l•f thm Jchu 111l-.c!'o pl n~.ic dul' H~: 11) rdh!..:h:tl tll ltuu..;nlllli:d ll~h l from the lOp :md b<..1lh•m 'JUJI.h..:t: t~llllt: 1hm 111111

I hin l' ilm Interference Due to Reflected Lil(ht Thin Film )

~ l'tlrallcl

( ,,n~uk1 '' transprucm P••ntlld l1lm (Fig I 3} tll lhh:~n... ,, lomd n·l rildJ\~- tnd~,

p \

rJ~

,-\ an..:ide n1t"'lll the upper :-.urfacc nltlw ttl•n '' JMf11)

,.,.~11.:\.t..:..r .th•n~

·\H 1

nthl p:lrl l)' rcrr:.tct.;d :tlnnt A H. ,-\1 R, pun o l i ll'- IUII!rJMIIy rdlL"l"ll'i.J along IIC .1111.1 tl n;clh ..·nh.•rg.;s ~-'~UI ilh\ng ( 'R1 p;mtllcl w A U , T lu-. \l'lll cunltnut• hu1hc1 m1hc ,;Ui h" Wit\

l"tut' lur i.l ''nglcm'"- hkru r.1~ •••·•umOCn•l p.tr.cll~·l n•l k..-tt•cl rot\' M,,· I\H. 1 t ' K 11 •• 1 I,.,.- 1111111 'uri.JI.."l' .uuJ h.a~.l. .... urt.1..:c ullh • 1h1nlllsn t...JI1 ~· nht .rt ·d Sim!IJrl~ .tnumhl·r ol p;ar:-~ lldr.t\·'-Ltl1 l'l\.'! ••hL•inct.l fn-•tn Ill~: ll.tJh.fllll h.:d Jll •nh ~11 •I the lfl\·Jdt:tU , ,,, ... l , ~l' Hl 1 DT: llh.'~ pltt.tlll'l r~fft"ctcU r..~' h.t, tng_l' ll~~o.U\«.' p.llh th l h:n.'lh:C 111 l"l'l w~.:n th~m!-!CI\'4!"' whtl'h cuuse amcricrcn.:~. bc.;••u ..._: tht.•) ,,r,• .llll·oh~.-· c ctll Ucrt·rullotolion or Opricul l'uth Uifi'Creti\'C Dr.t\\ f".\ norm.• lin. \H 1 ~u\d AM nurrll:cl lu ur. Th~ .tn!!lc u l m.:t,h:nc~: l~' 11nd .lll ~h.• ,,, rdl'l.tCIIOn IS r rmJUC\' CIJ backward h) lltl'-t.'l ,\£oiL r I ktt: L .-\1•( -, thr 1 .l 1 ~o frum •..'v\11/:~. AtJ= BP ;:u,tiAE=- Lr ; r Tlt~o· '1Jllic:.t1J'mh dift'crl"nce bc-Jl\Ccn .AR1 ~mt.l CH::. ''

~ ; JltfMJ + BCl l - ''" . II . t\NIAC J1 = ..m ~ · n ,. -= C'fJi'AC

ffmm _L.\('N Jnd J(' \ ;o.·l)

1 · I.V = pOll \ = JI(Afl + 1/C) -pCM =JIIMJ + 1/C - CM> = JI{P/J + /JC - CM) p<I'C - CAll I : Ali ; 111'1

Jl " INICM

I l'.;JtPM I

lnWt/t~n•m·c•,

/)i,Di a c1im1 atttJ l_jolnn:mtirm

165

f 1------+-~--~~----------I

't :

...,_T, lti~.

I.J

~f'M.

Opticol p:nh difTfrtne..- in par.tlh:llhin fllms for n:nt(led ht•:,ms

cos r· = I'MIAP. I'M = AI' C<>S t PM : 2t

,;.._ iAI

+ 1:.'1') ct~~ r (·. 1\E = El' = tl

..:o~,

( 1.11))

,.\bove equtttlun m ihe c~se ol r.:O\!ct~d light does nut represent the correct p<1th differ~nce het we~n 1wo tt:Oet":ted ra~·!'> .\1( 1 and CH ~ hut only the apparcnl. 11 hu.' been

cstab l i~hcd

uu the IJa.'ih oj dt·r lrtliiiCI,~ti rrn·tllem\· tlrm. when fi,~:lu is \llljm·~ "} W1 ,,,,;, ,;//\ dt•m, t m;·,/mm I Arr mc;,Jium

'' tic•( lt•tl m pnhu A. from tlrt•

mh:J(,tl!l!) n pluur dm:r.~t- ll, t'tJutnJ!t•ur t~t

Therefore, Lhe correct path

difl"cr~ncc

!'"'" J(OPI't~m t~ )J1_, rWf'ttl'\

m 1111 ...

~d.$C

will IJl"

I I. II ) C ondition for bright b:md in thin nlm for rcn.ctcd

li~hl:

ll the path difference. from eqn. ( 1.8) he.:. = 11.l.. where 11 = ll. I. 1. ). 4, ... c1c. T11cn ~nnstruclivc imcrf•rcn~c lakes plac" 111 .:n'c of thin film nnd lilm appear,; ~ng h< when 2J,Jt ct't'. r i )J2 :: ,;. (1.12)

Condition ror dark ba•'d in thin film for rcne.c1ed liAht:

If the pa1h difference. fro m cqn. (1.9) be~: (211 ± I )An.

=o.

\\ ht.!l ,. ,

I .2.

:~r1 ·~:u' tl.u L \\hell

~111

ro' r J. Af2 ; C11 .t I))./~ 2}11 I.'H' I~ IIA HI ill+ I Ii.

1he t.'nndmon lur hng.ln tuuJ dark h:md 10 1hm til m uuc rh:n:nl'C" 1..·qus. J ~ Jn,J I J_l J ..ar,: JU••l tlJll'loi' .'IIC 10 tht.! g,:n~o·ral I.'Clrtdllmns (\'qn' I ~ uml I .,, In' ' lltl'rh.·h.'IH,'t.' Th.11 , .... Llul.! h• lhc ex ln. pha'c dif!t!rcncc tr occur.; ~11 n:nc~llon .11 A. Irum 1lh· '\llfl.lt't..' n t 4Jen .. ,:r 111\Xhurn It ~houlJ he remembered thai Ihe uucrkrcnc~ J'MIICrn \\Ill llfH he perle.·~· hccausc imcnsily or the r:•ys AR I nnd CR~ \\til 11{'( he •he ..::mh· .1nd rth:lr ~•mpl 1tu~l.:.; urc d1ll~r~n1 'I he ampl1lttth.· ... \\ rll ~I.' I"-''" ' cu1 th'-· ttllhn•nl c•l hgh1 h:Jb.·h:ll .uu·l u~m.,mltlcd through th..: fihn:;, -lllt.:rc ' ' ;.t -smull 'hllcn: nc~ 111 thl· .tmpi11Udt•, ul !hl' r.a~' ·\ R1 ami CR1 I h..:r,·l,ll t.' th.: IIHI.'n'lty 11\'\CI \,IIIJ,ht•, llCII t:CI dllrk t'nutc' \\Ill om be nh,cf\cd h•r thc 't' li"l'' .1h•11t.' uf UlUhtpiC" n:flccluln. the tnt cn,i t ~ nf the mimmom will hi..· tcto

~,·um plch.·ly

.uat

Rut 111 lhL· L

l \t'

1.5

l'hin Film Int erferen ce Due to Transmiltccl l.ighl

hpu"· I .J ·hm" the gl.:vnu:t•y \ II the ltflO\nlJU~tl light Du~.: te~ ' unuh.aocuu' H'lln unn .JOt.l r~..~frll..:l ll tn \\\.." ttht:un 1\\'0 trnnsmllh:d r.\) ' HR .~.nd /J(! Thnc r.J ~ huH· Pti£IO!Ih'tl frr•m -.....nll' poin1 ~otlr~~ S h.:.~n cc.· lh('~ h~l\'t' ,, L:Clll,l;nll phaw t.hfiL'f\'lll'~ .mtl1tf~ m ;1 Jll'''''nn l (l pmd ucc ~u-..u.tin .:<l mlt:rkri!lh..'~ v. hen t..'nluhme..l lll!! ~tlct.:IJ\~ r1tlh thtfen:ncc h\! IW'-~n Lhc ro.ys 81< i10d (){! b th-: r'illh \htfercn<-.: ..l

= !J\11<

I CD 1

11.\

' i

FiJ:. I ..I

Optkal prtth diCTC'rcncc in pl•rQIId Lhiu film., for lnm:ul aittcd

h('~llb

lmcrft'rt'tlt'~'.

Oiffrac·tima wul /'ulan'.HHimJ

167

Frulll .JJJM L) :uuJ JBDN 4wh~•·..: RM nrul l>N nrc pc1 ~'M:Udiculm on CD und lJN.

1\'"'rcl."tivcly. "e gco tfiNIBD t , 1'-tMD/fiDt = 11/V/Ml>.IJI> =JI.Ifli .I= JI(IJC,. C/)- MDt = p(CI',. CD- MfJJ

I·: tiC= Cl•t

.J = JI(I'M)

Cll'> f

I I

I~M = I'H CO'\ I rM = 2t ~.:u' r

1'.\1/PIJ.

Su. p.tlh ..lllh.•r«!f\4.:-.: bct¥r.t!cn BR .1nd CQ

I = Jl f'M

/'R • 211

=2111 Cl" r

H.:r..: 11 "h<lUid he remen1h.:rct11h111 mstdt lilt~ tilm. rt:fl,•ctw,t 01 cltff&'rc·nt pnmu r''"" rll H mul Cl. W/..t•,, )mm lite> .utrftlt-r uj t/;r ldl'rr medmm (dlri, 71un m1; J.lr(l pltuu dwu;:t iC take., phwt· m tlu' t'llSt' Su (·nndhion ror hrieh1 lmnd in iran~miticd li ~tltt i.!\

Q.ut cos r =- uA

tl 141

('uncfitiun rnr dur-k intrUII'•miHI.'tl liJt,ht i"i

I 'lptn.,., r = (2n ± 1) }./2

tl I it

b ·mn E'llh. ( 1 12. 1. 1.\1 o111d C1. 1-t. I. J5} 11 is ch.:arl) tnUihl lhtlt cun~ohlzun' 01 bn,l!ht .ual J..1rJ.. for ref ~c.·rcJ 'ldt! nnd lntn,millcd !\HIC' ~1ft:' 111';.1 comrJ~IIIc."!OWf) l\1 c~dl ollhc l.(o

lnten~ity

II h.t,

~l!n

Distribution

l<\und lhat for n<•rmaJ

inc•d.,~nce.

about

rcllcch!d ju1d 'Jh~" •~ tr,,n,nl!Hcd. l11e anlcnsuy t!I \CO h)

..J'"~ t.)( th"'~ 111(1\ft:m

h;1-l11 '"'

,,r lhc l&'an·Hnllt~d '/ J hc:tm '' 1

II 161

und

1.. -1,+1,

Hctc 6 '" the 1>h:.1M: difTcn:ncc, ,~ the n.:Occtftm cvcfficrcnt, I, the mt~.·n~lt) uf rcnc,tcd b\•am .lOd /o lh~· tndd<nt int.:n&it)'. When It b minrmum SIO: 8/2 .:.&.0 )!CI IUII\IIl1U111 \.aJU~ I. Fur n:lle..:wncc ·l''t l'l\t.~. r; U.04 Puning thi' vah1c o(,.::. in cc.1n ( 1. 16) we get

11 rnin 0.8521 / 11 85.2 1%./1 nu\ = IOO'if 4 Tmmnnllcd 'lt.IC I , tlt;l.\ = In -I, IUn =- 1-4 79%. /, ml• =or~_, Rcn~clcd .. ide

I. Ju the rct1cck•d <.Hie. 1he emcnslly ol Lhc intcrlcrcncc 111axuna wall ~ I ~.7CJ' .. o f 1he mct~cm uuen!>UY und llh.' a m~.·n,ny e,\r lhc mumuu "all be lcro. :!. In 1hc lnlfl"illllllcd 'uk. the euiCO'II) of lh\! nl.r\lmtt ''Ill he IOCJl'f otnd thl" •nh:n"H~ til th.: nnm 11111 "1ll he M5.~ l'·t

h lllC~II"· lht..' Vi\olhdlly ur lh" fl'in~~·' i ~ Olllt.'h Ju~hcr Ill 1hc n,•ilcctcd \)''i.ICru th:lll Ill the IJ30Sillll1~ll "i}'SICill bc-I."DUSol.! o• tJnr" lrmgc lllll"ll~ll)' I:M:IO~ ah!'OIUicl)' ten• lln". 1hc fung..:-.. .arc more :-.h.U'Jl 111 fdlc"·u.'\1 light, bc-cuus.\: ~o ntr~H:.I hclwccn d.trl and hngh1 fnii}!C' .arc much hcth.·r 10 n:n;.•;.·t\'d hght than lrun,miUcd h,~;lu ~t). lnr dun lilm cxp;.·runt.·nt mlhl' I;Jhontlm~ ~t.:lk~tcd ~hJ\· \\Ill !'!\· ht:Ucl lhiln 1ran,IIHlll'J sidt.'. Orij~in

I.7

of Colours in T hin Film

'"c kmm t h~t wh\'ll wl ;,.. 'l'lr"l·nd tl\'l!t \\-tat~r. 1hen ( I ) dtffch:nt L:ulour-, w II b..: 'c..:n. i.l!.. th~ thin Jillu \\'ill upl>~.lt a~ ~o lnur~d and {2• tilt,,\! l"Ohlur~" ill al~n~..·hangc J.ccordin!! tu tJ1l· Ufl~k uJ \'l'um '1ll\\ the,; C.IIIC,Itnn FrLltn our duily

b wh\

cxp:rh.•nc~..·

t 11 \Vhcn ~unliglu which ~011'1'-h tH ~\l'llt.'t1ltU in. tse\l'n ). \1 IS ln\.'tdcm tul th~

thin Olm. th..~n somt: <'~I 1111.'111 "'II ''llt)Of\ l,;\•n,tnu.'ll\'c Ct)llt.htwn (l~<ln. 1.12)

\olltl\t.• of them .VIII \ali~fy dC\IfU~lt\'.,: CclOllllmn (cqn. 1.1~ J tn Ull\:rl crenc~,• .tiler rcpl!atcd rclltxllnn frurn thl' tlun lilm. '-tmt.:t: .111 ~·,t·n ru1our~ h<vcu K'l t."annot 'atiSf) the l'OOiilrtll'li\'C cc.•mdtlh..ln oil u tun..: Jur '' p<U1h.Uiar than film t11 panu.:utu lhi..;l..nc~\f ;and rt:fr:tcth·c indc\ t R.I • Jl. ' " m r! l't'HIIt tltt' lith! film u tJ/ <llhl

tl/J{WW II\

t·o/mnnl,

lfm• to IIIIHillg Of .\Oil/1 \HI\"t /t•nKIIH. Otll ttj \'t'l't'll

f:! • Nc)\\ al " part kul.u JlOitll ul th~: tltm l al1~1 .1nd tor~ p.1ru~ul:u p.ositioa\ ot th~.· l"YL' 1hc. ~•n!!ll:' Hf refr:tclwn r ''"'11 <Eqn I 1:!) he- ulso 11\cd. ~o tor tlm1 p:tn icular t'"(lh~ !tll~IC of \"hiOO). lfnd.nt."" I .;1ntl ~ f jJ.It flilrllt"UI.tr WiJ\C l~n!!lh 1}.1 Wtll "all,f}' C:OI"Ir'UC:Ii \'f.~ C:OIIc.fllltlO lf<IO 1 l _ t .u\d Hill) th,tl C('I\\Uf \\ill~... •,•n 111 1hu1 :m,!-!1~ <'I \'l"h'" (j mfl:f, oj

111 1 • 4'

1 ''

dran.~t·

rlwn

,.,,f .,

({)IJU•Itlhrr

h,• ,an. limn ,:,/oiU' will 111 I \''' ' rh n.,;l,• t~l 1f'''' dm· w tlu• tt~l/~ rn11 pu~itwu of c \ ,. ,,,. nm .\f t dtJI,'tt w , •Iom' t .\) 1'hc condi11011 lor llll tllma ~n!lm.t·umll , ... r~.·\ t:f'>l' tn the (,1-.c nt u;m.:,mlttc.·ll ligh1 Sn 1hosc colcurlro whn:b arc ab!<iCnl nr 'upprc..,~ctl m n:l h:'-'h:cl hJ:!.)H oaj)jX:ar J'i nucnsc c.:u lour~ m tran,.nnlh.:d h!!lll. ro tiU'\ 1114' nmtplc-nu•m,, r ,, rtwlt ut/w, ). u tfl

I.K

Necc.~sit~

of a Br uad Soun·e

hw:rfcn.·ncc fnngc .lhlnn~t.:d 1111hc calc ul bc\lu.:l'' I luyc.l'' mn rn• ate ptoduccJ

hl lwu cohcfi!lll '-t•.uCI;'\, 111c \tllll l!c shnuld hi..' n.1rrow Lhc.rc But in the C!t'iC ol ulh.!rl crcnce m thin 111m,, the nnmm "lllln:t.: hm1h tlh.' n .. thiht~ flf the: fi1111 <.'vn"1dcr lir't t1tlnn t llm :md n tl:tiTil\\ '"uuu.~ '\ hg I 5taJ Kay I produce~ mtcrlcr~nc:c

rnngcs bcc;~u:;c

and 4 r;::u:h the ..:yi!. \\hl.!n:~t ' ray 2 mc~.;L' the

,uri;Kc ·'' u dirfcn:nl :mgl~.· rmd gch r~Ottkd uloug 5 and 6 wh1ch 3te not n.:o~d ung. t11c I!)'C T·tcrcforc. unl)' punion.-\ t1l 1hc fil m b \ lsibk ami nnl the: rc.-..t But '"the ca..~... ut e\fcndl"tl !ooOUrc~ ol h~ht c l;ig. I 5b). the im.:hlcn1 rny~ I 1u1d ! 111\!CI the ~\llf:tcc 1l A :u1d 8. ami art! rcOed!!U .along 3.-1 and 5. 6 All of them ;each the eye. So Inth~: cilse t'rbrond source: oi ltghl, the my' inc illcnt ;u thffcrent .~nglc:~ on the film :1rc .acc-ommnd:ued h) Lhc ~yc. J lld lhc li¢11.1 tH view ls lnrg:c

---t 'ig. L5

•:•J hrt..-cl uf Jmintcd ~m urt'C ur ll~ht 1111 thin film: (b J F.ll'cct ur hnmd ..uur"" "r ! i~ht mt lhln film

t.\1

Fl'inj!t:> l'r(•duced b) Wedge-shaped Film

L:t u 10 con!!-idcr (\\ u pltJll' '\•r l -.ll."l! 011 Jnd O lf 1, ioc;l in.:d .11 :ut .tllgk (tcudthiu ~ :1 wcc.lgc ,.hapt•cl .tit llllu The tlucl..uc:r..... nl the nir film I j,. lncrc~ISell gr.•du.JII ~ from 0 to II (Ftg 1.()). Ruy • \IJ tncu.Jcut o n the wcdgl' lilm with tmgk "' incidence 1. Pan ~H which rclll!tLcd alon;.! BR nnd pnn will rMractcd ttiOn)! 8( with nn~lc of rclruction r . At the pvmt C 11 i~ again rdlcctcc.l wuh •mt: l ~ t)j rctlCCiiOJ\ (r-+ aJ ;IIUIIt! en .tnd tin:tll)' emcr!!C:S a:-. OR, . IJF :md /)H ~ICC th.: perpe ndicular~ dro\'n trom IJ to IJR antiBC. Angle between two pc~ndn:ula,.,.,

IJQ """ CQ" a. IJC produces b•clw:.rd meet fJI' "II', 'u LCf'{): L CDP : Cr +a) ni\d lf,un :>CI'D. CD ~ CP nnd DM ~ Ml' = r. When the :urI lim ~ newl."!l.l wath c~ll -e~t cd monoc hrom:JIIc hgtu , a sy:-.tcm ol cqllid1 stam uuc rfL"rcncc fn ngc\ ore observed wtuch un: purnlld m Lhc edge olthl· wedge. ·n 1c nncrkri.ug ruy~ IJR um.l /JR 1 do not c ntc.r the t!yc puraUd 1u t:u~;h Olhet hm the) :tppc~•t t•) d ivt::1gtJ f 1'01n a poi IllS ncar the riltn Thus the i mcl"fcrc:ncc th:u take:;o pine.: :ll S •~ ' 'inual 'Mle eHt:ct of intcrfe n:nce "i ll be best wh~n lht· angle:: of inc1dcnt:c 1s 'mall. In order 1n com.idc.· the interference- bc..:tw<.''m the wavc:5/JH nnd IJR 1• we tir"'l c.:alc ulat.: the p;uh diflcrl.:nc;;e hctwc:en them

, ,, I 0

' ,'' ,

~1 ('

•I

' ,, '' ' '

,' '

"'in~.-~_·

'Ill

" ' '"

Oplkal path dirrcrrure lu "~d~l' 111m.. tur n:Cil• tJtd lte;~ru~

i/:,jn r

= ~tlfi( +COl

11.171

= lJF/8£ i..:_ IJF.;;;: J.I.}JL

.1 - 11Wt "

Fmm

lr-•m 1flrn. ,in r

wha-e Jl

s t IJ.:. l.h

=BFfBD .mtt fwm cc ... ct •

111:, ;

\nFJI

wl l

'", .:. BflltiJ ,., - ul./'

.J~ I'/I

£/ 1

h um dcdrcm1.•g th.-:Cic: th~Hry

( lr

=/'/) LO, I' ""Ul-= :!.1 CQ:\ tt •

plllh '-hftcrt:OCC ),/1.

SH lur t·mutru~til'f!

.10 J

hghl il , .. wdl ~ nm\ 11 that due t ..l r\!ll.;c llnn

IJI lhr (1111111 1:1 ) from the \Urfacc ul oplic:lll~ dcn'a mcdoum ~flrJt•n,·ul·l· lr f11

l:(l

r'nterftrtiiC~ .

Jll

cxtrn pha.\C

lle:'-.-IIJ'

c..t rcch\C! urr• ~...:aiJ).Ith difference

j..,

lp1 cos (r + all. Al2 ; ul 2t..:o:-. fr+ a)=(,!,+ ll }.f'!

H. I . 2. ,\ .... Fo r dt·struclil'e mterfercmce. effc·c uvc opucal path difference

whCI'l! 11

!) .221

l:t

2Jic

c"' rr -t a)± ?.12 =1211 ± IJ)./2 1J1I cos (r +a)=,).

r I.BJ

"here''= 0 I, 2. AI , ; n. , ;. 0 1.1!. Ihe J't;:rt) urdcr frin~c \\ JJI be.- c.l.trk. it will l"UIUc.' ..tt the IUOC1Jull of lhc two plate~. \Vhen 1he :1nglc It 1.1.ill be zero, tht.•n ''t!dge film become~ p;Jrallcl ftlm :md E4ns (1.22: & 1.:tn v.dl hc..:u1m: Equ-.: t1 1:! & l.l:tl Frin~te

1.10

Width

l·nn.g-: "ILhh uf th.: frint;J.'' o~cumn~ l.ilh.~ tu thin Ill Ill h\h:riCr"'nct.· !o.':.lU N' ~.,Jculat~d a:. ro lhw.·:-;~ Supp.>-.~ tl1.1tnth hnght fnngc uccu~ at P,. ·• dhl.lm:c \ ,. Irom U I tu,~n'''' oJ d'h! tur film at l'n jo; ' •· A'lp1ying the Cundillon for l:ln~ht fringe.· tF'i~ I 7). we get lrum r:qu.uwn ( I 22)

2J1I CO< (I + (l) =(211 •

1 \J./~ /I,

o----x.---- ,, .\.,,--

fiJ,:. 1.7

Here

Fri n~c

";dlh 111 \\t'd;:t.• ntm

1.,, rhu m.1l mCJdt.:nc~

t=U ~~.. co~ fit)

.u - (2u

l•tj~

'" = X" hUJ ll

NO"- f rlHn Fig. I. 7

14)

Sn obm c c4ualion become.'

1f (n

lX,JIInn a cos a=

~2n

!XIf f1 san a=

(~u

,._ I ;iJ"!

hnghl fnngc occur\ :n P"o~ at

1 ))J:!

dtStan~c

1I 2Sl

,\,,. 1 lnlm 0 lhcn

2rX,.,JJ1 """ =12(11 +II+ 11.\12 ~ (211 .. 3).\/2 Subtr.1c1111g tlu.~!'.e cwn equ:UJOn!>, we gN :!(X11 ... 1 .X,.,)Jl ~In a- A So fn nge wuhh

Xn)

= 2 sin UJ.I

Wlum au tlllw wJ..t>, in ilttgffr. Bu1 if a • ~ very srnall. then sin a= a.

( 1.2731

l h<n

[ /1: i./lei~

I. II

Nat ure of Luterference l'attern

Fr0m the expn.'''HlU C\1 fn nJ:C "tdth \H'

I Ilii!>.

tnn)!l. '' 1\hh Jl

h~m.•

tkp\:nd' Pnl} un lh~

II ~7 h l

,._..en that

Wol\ dcn~th

A. R I

:.tntl :.111~lc

Fur rh1111Utl lllt:idcnt.·~.·, : 0 :utd

,,;nndtllnn lor

hn·~l,t

••n•l

1.. \Ct ~ o.,Uiall, :-.o cc.t\ ' ' t rt)

lhl: for n

.\'il u l11'11 ""'""' lm'"''''''' lo:ht '' lhul, .mtlfm mr J1;; I. rlwu Jlllrlirlllttr ",~,/~·· mu:lr (".( ,t// tlr, fnn,r,:n 11 rl/ ,·mm· of rtJitdl tlih·lm·\, \\l."d gt: U

I SH the

~l.1r~ ~

I ~I\ t

Which .,,.,. cli::p.:ntkm ~·nl) 4111 r "'' IOt'll•t\:hrnrn.uit.: r..ty' J nJ lu r pa.rucular \,tlut..• ••I p Nov. \Uh.:c 111 the t:.;.a~· ul w~i.lgt..· ~o.h,, ~,j fil m 1 rcm;un' C(IJP,t.ml m t il~ ~h r\!C.:liH11 p.trnlld ht th• l',lj.!~o' nt llh.' "'-'i-ll!\' .nH.I llli.'rt:3(1.'' h lll.."-.uh .tlnu~ th,• ll.'.n~th t\1 lhc "-:"J.j.:~.· lil'nCt: \tr,lh;ht JWtflllrl (nll~t'\ of t'QI~~tl h'idtll. pamlld In tlu edv.t• oj tlu 11, ·lc:• ,,,. "'''•liut ,/ t1hk'l HI) l,j thl;! fn n~e .. wd l mtrl."~•w "llh ln~o:t'C: l'...C u( thid.nt: .. ., Ht .J .. iu C'\{U;Hiwt • f 2SI. Such (riuge,.. .m.! c.lllcdj ttll~t'' Hj t'I/Utl! tlurl..m•\\ un.l t''l" 1 I ~· • f\' nllt•t!Jiw 1 muluttm tor {rttiJ!,I'" n/ t•qtml \Htltil

1.12 Thid .. nl.,, ..r till' fl

\\~dJ.!c

" p~o,,'tlhlt.' ht JI,,_.,J'IIIf\ tltL JJ,Uitt:ICilll.llllll1

\\ If&: \llthickn!..'S"i nf \&:')thin 11 •11

h~ 1ftc

\\. Cd_;!Cll·"'h, tXJ talm 1 h~ \\t!dgc I' lltnth:J h~ pi.J"-111~ the '>fl\.!l-1111\'n "ho.;.c lhlckltl' '~ tJr ~.h.am ~.·trl I' 10 h\! mca'\ur.:...l. 1n l\1.'1\\·~·t.: n l \1.11 upte..::tll\ flat t!lus' pl:1l\!~. :u ~111 c 1.:1111, wtul~.· th..• nthC'r end 'hould h: 1umcJ cF1~ l Mt t\ ccurdm!! 1t1 ~~ 1h111 film m tc 1f,·n·nn· th,•n() for ~.,1.1r~ h:uul the ntmhthm I'

'!Jll

LU~ (I

tl.

= , A,

~_J~"-----------fi~.

J .8 Thickru:s..'i

or Ihe wMge

hlf1!1ft:rt•m. <'. DifjhJcTimt «lid Pulmiwtimt Sun:~

nngh: or illcidcslCC i i!oo \ CI')' s rn:t.ll, !>U :lll~.lc of n.:fr:ll:lson ,. ...m.tll 4utd .111~lc ol the- w~dg.: ats aj;am s-mall. Therclorc 1

t.•o..: (r ~ u) :..

I 7~

ot.llt-0 \'Cr\•

I. Jl = I tor utr

=""

21 Now tf ''' lh\.' kngth ul the wedge. n the nuntbl.!r ol dnrk 1he kn~lh I .md {llh< Iring< \>idlh. lhcn

lrlngc~

uccurrcd In

" = 1/{J 2t = IAI/J

11ctlLC

f I 29l s,., lhu:knt:"<\ of .1ny vcn chm spct:uncn cnn be dcttmun.:J h)' u .. mp th\· tnh!th:r~tl(C te(hlllt.llH: m \\l'd,t:c·sha~J film

1.1.'

Tl·,ting the Flalnl'SS or Surface.~

ll u wed!!". 1 htrmcd between hHt 'urfacc\ OA Jnd tJH '' htLh .1rc J.h:rl"l:.:ll~ pl.mc, thcntfh· .ur 111m grmlu:tll)" tncreobcd in thicknC.\\ (rum() hi A Due: tn thi, intcrl'crl!nu: fri nge .. wJJ t.l(t'Ur. which arc of cqu.~.J thicl nt.•, .. ami p.tralld tt• th\' cd~e !If th~· \\COgc Shcc t:.tch fring~: " lhc locuo.: nr 'he punw~ .u whtch 'h~ lhn~kl1t~~~ tc~n . I :!8) OflhC film h!JS Q COI\SIMI value (rip. 1 -')) • ..,o thi'JlhCIWIHcna nm he 11'\Cd .. .. ,.n 1111J1ltr1oJnl .applu: nunn 1..1 f inlcrfc.r~n~..:c If lh..:-.c IIIII);\'' 111~ 11111 u l Cl)Uill l hu.:klh."'ol'- II mrnn:-. lhal ihc ~ur([!CC!\ OA i:IJh,l nu .uc lhll p.:rfL·dl~ pl.mc H

. ...-

---

In ttiLkt h• t..hl'~.:L Lbe uptt~o:.al flo~tnt.~~ of an) 'iurfott:~ "-~~ tJIJ. the.:. 'l..tnt.lanl tn..:lhud 1'- htl.llt• .m UJ"'Cic;.illy pl:me \Ufftu.:e OA ;mt.l the ..urJ.u..~ (J/J rhc tnn!!C.. •.m: uh.,cncd 111 lhc field uf \'icw II lh~·' 11r< no1 or <qunl thl<kncss U' ig. 1.10). 1hcn th< 'urfu« 00 '' not upiH.:~tJI~ n.u If thC) df.." llf ('(.jUitl •hu::kncss. t.l:u:n Lhe o.,ut1.1(t' ( J/J " "J111l'illl)' 11111 II OIJ " ""' upllcally fl.u lhcn the ; urfacc OIJ should be poh,hcu Jnu P""''"' ,.houhl he repc:ttt~d. When Ihe fringc-'i. uf cqu:1l width ;m: ub!'l-~f\1'-'d t1t:11 n\c.ub lh~ surl'3 cc 0 /J h:.t.!. now becnme optic:tlly On1 ( Fig. 1. 10).

I~ 11t--~ nf turnwthm

Flj:. 1.10

1.14

Newlon ·~

uf (rln;,:.l'' hct"t'l'rl '" u uun-nplira.l l ~ Out Alass l)l"tl•.,

King

When n pl;t.ntH.:~mv.:x h!n:" 1.1! l;1rj:c 1\.k:~tl kn~th.., rloa~.:.:d un :1 plan~ £-I:W:• pl~u~ ollhm film nl <!If, ... \'OciP...~II h,•l\\l.'~ll lhc.· In\\(' ..uti it~·.: pj th..: kn"i ~tnd the upp~r ~urf;Kc u l lh~ plittt• 1 hu:ln~'' ••I 1h~ ;ur him a-. h;r\ 'mall :u thl: poim uf cuntil\:1 ;mcl gr:tdu:tll)' im.·r.:.;a''-'' from lh.; c~:mtt: h1 '''11\I.;.UJ.., In LhL' L)pc ul Llun 111m irlh:dcrcllc~ rnn~.;.. pto.ciUL'c."c.l 1.\ llh m.mu-:hrtlmaltl hglll olfC cm:ul.tr Sin\.'c the ~~Ill\~~ 't1fl~ nllh~ plomP "'ullh'' lnh h,t, .1 "rj)h~n ...tl -.urfacc, M1 the thid.ncs' nl the ;.ur 111m will he L'on.... toml ,,,cr a nrclt.: ur pm1t..:ul.n rndi\1 .... wttlt the pmnt ul COIII.JCI () d"i Ct'nlfC

rln1' '-''lli,;t'nlnc.· ,J,tr~ tlllll htl~lal nut:-"\\ til hoc rruducctJ \\ Hh

the ptnnl ,,r t.·um.tt.'l t) ' ' ' 't'lllh: A' dut·l..rh.:'' nl lht· .tit film lt J incn:J...'t.'.~. tlh)t:t, (11,

Ul lhc dr.:ular rill~.._ \\til oll"'' lnt:no.~.;C"i, ~(~4\nliug It, cqu:,ll\lll ( 1 .2 ~. \\'hl.-'11

H., will be I.Cfll ll:qn. I .1XI. M' CCIIIr.tl 'Jl'\1 wil l he dar"- TIIC"I: nnw· oiCl' c.\llcd N!o!l.'. lun ·.,. t~ng:-. I F1l!"· I 1-l •.md I ,t 5). When viewed "1th whth' h!!hl. conL'cntrk \:111:'h.'"' '~ uh dil fcn:nl Ci:11mu' \\ tlh Uotrl "' centre arc lnund Wh.:n mnnut:hmm.llh. h~lu i' u~cd. hngh1 :ltH.I J.trl CHili.CIItnl: rin~' :1n: prnJu~.·.,.·d 111 Jh~· :tit liln•. wuh ll.:trb. •teo ccru.rc S i' 3 wurcc ut monodtn,matl .. ll~hl :.tt thl! h'C.'U' nl th\' h:n..; tflg I 11 J. \ fMr.tlh:l hc.:lnJ u( hg'rt r.• u.. HI! the pi.IIC r; .II..:~ The ~Ia~~ pl.ltC G n:Jlt,ll'" ;' pan of th~ Hit ~t.I~·H lu•ht '"'' .mh 1ht· 011r film ~·~~ !t~,cll lt~ I he· 1\'n ... L omd thr gl.~"'"ll1.1lC Th.: rdl\.'o..lt..d • ... 1111 ll&lj1 lhl.' Jll 1111111 \lt.'\\\!J \\llh .. mkr\I...Uipt.I=-

i: ''·''"

!hg I Ill luh:rfcr~w:..-aa~"' rbrc .•nd .tltl."rn~ll.•t.Lu~-hn~ht urt:ular nngs J1l:! prnc.lul"~d Th1co •~ du~ H'lnlcrlcr..:n"·"· •...:t\\o..'~n 1h.: lq!ht r~il\.•~o:tc.:J Irum tlu: Jdu•,·r wrfJl'C oJ th.: h·n~ ;nul the ur~• 'llll.nc.· oJ tlu.· ~~·''" phth· P rH2. I 121

Tluwry:

Nt•wtofl :S

Ring)

Ht}7t•t.·trd Lig/11

U·t lllo suppn"il' the r::,hhO' of I.'Ut\'~Hm.· 111 the lt:l" '' R :ultl lhe tair nlm ul 1h1ekness '" ts ut 11 d1M:.m-..'.: O{! =- 1 •., frNn IlK' P~'IIH of cont:1ct 0 tF'il! 1. 1:ll \\ht•tc nth fnn~L' will he hultH.al. In Ihe. C~t~C tlf r\!tle~.:tcd lii!hl'ihc condiiion h'r bni!hl lnnvc b ~Jllw COS

where

=-I. 2. 3

For rwnmtl

r = t ln - I ))./'1

I Here,.., (J. ~ llll'C the cemrJI band (II= 0) ,hould be t.Jar~J

mt'l<h:n~~·

r::: o co~ r :

I 2,w,.: •2n -

whl!r~ " -: I . 2. ~ ... t!\!C~fll 1~ro.

1)).12

1I . 1111

{

I ,\u him

0 h~.:o

1.12

t-ormulion

nr Nt'"ton•s rln.g

[ !pt, = w! J \\ he re u

11.311

=- 0. I. 2

" =0 whl'll r -= 0 :11 pntnt 0 .

At the pornt ol coni<~ I 0. 11 :: 0. i.e .. tltt n ·mml ham! of NC'wttm \ rmll "'' tt.:flt'Ctc•d 118/ll 1.\ dar/.. tFiJ;!. I 1.-). Since! the conllition for dar~ :tnd hrig.ht i'\ reverse in I he cn,..c:: of 1111n1:-miued light So fur 11'1111~\'mitwlllight thl' t:cmrnl band 11'111 11< ll'hitr (Fig. 1. 1~ l

-----' R

'• • ''

•'

• '

__._ I ' I

fiJ!. I.J.\

Formation

or Ncucon·, dnJt

1\~'\\t nu '!-' riu~

iu \\'hilt! liJ!hl \\ h~·n whnc flvh l '' Uo;;Cd in~1cad <H rnpnnc hr,~m:•w.: ,,\d111111 hght shcn "'~ u.ttt"n I I l01 w1ll 1"-' , ,,tt,llct.l :11 ;t ,hlfcn~tll \aluc "' I Hlu~:l·n\-· ..... ,,,f ;.111 llhl1) 1.: tnt tlllh.·r ·111 \ ,t.lu~: .. ,,, lh~.." nrc.kr I ttl "uh d 1lkr.:n1 \'Jiu.: ·•I 'i.o the nn}!' "''II ·•Pp•·.tr .·nlnqrnl Aut at,= H "II).- fl. ''"" ,,,,. f I' ,,, 11'111 bl .I { Jr•t rt'/ln It-t/ lr.~hf muf a\ t/u, A"i'.h (IJ uf tltt 1111 /lim Ou 11 ' " ' tl~[/t'll Ill orrJ, f Ill' rl/th.· filii!\ ll':llufiJ'fiiT n-llh th}Jn('ll/ l'nlnur' A. AI l lh· ...;II lit! hUh! tWi!tl.tpptn~ t'l ,hlkrc.'IH of\kr• \It I with thllcrcml i. ttl"" \\Ill l:t"" f'h~< ~ ~~~ (t11Hut lll ·' p.uurul.u rm~ ~ .umut he dt,hllt;lll.,hcd \'CI') ··~·uu .th:l ) ~tm rmm lh.l' thenr> or circle (Fig. I 13,

_.,,,I,,,

EF x HE= ()E '>< <2R - IlL.

fl~.

1. 1-'

Nt ~H o n •s

rlnl! obstf"\'td in

n.'Ol•CtctlliJ,:IH

Fig. l. l5

Nt"· lon·~

rin" ohstrH!d in

lrUHSfUilH•d IJght

llllt'rft!tt'l/t t•,

llul £/· ; H£ =

1'11 =

/Jiffnu·rum mull'nlonwllinn

177

nu:hu:-. nl tilh ring ou1Ll

= 1.,

OF.= FQ

I •'

SU""-liiUiill!! llw. \'oiiiiC ur '" In ~qll:ltl(l11 (I "lO), \h' ~1..'1. lnr lhl..' lllh l:mght nng

111r,~ : -r;r

r,.-'

1 ( -11

I )II., I'-

(~II - I H<.l

2!1

:l~l

Replacm)! r,. • I J,.f'). w~ ~.:1. d~.tltle!l~f "' 1h~ 111h hnt:hr nug t/)") .JC1ti - II !.R

(),;=--'1ft [

l flu,

lht

/)It rx \

2n - I ]

CI1Jt

di:uuct.:r rll lhc nih hnt1hl ring_' ,In:' (lfH(l<lrlllln•ll lu lhc !ooqU.tre mot n(

odd na1Ur.tl number, 1 ~ (2n - I ). Snnll:uly l<•r the nih •l:.r~ nn~ lrom cqu:uwn 11.31! r, =-~1\r.,. =n}_/.,'fp

It, :

~ttARI!J

( I IJ'

I.C ••

Tim~ the d mmel~r O( 11lh IJ;trl;. t lngc> dr\! (lfC\J'H)fliUI'Jill hllhl! '-~U.'lf\! COOl of OatUr.tJ

number n. \Vhcn J1

= I. fur lhc 11h dark nng ,.; ~ nA.R twhcrt n ~ fl, I 2

..-. hidt imJ'lic:' 111:11 Ihe r.1~11 ot the nng~ \.me..,''' '4(U.Ul~ ' '~'' uf n:.uural tu lmbcr, , T im.!.. Lhe ring' \I,JII beL"nlle! do..,cr 10 cuch 111hcr "" nHh~•' ui I h..: 1ing' hu.:n::I,C\, i.e .• fringe w1dth goc~ t.tn llc~rensing prtlgr"':,:tiH~Iy whh rln~ numbl!r. t-o the nnJ:S /Jf.'t'IJillt' rlwtnt'l un,J thlnru·r m ntta: numln·r' will mrn.·uM. wlud1 (till be IUcl\cd

111

f I "'

th~

h1llowing

l r

Wll) •

./I -=- I Fnoge w1dlh 1.e.. f r 2 - r1) •~ prupu1110nal to J2 ; JA 1·1 U.~ IJ ho:lwcen 1'1 and 2nd dar\; ring

= ~ l5tJ \\hCI'f!,t-. rrit.tg~ ~\tellh u• .'' ·'" '~'~' h,.·I\\~Cil r?•! .... •.. :w = "" ..! 7' r .uhl 20lh thnl.. rm~ " rrurMlfl um.tl h) I) I I"'\ r,'f "' ,1 4

rhu ... lhL· rnnpt: \\tJih 1/J, t)f lhl" Nn\1011 nng ,, lllVt.::~l) '4U;J! \! I HOI , ,1 ~he I).UUrJIII, I. C.,

of the rw.r: dt•t rc•ttu''·

/J oc.

i.~.. lrinkt:

llJih

rmpnnuuwlwlh~

1/ , II , as fill[: IHWibtr lltffc.'liM.'~ iiHcJ..Iti'M•

wtdtlt

d~creaJ·e ,·

{J~ _I

'" 1.15

Determination or lhe Radius or Curva lurc of U1e l'lnno· Cnm ~x Len~. Wli\'C Lcnglh of Lighll l~cd. and Rcfracli \'e

In de:.. or Some Unk nown Liquid Dt.nur.:h:r ''' mil .uhl

111

+ mnh dar~ h;mJ :u.:

o; = ~,JJ<,1 t O].,.., - -Hn f m IARIJI I hu .... 1h..._

t~thuo. \I

t.:Ut\.:uure o t

pl!uut-~.:nn\c\

len'''

II l!ri H~

n ... in~ aile fl,unul.a CI .Jll) Lht: rnd1u' nf L:Un.uurc n l pl.mn 'm"c.\ h.:n' ur h ug1h uJ m+~rhJ~.:hn, m.Hk hJ:!-hl nr thr tcfmctJ\c- iw lc' tl 'iltlh' htJUHI t-•111 h..• t'olt J l'UI \lht"l th-.•J Ln·Lc'n. ..ttl' ~h'-'n c .,, .,t//1 lilt ••'l'•ll tH·l utdt \ oJ "m1r unkllf''' ,, llllau.l ~~~ l•'lt"t• •

w,,,,

''" ' " " 1\\'illl,' .. .J\

1, .. ,,

\!'lJU•thuu•

' ..,"" h.a,·.: ...~.:....n rh.u th~ Ji.un.:t..·J "' •to:' 11 J.ul. IUH!. , .. h• ~t:lmcti'~ ind-.:x J' tlllU thL' rdr..Kti'c IIH.k\ ••l 11ll11l' II,JHI•I llt\t 1111..'·''111.: li t\."

111\t:f'•-:h pru~Hlrll,'lt.tJ

lku ..:. in tuJ..: t•• u l ni h J.1rl. till!;! \\llh :tir. ' ~'Y 0 1• Thl'tl

,I!,UIIl'l,'l

/),~.. ;;;, ~ , ).R

\\'uh lh~ ':unt.: 'caung. nm\ put 1hc- h llUtU in l"lci \H't." ll gilt'' pl .u ...· ~'nd plunP· Cl\111'~' I~'"· lhl'll tlr:uu~l"r til lllh dark m>g -.oil be l<lhl(·c.lru/1 'loch rh:Ji

1>{., I ..I~H1~ lhC rtJIIII t!l hi lHLUicJ, ltOC it«-" I'

,IIIli

.2nd

= luARIJt

Hf tftiUIICI~( U f

13"'mJ. =1, the

r.:l rm:t t'\'~

mc.k\ t.JI

lh~ unknnwn

liquht.

thC 11th f.lm~ 1111~ \\llh .ur .tlltJ

lmerj't~e•m ''-

1.16

Di[licu-timl mul Pnlurivmion

179

Non-Reflecting Films

On.: of lhe pr.u.:lic.tl ;tpi)lk;uiom. o l the Lhin liJm mh:rlerenL:e plwnOilli.!IUlO j., rhc 111at..ln!! u f ltnll·fc!flccung rifln,, wtuch :u~ t•,~o.·d In l':uncmo.:, hmo'-'Uiar, .ath.t lt:k't:HPC~ I h\.' r~n~.·cthm tn'l11 thl! cunll,'r,, h:n.-, Ul' a pn"im .:.tn he tfc.:.rcil\\:tl tn •• nuninuun h)· ~Oahng .1 thin filii I uf pl'• •flCI Ihu.:l..11c'' Sn th.u lll1li£C' fc1nncJ h} lhl" k1h or pri'm will be: hright J..Od comp.u:llin~ly lc~' C\~•wr< tim~ \U111hl he nl'cti~U tt' phntugmph lhi! ubjl!cl.

In nrJ ..:r h> make 1hc n<,n- n:n~.·ctiug film_

\\C dU'lhC J c~'"un~

matcrwl who!-!C

h'lrudt\C tnJcx wtll he in l'letW~CI\ that ul mr :uH.I ~I;''" flt.:n:

\\l' nl't:LI lnt:JI object t.hmuph th.:- L'•IDh.'r.l h~lh Ul the phutt•.t;mfllllc f1l.ltt.• licm,.: .:. lht: IllY' 'houhJ ~.i.lli,l y the Llc-...IIU~II\'C nmdJII\10 f••r rc:OL'.:h.·\1 ,jd~. lh~h' ~Fig. I 1(,._ fmm th~: poi nt'\. A and J~. in hcllh c;~ ..c,, rcr1ct·tiun '"'"-t..'Urring J11tlll the -...urfan· nf dl!mt:r mcUium~ So. C:\lnl path Jtlft!rcnl'c i...J1+ ).11 ur C\1m rhaw diff~·rcncc If+/(: 2a= 0 will uccur:as per clcctnnmapn\-•ltc thcnrv oj h:;!hl rtn''· m tlu-. "·a't the c•nHhtion ,-,r clc.:.•:Mucll'~o.' intcrlcn:mT i-...

tr1uhmis'lillll

11t

lt~hl fr\1111

II. 1~1

1.c .. upucal lhtd.nc" }JI = (2u + l •AI-.1, '"hell' n '' the n.utlt.ll munlwr tl, I, :!. ·'·

~<. '

II.

Ill

U1 =- l ll

l.+ll''

tlg. 1. 16 Nnn·r<'Oec.•tlu~ film tp. < JlJ "= Jlx l ~uw, m oN!!r w m~lkc non-reflccung ttlm over ~I.•.:-~. lh~ mmunum opth:!JI 1tw.1ncss o l th..: fihn (J;l} should he A./-l In lht:-. Co1:-.c, the dud~nc))~ ).. 1--l 1JI lhc 111m will he tnu: ror one particular wan: lcngt.h For th i ~;, purpo'-t::.. 1hc w~,~,.~ lt."tl~lh i~ ,cfeCI!!tJ fn 11l1 ycllow~grc:-en IJol'l'lll'll of till' :-pl'Ctrum \\-'here the cy1." 1:mo't ..cn~ l ll\·e. fhercfore. 1f the iocidcntli!:.ltt i~ wluh:. "nm..• hgl11 '' rt..·ncct~.·d al -.h<,rt~.·r ~nd longlt!r wa\'C: lengths and the reflec-lcd llf!hl ha~ J ,,urple hue. Th1" ~~ .1 \'Cry Uii<::ful mc.thod to dccrca::oc the rc:ncction lu ;1 nnn1nuuu ,;,luc Surh lhm t.:(Mimg \It ;1 hqu1d CJf thicknc:;:. arc known as non-rcfl(;clin~ !Jim'\_F t"!J prm."licnl purJffiSc. dumhk l:ty~.:t1> . 1 1c nloHII! hy ~\·apnr.um~ ~.:;.1kmm or nmgnt:sturn fltHlritk on thL' ~urfacc in ''.1cuum. or by chcmicttllrcatmcnl \Vhh ;u:id'" hid1 h.•;1v..; :1 1hiri h1~CI u( ~iJicnrl llll lhc ~Urfncc or lhc lc:n~ llf pri.\m

1.17

Totally Reflecting film (Sun Coutr·ol Film!

ro,·sun coutrul 1n tl1c wiudo'' g:l1b:o of C•lnt. bu~Q. ••r in .\UOglas!-t~. Hac we need 1o1al reflection oflhe ~un rny-. rwm the gl:.~~. i.e.. the 111.1jorit.y ufthc ray:-. will satisfy the l'Ondiuon forhnghl nes.' un the reflected ...ide. \Vc can u~c the :;;smc prhciplc

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the: p.uh th(h:rcrKc "'II be

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I wl;nn

tlh ('f,)J'I'C'r C\J1n,• .... tt1M

(1/lllh £:xp1.un rmm C'l)U.tlltlll' \ I J5all F~rt.:un \\h}' th~ ~+o~'lcm cu Ncwton'~+o tut~' ulh('f\C:tl hy lro~INilllh··l hp1u ,.. ~.:omp1tm~o:n lu l)' In llul•\h..en.:J by rcO.:cled light Wh.11 "'II b..• lh~o• n.thar~.· ••lll11..' 'c"tuu· .. nn~. I( 1l~ c\p<rim<"m h pcrformcl1111 lhc: 'unh~h1 •llwh lu "'unlt;:ht u:HII<JI "'J'Illt uf Nc\\ll)ll'> nug ''lll.tpp•cuJ d.Jik 11..,. H.,. -tit !1111 nlh>l 1111~..,

Jilh'h.:lll

'.\illloc ll,h111rc1l

1. ~tlt.:rcnl

)...

wn,liol~r

\\ llt'IC'

difft'rcnl Uhl['rfo

wall .tl•ou '"' d.tJt

tl·"l

\."qUIUII'""' 1.;1.11, I .H omJ Se~,:h •n l I

I B. l.)(FfRACTION OF LI GH'I I.IK h

Opticsol J)ifl'raction

''Jr.. run' n from nunnnn1 \'Xp.;ri,·n.:...- 1hrat tf :m ,,hst~tdc '' Jll:u:t,llll tlh· fMih •'I

li~;.ht.

h.ur 'hdtlU~\ i' pni'l1w.:L'l1. whidt prove.. th~ rc-ctilint:u flllll1.ti!•UI4tlt nl thl.' ""'"''"' nl Nt:\\ h.ln·, t:orpuscular Lh.:ory But it h~ aho lx-l'n n lh~f\C-.1 lh;,tl \'l1c:n :tlll:.JIIl t•f light p.t ...,c, l ltro u ~ h .1 venr .. m.1ll Of"-'ning 1 :1~ I ISC.It. 11 ot ..

H~ht tlll

'Jlrc.&d" n\t•t ,,, 'umc dh!nlllHt, tht'! re_!:!IOn nl lhc ~comc t rh.'ol l :-.il:llltm .th:.l Tlu c:an he e\pl:unl•d ll~ <.'OO~>Ilh:'lltlj! the w:tvc n:llurc ol ll!!hl h~i>" ..:ounU "·' c \\h,•u t~n-: "''uld "''I)Cd the b'-'Jhill\jo! nl lhc li{!hl beam n1·ounJ lhc cl.1~~ 41l .u, tlfl<J•l~h. ~! l'h l.l.,h.· .•mllht.' •llumumluln til the g ...·tHtl~otlru;al ,h,tdt.l\\ .tr\:-U 111 ..ttllh \'\h.·ut

•\l.:L:orJml-' w 1he llun~c-nc' wuvc them)'. c.1rh progrc~~h ~ \\~h· ,,wtJuu·~ 'l.'cnndar\- \\,t\cl~l' ;md lh~!oot.! M:conUary \v:avdeH- ~a} M1N1 onpm.tllll~ lr•.)tn \ll l ltJII~ j'•UfU Ill 1111,• llrl~lll_.l :o.pht!n.;~tl \\:l\'C fn,tll 1'-//\" {Fil! J )~) . IIIUlll,lll

l .lf'hlt.l '''!!111(1

Fig. I. IS

Cn) l...iJ.!hl fr(IPI u llOini SOUI"('e Cs) IJ:l~~ht" lhrough nn :lJU.•rlurt• MN tbl l.ighl frnm :t 110in1 ~o urct• ($) obslruch-d . hy on ob~I:Jrlt• MN

I 88

F.nxmt•t•rmg l"'ln-.oc'

l ntcrtl!f1! wuh ~:\ch other. wh1ch :m: nOl blocked hy th\! smnll ot'tst:1clc. Out! 10 \\ hu:h h ftCII a .wwlf ttfHtm h· Fil!. 1. 1~{b). wlm\'t· ,\i:c· u nmtJillmhlc· {(} thr wm t' h·nNtft of the· fi~fu 11.\l'tlt~ l)lm:Cll m 1h~ p:uh uf th\!' h~;ht. 1hcn llgln rays bend

ruuntllhl• cUp~ nl th;tt ob~1adc :mt.J the 'h:td11"' 1\1nncd h) the ,m.t11 oh,1:u:IL• :trc IWI \'cr~ 'lmrp Tlu\ 111tcmmtt'lllll~{fu•ttdmg n{ fit:Ill mum( tlu• nJ.r:,• oJ fm Olhttlr((• or tllr· t.'IIC'ruaclrmrlff tl/li r:/11 within Kt'unwtrwol \'luulou

m'f."tl t \ f -alfrtl tfrt(nwticm.

Bul rn ~cucntl lht:' 1lhutnnu11on 111 lht! !!I!OIIll!lfh.';tl ... hudow ure1.1 due 10 pouu \HUI L'L' "''' ..:ummoul! 11hq:rvcd. bccau'c fil,tl) the h ~ht "<~tnl ~c-... .m· nnt pc1i111 'our...-c' oiiHitor ;an extended '-oun.:t (I( hFhl 1.'\Cr\' ptlllll nf lht: C:\h:nJcd 'UJ1",tcc lmm' ,,.., n" n d1rfnu:uon p~lltcrn anO :tftcl th;ll th"~ \\111 n\c:tklf'l "nh ~a,•h mh~r. s,, "'' ... ,nrh: dafft-;h:ll•.ln p;mcrn can hi! u.knuficd St:~ondl} the C'lht.u.:l~s whtch .m: ~~o~r.tll~ ur.cd. a 1c n l \'CI) lurg4" "~>llt' ,·nmp ;1rcd In the WU\l' length n l hght u'cd. , .., pr.•cuc;tll )' nu t.f1flm<:uon o.:cuOi. Auguslm JL·:•n l"r.! ,ncl 111 IS 15 ,:ll!~o f~ICto111) t.'\fll.tined the diffrac t10n ph~ llCll\lCO:I, I.C., the bcndlllj.! or lighl round the ,•d!!C HI .1 'iiH:tll Ob.,l;t\'ll' :111d nl~:o lhl.!' £C('11h11l'Hf (lTOp~tgDl lfln Of l1ght h) (.;011lhlli1f1~ Ill\• IJuygCih lh~Of\ rtf <;CC01ldM) \\ il\dl•t , '' nh the prmCIJllc of lmcrfcrcnct•

1.19

Fresnel ll alf'-pcriod Zone·'·"

·\~c11n.lin~ tu Frc,ncl. the. rl·whant cllclt .at aJl C\h:nMi pumt

due ttl.l

\\il\l!

fmtU

'' lll lkJ>l'nd nn dtl' ft•llfm i11g (aclm'o,' (II

\ \\U\'C Jmnt ('an hl' dtVHh.•d llliU :1 lutg\.' IHUIIlll.'l ol 'triJh

(\I

/UilC' WhtCh

.ar~ ~.atl~d

as frc!\ncl'~ 1.011~:. u l ~mnU urt.!n ~nt.:l the rc:,ultant clle~t ot any j)llllll will be the ccnnh lfl~d dlct.:l IHllfl :11l 't:n>~1J :1ry \\',1\C' COl:'IOilllO{: f'mm 1hc v:'lriou' 1.oncs CJ I he eflec1 :u .1 Jl'Uint due to ·'")' p;~nit:ul.•r /nne will J.:rx·nd em the , h ...taru.:~ or lhi! I'Mlilll fnH11 1hal /UIIC 1.lt Ill" clfC\·1 al J pf'ml Will :1l..;C' \Jcpc:nrt ''" the- ,hht~ulty t•l 1h.: Jl'IJOI \\'llh n:fcr,·n..:c IU th: lone unJc:r -.:•m._,,l(r,dtnn, \\ 1th Ih.: lll\.IL'~I~ '' rh.: Hhhttull\ c:lkc.'l \\Ill dCHC:<I"i-1.!.

l .c•t "' n ,n, itJ,•r .t pl.tm· \\:1w fmnt H'1 U'~ 1"-'tpcndieul.tr hl th~ pl.u1~ of lhl· f"'P""' pmpag.tt&ng tlh\1\g 7.-t.hrecuon CF1g. I J')) .uu.l /' ,.., .tnl'Xh.'mJI pomt at J pCf1'l\:nrht'ulnr di,t:uh.\• b fnml wIw:!. In t-mh·r lt• dctcnuinc the rc'ultttnt ciTc.::t Ql the l'h tint J• du~ ll• tli,lurbJnrcs rcachinl! fwm tht: t.IHfcrrut poinh ,,j 1 h1.~ w(l\'C front. Fn:~nd '.., mclh•x.l. con~i''' in cJjvic.lini 1hc \\hOI!! \\'J IVe; lrmu 111 11 ntllll~l 11f ll.tlf-pcrinJ clcmenh ur 1 onc~ c:1llcJ .t., P"re\nd\ hall-p<"rlod J.oncr. ..md then lind the Ctllllblllcd d:t!ct from ~t il .£011l"S .u J' Wtth 1-' Jo, ~entre <.lr.:l\\ ~pher\!~ vf rudii h + )J2. b + 2)J-:!. h + 3)fl ~:tc Tl'I~M! ~pht:tc will intt.:r"S-C~I the W~W~ fruOI n ·, W1 in t:4,:)01:Cntnc Ctrck~ JS shown HI lhc ll'ig. l. l9;o, hi. Tho radio oflhc nih c~rclc lrc>nllhc :ohMc Fig 1. 19iu) woll ho

R,.: [(II+ nAfJ.I! - 1,' 111':

= Or

(1,·

J,,,). I I + IIAl~blln !lAO)

lutrr/rrt-tU't',

I RCJ

Diffmoum fJttd Poluruntimr

,.,

I hi

\\hen.: th\! lcrm , !,f /-1, .. n\!~Jt:;,:h'tlln ~cnUI'!otfbHiliO tthA. htcau'~ It > A The df~J o l 1he :mnubr rt:pit,, hct\\Cl!n I\"'' t:f'n,c cuti\'C cnn~,;.;ruru; en-de~ w1ll be 1rR;, 1 - JTR,7

IT(Cn + I I hi.- nh.J.)

;rll},

CIAII

Thus thi! ttr<a~ nl a lith~ o.nnular rc~1nn-. <Ill.' ha\'mg 1ht: \·:due {!thAt. whid11' nHI dc:p~nth fHI n. ~~... , ulcr~o.tsc ~ lhtd. n ~"' n l 1\m~ decrl!ti',.C,, tmnu/nr rt•tim; httlln!t!ll rJrr (tr - lith md t/rr· nth r·1n -f,., ,., J..,w,ut (1\ nth Jtai{-Jh'notl :mu NnY> m;conlin~ 111 1h,. h ):' I l'lt .u. the po.tth dtffcrcnc~ tx.·twccn an~ '"" CI'II\M.':CUlhc: 7011C' '-.ll~ Q lf•l P- {}.J'::: A 2.. wlm.:h (,:(l0C"Pf'll1h hi rh•l.'C tliffcrt•nc:c ( 0: 2{ ~ ;r n( ( r.-1 a.c the) .ttL~ Lilli of ph~L' Thu"' the :..ccondary \\IL\'C'

71,.

= J

reaching h) I he pomt f fmm J tfl'crcm Junco,; :uc contmuously ou1 of ph:l'-C und 10 pha<\.C with n:.fc,·cnce 10 the LCnlr.tl PI' the (lfl<>t hatr.permd t.One . Let M 1• M1• M" \/..1. ~lc 1\.'pn:w nt 1hc :•mrhHadl.">: of \'lbrnuon of the ~•her p:•ruclcs m I' du~ In 'iC•.t\n.J. r~ \\ 1' c 1rt-'lt1 1hc l '' 2"" ~,...1 ~h.' h:,u pc;n<'l(l zon~..\ No\\' lir:-.tly .,, \\'C ..-nn'iu!..:J .....t ile r thnt .1s. th(: 7.Hnc:; gowg out wuhJ Irom 0, lhC ohliquuy IOCfC3!'('!> and hcOCC' nmp)IIUdt"S rmm dlflcrcnt lOll~ Wlll "L' continuoul<oly m lkcn.·.u,mg nrd-.:1f 1 IJ;. J : ()) S~..:uudly tlue 10th,.- phase dific rt!nc'-· (;tr) hci \VCcn any two con\ecutl\'c 700C\ ,r the d•spl:1ccmcnt ol 1hc cth..:r panu.:l~.· due 10 odd number ?one' 1~ m jXl:O.itl\ c Jiruclwn. then due t<t cvcn numhcr ut t.OO~;.S the d•~p hl(.;I.'IIICiU \\ 1ll h..,: nl u..:,;oli \ C dircc1ion ot the s;unt.' mst:tnt as ~h,m1 n in 1l1c (Fi~ . 1.201. Since tile omphoudc

is gr.>dually dccreJ\Ing as'""" numher< are incn:.a."iug. \d antpliluJ~ nf :til)· 1onc c:m be appruximatel) taken :'' mc~m uf 1hc :• mpli1U(h:~ dut! hi 1hc 1unc~ prcceuing :ond succeeding 11. "' lor c!!\;&tllJ'IIe

1 1.42)

So the resullont ampUoude oaahe po1n1 I" will be:

' ,...i~. 1..20

c; ruduul dct'l'l'USe uhunplitud\'

Nn'' lh~ :.bu\·t.: ..."4u:umu cun aHo he wriuc11 rh

[-M'2

I ; .If, ~ +

M +

,\/, T

l [T.\/, ,\/_, +

-f

M,:!. l+

Clc

\\hu:h '"·'"h..• trnn,lormt.-J m Ihe lnllm\lnj! \\il~ h) ll''n~ dw l..;.(~n II ·U.J

A- 2 +- ~" ''ll..'n''''''~l .Uid

No\\ \dH,'Il n

·~ ·->,

then \/,,anUM,. 1 -) 0. rh..:u tht• n· ...uh.uu .e!iipllttuh dul• tu ht:

llh· \\hnll.' \\:1\'C frunl 1t'1 \l'.. \tr.ill

, .. A-...

[ M, }

~- .:. ,\/ 1 /1

<I 451

1 hu-. tltc· tc·.,ultwll IItle fiAtf.\ (If P due tu lllh'bltrw·tc·d ulw/1 mll'c /111111 n an/\' mil· Juunlr of thm,/ue 10 1'1 lw(l~pc·nod :w1r;: aumt' I h:h.' •nl) hullliH'IIh.'~l ollhc I'' hull p..·n•~ Jnlc 1!\ clfc4:11n: m producm~ Ihe tllumm.HJon oJitlh'l'4'1iH /' Su "hen :tO •• h,l:u:lt: I lin: '1/C h:tlf the :lr~:t (II I he I~· hall-perlftd /UOt.' , ... phu.:cd at o. chen lhou w•ll !'Crccn the cffe<:t ol whHk \\a\lo! ln'm an~llh(' mh•n,uy :u P dm· tn r\!'1 ''' the wave trf'lnt will he 7Ctll "-n\\ whtlc 'nll~ldcnnl!, the n:cttJin.:nr rmr··~·llllln PI hght gcn.:r-.111~ lhc <iii/(: ••I the olhl<~~lc u~cd '' l;~r gn:oUt'r lhian tht' atl.'i• ,,j th,· I'' h.tlf pc:ml41ton.; aut.! lh·mx h\·udtn).! ttf 1ij!l11 t.t)' :uowullh~: c:cJ~..: ••f 111~ ,,h,l.n:lc. 11.· lh\· ,Jilfi":Jl'litm t!lf~L.J ~....uwu1 he noticecL /Jw if tlu "':• oftht olt\lti• b· f '.\ \ 1/mn tlh flit 11 u{ tht• I hrtll J'l'rlf•d :ntw 1 ·Jrh)d 1 t .• h'ht•n tlt1 ,'fl':• •'I ,,,. ,1/hmd,- ,,. t'ilf''l~'"'''hlt' m

1/lt htll 1 1.-u~;f/t

or on

r)., Uj t/lt' Jig},/ rt"it'I/ /Jr,·tt t/

t\ fti'.\HJdt'

If \111' tlfllllllllltiUIII Ill 1/tt•

~:rrmt«-'l,.wal

\lrmiiJU' f'r'J.:IWI, \1'/m·h pror~~ 1111 ch.lftm·thm ph,·umur mt I he aht1\.l: :m;;ly~a .. t•tm he u-.ccJ hl ~tud) the dlllr.u;tHUl •'I ,, l"l;uu: \\,1\.C hy ,1

l.'ltl'UI:u !lf"'CilUI'C l,.i.'l lllc pwm P :11 u di-.tmtl'l' hula t.'ll"t.:uhar :Jpcnurc nm" ll'>11h.'

nt4ltlf ... '' J ~'I

the clr~ul:lt apcnure incrcuo;.c~ Jrnm t.~~.·r4' tu th'-' r.uhu., (1llhc I '' half· fll.'nuu '""" tR,, vi•J. I the mtcn>ily 01 pmnl I' w1ll he m<~xnmllll. "' 1 h~ rc .. ult.uu ;tmplhudc

•~

(M 1) Ho1 a.-. 1he r.rdnt.:. nl the

R1, mlcn,ll) a1 F will

!'\:art'-

(R'!- . ./~h).) lhe lll1cn:o.lly S{1

((lr

0/1

nnd

~·rcnure m~.- rc;•~c'

mnrc 1han

dcc.·rc:•sing and when the radlll.., ,,t th ~· :Jili.'rtun:" Ill,. I S IOIImnum ·'' the: :'1111plllul.lc eM, M'!) - t n

:HI CtrCUltlr :-tpcnurc whenever the

dJ~Ianc..-

h:: N./lodd mulupt,, of w;l\c h:ng1h ,;.,, puu11 I' '"Ill b< hn~ht!!'' 1..)/~

= h::; Rf /even muiHplc or Wl,IVI,! li.'nglh lA). ft Wttl he d\lf~....... ,

11.4(•) 11.~71

/nlrr{t•n•nn•.

Diffm• ·lum nmll"o(ariwtwn

ltJI

J. 20 Zone Plal e zone plate 1 ~ n $J>ei.:WII) c-nn!-truCled !.Crce.al such 1hu1 ll~h l uh:~.tructcd I rum\!\ cry

:•hcrnah: t 1,

l'fmC "''

:-hown

Ill

Ih..: (Fig 1.21a). Kudii nl che /One'

;U'C Pfi"'!pOrH!!IlOII

lhl' ~quare muh llf th.: n:uur:al numh..:rs .lCCJll du&l_! an I hi! tl~.-Jn t I ..H)) Th~.·

,,~rr~ctnt!~' ~~r

Fn:-'ncl\ mt·thod in Jh idmg the who!..: \\'~1\c ih)I1J \\ 1H , (h!! 1 19. I .2 1' unu h;&l(-pcriu~,. 1'11111.'!\ ,;-an he \'crincd v.. llh lh help. I i crl' ~:\~U numh~r nl J',flllCS ~tn: hbd,eJICd \lllh!U lhc~ \\>ill Ubt.,IIIII!Jcd I he Ji_glll \\:t\'\: l:'"

FiJ:. 1.21

v i•

I ltJ •

I!)J:!

·~ j (a) Zone plntr lb) Z<•ne plate \~ith b t0:1d ~11urc.- h:J Zum·J,htl~ \\ ilh 1whtl

' uurcc Lt.!t "' Cl.ll\'ldCr ll pmul/ 1 !II !I pCrfR'Udi<.'ui:Jr ch,t:HIC\' b lmm thi!' /tllll.' l)l:n¢

ol !'i.

,1\\)\\ 11 1111hc CFi~. 1. 1l), l.~ I bl. If the source b ·l' .llur!!C J&~ l .uh:.: fu11u lht~ Jtull' pJ.tlt.:. ,, h1 1!!IH ~pol w1ll ht.: uhs~r\'la,l.u f). As th\! ~ll,tanc..: {lllh.: ...,OIIrH' lnln• l'llll\' JlhliL I!\ lar~c.thc mctdL'Ill wuvc from can be taken 'L~ u plane \\.J\~ fruut \\.1,1. tht.: '"'·•ll•ul!.l of lin: torle pl.tti!. t\Ct.'fH'I,hng to 11tc (Fit! I 2 1). ev-en numh..:r nf _.wnl!~ LUI t\f( tht> llgh1 and bcn('C the re!>ult:tnt :lmphtude :tt 1hc pom1 P due to lhc purually uh..trtu:tcd WU\'C lr~mt from lhe :~.one JliUl~ "1U be

~llli..:t: sltl ;J.Ulplitudt:' IHuulh~ C\CII nurul)f.!l o'

lh\-· r.nnc plah: (i.e. M~. \I~. ;\h ch.:

tJu:

,.,.i fl-mrmlwn·tl :m'''·' ar,· Mm·''t'l11'd. 1!J•• m/('11\tiY I_\ IIIUI

I'UIIC pf;_tit:' .ua: ~llhllucrnJ

I') rh.a m th• m I" 11•, nrdml.! rt• ·'lfll. r J A~ 1

=0). ')o itt.\ lltlt'tt .,rwg :, tmt.

It ,t:l•'dll'f 1/WII tfllltlt/ti'll 1/w 1\'lm/, tWI\'r·Jttml h 1'\(10\tllll• tlu pnillt p I l·H. ch~

~in...·~ .h \\o: ha\~· di:-.cu~. . l!d i 11 earl ier )..:,·riun (Fig I ltJ ;1n,l "'In h.·-..uh.ml .ttnpltlm.lt ;,II p d.IC In an unnhstrm:tcd \\ii\C rrot11 H ,,

I t" ~o'~

\\hl.'n a par.tlld hc:ut1 of \\hik ltg.ht

Mt 2

I when

• "I

II.~~~

un:tdcnl on the Lnn~.-· pl.•tc. dtUen.:nt

c,;oluur.. tomc to lt"k:u' :u tl(ftmmLpotms ulong the l ine (0P) (hg. l.! l 1 lluto,, the lum:auut uf :t t.ont.· plate it. ~irml:~r tv that f..lf ~·tmvc\ len\. J~nnn the 11-tg.

1.21 hi II\ clear th.u thi! t.onc phil..: is g1\'ln.g the convcrgcncc dT..:cc "I IipJu b-:.un' fu t· th\! miJ uurnht.••l!(.l J.c)nf.!-:-. 111 the puint /; like- tHtwcx len!' The locotl h.·ng1 h 1tJ Ihe t.nn.: plu1.: :.t\·c•,rding 1u tbc Cfig_ 1.111 \\Il l h~: 1nnu Ctln ( I .m1

F, =,, =RII'IIIA

11.4<) I

Thul\ a t;Ctne pi:He hat- difrercnt foci ror di rfcrcnt WH\'C•lcngths. which shOW.l\ th:ll the /.(liiC p1:ne suffer (rom consi dcr~'blc chi'Otnatic :Jbcrr:stiun!-

192

En~tinrrring

Plrnit•_,

The len:. funnulalik.c COil\'l'A kn .... 1 c.. the relatjou between ubj~Xt llh.tant.•c. Ui_!!,tancc :.tnd the Ineal h.:nglh can uhn be ubtwnec.llor u LOne pJnlc in th~· inlluwing W..t) lc! u.., t:on ...illcr J poiur ...ourcl· J.l S. XV is Ihe -.cction of thl" Jnnc pl:ltC pcrpcru.Jjcuf:u In lh~ pl:llh,' nl p:l(X'f .uuJ /.j j, pe.NIIlln o r bright image UO til\_' \Cr..:cn th shown in Lht: rH}ot I 21c,. ·nu.~ di~t;mcc from the sourceS to the/''"'-' plate i:-. o anLI Lht; ilhuuu.:c o l thl' poirll 1' Jrom th~:- :tOill' plate j..,. b. OJ . OL,tR,. R,_ clc.) :ttL: lh~ r.cdii of I''· ~ntl. l'h.: h:'III-J')~Jtiod /HIII.'tlt.. Tl1c lllhiUou ut the -.crccn is 'urh. lh.tl hu111 mil' Jnlll! hi th~ ne~l then: IS :.n mcrea ... c n~ p~th lhffcn:ru•.:~ uf ).12 . JI11 41~C

Tlu1:-.

!>/'

,\() t ()/'

,\/ + t.,P =-II -i SL~

+ /J

)J'1

f..,p-; ,, + b + 1JJ1

.\1. 0 + L,P- .\f' • ).12

I.C.

where /. 1 •~ un the periphery t\l 11h.' bt ..:m:k 111 the the lsi ~u..:lL• I'\ Rt• Mt lrnm a h~~ tF1J,: 1 :!h_· J ._\/, .. 1.,1-'

,,P-

'II

/( ., ~,

I.e. ).f1

i.e.

- (It

ur m ~:cncrul

:AIR!: FI

i..l /(I- ~l

l I l

f ·:

I•• I·I

h -

I [ t•

•

-F.,

nAif,,. -

plate nnd 1he rndiu ~ ut

,'h~ -; R,

I I'' I;

ic.•

wh~..~r(

R,,

L.on~

J=-

I I

I I '\01

I I ~ II

II '\!J

.md /> .m: the uhrc~~~ unO un:1g.~· <JJ,tunct.• :tnd f',1'= H.~ In). :m: the fu.,.·.tl ltJr LJII h:tCJII Y.,J\~ ICII!;Ih\. ·11lUl\ ltH1C pi.JIC IICI :l~ lJ C\lll\c.rging len., \\llh

length~

number of ftx:.l which J~.:pcruh t.'l nthc number of the: Lones (u) and cJjffcrcnl w;l\\." length' (Al

lmrr/c'rC"nrr. f)i/Jruction mrd l'olaruatum

1.21

193

Comparison Between Zone Plate and Con,•cx Lens

II j, \\CII L tlP\\ 11 thfll

p.Ulu.ul.ar '"oJVl! length of ltghl t:t!O\ C'( len' ha\ I! 111\l!

hM.-;tl lcnjtth. ~l-<IU~t:

IJ ~ ~ II,

" lu·rc Ihe l t~"·"l h.'nJc!lh. J' ''I heN I uf Ihe matcnal ulthl' len' anti R1 H• .u,· the wthr ul ":un .uurc Sur~.;.: lht: N I of Ylltlet rrtys 1:0. n•nrt! 1h~u• H /11l n.••l lt~·lu 'I' -,.fl, l 'u' 111ld h ~h1 '' til f\'LU' m!'::ttC'riO the len' lhun red h~hl. whet,· ·" 11 Pill ~qn ' I 1 I 111 " ·I~·'' m '\tne plate foca l length violet v. ilJ he mort! th;~l lt ~C.al lcnJ;th ol r~.:•l ·1... 1 )., <<~,I Whtlc con'itru~un_g: tilt: 1.onc plate. 1t Is tonstnu:h.'d accordan~ 10 the t1tg. t ~ I t r~tr ,, p.trlh ul.~r va!u(' nl h. But .Juring llh: exp..:.lll&h.::lll '~'th 1mh" rl,th' th\! Jt,Li1111.:~ h. I I! tiH' llll :t~(' d ....t:lllt:~ (Fig. 1.2 1) l.i..'., t h t: ~1'o,l11011 uf f.J l.Jfl h1: ..:h11ngcd 1'\il\\ •.-. lhl' M'rtc.n ' ' UHWl!d nearer 10 thl! /.nne pl:llc h v. ttl rcdUi.:t: thl! \11\';\ ,,1 lhl! hoi! I ~rH..J clement.. : :~~,;cmtfmg tO \!((n. { 1.41 J (/diAJ wrll ahu t ..·dm:t•

,,r

..u ulmc nunihct o l h:1lf-p.:nud dcmenb c:1n he prc.M:nl un ~:•~h /01\t.: wlud1 '' ~lltl.'atJ~ um-.tntL·tcd on th.: 7.0111.' ph1h:. Now il. P., 1~ lhc J)11\tlwn ,,1 the lflM!!C when t::!m I J hHII ~ pt'JU!\1 ckm(.'llh ct111 be p rc:-.cnl un cndt .;un\I IU,h' t.l/ttl'l.: nn lhC: /HOC fll::lll.• then (l'IC.'..tl lc.•J1f lh uf lhc /OOC ploJIC " ill hl· I

-~ )

Sa) lur ,, p.trtKul.tr pn~•hnn ,,, lhc :o.l;'r..:cu c~ch I.C'\n~o• cuntmn lhr~l!' h.tU p.·uil(l dcnh.·ru-. , ,_c.· m::: \t. thcnthl' I•~JI Jength for the I:..J iwl t~rctHllilt'll'-'lt.s: 11;:; It

will b.: I

I~UJ

wlm;h \\llllx- n t\ lhl' li uc{0/'11 Hg. 1.21cl ;t.-. P 1• Pl. P 1 11nd Hut ul .tll lln·w thn.·l· fl 1 wall he nu•,ttllh!n\e, ~ince ;,u th1..; p01nt rcsuham ampluudc h lM 1 ) .. wlwr\" "'' Ill P , resuhant .unplltude r.; t M 1 M 1) :and tU the poull P , n:suh::un ampiiHith.! '' !M 1 ~I + 1/ll

P rnhlcms o n

l h~ Zon~

Pla te

A111!oUI\1C !llll:mc \\ti\C dl "·' 'C lcn~th 5000 Aii. inli;.lcnl '"' " .O:Ih.UIJI oiJA"Hlll~ l'f r.ldiU~> 0 ~ mm C'ak.ul:trr tht' pO>itllun u l the! brrghte'l .md d.trlc-'1 \rnt 1111 th"· ..tl,lllttlll

I Htn\ l·qn ( I -if'l an;J I_4..,.J fM hrljthTI!t:l 'i.ptl~ R,: = h}._ <;o ,h,run.. ..- ,,n rhc a.xi .. " h = OP = R{ I A = 0 OO!i/ '_l x tn _. ~~em For d.trh~\l 'P"'' ,, = OP = Rj 12b). = R1' 12 x 5 x 10 ~ = .21 'm ~ With .1 tunc plutc! (('r p<1int .. oura: of hght CA. 2 tiOOO A). 1h~ \tnmfC..'I ami th(" nc:\1 ' lrong..:...,l 1111UlC~ IUl" fonncd (ln the axis nt 10 em oml (; nn. re\pecll' dy. Irum lilt' lone JJhUt. Buth the mt a~!..:.~ un.: on lh~ ~rue Mdc .u1i.l ,;n the ut h~r ~ hJc

Qt th~ w un:e. i\\w.. 1,.\.tlcuhth.' In) 1h~

lhl! r:u.h u' \'rduwm

lhr;: di:olonco! •ll tho:

41( thL' hllllUl'. (t.' ~ ptiiiU(J:ll

~uur.:.:

lrmn 1h.: 1une pJ,1tc\

{CII.:,tJicllgtiJ.

h»t I" l'.onc,. =- I. nthllu l .:~ ll'otl);.:'1 unut:c m :. I h 'r n.:x• 'trvnJ!~~\ m Rf lA ~md F ~ 1\'1 ~A

= ~. Ml / 1

.s:

I 10

,l = MH.,

.111<1 -!"

dh1.11.;,· PI 1lw ~nun,:..: f1 n111

1h~ l tlnt,' ploil~ - d -

l.U em

B) 'Ubl>titulUIJ.' t ht.• l .tJuc u( o 111 1he Qt'lll' ,. l'cpul lnn

6 ' II\

R'[

l~J ' ,'o J

lh subJ·IItUlilllo! tho: , •• luo:

1.22

Llf

·~J x tn

ollh1 ).,

th,· ,,rm\lr J.I IOl' 1.ll

l~nlo!th

tr,. '-'Ill bt

l<'resnel and Fraunhofer Diffraction

OiffraLIIOn phcnORll' thlll \\l.!!'o con cu i)· cxpl.uncd h\ Frc.!-nd a~ 1t i ~ Uu~ h> the mUlual mH.·rfcn:nc: tJI "iCetHu.lnl)' w~l\ deh uri~m:tllllt! (rom ' ariou' J>lll nb nf the w:H c lrun1. \~hiclt ;m: nul hlvd.c:d u t'r h \ th~ uh~1 .1ch: H.::re he :.tpplicd tht• llu_yg~n·l< I'H'IOl' IJllr' 11 ...l~u,nd.u ~ " :1\ d~·l ... "nh th~ pnnctple '•f mterrcrcm.:c D1flr.lt..' ll\l0 ph~nmn ..•n;.t c.,.n hi.' dt\'llkd an M two dtlfc rcnl c i:I!-!'C ... ( J) f rn n..J\ tf.t.' llc/11111 I whll~' ! lh •lll~t· llhl SO.::h~t~ n bnth .tfl! rJ.u.... J !II I lill ie d i ~HIOCI.'.... fron+llll ~ •t h t,td l.' li;J\ Int: ... h.up cJ}!t:. No lcn:"'c!'- or llll ll•lr,:,.out.·

U\l.'d w m~tl-..: the r.i)' I)Jr.JIId t~r comcr~.!l'nt . 'I he ml·sdcm \v~nc 1ro111 1u the nb!'1udc I!- t:tthcr :ophcrit::tl,,r '")' hnJrit::tl But \\hen the: 'nurcl' '' pl3~cd at a l:tr}!e d l!'tt:lncc thcr. the !'tphcncJ \\ :J\ 'C nout w1 ll b.:cumc as an J>lanc wa''i.! from. ''hich we h 'I\' C uhc.1d: di"cw....,cJ 111 "t'Cium.., I 19 IU I.~ L (:!) 1-tuuuhojr·r ,/rlfw•·tmn ~~ \\ h\!f(' the <;t,l_ UfCC and 1hc '\Crccn or lt·lc:-copc. 1hmugh which d irlra ~:t itln p:tttcrn 1:.. ob~c rvc d nrc phu:~·d 011 mf101y or dlt.!(.:lncly :noutiout)' o.<.. one d~ut "'~' l'CC\1111~ p:oo:o11• 1with :o leu<and the difl'mctcd hcam .... tuctt~"'<l 11111he ,.crccll \\tlh anmhef leo' N••\\' 11R\\ ;tJ\l., \\L' Will dJ Sl'U'~ FmunhntCr Oifl r~clion

1.23

Frau nhofcr OifTradiun at Single S lit

L..-t :• monochrom1111. par.1lld beam ol light b< mctdl!nt u n thl! !'>Iii AIJ or wuJth a (F'Ig. )~}. rhc :..C\.'OIH.hH\' \\a\C!<o 11"<1 \l'lllll~ uJong ~ am t.~ din:cu on COI11C IV focus 1ll M~r If Lhc wadlh or the slu il h. t.:ornp~lntbh: wuh lhe W<WC ll!ng.th of the monocr.un:Hil.: lig1u u:-cd. th~n :-l.--ccmdouy w~•vcs will also dirfr:lct ::u an ~mglc {) nnd come to fl"K!U<: 01 /) 1 Now co n~idL"r twn d1ITracLed beam'\ AA 1, IJIJ 1 fmm 1hc

luu•rfi'J't'JU'C1, Dt/frut rion am/ PolwLuuhm

195

''' u t•\lrcmc pt"'llnt .. of tlw ~ingl~ slu (FI~. 1.22). If th..: p:llh d•ff..:rcncc ;"\)' bcl" 't'en ''"u ~o.Jtllnactcclmy' ; \i"\ 1 uuU /IIJ 1 1.-. mul1ipk of A then 1'1 \\Ill bt dark~ It i~ ..o. ~'"'.U''l." wht:n J\Y; A Lllcn OD-. All. \\ht'Tt: () ;, 1hc mu.ll.llc ptlllll ,,f lht• ,fit fhu~r.. th~ path \hfh.'rCilU: ll\::1\\~Cil n0,1111\J ()/)I' }J'J.. "IIIHL.III)' p.tth tll ffcfl':O.:c ~l'"ccn t)J) !tnd AA1 ' ' ;tg.un ).11 • •md \\hen path difference j, ul Ihe onlcr of ).1"1. then thcs.: two rays w1 ll ~wtt <Jc.;tmC'I1\'I.' mh:rf~.·r"•nct• :u 1'1 Thu.... for cv.:ry (l'l1int tn the up~1 h.tll (JJ\. then! is"' ~(>rr\!~(lOm.ling (lOIOl 10 th\! 10\u~r half 08 .ttu.J th..:y d.: ...lrn) l':.u:h (It her b)' intcrfcrcn\:l." m bc:I\VCl'O thcm~ch·c.... I km.c the dlll\lihon for tliffuu lioil minimu ''

I -1=-Po.Uhlhn'cren...:e-:. \l where/)= I. 1. 3..... .utd r'i= 1111.1..... tlif(r:rent:c

.,.,1nO

1150)

, =-;: fn!»in 0'

1'hc t:tllld i t n111 ror .Jiffrt.t'litJII liltUWW

i!>o

( 1.5Uhl

Thi! tli rf1'31.!1H11l

p ai1Cm

due ICl Slllg_l~ -:(11

COUHUU.... a ~Cntntl

M11 {I''!!· I.U}. lo11ow\!d by secondury ma>.una Hnd

bn}!-IH !n~tX HIHIIIl a l hf•lh lhC ~tdc..~ of l-'i1!. ( 1.!2) The ~econd:tr)

nhn llli;t em

M,. l uh.:nMty d1stnhutHil 011 the scr~(n t~<t. Js -.hown tn 11111.\HHU ure uf much I~\ inrcn~ il)' unll 1hr11 ultt'll~I IY tall<. nU t':•pu.lly (rum th.: 110nn Mu OOT\.\'llf'd~ Sccondm')' mmimn '' 111 come when the path t..lini::rcncc bciWCl'll IWO Uift'ntctcd be-ams AA 1 :md 88 1 110 .t 2A. :V... c:tc l f th~ len, / . In Fif,! t I 12l ,, very IIC:.tl Hllhl! ,Jh onhr '-CfC\"n i' far J\\:ty rmm lh< len• L chen

,;n

•IJ

'= M(,l'1 (Fig l.22l. rri:lngJc- ..tB)' that

"""'" f•s 1hc foollenglh co( 1hc len'/, nnd

801 t'mm Fig. (I

~2)

it is dc:tr (rom

Lit~:

>in Q

=II Y/<1 =J./a

~If=

So.

Alii

i-.J

{: -

whcfc ' i'\ the d t,t.ulcc of the liror;;t ~cond::n')' minima P 1 from ah..: cclllral •u:•>.:tm, 1 Mu So tht.• Width ollht.• l:t.'ntr;ll m~1X t mum is 2r whe:re I I 5UcJ

f rum thc l'~JU.tLon ( 151k). \\.C can conduJc 1I) \Vil.lth uf the ,.-cmr.tlma.ximum is pru~>tionalw J.. \Vht.·n). t=-- mure fur ret I th..:n width urllh.~ l'l'lllr:illll:I.XIIlllllll will be lllOf('. C!) \\'ii.Jtll ol l'('ntr:llmaxunum t!'l tfl\ t.'r.-.c:h pwp\U1!0nHI hl a. ,,JJth of the !~olit. So if the ~l it '' mtmn'. wu.llh \•I tlw 4.:Cntru1 m.t\1111\Un wi11 he: mur~. {J) Diffr~tction ptUh.:m con~l,l!oo ur .thc:mat~ d:trJ.. :U\J brittht b.tnds wilh mullt)Chromalic light. \Vith '' hitc li~lu LCI\11:1I b:mc.J wtll be whHl' bc:l.t '.I~C :11l ti.:J\'e~ \\ttl supenmpose at lJ = 0. ;u c~mr.JI rn~t \llllUIII Rest

••f the dtl lmctutn h:tn'l will he culvun:d b..:caUM' (Jd~pc 11tl~ on A

•.J) Wh~~.·n

0 ,,.,II be ~maJI. so width of Lhc t:cmrol nu•x tmu•n ''til he -.m:lll {&nd '~.;un1l.;_uy rnm1ma nm.l maxtm<t w1LI be \'Cry du~~ tn" cntr.t111M\IItlllm nul II It ,, '111<111 I be n lht;:) au: {Ill wdl sep:.tt:"ttcd. w1dth .._1( th~ :;In

I .24

1:. lar~l!.

Fraunhofcr for Diffraction at Double Slit

Ll'l mnm...:hrnm.llt light Iall 'm a double ~ l il Fig. ( 1.23) AB nnd CV. p.lr.Jikl li) r:a~.-11 'tlhL'f .uul 1"-'ll'ICiltii\.'UI;u IU I h(! pl.lllc: ur the p;•pcr The "'II hh ~·· «.'tli,·h ,,,, " It JOd th~: ot1.1ljUC pun ion .... It I.1.'11IIC \\,1\'C fmnl he irH.:id~lllllrl lhc ... ur(.h't' JJK ,UIIJ .111 th.;

"l'LIIIU.iU) "J\~., ti ..L\'dlmg In .l d i i"'C('III.O p~t r.tlld l 11 (),\1

••l'llt' l•l

f'•~o~.·~~··

11 • -.; ' t/, '' tl~t• '""iiiuu ul "·,mtr.ll m.t~lmum ~h.•r,•. lhL" Jtllr.ao:tiun p.Htcm hn.."i tu h.: c:o n~ICkr~d tn IWlllltllh SimL" th..: ··lit... .m: \l.!ry n;trnm. "'each ..tift will ~iv~: rio;c ltJ diffr.u.:t.:.LI r.-y ... Thl':-.~ t.hUI.IliL'tl r:.&)'' fhcll mh.·rlc~ \\ llh UJlC: oiTltilhl!r anU g:IVC-timsl pnll~m 1'/u" tlu jiuul (hltkrn i.\ u

WJWff'tHI/lml

ufintc•rf,.,rm·r JHlW'IIIIJtrilif/rtwlitm Jlllllt>m 1Fi!!· t _:l.h ll"fm

f-1~::..

1.23

l>ifTruclion fnun duuhh· sl it

lml'lfi"rt•nrt•. IJiflmcwm am/ Puluruutum

tlJ7

p.1ruculor din.:c,; tmn 8. •olcrfcrcncc m:uuma and diffraction inlnlmG CtmdlhOI\ •~ s~atisncd 'lntuhancou,ly. then Umt ~pcctrum of pnrhcular nn.lcr 4:s.ty M, when lo '="h. 111 the Pig I 2J) will be otb'\C:nl in thm Jin:t:Hnn ( h g I '24l

~~ .

r lnttn•ul} "'

M, , ,_..-·IJIItr..:IJ<>n p.m~m \ M '

Jnt~tfl.'ll.".tl~t Jl.l't..-nt

f',J"I

fo"i.:. 1.24 Diffnu:lion pi.llh:rn

du~

tu duublt: :tlit rut 2a = b

Lruerfcrence 1\bximu 1md Minima Let U!<l <.·tm!<>hh:l the !!occondary waw~ thifn~-t,:rcd an .1 dtrcctJon mdnll'U .11 .1111an~h: ll. w1Lh initi.al din.·crion. So 1hc path di(fctcth.."(! bt!'l\\-el.!"n the cnn~o.L'\:uth~ imcrfcrin~ '"''ALand(")' 4Fig. I 2.'\), from 1"'0 COO..C'-(Uli\"C ~)II, I\

CN;Ia+bJ'!IIl 8 Ntt\\' if this path diffcrt:llCL' i~ ~:qual to tttkl multiple ••t )J!. (J wi lit.:" c dtn:ctiort 111 imcrfl·rcncc minimu. Sc lhc condition of im~:rl• t"('lll • minimu f<lr tlouhll• ;.lu "

I fa+h ....mtJ =c2n± I~

II Sial

v.lu:rJ.: '' = I.:!. 3.. Ri''C\ lh< Ist. 2nd. Jrd ('rd<r tmerkr~n~c mtnnna. On 1hc: utlh:r hand tl tl " .;\t;O mulhph: nl )J!. 11 \\ill gtH. llth:rh:rcnt.:~ Ulll\1111il Su the l.!ondlli•111 for lm ttrfttt!llt"l' ntfl.tim., h

[ca+ /J) !!oin 8 = 2t1A./:! = uA ""her!!,= 0, I. 2

• gives

cemr~l.

I st.

2nd~

ll.51bl

nrdcr mtcr1"ercnt.· c ma.xtlllll

1~1g.

I ]~ ) So (l(llnl P1 m F1g. 1.23 may g1vc lh,•nll~rl~r~ne< 1113X1111!l lll 111111im:l 11ns11mn. \.h:pcndm~ up,•n the. p:.~th llam.:rcll~,:'C. Oiffruccion Maxima and Minima Lei u ... constd..:r the Rocondary WO\'t!.' "-•l lrJcted m J. dtrecuon mchncd .11 an ;~r~glc

0, Wllh th!! 111i1iaJ IJirC4:-.i<Jn Of indtJCIU light, ·n·~ p!Uh dt ffe"li..' fh.:C h-.•IWeeJl tU1.1 dtHr.t...:tcd ~•1m AL nnd /18 1 crmmnlin,g from the C\lremaltc' Ctl the 1111'11 ... lit j ,

(F1g. 1.2J) 8,\/ = tl

!'Jill

:-.:'(1\Y II ltu~ p tllh (,hfri..'r\'llC\' I~ 1,.'\'Cil

muhi lliC A. I hen f) \\ Ill gi\'C d l fCCIIOn o f dtffr3cuon mmtmum. whteh .:~1n be cxplatncd til the same w:,y. as 11 was done lor sm~lc ,!Jt. C'Oihtt.lcr 1hc- wuvc front A IJ 10 b~ rmu.Jc up ol L\\U halve!). 1l Ihi! p01th dtUcn:uc~..· hc tw,·cu 1hc (On-:'J>llllt.h n~ ptmH' ul lhc upp;.·1 .md 1h~ luw~' hulr ;., ~q ua l to iJ'1. lht.:n ;1U 1hc ;,ecnnd~ll)' '' ~we' will imel'l'cu! t!e,arucll\'dy Thu~. lhC lhfC\.1100 fJ. may }!1\\.': thl! dlrtcuon or <hfrracuon llllntUhl I ht:n 1)\.'l nl / 1 1 (i-ll! I ..!JJ 1uuy g~'" ddlt;_u, tuulnnnttll.l pmilhon llt'!ncc,m ~cncrul.thC\!nlufumn hu dtfttllc-tum ttlltttum 1-. . /i;\1

\\ ht.·r.,.· I' : I ,

C\n.'pl

t\'rn On

whcu H1\f

~ tt

<Ill

II= JIA

l ht: ~oHhc:r

hand.

sin f1 ~ <2!' +-I )A./1

then the t.IJl"CC:llliU 0 \\JJI ~1\C lht.: du't;.,:lh.U Of tf{f}inrrum tiUI\111111 . l:i!!ttr\' 1I ~-1 J ,ht•\\' I hi.' M.,,unLI.uycun•c. w-hich rcpi'C$C1H' Ihe intcn\11\ tli,arihurtnn ol ,fiJlrn..:uon J''•ut~n' c.ltl~ (o doul\fe sill. anti rhc mner line!- rcpn..•!<(cnt lht' t ntcn, tt~ ,J,,1Hhuriun dll\' "' lh~ uttcrf~fcnc\! hclwc~n I h.: diffracted lil!hb lr,,m ~ollt lh\· ' I ib. T/u ••ttml{l\ '"m·c.·d rmcorkrcnn~ pattt!m i \ Sti(Wrimpc13t'tl mr lhf tft/fflh 11n11 l''"'''m of the· tlc•uhh \Ill I he n.:~m nurg1 u ~ally lw.:cupu::d h) 1he I..L"IItt.tlltt.IX Intum u l lh~: ,iu.l-d~.· .. Jh ,llll;u.. liou po.~lll'flt j, ntH... ~upcrimpo'\CtJ b) lh~ C'()U;tlly .. p..~.nJ uncrl ~rence m:l.\JOl.l und nHnuna. ·rhe mtcn.!-IIY of t..hc cemr..tl m.n.:imum tm duuhlf: .,Ju l "i four um~.·... tlum the im...·nl-lt) (1f the ~o:ct 1lr:1l mnx tnlultl If'' 1h~.· '"'!!k slit ;, .. \\C \\111 "'0.:\' i t\ !he lulkm tn~ tli$\! U :o.:~l{) n S:. The m ccn,ll)' t'l th.: (1\hcr 'iCt:t!UJttl') UW~ Ill1 ii lJrt.'

tu:t\Jmum t hl'

gmduOJIJ)'

the; I\\\, :..:uJ~,•:o; HI th.,• l'l'nll',d d iiYrac1ion h) J futhft: ,Jrt \\ uh

tk..:rc;I.SIO!! On

11'1\'lbiiY tlt~(ribullu u

due

1(1

l~J h '':. .. ~.howl ul l•tg. l.2-~. \\he r~ the I'C"g1on of 1he cemr~tl otmJ 'e""unJ,Jr} nt;l\tmtt ,,hll'rih."lll\.1 fh.IH\!rn Juc to douhle !'hi '"' 'UPI:rtiiiJXN't! b,· 1lu: ..·quail\ 'f1·tt.:<:d 1111\!rlncn-.,,· rH.U. Inl<l llf km tntcnstty. For the case la == l•th~:r..: will he II VI!

tru,·t'krt."Jh'l" ·n.t\tnt.llll tht: ccmml ()JJ fructmn muxnnum Tlurd IOll'r kl\'!ln' ll!a\tnlll • \J' I \\ 1IJ ~ H1 ,1 p1•,illltll l •l J If'\ Jrl h-:.«.:1hnl 1111111111a, :OOU II Will :k: ;lli~\.'UI j"(~o. I 'I d~.·loul-.. "L'c.'lt••n I ., .,:;aw t.l•l

l.25

Frau n huf~r

Theory of Diffraction Gratin:;:

Onto: ol the mo... t uupnnant .tnd lntcrcsUnf; :lpplicauon~ ol Jal1rUl'th~n '" thl' ,lill rnclu)n t:r.alm~ II -.·•mw..h uf ·' l:uge llt.unhcr of cxtr..:nl!!l\ nJrto\\ ll.lt.1lkl ..;fib SL'p;lfi.lttd by C~Ull f (lfJ~quc :..:p:u:C. Titl'rC 31'~ t W() typc.s o r gr;tlll1l!. lr..tn~I1U~:c-tull fr:Hm~ <tntt rcllccting ~-r:ume.. Tr:m...,ni ..,iun ~1.11 ing' ;tr~ prepared h) ruling fine lines extremely dl)'~ W£.l"Lhcr un rn~.~ 'urt:u:l! ot a ~Ia-.~ pl:uc by u!'mg ;t tin~ l'hruv r.lumh_m..l pt•IIH In 1h:11 d J ~unnncJ,cr:uch~..;:l(.'l m. • lp:t~a u c -.p:u;l." :10tl 1h.: tmnsp:m::lll spac..:- 1n hctwccn "''" ftth!S ;tCI OS ~~~I.

f 1gun: ( 1..:!5} rq')u;,.,:nh tl1c :o.\:~hnn o l n ,gr:shng whose s.h1' urc l>l'rJ>entliculur pi:Ule- nf 1hc p·apcr Onl) lOur slil' have been ..;hown 111 Fi~4 1 I :!51 bm m1 m.:LU:'I gruu ng con(.HIIS 'huu!'~mds ol thcm pr.:r \:Cn1imch:.J, Tht.: '"'idtb ulc;u.:h ,),, '' o tuut th.,.t:utn • ll->'1\\ I.'Cn 1\\U s il l ~ 1!-> h . "Ill~ d1S.rance (o +h) J\ J..mhnl m grmJ,JS

d~,~

sins pet· cenumeter of the gr:lting: b N then Ia + /J) N-=- 15.0()(} lu1c. per 1nch. then

C'f('lllt'llt. II number o f

em But d

liN

/?'r-ifaenu· IJiffraction ami Polansmum

199

~I 1.25 l>ifTntcfiun und diiTntdiOil p:11tern from dillroction

Fi~.

("+h)

15.(MXI

~Iii

(·.·

inch~ 2.5 ~

cml

,,- f,-()Jlx 10 1 cm=8000A

a.c . .So the

~~ ~ 15~ = I b

gn:ttin~

W3 \ ~

length rf , ,,Jium liJ;hl (-

onoo A) b

tompantbh: IV the

llb,t;~rk

,jlc (= h). whid• j, ~':o.~·nt1.11 JHr •llfll .tclttllt.

To get the Fr.wnhnfct t.JIITr..~ct l lUl p~ucm m .1 mu1~mi.ssion ~r::uin~. tl11.' rn..:id~..·nt wav.,; front mu't he pl:mc ruul the Ui1Tr-Jc1CJ 1i~h t i~ collt::ctcd o n lhl! l;CtN:n with

the help o f Lh\! len' L. Le t. .t ptlr.tlld bo:am ol monochromauc lif!ht u1 \\ a,·c length ;. be mcuJc.:nl till IIH.' tr;.ubO'It!<."'htn l!.r'Otmg. The problem of tindtn.~ the mten-'\ity of h,gJu trJtbtutucd ll~ £;1.11111£! 10\oh·t·s. Ole prmriplc' of mtcrCcn:nn.: anc..l din'racuon StnL"\.' lh" '"''arc \Cr\ n;tnt)\\, c.·~,mp:u·all\ t= h' th..: W•IH' l..:nt:th •II 11~111 M:'l e;tdl !<!'" .,:-. n-.~ h' d1f11•.:u.:tu.S r''}' lhcsc dlt1'racl1:'d rays tht:n 101crh'lt: wuh one anotht:.•r tn rrn.luc~ the flnnl p.1u~rn I hus. lbl' liual pmtun ' 'a \'llf'··r pP,Hiimr of tlll!'t1('Tr'm'c' pmtt·r·n rm ,fiDml'lum JUI/I('rn (FiH' C\iO:-.t~llll~

1.25 ami 1.1h)

of:

I \\'iddy~:!!poK·c:, l tllllr.u..:hun lllll;\ Ulld Clum\ll i"t\ pritn3f) mllxuna ) ..,lh.:h o.~-. M, . M,. ~ CIC ti-1A I :!.Sll!O hnlh lhc side' or ccntrnJ maximum Mo. :!. A large number fll Iami ~ubsh.fl.lr) m;txinw ;md minim:1 in hclwcc:n l\\ n primary muxima ()0 bnth dw !'ides ol A/11 I Fig 1.25).

Condition ror Prinw~ \fa:\im3 Let n pla ne W:l\ e lrnnt bt• lnr1dem on th~ grating !-Urfucc nommlly. By llu v~..:n ·.. principJ~. l':tCh ur lhc.;t• pninls ill lhc , !hr. .;ends '\CCHIUI:try Wti\'CICI' tU nil din:ctions. MoM of the secondary wa\'CS proceed strrught und when coll(•t'l<."d h) lhc lc1h L p~ttdm.:c u ~lrml~ hnt~hl ponu itl A/11. It j, known d' ccntml ll1tiX 111lllnl. Ncx1. consider tht~ l1ght diflbcrcd in lhc dir~ction makin£ .m unglc 0 w11h thut uf inc.:idcru beam. The t:ollcctin~ lcn11o L :th.O i-. properly rotaled such 1h:tt tho\c diffrach!d r~1ys i nterfere wilh each other nnd get focused a t M 1 ~ Tht:.> intensuy :tt M1 will depend upon tt.c pnth difference between secondary w~evcs ungim11i11g

1ro111 1ho corrc.pondln~ poin~s A on.! Cor 1wo ne1ght>urmg sill>. In hg11rc 1.25 , \8 =a und IJC-;; b. So the ,,,,lh d•llcrcm.:c hctw ~1' I\\U inh.:rf..::ring :-.ccund:u y \\·;1v.:' Jf\llll i\ 0111cl

f i'On\ IWO (. l.lll\t'f;UII\ C \Jil:-. I~ 4

P.llh Jillcn.·n'.:c - ..3 = CX

Thl'

p~nnt

,\C

'II\

0:: (a i It)

\II)

M 1 will be ofnmximum inh:n,tly. tf 1111, p<tlh 4.hll crcm:c 1:-. C4.1UU11n

ni... f'1•w• (,,t •• pan u::uhu· value ol J,ff,al' h.:LI :tnstc lJ:: 8 1 '' hen CY ;- tL

''c." HI

gel hl urde1 primary ma:d m~t a1 M 1 It lhC' diffracacd angle () h mrn:a.M.:d Lo 0 . ..ud• ahm p..11h d•rkrcncc C.\' bc1wcc-n ''''"l"·on,~,.·,.-uuvc mh.:rfcnnp. ray' from A and C "~A 1hcn1hal wtll ~tve 2nd mdl!l p1nnary lll:t\111\:t :tl M ! anti \tH) I\ , Hcr1e.:e th\! !!Cllcrul ~ondit1<>n of iiJit"ljt'I'~IWt: 1nmran m.J.\'IIIW i<:

I f•ulh d1fltm:-m.:c =

c: • o

I h)..,, .. ti,, =- nl. j

11.53a)

whc11.: n :: 0, I. 1. l :.~nd 811 =- ~tngll: ,)r d tlTr•.h.IJ\10 lur nth. Pnma11 ma\lma J~or n =- H. tu::: 0) g tvc the d1rccuun c.1l Cl'nlr;tl maximum Mu Condilion nf :;ct:-ondury minimn Wlwu rml h , hfl..:.r"tc~ ex.:: l nrul •"'t'\' uf t.hff..u.:IHIU fl,. l f-1 md~r rritnill')' Ill \1 1 ''til L:Ctlll~ tFig I 25). No" if the .m~)&:- t!l dtUe.u.uun 11 1 be mcn:i.t~~d hy t/81• ' Ut. :h tllat lhc po.tth JiffercOLl! CX ht:IWCCI1 l\\H l·lm\CI.:Utl\c IOicrfL•ring 'l'COih.hlf) r.ty!- h1r J\ an..l C incrc~L'L~" hy )JN. lhl!n the p;uh ,lit'f.:rcm:c ht.:I\\'C<"H Ih..· i,C(.;fmdar) w;n•~ .. fo1 h~t• cxttcmc puinl-. A o.uuJ S t.ll tlu: !!.'· '''"!! \UI f!.u.•c whu:h \.'Uill!U11 N numh~.'f fll -.JitS will be. AIN x N =-)._ New. a~!lumc lh;l1 1hc whot ..• \\;a\·< fmnt b IH

he til\ ttlf:tt

11110 CWO

h:tiVC:,,Ihnt !he path !Ji iTt:I\.'!ICC hct Y..l!Cll tht: LlliTC'ij)OihJilll!

hahc' will be A/2 and .tlllhc ..c... nn,J~u') wa'l!' will intcrrcrc t..lc,-.UuLtlvch lhus rO" +dO,, '"'JJ gh·l! che lhr~llluu ,,f thL" liro,l ...cnmilotf) minamn .1f11..·r nth J)rimary m:•xirnum Simtl:trl~ 1ll'm hi}!.hc1 \':tluc t\f tJ(J = tl8~, CX , .. lllo,.n:o.~o,t:c.J b) 2)/N, then the p;nh diiTC'rcn\.c ~lw~..•,:n CWO t'"s,tr~mt> f:.t\S o l lht: ~ruling '11rt•1cc from A am.l S w1ll he 2i.ll\ ~ \ ~ "'i. I hen ,~..hulc ,,.~ ... c fu-n\l w 111 he dn rd~d wlu fuur p an~ . .tmJ 1'mt 'cu•mhu, llllllllhU will be pwllul-Cd anJ 'll Oil ·n,u ... in gencntl fol gr.tdually illCI'l'.t'in~ 'aluc t1( dB rrvm 0'1 Ihe path d iftcrt.' n..:c hL"twcen two co n:o::~cuti, ...• r..ly<- Jrom ·\ :md C ~ocs on increasing a..' l'oint'

,1r 1hc- l\\C)

)J/11. 2)JN,

\ ,V- I ).l.. a nd prndl•cc:-. m lht:~l' ;~t~glc!.> the I ''• 2nd. 1HI ...

N IN- I )lh (\rdcr scoondary minima nftcr nth pnmary m;tx.imum SH !Ill' numh\!t<Jf •H.:~ond>~l)' lllinirnu in between two prim"() nua:wu" b {N- I) .mU number uf 'k'<.'ontiJI')' ma:<inu 1:0: :lUtonuuically (N :1) Thus. the Cl1ndition for I st sccondaJ') minima ufh:t n th primary maxim.-. is ( 1.53b) w hcr~:1 s

Ihe condition for I SL ~condary minimu .tftcr (.'Cntml maxmnnn JS

Similarly. the condition for 2nd ::.ccvnd;uy nuntnt:c :1Ucr I 'il pnmary maxama is

lll + bl <in !91 +dO, I~ i. + ~)JN

l mcrj't•rellH". l>fffr(lUion wrd rolarisllliOJt

1.26

Resultant Lntensity

Rc~ull;tnt

wall hoc

t .2b. t

10 I

mtttn,il)' di•.~ributir1n f~o•r ... inglc ,Iii , d(UJhli! s lit :md Jiffnu.:tion gr.uing.

d i..,C li..,~U

uuc

une

ht'~:.au~e ~til

uno rel.ttcd tu eoach uthcr

For Singl ~ Slit

Tile (in.al mtcn'H) .11 .tn~ pumt mot) t"C ~ttll."lhkn:tl h) o~ppl) mg the thcof) ut Fruunlln(cr diiTnt~liun .11.1 ,jnglc ,Jit lri~ 1..:!2). 11tc v..t\'dCt\ pnlecc:ding rrllnt .lll ptlllll' an .1 'ht .1h1ng the ducuw n fl. •u-c: L'<JUI\o~ l ent 10:1 o;,ingli.~ v.a\~ ..,1~1 r1111~

Irunt lhc mtddi< point <>1111< >Ill It the wtdth o l lh< 'mglc 'Ill "dt' ldoo lOIII II '-'4ual J'MI"h :n~d the o~IUJ,htud c ul lh~ \\ :n'C frum tJt:h j'KU'I ,.., u', then llw ph.t"oC Jiflcrcm..:c hct\\Ccn omy I\\ II \."dlhL'\.UII\C \\U\'c' hmn lhc."c 11 ·pan' \\()uiJ ~

Now by usinJ,! the method uf \ CL'Ior •.uJdJuun Lht> acLu:ll WII\-C from u ;,mgk: , 111 tl\

H~nn:,

A .:.a

~HI Cl ~

'Ill

c.rln

=tt

rc~ ullam

• \Ill (.( -

mnpluudc A of th~

c·:

a/n

fll~\ef}'lllotl1 1 11

where

Thu-.. the

lntt-:0'11)

I Jl

.til~

rumllur ... m~lc

I= A ::: (nu') 1

~Ill (

\\ Ill b\·

' 1~~r.r J ( 1.541

when

' •> =(tw ')~.

" .u lt...:ncc lhe

inlcn'il~

M!l.£: I

uf ctntrnl m.t>.lmum ut M 1 tlu..: to

1 = m 10 a-u

( a,· a )= 10 :~om ·

--,-

~jugle

)lit (Fig 1.12). ..._

\\ hidt i-. tn;aximum

( 1.54aJ

1.26.2 FCJr Otiuhll! Slit In douhlc ~I t b . then..~ we h;,,·e two C't'nlrJI l11ffruclcd \\~1\1.."5-o. L'Ut.:h nne fm1u the 1mtldlc ('l(UIIt l)l 1bc rwu s il l~. Su the p:llh diffcr~nl"c l x:t"l!~n 1\\U CtliiM."LUI_h·e r.t\'' lron1 '"" l.:('hl'I.Uii\l• ~li l5 b. lo t h) .. rn 0 fhg I 2.\• CN: fa+ In ..m 8

N,•w lh\" fm:tl inlcn,ll) in a d ircclion fl. uf !-dirfmctcJ m'' l'·1d1 uf ouuplitucJI.' ,\

~Uti' (~In tl/il) .utJ h~l\ in~ t.:tl1111lHll1 f~h.J'\! tfiffr.1dhll1 =-f1-= l)~

ld -

hJ •un fl.

\!!\0 h~ ~o..llculatcd in ' he follnw mg \\ ay: t\!!ilin h~ "'Ill~ the llll'lhod ul \CCWr :•lld111nn 11! .unphttuk. the n:,ult~mt .llll(tliluJc fu•m 1-,lit' In ,1 dirc&:tion 0 \\ill ht'

I hu.., thl'

lllh,'n'll~

I o.il

=- ttil

oHI\ (lliHII

, sin u

2/J

!\Ill

,m fl

<Fig. I.I'H

IPI

tluuhk ,1JI

I• CA'l.! ;:;: (na~i- sm:~ fA .,ju ,~II u ''". /l

rt~ln

Mn;:.. a

cz-

~.11' ,m -

I ,,l .:.:mr.11 m,J\Imum rn dtluble ..111 0 =- tl I hcr\'IHr\.". ,,_ u. {J =- 0 "ln!.!h l!l'c' .., 111 ~ .,. , ·•• uru

fl :;;

I .tnd

ttl

,jn ~

'fJ

-:t-

11 -n <-sn· (1

= f2l- =- J C)\~ ,..,in~· I'Hu'J"II.•f, ruiL.')

I knt.·c th..: iJllt.·n,iJy of ccntrnl ma:dnHIIIt at M0 due h• Jt1Ubk ,Jn

LI ~ ~~.. ] "h"n u = n ""'' ~ ~ u 1"flu,. lht: inh;no,it) of 1hc c.:cnlral m;p,jf11,1 i11 \::t ...l' 11l i.Juuhlc ... Iii

j..,

() 55al

j, fuur tluh.:' th.m thnt ol .... ug.h! 'lit. The mh:u-.it) thtnbu11on shown m f•g t 1.1-iJ corr~'Jlomh to .2t1 - h \\ ht'l\-' II h lhC \\ tlfth tl( th\! ,)II Ulld /1 the Opitl( U~ '().il'lll_g b-.!1\\\."CII I\\U \hi'\ llHh lhe p~tlh:nl due cu thtfnactiun ul u duubk .\Iii, ~.:un..,io,h ol' 01 d iflrJl'tiun pUIIt'l'l1 lluc tu the individual "Iits o f width u each. which i~ SUJ)I.!f·intJ'>u\ed by th..: in1~1 (ere nee p~tll cm m..tximum and m1mm um o f equal 'pacmg du..- to the intcrrcran~,;-e uflho~

lntt. rfetwu···· DijjrllC'tion fmd l'olanmlt(m 1

203

1wo diffr:tch.:U b..:~un"i. The ~pacing o f 1hc inrerfercncc mw(tmum .ami n1mnnum 1:-.: t.h.•pcndL·m tm the v;~luc\ ('r 11 and h

J•.2J:,.3 l•or l)iffl·m:tion Gracinl.! Nu" tn dtlllulllllll ~ 1\tllng, th~tc ;trc N number ot , hl\. "in we h:l\\! N-~cmrotl diffracted \\;t\'t·. u nc ..:acb h..-•mlhc nutkllc poml:-. ol lhc !-Ill' Su lh~o.· p;llh t.l.rlcrcu\'l' ( CX) hci\H't:ll ''''n (OII~<'cuuve r.•}'' fmm 1\\--0 oonf\c:cuuu• ,JiJ, I ' fu"" In""'" II ( r:t!! 1.2)), tht.'tL"Inrc Lhl'" L·orT~!>pondtng phase daffc-rctKL' '' ·

r fJ =

+h)'"' 9 ~ !{J

r..... b)"" o

\~,un hy u"tn£. lht: llt:lhod nf \f.!t;Wr ;u.lc.huun nm1>hhttl1." IJnm \'.,h,, 111 "rhrt~o.' lltm 0 will he

..-\

t ll

.ounrhruJ~.:

th~.· n.~'ull •• nl

* .. in a ~m Nf2 fJ/"2) =ml - - - - rt

sin (2/J/21

• ~m 0 sin NP I • =- tw - ---

a tntcn,tl\ -1- A

.1.nd

"" {J

hm ll) ~ co:.m ,\:fJ • • =- l ro ~ --a hm/11

T1w nM:\tmmtt tnh:n"L) ''til ~''cue fm rt = 0 nnd 1J = 0. I.~ from \!lfUJlton-. 1 I "I untl 1.55) \dLl'n 0;:. n. \\hich ~ i'l' ~ the po~i t ion oJ cc1•tr411 111.t\m1um \f1to \dh'll a

o Oo " S11Lh~.-•

Irum

It -

I .•mu ~hen {J -, 0 "" N{JI ,;, (J N ltllt'11\ll\ m •t'Uiftll U/11.\mUml M 11 mt.:.l"-'-' of d tlh .h. I tun gr.1tln}! ..,n, \\ tfl 1,..

" niuumt w.

~o.'~fll,ll

'' ~

N 1 1,

I 1 I ~71

Her..:. 111 ..:quatJtlO ( 1.57) lht: ructor f-in~ aiel- IS r.:spnnlithlc hu lhe thlln.rCIICnl cftccc due 1u ,,ngk ~Ill ond 1hc ndduu)nnl tuctorsm 1 NfJI"n~ Jj '' rcsp<:m~thlc for the inu.:rferr tlCC cl(cct'i of rhe dift"r:actcd r:t)'~ from N·shts.

Primary Ma xima or Principal Maxima The rc,uhnul tntcn!'\11)' I will I">\! nHlxtmum when denominator vJ ct(UOtiOn ( I ,5 7l 1~ t.cm. 1 e "hen stn fJ= 0

fJ = ± ,,. wheN 11 = Oo I. lo 3 . o o

1-lencL":. fm· uth onh.:1 1,1un~tr) mnxin'ta cnndititln i:; {J =-1 11tr. 1.1.!. IT(tt

Whert> 11

::: (l corre!.pond:-.

+ /1) MO 8 _ + A - _ '"i

to n·otral rn..1ximum Mu :md 11

=I. 2. ~

.. CC)rr..:sp(lnd ~;

w I !'I unll: r. 2nd wt..lcr. prim~u·y nHt'(inm M 1, M 1. Thr t stgn 1n e<IIL ( 1 .5~) ll.h0\1.:. thnl there OI'C l\VO prmdplc nl:lXIIna c'j the same nrJt:r lying ( JI1 \he lwth ' Ides ,,f

lht.• ,·~.mlrul HU.:f'C11'.it.'"

muxnnum

Rcsuh:uu

Th..• mh'll'IIY

gntl!-.

un ll-.!cre:J«iillg

1111cn:-.:1~ d1 , 111htnion ' '

'hown

it;;,

the onlcr of maxtmot

R!!. ( I :26)

""-

CUl'.C I

r)J\fJ.r~. -"_I

R<'SOIUint lntl·n~it.)' dis I rihut in n

s~.~ 1.. ,1""nla•ll ufCUI\'l' ~

.,r ~r:t linJ.! •._JH..."Ciru

Suhooidiary fJr SC("ondary Minima and Mo.•xima Condition of primary maxima rmm t:qn. ( 1.57 J is {3 = ± utr. But wh.,;n /J :- + ,;r, Chi.'" num~mtur nt Ettn ( I .511 j.., ;~l ...u ti.'Ht, ht:c:ul'l! ..,jn Nf1: 0. Tlwnllu• n•.\ulttmt

mten.-.ir..• , ,,,1( be- ml1u"""" So lh\.' \:Ondition l<lr nuntmu '' NJ) = 0. IT, 21T •.• ± KIT

N{J=± Ktr

lmrrfrrtrrn·. Dl[fmc·tum anti Polan.Mtlfm

:!05

l.hu ahen ahe quc•llt~nt (cqunllon 1.57) become!\ U/0 wh1ch 1' tndctc:rnmmh.: 'f here: ron: N{J = ± K 1r F-r•c' 1he: condumn l'or nummurn mtcn,it>' for rtll \'::tluc' of K. excepl H. N. 21\' n \ Hecnuw for IhoM: v;tluc\ (1( K ~111 fJ wtll be um.

wtw,:h i!'''"o; rhe pnn1Hr} 11111\llllll Tiu" J.: cun gcr rtu.· value I .:!, (,\ I J omd there arc (N I) '\lthJdl~f) mrn1m:t nnd tN- 2) c-.ubsidH"try ma>.:Jm:L m l:'etw"·~n Cl.'llllal (Mol and I st OHler tM,) pnmary m~xnnn. Qnd 1n hc1wccn :.&O) '"'' J)J tJll;u;. mnx1m;s .,, \' tm-rt';l-.e,. th-.· 111 c:n'U> of ,uh;,.i~li;lt} Jlt;t\Jm:t dccrca,~c; r('l._,,,, t' hl pnrn.J") nHl:C:JnlJ :Uld hcrnnu:' na:~h~ahlc \dum N tk!comc' \tt) litrgt· tntemoil> or the Prinwr> i\l:t\inm u:r <'IC we 1!-:1 from cqumwn ( 157) Fnr fJ ~ 0. Jr. 2n.

"" N{J

"n tJ = 0

\\llfdl 1:0. 11l11Cit.TilUHllh' N1w~· hy •'PI'I)'IIlJ;. Lt H,•.:,piHtl'' rul!.!. thc limiung vaJuC": ofthi\ L:.sn ht~ t ...alt:ul.llt-''1 ;'" fullu\~'

"nN{J

Inn -~-··· "n/J

d!tlfJhmN{Jl

,,_ . ., ,1/i//J<s•n/Jl )un rJ • · ..Jf

11m~;..

lhC' f('_\ftlumt

iiUC"IlW\"IJ{ ''"

Inn

'' ''"'

.,N{J} : ,.,, .. . { <~n' ''n" {J primttn llltLrima rrom equation t I S7) ''

i:ii.JJ

1111.''~' ma\ttn.t t,\1 1• ~I . 1 un N~lh Mile:-. nf tlu.· t:l.'ntr.tl m;1\tmum t \lut .u,· tJUIIt• i111io'll-..t' Rulth•·H lllh.'ll\11~ !!U"'" un det:reJI .. mg a~ the: unl~r uuuthc•t utt.:h· l\,t'"

du~

w 1h.: 'Uf'CI"f'lt.,IIUIII•if tnl~·rf-.·~m:c

1.27

p:tll~:rn ...tn'l'"'" clc:trl~

'"Fat: tl ;61

A hsenl S pe(l ra

·nll! condiuon fur l nll"rfcr\.'ncc tuJ:-.tmii I rom ctJUauon ( 1.5~) 1~

'" Stmtl:srl~. condtuon

~I!) sin 0 = 11.1.

lur t.hfTrJl.tion nunim.a t'mm equuuon ( I.SOJ ''

, ..in 0

=,,;_

whet ~ n :md I' .m.· tnh.:ga.... n :: U. I 2... .tntl p = I. 2. 3. I( tfh· ,,aluc uf "nnd h ~'r"' 'uch 1h:u hnth I he ~quath1n~ nr~· ~;,11sn(d simuh~m«.•cut,l} h,, ""lm,•

J>ankul.u ;.lu\!t.:huu 0, 1hcn .slthuugh lhc d1ffr.11.:tcd

r.ay~

from all th.: 'hh •H Ih-.·

gr.lling rcinfon:e coch other. hut for r:a..:h slit. rays from the upper ;md l.-wu halve, d~'truy c~u:h (ltlwr .md hence the fC-)Uitum ina\!nshy h Lcro. wh1ch mean' th.U the 'JlCClruJn 1h:11 paniculotr tlttlcr wi ll be ~th!-cOI in dut tfircl·tinn.

lly

lll~ing lhl! ntiJV of i!h1t\'C l \\'0 C<-IUothOII'

fo + In ~in

()

a'itnR ·-~

\\'l'

gl't

,1 I'

I I hilt

C't~'l'

I IJ

"= 2t'lf' =

=b, i c .•

\\ lh'n th!! V•u.hh n l the ..,JH 1'- cquul Hi •)Jlol~,:tt), tlu·n

~lit"'

1. 2, 3,..

Jlt.llllw

~n•l,

41h. ~lh ,.,, •mk n. uf lh<

t>rim;u ~

\\ ill bl' m ,~ jn~. l".t.'c 2 II h :: .'J. l.c 11 =- t• tlu.·n ~.:\\.'t.'f"ll ~.:cntr.t l m.t\Hmnn (n = 0) :til uthcr ntd~ r' nrprimJl) m.iXIImt P i s. \1;-. J 1.\tll h.: /CHI lll~ r.,_•,uhnnt c.hffrtiCllun p.tncrn \\Ill lx.· 'imilar to th.H dw.• 1U sm~l~ \ IU . CaS\: 1_ When J• =-1u. 1 t..• n- lp ...o th.al llh' 3nJ. 6th 1Jth order-.. o f prtnlOIJ) tntl\IIIIUm wi ll ~ mj,,j"F 1'1Jj., ... o,.hlt\\U iu H~ •1~·1) IHU.\InlU

I .2X

Maximum Number of Order of Spectra in a Gmt in!!

Tlu! l'l\lh.IHinn rnt nth

tlrd~r

prin tp.tl m.l\lfliOI tor lP'·llmg ., (.t •

'Ill

0,,

nl.

II to! I II g,rutin~ dcmcn1 {u +hi<.:!).

u. ,, <

~1.. 11.

<.!

u,' nnl~ hi ''rtlcr 1' ~,... ... ihk: h• 'L~ Fnr •• ~r.tlrn!! w.th I"J>fHt lt n ·o,.m~l (11 .;.II)

(to+ IIJ

F<>r ;ocllum light,l Su

2.-i..l/I'J)IHI l.fll

=~RI/1

,('t X

I •

lllCh

~-5.-1 l"rtU

IH ·l \.Ill II.SX'J \, 111 1 em

" lfl ~-'7 rn••-. - H5lN "\ ;o. HI ..1 - ....

Thu .... 2nd MJcr 1:00 The ht!!hC!\1 order Jl0'''hlc hl M'C"

1.29

Dispersil•e Power nf the Grating

T he ch;\OBC in th(• :mglt: nr thffnu:uon pl"r llflll <lt w:.v..~ ll·ngth o l lighT u.;;('d I\ tJehned 3S the t/i'\{11'1\H'I' JIOI\"l'' nl lh\-• !!l:lllll~ nH,• (.'UI1di1IOU l or lflh nrd~'l pnncip:al mrt:\im:t '"' ,,, -t ,,, '1111 (}

,A,

l*r(Jtn lhJ'I cqunuoa il is clear th:u fo r :\ r:micuhtr \~lith: of grating clcnlclll V' +II). A is dirt~Cd) proportional To 0 Ko\\ dsfrercnu:ntng dbove condition \\,r.l ). we get

"' "h~rc

N = __1_ (u-+ h 1

~lJ

Nlllnbct ... r line~ t fn illt·n!_!lh t~( ~r.llmg

hll '>mall \ .IIUt'' uf e. C(t\ H= I. Sf) Ihe <lll£.UI.tt<II,\J)I;r...mn d(J j, thr\.'l.' lly P "-'~l\lnllln.tf 10 d}.... Sudl u 'liJCCirum" called (lfl(flllll \J'fUtlllll rhu't, htl -=~Ill r I n~ I. il h deaf 1h.u 1h..: cli,pcrxivc pll\\>Cr t/8/tll dcp..:mh Jircctl~ nn; fi• n-th.: ttrJcr t~l' 1h.: ' I"'L:-:rrum . •Ultl tii) N·lht· number uf linc.Junll length 01 the grnlmg l ien: '"'l":"i' l! J'Hi'''•·r tlfJIIIA.. J?i' ~·,., 1h~ :1ngul:lr tli, l'··r,it m l'~r un'' t.:lwng..• .,,,

,, uvc h:nl!th. But when 1hc ditfrnctcd

~:.m

r~cor..ted

on phowgruplm: pJnL\!.

tht;n Wl' ''ce!d lint:nr tlio,pcr:-.iun, lltll liii!;.Uial. lf .fi' till' fp<.";:tl len;;th ul lht• len' u!-.:J tH rc~.nn..l cc.J JliTF.telion pattern 1111 the- photogl.tphi..· plluc. tmU ,_1/ 1.. dtl' '"p..tr.ttion nf 1\\-o li11cs h:t\ ing ''ave knt!lh A tm<.l A. ;. J). then J O = d/lj ~em 1hc hnc:u <l i ~fH!I'i<. i nn f)<:l uui1 \\:t\~ h;rlgth fl11111 Clptuliotl ( I f'I:!.J i .. •II I dO til ~ ,,;..

nl/'

+h) Cl.h 0 = ~.~)"' Q

I h!nn · Chl' Imc:ar >epJr;~tion dl hci\~Ct'O ";I\ t.' length ). and A + tf). m tht: nth o1nlt.-s ~-> tUr4l

1.30 Spectrum formation and Spectrum Lines

Overlappin~

1r11rn t:q u.111110 ul nih Hr-dcl pmunr-\ llt.t\lnht fa+ bl .. lu 0,.. = u). It '"dear lh.tt lor :t fKti11Cillnr nrder u, lht: hghtnlt.hlle rcm \\ave k·ngtlh

\\til he 111 chffcrcnl dirc~.·uon:-. For ht:.ln or lungn \\ ·l'·e lcnglh (red t \\Ill bt.• t.lin·r.u:Lcd m~o.lrc than sbortcr ""'c length (\IOicO llm .... if we u:-t.• while light m .. le.;td ,,f m'mut.·hmrn&ttu: ligh1 i'·'Y Na). then ca.:h \hi\~ kngth wil l ~we it~ nwu ptiiH.'IIMimaximum in each order .C\o \\C gel 'JlCC.'Irum rorc;tch ordct primal)' max1ma. n:U hemg the outermo~t :md ~.~iolel being thl' mm•rmo.sl po:-luon But. h,r CCntr.tJ 11W\ill111111 ror "hiCh II~ 0 . fJ ~ (t rot all w:wt.:lcnglh .. \'vfll<'h ~ 1 \C .. whhe C4.'nlrul maximum M(l.

t.hOntct~d

Nnw tl lht• m1g.le of \liffrm:lu)u f) iu C'-JUialuUl (u +h)

!oil'

0 ;:- uA.

oc lhc ~.lmC for wavelength AI 1n nrst order ( 11 -=

I,. \\ .w dcn£_1h A~ in ~nd ~.~rdcr

(n ~ 2). ;utJ w;tvdcnglh A, til lrd cm.l~o·r (u ~ H Th.:11 (II

+b) sin 9 = I · ..\ 1 = 2..\, = J..\, = . • .

l lcncc. the fin~• ord~r spcclrum of w,tvc length At \\ •11 be O\'l!rlappmg \\ uh 2t)d spectrum of \vnve length A:! ~u1d 1td ltrd¢1' "P'CCll'urn of wnvc lcng1h A.~ m Lhc Slime dtrccuon 8. i.e .. :JI 1hc same posiuon ol 1hc ~(·rccn.

fH'dt.::r

10X

IO:n.;uw;·tml, Pln·\u-\

1.31

Determination of Unknown Wa\'c l.cnv.th DiiTnH' Iitllt GrMing

h~·

Dinl.llllllH }!1:11111}! ' "" \Ct ~ uuu.. h u """..t In l h~ l~•hur.UW) htl th~o.· ~U.'f.'HJ;ItC Ut(.',a'Uil'llh.'nl

t'l V•:t'-'C: h.•n;Hh t\l h~hll!l\~ll ~) ~• '()\lf..:c hy lhill!! :-.('k.'\.'lfOill~h.!r. h\(\\'nllh'ntut itmmttcm~nl '' ,,, \htn\ 11 111 F1,t: I 1.271

'"""'

- I

I ' \IH'rir.ncnl!tl ,o.d Utt rnr dt:h·nnitndilm nf unknll\\11 dill'roc linn h · n~lh h) a!nllinJ.:,

I· II!. 1...!7

l\il\\:

lm1t,1l ,ldJn:-.lllh:nh ,lj the 'lll..:l.~lnunt'h.:r \tl\.' m;t'-1..: .md 111.., oh.ljU'IIC,IIN pom1Jid

'"'~' h~ \dlu,lt'f ~ m. ll~~td Tlw 'hlt.tl 1h~ ..:nllinhiiUI '' IIJunllllott.,;.t 11, lll•lll" Llllnnt.lhL lt~hl

rwt:t.tll) N:t•lil_!IH and ldc'LIIfl~ j, :Jdju,II:J Ill '\UI.'h .I \\;1\ th;ll tilL' llll.l!!t.' ttl th· ,(II ,., t~h l;uned at th~: pt''l11t111l)t tlw \·eml.tl ~T•*....'·'\11!..' Ill lhl• flchl ill \I~\~ HI tlv kll.'"tt'i'l'''· 1~fl\\ lh!! :I \ ' ' ' of C"OIIIIUiJit>l and h.'k~·i•p~· .lh' Ill tltt.: \otitic ltttc. Tlh.·tclt·,..:~)pc ;, n•tuh.·tl h~ ~U :.1nd c l:.1mpt:d ''' tJMI \.'UIItltl.ll•lr ;and tht: h.·t..•...,·npc ..m..• no,, .u Pl'l'J'k'ndu.:ul.u pn:ooillt.JII Nm\ rl\h.l.! tlw lr.III"-1111 ...\IUh ~l.ltm!' .11 tht ·-~·r•u~o.• •11,111 uhh.· '\lh.'h th;,t l:'r.ahny ...urr.u.:t: "lk'lfl,~ut.lt. ul.u ,,, pn..,mt.thll ll••'lilht: l'n·.mr •• hh·r ... n•heh!li m ..ut:h ·' \\,t\ U1.111h .. 1111.1\! '''tit

,nlhtu .•. •• 1111

·d "''lltlh"· ~hlllll~ .. u.-f....·~ Jlllll•hl,mh.'•J

·!' tl"

tl"

the ft~hl ''1 \ IC\\ I· I the 1\!h:,.,;,~jl\! TIH' 11lCo\n' l hol1 lht.-• p.tr,,lld h~ht lh•lll th -.:olhnMhtl f,tll' .it ,111 .m_:;IC' 45 ,,n the ;;r011111~ ,urf,t~ c .md rcll~."\.h:, ( t,t\' ~~· h h.:lc't..:UJ'I\.' 1)\.''-''"''t.' "·ulltttlolhtr ;md cd~..,~Hpc .arc lllllhlll) kept .11 uo ap.ul \u\' lhl: (M'-iluill ~11 1h~ pri .. m tahlc ic.. mlll:d :at ttl :tttdinj.! ..1:" - In thi' l~!tdiu.~· thL· pd...rt1 lt,hk j, ol}!olln n•t;.tt\•d thmu~h 4.5 IH the Ot'\\ pu:-.tuon OliO that .It th;\1 p.UIIto:lll,tt f'\htlull) ~C.IIUl!-' 'ud.11.'\! h rlu1111.11 IH I he .nculelll hcmn. rtw \\;-1\,·lt'n~lh ulllll' ~;J-Ii;!hlt..'Tifl he ds=tcnnincJ h~ rnc.t,\lnug lh ~,.· 1llll!k ol J,fftal·liun uf the l'llttJ~l ( .\11 iu' .. 01 untJ .2nJ ultlcr mtJ,imoJ (s\1 .J 11:.. IJ. fl1,111 the l"l'lltr.t1 mot\imum 1 \/11 1 •10 hnth ,jJ..., Then Cll I /11 II ,..

(tt .,

N Now

light

= Numhc.!l

()~. If -

h)= (il.tllfl!! c lcmcnl:: l h\•

Cil hn\:,fl lnu

\\c! c:m t:uk tlatc

M ,111 0" = nA

f muJ for .!IHI \tnfcr (1,, :

l~nt!.lh

\lf 1hc

~mtln)t .

the wa\L' length u f Na-llgh1 l'!r an) nwnuc hrttlllillll

Jutt:l'ji•rt•ttn', Dif(i twtirm mul }'ollln\tlliou

:!09

If the hght " not nwnochronmtic. :o.:ay w hitt'. thc.n fu r cotch '''her primary ma\101:\ 'lli.!Cirum w1ll t.:~tnu:, t!Xc~:pt furctntr.tl lnth:11 1.-:l'c in wtlt'r tn (ind out '".1n· lcn~1h (If :m~ f>.ttlt.'ul.•r colt'lur, thl' dtffl:u.'-t•ng ung h~·' !Il l! nutcJ fo• the I,, and .!nd ord~o.•r untl ust n~ the t.•quu thln~ t:!l' 'Cil ;\1\U\'C, tht;' \\oiH' kn);th ul that panu.:ul<~r ~oh.lut can he L'akui:Hed 0\trlapping 'l'k'L'tral ort.ft.'l''-l'JO he d\ ttldrLI l'l) u .. ln~ .. uitllllc t:OillUr fi ltcf\ ,\ ._ th~ thffr.t~llng .m)!l.: .. art" large (ut U<u.al ~t·:ating h:l\ in)! l ~. fll10 Jill~o.'"/inch . ,,, the~ ~an bo<- nl\-':t ..uu:L :.~ccurnh.: l y. The numhct '" hnc.../wdl •ut ~.:111) 1-. vhl.'n h~· the m.anuf:lt.:turl.!r-.... '') tu + b) t:Jn be calcui.ucd. ;\., tht: m~thod tk-\c~ not 1uqthc iJil) ~tn.dl tnt'il'un.::mt:nh )tJ n n nccuratl!: ,.•,Itt\! hf \\ ,iH! lcngJh 1.. !.:'<Ul n~ nht:1in~d fur 11 \niiH.'t! uf Iiglu whnsc wave l~n~th '' not llw" n

PROIIL £~ 1 S

\ p.lr.tlld lw;ml ul tnt)mlchmmati\:

li }!hll:~ullmn:d It! I~

m,·ukul

Ol!llllall~

un.1

pl:ln.: uamn\I'"U\1'1 gr•• I'"~ 1\aVtnJ:! I :!50 lm..: .. t.:m omd a 2-Jhl ••tJ~:r ·1'1\.'Ctrallm~· '" t'lh"--.•r.•cd 11l h.r dC\IIIINi throup.h 'H t':1Jcultth' the "":\W t.•n~•th nl lht.• ' l"'tt'Cital

1nu.• tu i I') , jn

\I "IIIIIIIl

o. c 11A.

(11 +II}-:

Th~rcte~r.._•

111.:!5U. II-:!

.. ,n lO'tl1ill x:! =- 2. x IU

tf~- \1)

'~;m

llu\' UloJ~ uh.J\:r.. o,o ill he \ jsihlc if the ".ave kn~th ~11 1l11· mnJ\·nl mali.a!J(II1 j, ~89J A .uuJ d1.: nu~t~ bcl' uf hUt;.!, un the g.r.a.un~ J., .!5-1UIInrh" \olulum

f lcn.,;c m.t:.oin1\lrn ndcr will he 16.

I h.: :-...:p.u.at•un c 1 l ll~ two :'-Ja·lu1es •mean ). = 581.),:\ A 1ut Ih..: :!nd Ndt:r "IX'"t.:t.nuu •1t .1 lmn"nu-:s'''" ~rotting t'r>nl:llnll1j! ~nnu hn.· ...tcm '" 1 ' n11nuh.''- luc nnrmal IIICtlftnt.:t." Ill Wlmt j, l hC" dtff:tcm:..: iu w:t\C Jcn~th llf

the lWO }t:IIU\\ hnl''-..' ui• Wh.lt ~\Ill he Ihe lmc:tr '\CJ):ir:num 1f thq are recorded h) 11 c.::uncr.t ''' J\•..:-al kngth Jll \'Ill '' \t1lmhm J)i.;-pcr.. l\o.' ruwer-== i/IJIIIA =- " " "

II)

t/A~ lu+b)cosiJ JO

+ M '-.U\ IJ

'lU::tJ'I:.lUI( ·~0\.

t, Ul

:1(_

UUH. X \.Jiut Ul' • YU/8 U!,

t Ill/ I

I•' '4"1'unu •

nnl':uur t • CH~ot

= tf/

t•l~ •~t~Ot

= c;y

,\' • ,,, "''•11

r·(•J'l' • u

•·~ t I • ' " : '~'" +II_.; • 01 ,,_

1 HI ... U!)flt ... II

WfU.i•u•:,J 1: 1u1 'r 1n ~ ...,uu lfH 1

t u~

OllC'Io

a lh Ul

1 ''

uu f'~!I\1\Jwu .....Jn, .. ,

'l''

1;-

Ut .. H 111 ·' Il l~\

•r 1•• ,,,,,,... 'fill ''\"f\

yu.: '"'6 u•~o ''I • "' I~<•U'f,.l\

1 ZfiiJt!d ~~ Uf ,)J~I ;.\It" tUl,';~ll( \UrtU 't\~~lf

'XII

.:'" 'ffto IJil.(jllol 1\.lU .JCU v um ~;J Nllf r

IV (JS.Qtl ;tUIJ I.JI•tl' lMH .._, fl"'~qnu.Jtf,,. t.lflh'

J•'

,_,,.;r .:t""U:'I·n.lUl t••tu'"'' '"IV"" tl11urt:i' ll•tLW'Hif(l \

mr-_:-~, r · UJ.

I'"~ 111 \

fta ... Uf.IH:k"J_iPI' ;111(1 Ji.l .Ji)Ur

••••i-s:

pur\' U;;.L\

"''f&.iU;1(

•t\o l tlllllll't•l•> ~ 1 "''//' '-'1'''' 111 ..."'UI( I:Hl,l'll• h•l ,,,,.,,.ll'd.h Jr.J1ltl

;1\t'IY.

·'Ill f'll' 1 •ttoiU.lf Jl"101 UP IJl I" 'l " U.1J :Kulf" rJ:tiiU''I r ~q I''TI'IJ~: ~nh,')oll \II u 'I lll:'lf·>\11( CJIMN w .....'1~\4'4 1U ifUtH•Joi ~II J.\l,.llltlll •.lJ, 1iuqr.Gi 011•1•111" \• lll>.ql' ~ IJI• fJI

: 1 ;J.JJJQ'~'>I•It ~~~

-.-f,

• ,,

dtu • r•!flf , ,,, IU~f"''

.--.,II'"" I'J p.ld~ ;,uJl'• u;H(I .,,: •

\\111\

•fii'IJitpm

q l'uL• ''

MUIVI•U U:l:lll"'rJIJI\1

7•/.: p Ul'!l; 11

yu '=H Ul\. (1/ ~· t•1 "' '""If'\

~'U.'IJ.'jURij

, :loru•a~ r 01 ~.-.I'JI,.,n:d.. m•rt....-11 I"

•''4 '~•'lll:n:J!•l Ul l

J••

JOJ , ....,_,,11,., .w· ~u••tllpth.•~ \fl'~ ''·"t \\

t"WI\ftU

.lHUOj•

'"'tl

;)Ill lt.lljtpl" •''II II IU.:'!')1.11! ·'41JIW'I\ J'IJ,I,'IoJ.. "'ln>IUI'\IIr\.f \\

(J J >.~ 1" ~

lU l(tft fN ·rJ\ I~

•If '"'*I d,u • t•1t· 1

"'I'' -\ •qn."JutJ JuJ 8 I•' .lnJI"\ Jt·tn:uued r

~(II X(.L

1C'0l

•r

OJ•f • l/'aUIII II'JI'dOl'oJII,,UIJ

Yt'.flf'l • (1'111' • U•lht~·lp Jt•_;,ut·J '•• 1 \ tj\IUIMIJ"'_....: I•• :-.~If

""''II·'\ •'V.t

U.'.'l'l\l:'lol..l ti):IU~J-"':'r'l\

~·,, -. m,.,mwLlCS'"

Ul " L; L '

"or

1rfOOU')

'1(

L~L .•

I•' .>."~IJ-'J~III"\ .'l'loU:'IJJ C•.

t~·r~u

iltrtlt

~ .. ,_~lf_iO,. I'(

Ul ..

t"h~~,

p -\•"P

I I' ~ YJl

L4 L • 109 x US I )Jta, i' ") (II\ 1 : tnu \ ~ :flfl u•"t, m 1( n.s~: r ·;: • ., ·cJI •u\11 : •• .. m "l''

Ul'IJWJ t Ul )(

'fi\UJ,/ i·mJJ.,m:.·u·l

C) I~

lmt•rfrn•ucr, l>if/nwtron and /"n/nn.wu rm

111

QUESTIONS U rhc h(!ht nf -...... u- h:nt:rh A 1~ cnudenl 1111 .1 ~rill Ill# uf '>Jl>~crng c/ otl •m .m~k If' o~ntl 11 9 '" the .an~'-' ~Jt \.lrllra<.trun, then ..,b<•w lh••t th'"· ~:~.mdruon ot ;.llflm\ hl•rl rn:uwna •s.

-l

UJ>e.:u .... th..- ph<'n;.•ttll!ltnll "' h.uu1t11,fer JJtrr-~i.'Hun ·•l .r ''")!I(' .. In .unJ obtam lh~! cunt.liuun (or fil"l mumnucn m lht: 4.h ffnn.tu.m l'·lllcrn Al\.1) uhlmn the hnl!ar dJ,.umt:~ ol first mmun.1 fwm l."<'n •r••l m ot~u nu m lh\c:: t.:on ..l.ltJt:ll\111 ol .a pl.utc J rll tJ~ I mn guung ft•r \ IHunbcr Ul \hl<t.. Ohram rhc L:1Hh.lltlon rttr fif"\l \CL.1111ll.lf) nunnn.t otfh!f the •.xnlral mn\lnuun. Ahn 'Hhe lhc gcnc•••lru.ambc-r,,l ~~..m1l11n mcniuM olll,J ntcmhrer ••1 ..c~(mdu rv m.l, ltna 111 bci"''-"t:'f'l l\\0 pfilll:aty nl1.1.1i.lll,l.l Wh:u ,s the- lund;.aJiic(ltall.'rtkrla ht.:•"ccn w:nt• knJ;Ih ,,, 1i£hl u-...;J nnd nll~ r ::.dc ~17< In urdcr rn gc• \11ffr.a.:unn 1 ln~tc.ad ufNa-li~lull \'tnt.: h~bt b l»-CJ (,•t lhffr..~.~ut•llupenrurnt, v.h.._l "'II be Lhe m:tJOf ..:h~tn)!C m ~.;cntr:alm;;~xrmum ::md pnnUt) rhonun:t., (1/tmt · In suni.Jghr '-'C'ntr.tl llM?.Ullll will hi.· \\ hn~ hf....:t\u~ (o + h) '" " 0,. ~ ,,;. fl G (l, tt :;. (),;:till' will mt"t'l Ill t.:CIItntllllilXUIIUIII. hUI 0., \\ill "" lhfJcrenl Jur ~tfTncm

(t.

A.. "0

.111 l~rtlll:U') n\ol.,.tnl.t "rll he o1 w hnrr h•m~l ) ia~·r.:..t..,ul~ the numbl:r ~Jf ,~.~,., '1\'' 111 "' dliTJ.tt;INtl gruh n~.

1:...\pl.un why Ill

Cit) dccrC':t.'ling ,,,._..w kn~th. (ui • mcr.;o.t-.~ng gr:-.1mg ,ra.:mg tr• +IJ); •ncrc.!lo.;C, t h~ 1111\:0"11) Of lht m;l\lnl,l ul lhC ):f',!ltn~ 'J"'t:lr.t'

t //11111 E>.pl••in llutu C\IU.IItut•

7 H

l,l)ll(:

h/(rlmn lhc ludf 11(fltltl ;uuc m rchaltun lu ;1 pl an~,: \\;iH: h oul. S how lh;•l the lMIU \lt :. JX'IRt 1-. h.lfr ul \\ "'"' wnuhl he t•auM."lf 4

.unplltui.S~: due \o a .:•'lmpktc by lit.! h.t .feme

I.;;,

pWtc anJ lil"' JS II fii.Jdt"' 1 r:~rll:tln 11'"' IIH\\ 1,1 ,t:l)f)C,: pl,IIC :Jt;l~ m.c •• cun , e.rgentlcn.~ l·,t\ln!! tnuhrrlc 1"\l(;t l>cn\t~ M nJllc"roo for n~ foc~tllen.g tb \\'hat n

""""<

\Vhott '"tile l!td ru.. i)f tile ''' ''"""' in ,, l'••n~,: rt.•h.' HI IOI:.JI ll!ni!-th !Hem tur h1!hl 111 \\,.1\\:

lcng_rh

iill.lfl ·\

I C. I'OI.ARISAT ION O F I.IG ti T 1.32

Polarisa tion of Wav{'

Whcu "111:ri1xlic cli>UIII'allC<'Ir3,cl<lhmugh u mmcnal mcd1um, li~c iu wmer or in :a stn~tch(d s-tring. p.u-:icJ~.., tn h!> path nrc 'et into 'ibmtion lt!.atling tn a v.•ttv~ 1>rop::.goUhln thmugh thut tuctllum. Thc:t~ Ql\.' l\\ 0 wbil:b o.rG cuJJI!41 ruoJc.., llf \ ibmtion

1)~' of vibrotion

a.re

I)OM~ibk

Fu'M I~ the Lt.mxiuu/inuJ WrJtlr 14 ··lbnllitm, in " hich r.u1tdc~ o f the medium \'ibr:uing :tlon£ the p.:u h of the '"'aH" propag.uton. Scctmd b. the Trmr.rw~rst' motlr of l'lbr11tirm. an \\hich pnrlick' of lh~ mcdrurn \'ih nllrug in :tny pa1h "hlch j,

perpendiCUI3r 10 lhe p.uh or lh< \\'3\'C propagauon. In longatui.Jmnl mode or \•tbruuon 1here: •s only one pos.sibll.! direc1ion of vibration of the panic I~ is possrblc that1s along the direction of wove prop;,tgaliOil.

Uut in f;;l\c nl ll.lll,\<'('~ rnodc or Vthf':IIU)f), 11tt.:rC .m· tllhnate tltu:t;IIOII' Ill "thrattuah :uc pu...~ thh: lnf 1hc panaclc' whtLh :arc Jk'fPL'Odtl~ lilar tt • I he lhrl!I.'Hnn nl \\';:i\'C prtlp;t~UIH)f\

Nctw 1I ;tiC'II Kllau t!'. ttt'\f10!-.I.:d un the cl t fl\"tt~nt J'"..l"''hlc tlnt~\'lton' t •I 'tht.Umn ul llh' p;~nu:l~.· .. pt·rpcntlt~.:ular In 1hc path ul .t \\,t\C I" "P·t!!.tlum ...u lhut tlic:u \ thr.tl tiJil'o

"· ht.,; h 1'

.cn·

~.:onfin~J HOI) 111

pcr~mhcu 1;-ar to

n 'inglc- pl.tnc, t .l' .. unl} .tlong u11c din."t:ltc>n th.: dirc<:llun nl wnH prppat::ttlnn 1h~.·n thal uut~tHil~

\ti.l\l~ l"t

Colll.,::d tmlt111H't/IWIW' lnn~lnthnd ,,.._,c thcr.: I:\ on I) ••nc po .....tbk Om.:;: tum •lt \'I~Tutum t•llht: p.n1t.. l ~o: nit h.: m\"dnnn '"' P'h'thh: Ibill j.., ;tlnn);! the dmxuurt ''' ".a,·c pntp.t!;'-tltun ' ·"' the '' ,1\i.! i._. .tlrc.:td) fl'\ll;m~.:J .ll{lfl~ the tlin:, ti,m tll ".t\ ~ prnp,,~;tllnn. '"'' nu nthl.'r f'Hlli.111 .. 1111HI1 i"('(h'othlt" Btu rnt lr:IU ...\\"t....: \\:t\'C lhl.'lt' ;II\' lllllllllt..• po-. .. lhh.· thr..:t:lt(lll~. •lllllr\.• r>.:rp!.!lldt..:UIUr tO Lhl! (.Jtr\.'\:lhm Ill \\';,1\ .... prtlp.tg;\IWO, ,._t tralhVCI'M..' '"""'can he pul.,ru~d m ;m mfimt~.· \\,t) ~P\\ \\ h~.·n th..: \thr;UHII'I of lhl.' p.1thd.:, '•IIIII,: 11h.'Jitlm 1"'''1"1!11 1h~ular In lhc potlh ol lhl' tr:JO"t'I"W \l,l\' l' pmpag:U ICII1 ()l'4:llf' Ill :til I'N'''Ihk t.hll!'LIU!II' \\ tth ...,,u;il 1:1\·mu, th ..·n lht: mnyotng. w:1'~ '' \':Jtll;;'d rmrmhtrt.\r·~l II th~.• \lhr:lllmt ol th ..· ll;tntt.:"fc, ~k.·..:u 1 n only llOC p l~uh~ or dtn:('lton which'" Jl,·tpcn,ht:ul:u IP lh~.· \\;1\l' pmp.IJ!ollft'fl tlwn tht: UUlJ;!HIO;! \\,f\t.' ' ' (olllt:J fl/0111' ('rtltln,t·,/ \Hllt" ot 'llt•·,u/\ fN'Im 1'' d \\'hen till' Vthrlll 11m ul lh,· Jl.lrltllt"' • ' ' ' ur Ill 1111 •r~ 1lli111 urw l"'lf'Cn<ltt.:.ular 111::tnc and if it \\ill ul.'~:ur in .tU) 1'"-'lpl~ntJtl'UI,H J'lanc ttt Jltt:&.lhtn '' llh m• '"' Ill' ''UI than ~mothl.'r, them tiMt nutgoln~ \.\ .t\. c: 1-. ":.til··• IJt<ttnoll\ /'"'"' l:.t'tl l·nr n

1.3J

J>nlarisation uf Light

\\'a,~

luh:rfcrc.n~c

.utd dll!rucllnn Jlhcnomcnu pm\ctl the WJ.n· llJiurc ul hght .uHI ;1l1n aht: wdHmu''" Maxwell's dccnomn)!ncuc; tltc:nr) nl lt~hl. lt,..h, W lt\'l' '"' \'dl ._IH'"" "' tr:u"n: r-.c clc~.:tronm!!n('lt f.: wa'c: h•r ·• pl.tu.- t.·lnlfOtO:Jt'lll'IIL ''':"c tht.·H· ";an f .. ftdc.l H·· 111r • F t .allJ 1\/.ftdd ·1pr f Ji' ''hu.:h .• r..· ~rpcn<.hcubr hl c.1d1 •llht•r ,,, \\ II ,, .. h..th "' llwm l'•'rp..·ru.Jtt.:ular 111 the dtr~"\'1 1\m nf prup:•~•llinn 1 jJ = prnr·•l!.•ll••n h't lt'rl•ll th~o· l1-;.'ht \\ ,1\C

f'hul

\\h) ChC hght

\\',.a\~o•

(,llft:tl •'' rr.JO..;\ ·r.,~o: d..-~o.lf•l11l,t.gll~11..:

''~''"' .m~l

h•r 01 hnt•Hrl) polnn-,cd h!!lll \\U\'1: prnpngdlln~ dlunf /·,1\ 1,, llw t·lt.:hl \/-lid ..l '''t.'htr., ;arc g.l'ncr.tll) \\rtlh:n ""'

if.\( .. II = E.,""' I"'' fJ. anJ

IJ\'(:_, II= /J.,Cf.l~ (IIJI

I. ;;: ,.

=E. =IJ

jJ:_I.IJ\

= /J :_- ()

tl 65J

\\h!:IC t1J

= Angular

frclJUl'Dt'~ .::

1n{

1/,JJ,,I" =H~h"h:it)OIItghl\\;t\'CIIIII'~~'Jl:.t!.:~(.lll1= ~ < lll"'lll/l'I..:C. ,u•• 111 -) pcrmc~lhtllly :uu..l pcnnuivlly ol tr\!r 'Jlal·~ 1a1n ! '= • =

In ~t:11cr.tl, :m 'mf11mr) hj;IH beam:-. (:OI!ltn~ trntn u l.unp t•r trout 'unit~ Ill oarc ruutkuu m t'h"'~· uud \tnpolttnM:d, t.<:. t:l c.-:ln~; \'t:c.:tnr ll:. • und m:tt:fWliC vecltU' ( /i) though 1hc} ;,r~ pcrpcndicul3r 10 cad1 \llhcr (ln a plane. 1r:mw.:.-....c to tht: dm..oc,;llon tlf p f<lp;tg;tlllHI,, bul kct.'p.s on ..:h:mgmg thc1r din.."CIIHII!- 111 ;, r.mUmn

lnlt' l It 1 rtW4'. Otj]ftu timJ mul Polm i.wlinu

21 ~

ua.umcr ll' "'huwn 111 fhl! 1.2Xa) \\ h~11 "'Udl .1 hc.uu III~Hit:nl 1111 u pul.tn"~lll~ (poltJri!\~r). 1h~ c:nlcrttt'llt h~;tm ,,f li~hl \dll bccomt: lincarh p<\hu'l<w:d ,, ieh us clccui~..: \.'c.'Chu c £ 1 .mJ m••gnclu: \'CCLor- c 8 J U'\t' l llallll); in p;m kul.lr ti l tl'lUOil ol\ ~hnwn in Lhc (fi,l! I :!8hl Dlffcn.'llli~J'IC' ul pttl;m,in~ til:\"icC'o .trc.· l't'!o'-lhl~ \\hich \\ lll ltllJll"C lh~ ft.',IIII.."IIHII 'ntiMt II "-ill.1lht\\ U•pa..;, ullly unc

""''·ir\i

t.'il01J)4'th.:IH t) J l ht.'" dc:lw: \Ci.'IOI .111!.1 fll,l!;ll'-'lll \\!t..:hll. l'he \il tC~IJUU ur ciCCIIU;

'l'4.'h'f ~tnJ mat-:ncuc

wcwr ot the \!lllt:"r~cnt l1t!l11 bcJOI dcpt.'Jh.b oulh(' <.nerumum

••f the pul:ln~cr

·+-

•

i·ll

flf:!. 1.:!8

....

fal l' npoh.uis~d lk·~nu 111m in~

alunR Z.·:l.\i~ \\h~n R•\\'Ctor or M· H'('IfJI' th dirt•t:llun In ') plane. I h) LJneiU'I) pohui.}td li~ hl mminr: nlnnJ: ;:-a"\i:o.. " hen f:. or M· \«tor "hkh an• nrthneon:allo \"tu:ll lllh'4'r, u~dll;,tt-"i •t~11~ ~·lullJ: J JHlrtkuh•r dir.:..:tiun run ehn1o u..;l~ dm n~in}!

1.3~

Production of Pol:1risl•d l,ighl Wave by Different Polaris ing Ue,•ice'

(A) l'olarisation by Dou ble Refract ion ur Bir·cfringence3·•· 5 fJoubl£ Rt[roctiml fir /Jirt:/rin;.:.rnrr

Wh!.!n 01 ht..'~lln uf lllUIIti.:hnm~;~la- hvlu ,.., lllt.'t~lcnt uno1 pllllaC II:J11'f':ucm wedunn hlc ~Ia" llJH\1.:'\ ••~· h• :t "''n~k fdctt.ll:J 1.1). ·"the adr.u.:ti\t: 1n<lc:\ ot' f!b·' ' '''~~me- c\el)''"hL"rc ~ittun tlu.· ~l.a· m;tll'rt.•l 'l h.tl I\ p..- n• m.tlcn;~l.., .m~ G\llt.•,l "'ngly rdr:•c ling lll<lh:u;'l 11r th\.' twlm(llt IIUIIt•nnl Ou\ in muny cry...,tJIIInl! uptlt.:;il nMt.:n •• J-,u~h :a-. ,·"lcalo: <t':t(.'O~. ~t u:ml (~eo ••. K l>P o•ou~:O.IIJIII d)" h)dNlM,\.'11 phd,ph;lk 1\ I I! PO,~'\\ h\.'llli).!hl IU\!u.Jcr\1 un thrill the~· £1"l' rue 111 '"'' rcfr.~ctcJ fJ~:-.. on,·'' ,·nlkJ mJnull) r.J) cO-m)'), winch Iolin"''" lite Snell'' l.1" tJf 1d1;1\:l!llll .aml 11thc1 '' c.ulktl e~trJaH• \!i u:tt} r.t} (/· my), lllC.~ \"C~ItN.:II.)' ul ll /-1.1~ 1 '' \,uuc 111 .all d trediUII\, ...u tht• refr.u.:uvc.· imll• \ Uut th.: ''"''ludt)' ol C/-rnylt.., t.ltll\.'f\'nt tn ,, \Hi h:r"''tll d1 r~t·t mn R~..1 the r..·tr.u.:lih' 111de~ uho 11 1!1 \dl) •voth ~~~~~lltlll lilt I E-r.t) ). Tht)>~ cry>tullinc lll~tcnah ,trc .:aii..:J tm·uatmptt U .dlt'tiUI TI1b olD·i,t11mpy .lri\C\ llw: hl datil'n:nl IYP""""' HI .tmmt;cm~nl u( Uh,IIU' 111 Jdr cr~n t Ull\.'t.:llutt wulun 1h-.: muh.!nJI St) eh..: 'fll'~.:d •~I l t~hl a~ wdl O\ n:t"a-Jdi\c lndc\ Ill 'ud1 mutcn.tl"~ dcpcnJ tln thr: din:cuun Thi, ''fu,·Mn(\ pht•llomrno i'i •·uJ(,.,f,Joublt.• rt•/rt~uum m /Jtrrjrlngt.•nrr mullhow mt· enllt•d Juubl\' ll'hwtin;.: 01 Hu,•fJ·Jn~4"111 r·n·~tuh ThO"'I..' un-iMllfllpi~-. t:r)"'IHth '"')"'t.allll~: u' lfiffcr~-.·nt fum t,, hut ~C th..'r.JIJ~ the' ~au be rOOuc..::d inlo a rJtlHnbohctlron a.' 'h11wn in 1hc (Fi~. J .~9u). A t l \\ o nppoMI;,'

"7"'

~onlct' A&.

II of rl•..:: rhntnbt•hcllntn .t.llthr: an[t)e') arc 41blti\C Now af 11 line dr.twn

1hrmt1_tllA & H . ror ;a ,ry~utl \\hnsc ahrcc~dgc., :~n~ cqu.al,thc n thutlinl.' will male-

'f_-• • TJ ' .7 .",., '...

___...,..I . '

1·1~.

(~t)

l.lt,l

," J_.c .., - ·-''!-

UiJUhl) rcfr;trtin)! c·rpl:tl C:·tfcilc•: ll, .• Splil up ur 0-r.t) & r.rrh lt1

l 'uldtc '''I"·' I .tn~h· \\ tth c:t~·h of 11u.· tlucc.• cd!!C" Thttl ltm.· 01 llt.tl dlt \!1.: litlU

\";_, \ny ,lunltlll1

j, ~

.t)h:d ''l'lt•

I'Otfnlld w \1-l i:o. Jl'u ortic uxi,, i ~.:.. ~.)J'Hit' .t'<i' j.. t'UI\ ~ llwd tn'tlk· the O•tubl~ rcJnu;tjnl= Cl}'t.tl nut J ll\t:J ..tnu~ht lin~.: llh ·\II

llni•.J\i~tl

ltn~

u nd Ri-;.u.i:ll tr\'Stul

<·ry ~t.t l whu:h .A.fl.! hJ\1111; on~ dlrc~: uon ol opuc d>.t c-.. the) or< "nown "' C.' I'\ -.1.11 IC ~

Ul\ht\ml

I."U)nll•. 4U;.irl/ .t r~· 1111h1Xt:lll.

Cr,,1.tl' \\hld1 ar~ ha\•ing two din.:ction~ t'f uptK .J\t~ Ule\ arc .kunwn ·'' ht ~~,t.th "·'·!!·· homx. nuca .1~ bi-axmU. I lim' IIIf ~lfl: tiH: Jiffcl'cnl Hllpun.un fc;tltlr~.-.. h.:~.uJm~ J\•ulll,· rdlil~lh1U u1

.t\htl

Utrcllln~cnce :

b,t:lll ;,,.hh•m w1 tltr tlottbl\ n•fwl tmt: c 1 \'\Ill( uhm~ ttt•tl• the• tlfiiiC tl.\1 \ th,•n It H'l(( mJf ltrntl.. Wit• tu o ttn•~o·. ,_ • ~ltmhf,. t(jwc·tum '-' ul"t'llf al<mx opt;, .1X 1" I or the til her dtrccuon" ~"' !ihO\\n 111 th~ (Fi~ 1 ~lJh1 nKtdcul light \\Ill hn:;•~ I llto rl~·my ;tnd O·nl)'). whkh \\"JIItr.t\ ~·I \\ tlh dtih:rcm 'P.:C."th h••th ,ll'l' pia Ill." ('M)J:triliCd and h~l\'C lllUIUally <mhngunal rtmC:\ ()( ()OI:'U'I"flllon I he JOl,t('t'rp:nthcuhtr-:nmponem) rt!pr...-:-.em the tJ-r..1~ and ln•c \I}:JJ,IJI\•1 ·o•upHtU.'1111 •cprt.:,I.'OIIh~· fnty 111 (Fi!! I :!'Jht .;;,, "ht.:lllllllmpulmt,._•,l

It the.

HI\' ~~r

cl U\ or pumllt Ito

h~ht

.n...·,\.knt n~•mtaHy on !<ouch lloubly rctr...cttn!o! (r) .,,dJ 11 r~~'>lvt.!d into tw,,

uuh:t~n\h:nt Wd\'C~ ( L-ruy um.l (!-my~ wfuch lru\'('1 w 1tb Lhlll·rcm 'dt'lt.:llh.'\

Bolh fl··fd) :1ncl 0 my• ot t &: lmcarl) m plunc pul~tl1\\'d I he v1Pr;Uwn 0-r;,ty ,., :11\\':ty'- rx'' fJ\'HdiCUI:u HI the plllU:lp;ll \CCI Inn

t:fiiYC, pUIUiill)!, (0 lhc

ul lhc Ct')'!'ltal. wherea1<1 tiHH ror £-ray iS p;tttllh!l to th~ pnnctP~•I"c.:'uon nt lhl-' ny..,t.tl l'rmdfml 'it'Cftflll t ,\· thr plant• m n en \tuJ nmwuunx tJu.,.~·tr•m a/l'lfli(UIJ:II(UIII OftJ

o.l

the

optU.. UHJ

II thl! \'e!lm:U) uf (/:•t:t} ll' C\l'I'Y\\herc 11hlh! rh:m (() r.t~'l. 1.; \', > \', ..

thl'n thatt~ t'~ ... r cry,lal h. caJictJ a' Nrgmi1 r ,·ryuul f,· .t: ,·at.·llr-. u/""' R J for o~rm· '\ mufl' , , , , 1\.1 .fur £. l'tl\ ; t'., n.. ~ Ill') \\' hc:n::J\ II lh\' \ t-lucU) ul ttJ·t~y) 1\ c\ ctywhcrl! mntc 1h:111 (f."-r:')' 11 c. \ .. > \', th\-"H th:u l)'p..! "'r)Slotl l~ <.'ailed a~ Posiuve c:r)'MUI tC.!! .. quur1it'. h'IW.\f' H.I.Jnr ~~ ''" u mon• th:m H.J fm O·rm '·'·· n .. > u J !' U'ltt•n '"' · flglrt lwum inc·idrmt l'''"fJ•'IIdit ltlllr Itt tht· optir· t1 d.\ ~~{a ,(, ,,,b(, '''/'rtltlin,t: rn •tal. tlwu ctl\tJ F.-m.\' mul 0 m\ u til tWI 'f'/11 llf' lhr•Y u1/l mm't' m tlu• \l.ltW ilirertion bw H'illr dij)ut•nt sp~·t•dr h Fur nc!!altV\.' cry:.t;tl like calcite. velocity nr E·nt)· io., m:t,,;irnum lll n ,;ht

/ntak·r~nu.

.mtz.h.• lO lhC Optil,; ;o,i~ nr £-my ... mine mum

\\'hen!~ ri~ ln

fOr

Di{fracnm1 tmd Polatirlllirm

po~iti VI! c.:ryStal

:engle 10 th\! optic

!. 15

liL,c {)Uafl/. \'CIUdl)

:1xi~.

TI1is property ol d('Uhl~ n:l r.tcuon or b t refring~nce can be u:.t\.1 to (!CIJtulunM•d \\to: hot\~ 'ccnth:u \\hen ltght 1 t\~1dCIH un an tmi'\Utroruc lT)'tal t hcu lllt~dt.!nl l1t!tn w11J 'Pill up lllht 1::-ra~ and O-ra). when bolla ::ar~ pl:ml." pula•i-.cd ami t1n::u pl:tue nf \ 1hr,dlflll' :u·c on ltngonal tn t.•.ach other Nm\ a ...clccll\'l' uh~nrymon ol nne '" a .;,unpl~ method for e hmin:ll lll)! nne of them. w1t1ch '" lil!ht A~

kmlwn a..: du,:hrot"'Hl. Crys•ol like toumwhnc hu.; dtll~rcm co-cllict~m of ,tb~nqnn'tt f(n IIW !Wet lincnfl} j1<1l.tl',.;ct! IJ~hl, tnlll \\ luch IIICitiCIII 00!1111 ~Ill ur Clul oJ1\\ol on.: of tin.· hcam t!Ct' nh~orhetl qu1ckly and the mhcr COIH(l4)111;!111 p;'''~' 1hrnu¥h wJthuul lnuch ltUcnumiun Thu' il unpolu.riscd hc.un incidcn1 on cr}'tal. lhl· ccm:q;I.'IH bco:uu w1tl he: lmc~trly pul:m"Ved

ll. Polaris ation b,l' Reflection Ur~o.•w:-h.~r

pcrltHIO\!J

.)Cfii.'S ol

•

CXp'\!rltlh!lll\ IU \ltld) lh~ flt11.1fl:',_.tltllli

hluniMinH.•

•

b) ICflCUIUI1 .tt '-llffUI.:l' of diffcrcnl rn..:'-luun lie rvunlllhill .ut uu/won 11~/u bt·< oUIII XI'/\

tiii#Jift•ld\' fWIUfl.\l'lf n-Jun fl

rrtlt·c·tl'll /rom ,, ITIIIt\fWN'fll

me tlmm. nl ct ~lttu·ulm mndc•m tm~:,lt• t, u hu II ' ' kno\\ n "" .anl!ll" nr Un-:wslrr,, )..g" polm 1.wlum ''r llrC'\\ 'lh!r ' ,m~h: /Jrt'U'fl,·r 'vltlw \IIIII~.\ that ~du•tt 11 rayoj'liglu n:/let'lf:tlfmm 11 \mfm '· 1 tlll'u tlw IIIIIJ.f"lll 1~[ tit~ polun\I"R rmglt• '·" rquulw the rt•frann·,• uult'\ nf rlu muln111l t~/ uwdmm So n..~,~nrdtnp: ,., llh' 'lt_g. I ~CII. Ure\\SI~r·~ law suue-. tha1 t.m' =- }I f 1 llht \\ lwn: 1 pnl.m ..m~;- m!!~· olm~o:tth:nn:· and Jl • rdro.acti\C andc\ ulll"· 1Ul"tlwu1

',.,,Jon,,.,/

Nnw ,,,,1111h.: F'q: (I 'lU1 t.m J Lc:

=Jl -= 'in , /,in r 1 -='in 1ko.., '

o,IO 1'1 ::~OS I

I.C', 11

=- ')U

hul h) J.n,

= SJIJ (9{}- I)

Hf n:tl~cltutl

a r, Su r

+ r 1 =t)()

f-l t!nc..: ih.: un,l.!lt: llel\\'ct:n rcllt:CI(:tl und rt:"frttth.;t.l he;nn 1!. 90 .u; n .. '"ll\\-0 111

1.30

,,t

Su1hc t.·nn-.t"t!ut.•nce lhe Bn•wo;.ler·~ law IS lh:.tl whl."n the hglll "lltlldl'nl dl1 the 'Ufffil"l: Of the Cl)'liUl a1 a fi'Ol:tri~lllJ! angle. lhc rcnccted llnd rdr.n:l~d r:t\'' w1ll ~ :u nghl :mgle lU "ach othl'r. Thul\ II ~tn unrolano;.cd l)t!Uill lllculcuf un Ihe cry~t~t lallh¢ pol.tn .. in}! ollll."k.lh~n rcl1~ctcJ l'lc~llll \\'Ill be plaiC poJJJi.>ed \\hose plane (I[\ ~br.SIIOil 1_\ f~l p..-11lf1LUI.U HI llh:rbn.:ol ill~.:hl~n.;c:h ..htmnantFt}!. I '\0) 111l!tr:msmaltcdbl:am \\Ill he p.m1;1ll~ pol11n~d ns ~I'' ha\'lng the c<nnponcm nche.r Ill v1brnuon 1n 1hc pl(llh! oJ llll.'lt.il!llLc

C. Polnrisation by 'lot:ol Internal Rrneclion A Nacul prt!-lll iS n dcvic( which ucts as u pnlanscr. made rmm double rcfrnct111g

L"otkth: Cr) "t..al h• protluo.· pl.111~

pn!Jn,cd l•rht h~ tot;tl 1mcm:tl retlt:ction I rum a l:t}a of(',tnJd:tiJ..st .... m. As the /:,.'-ray .1ntl 0 nL} ~plit up 10 the douhle refractm~ L:t) 't:~l l• l..c c;tklh:. \\ lu.:h arc muvrng wllh t.hfr,·n.:ru 'C''''II} 4Ju~ tn Iherr Jtlfcrcnt r~lra~ll\ c 1ndt.!X. N,w,• tl a 1.1) cr ,,, n mnh:rmll!i ~~lllllv. tch.:J In ~t\\-ct:n IW\• h.1l n ..... ltlllw pn,pcrl) t:ol..:.akrt~ ..:ry,lal \\ho'c I{ I •1.55) he') 1n bcl\\l'l':n the R J 111 F r;t) ~ l .•IN6t ;uuJ f{ I nl I J r;ty ~ I fl"\S),lh.:n lor the LomrRml.'nl cO n1yJ the ln4.."h.lcoci.· ~mah: u l:.ycr \\.Ill h! :11 r:ltl.! l llh!f.IIUm .m,ltur the othl'r l'illllpHnl.!nt (h·ra)') 11 Will ·~ ·" dCti\Ct ntt.!~ohurn nli ~ prm..-:tpk ,, Ut.~J m N~eol pn,m. \\ lm;h conw.. h .,, ~-.1k11.: \T) ,1;11 t.·ut Ill '""'h .1 "•') 1h.11 j, •r ,, pt•r11t. ular n•l ,,1mh' 1..;h mal~nal \\ •H 1)1,· .1 rou.:a mcduun and 1hc lilt~!~ ,,1 nh.-hl,·n~,·,· h1r thai r-,,~ \\Ill he ~J'I;'ilh:r llwn thc-.;n Li~.-·al ~Ull_!k' a\ ,h,mnln lhL' I ri~ I '\I JJ ., h..:n thl... partkul:.u CUtllj'011Cill uf r;t~ \llll ht: dunmJll'd h} hiiJI tnh:motl tdlL'dh•ll flh~ pl11:n11men:.t 111 Ull.tl 1111~rnu l r~Ol't.:UI111 ..·,pl:uncol t;l\.',lfl) 111 Fah~.·r nrtt~ '),·..·tum.(._ h:tph.'f 5 }, \\ h~h: ~·'I h.: Ulh...·r ~om ron~nl 111 m~ v. 1ll h~ P"''L"-' :1\\ot)· i=11! 1 I \I ;11 , JUI\\' 1hi.': prop,·• I)' ~111 '~'Ink -.;1}-..lal ln whH:h .t b)'-'1 ol C.m.td:t Hott, .. m "tlllrt1JUi.:c..J 111 '"" h :t \\ol). 1h:tt 0-1.1) unc.lcr!:!uc:, tutal inh:m.tJ n.•I1L·lll1111 .mtJ J •·•} p:.tio'-l''- ·'"' :1~ l h1" nutgo1ng 1!1\ ht..•CtiiiU,.'p)!llll'

... ..

p;•l:llt'Cd

,~ ·,,., ~~• ~ •••• ... ·""l. ' ' - • ' r • .J •,' •

Lt .. , I~

I, ,

r •• L ~!I •' 1..1'\_~_/ -·~,\

f I I.S\

Analyser for

'!. •......

••

f 1\

·~·

t.tl

1.35

l'olari~ed

Wa,·e

.\. CnJS..\4-' d Nicol Pri!<iut \ .. 'hm\n mlht' lht: 1.3 1:1 I 'II'' '"h\.'ll 1\\P NH:u" ploKcc.l<~dJnccnttu c~u.:h 111hct. 1hc.11 Ull\.' tlfdn•HJ ;•t.·h. "'' .t p~II.JII!i.'t .m~l ,llhl.'l un~o· .h.'l .,, an .mala~(.'l \\ hl.'n rhc po\lllun of twu Nact•J, .ar~ l'·"·•lkl h~ \!',ldl 11lht!'r •'nh 1~.-ray 1'!1''1.':, lhuJUt-th the both lhr Nicuh ( f ··& I .:l l ~~ •- Hut "lwn 111e .'!nd prhm ,._ !!raduotll)' rmar~d tht· IIIICO'I.IIY ur the CIUl gc)tll~ / :-r:.~ \\Ill t!r.aclu.-11)' deere;::, .......md \\hen 1hC (\V(.l Nu,.;oh .In" Cft)S,cd 1Hg I 'I h). then nu hfiU ''ill ~·~uut.> uu1 110111 the 1uJ pri~1H. Rt!~:•u-..c \\ hen lh~ F ·i.JY l'ntcr~ tlu: 2ntlprhl11 ·'' lhl' t:ru,...cd ro'I.IIHII"I. I 111} wall :1,:1 a' .Ill (J-ray ;mJ 1' h)la.JI} ifih:l·nnlly r~ll~,•t' kc.t h~ the C:tn~ld!t H~ll,:un • ..,,; Jhi l1g,lu c-~m\1.!' nul ol 1nd prl\111 . hcrdnr\.' th\' ''' pn'm pwJuc...-~ pl:!n~o.' )l(tbrl'-l.'d hght (twl a.. un-Po l•m~crj ood the ~nd J>n~llt dch:"'l' lh plane nl polun:-.lthlll (o~Cl a"' uoAnaly!ocr•. The cmnbmuliVIl ut I'' umJ 2nd pnsm I' ca lled lb palariJC'fJJIC.

8. i\.hllu.s l.;n\ LciU~ l'\Hl~h.kr m~oUls.

n p~•lan~a \'ht,·h h:h fM" :txt~ p:-tr.tlll.'l h' t ·tlXt' tp:l" "'~" 11 will only uiiO\\ H.'l pas~ thl! plan\.~ f'""'l'lnscd hcum which om: pom1ll~l w

}..· :1\h) . Wh.,:u 0111 Ullpul;u'I'ICiJ h!o!all1 Ult:Uicll1nnlhc

w;.tvc ''ill he plarL'

po1ari~cd

pol;art'-i;rlh,:nlhc lt'illhtl~lth.:d

.uul phu1c ••I \'lbnuwn nl that

planL~ poJ:m~ccl

u·anslllHicd beam '"Ill he parullel to Y-nx.•s. Ncm 1r the pnl.Jn\cr ~-'Y 11 L"an Oc a N!Ct)l pri'rn or :1 Jlt~:n'(•l\1 ffll:&h:d abnul Z-a\JS. 1hcn fur unpol:•ri:-.cd mcJdcOI : m ~ cha ng~..~ o t tmcnl\ity fll 1he emergcnJ be:lm Btu 11 Urnru:tlly Jl4lhlrl'-\'d l~al1\ln\.'I\IC111 ('11 thl'- poluru•cr, lhCn :1'\ lhc rwlun,cr rniJICd nhmll 7. ·'""' th\!n lh.: lllh.·n.;n~ nt cmcr~cnl hcJun "1l1 .:hungc hul 11 \\lll ne\"n be J"cm

bc9m Ihere "111 no1 he

Nu\'. It: I lh cOIP..IdCr a plane pul.u '"~cJ

•

he:m1 \\ 1th eh~l..lnt: 'cl.."h'r ' tl umpl11Udc (/!..J oncnl~ m nn ohc Jlllllfl'<'f 11how rl.-.nc ut \lhl.&tlon l~.~~ AB• nl.1hc' .ul

~-; ') 1

nnglc (-) '' 11h 1hc ) .J\h. a.., . . hown m the ( F1p- I .t! 1 I hc.·n lh'"· ,JOl(lllluth.- nl

the c rm:rgcnl h'"·.un fnun I he Polmnid wlll he F ,, '"'\' f-' J ll..l 1111.: ulkll'-11~ ••I thcem c1~111g lh!ollll \\Ill \ ~It~ ·• ~cttrtluJ~

(

{

•

(

w 1hc Inil~'" 111~ ct(u.tthm I = I " '" (-)

l ncidt:m'l* of t•la nc IJulotrbcd h)thl on n oa nai~M:r ul ~~.~~ 11\.i..

II h7o

whcr'-' f, '' lh1• 111k1NI \ '' 11w uh·Jclcnl nhml! }" bc:un.r\b<.W\' "'""llMllt~l 1l,t,.,J rt pr~-;.cm lht.• M.ilu ... l;a\'. I hu .. It .a pluu,• p ct1ili1:0.L'd h&.·.uu llh:ulent un

ol rulaH,hi olllll d llh' ,,,,, Ihen lhr m iCil\ll) n llh ~! (.111-:r;cm hcam \\Ill \~I! ut.."'CUh.iln~ tu t)h' \1.tlu "' IJ\\ ~u~· lhl• pulmusd i' fill.tll'U 111 dt~~ \\'1\C ,t~~~. ~.:uou l"'he n lhl' mh.'ll'"tt) ullh.: cml•rgcnl ~om1 \\Ill m~.:rc. 1~ . nnc.l11 \'-Ill he m;J\10111111 \\1u:uth ~ l~.l " .s\1"" ... p.ualld u• AB founlt~r rmtttwn wzll dL'"Cfl'..''c du~ mh.:ll...,ll\ and it \\111 b'" /t:l•' nh-..· n 1h~ ~-.:..!> .. ttXI:-, t .. p~rpcndt.:u l:u tu AU. H tt '' 1l l tun1h.'l mtalt: then ol).!.iiU it \\i ll ~~.. IH.a\iiiiUitt ltt t h~ J'K><iili~.m AC unllo~!!ain it" jJi t,,• I"¥: Ill at u (ll:rpl..'ndkular P•"-lti(lfl ht:ft11T II n-oh:hl'' tu II' HriguwJ Jlf"jtion

pnl.unnl

n•t ,ll~' ·•~•11/

1.36 Supcrposilion of Two Plane Polarised W:wcs and Product inn nf Circularly nnd Elliptical!) Polari~crl

Light l...c.1u' c-on~u.ler .t UllliU~Iuum.:nu: hc.tn1 inc•dc.m on 11 Nit:ol llri'm ~IIIC I p~t,,Jnt through the t\u:nl 11 hc..:om~ plnnl' pul.tn.;c..-d. 111en ;tiiO\\ Um1 plane l"''l.lfl\l'd he'•m 10 .nddclll onnnull~ no a uru:lAI.ll dnuhl)' rdrti\"Ung t~ulcn~ 4""~f qu:.n?, who~t· •nn<ll.·m f.u~c ha' "ern ., c ui. pamllct 1\l tb upiK tL\b. I.e . the

''T)'''''

Opt11.: .l\to

phu1c l)ltbn'-f:d ll~ht lllCidCIII nurrnall)

to I he: nptic a:~•' uf thL dl)uhle rcfraclin£ ~, h~o.· pl.mt' nr '•hr.t1Wtf1 o f Ihe plttnc pulan ... CtJ ~nn llh.'tdcnt nn 1hc dnubl)' n::frou.:lutg '-- ')'1.11 ur~ ,,.., 'hm\11 m lhc t Fil,!. I.J3). lr 1h.u !-iLUullon ~~ we have UI\I.:U''-Ct.! HI the 'C:f.:tiUn ( 1.34A 1. rhe inddcm hc.:tm \\til bL· .,pl1l \.."1')' ' ' ~'1

t'ig.

·-·n

lnddl•nc.·.- nr plluu~ ,,u l.ar i ...t:d beam on Nicol prhm

UJ> tlllU 1!-ruy tmd 0-rJy. when bOUl arc plnne poh&riscd ouut lhcu plane (I f vrbrutunl\ :tu· (Jrthogorml to l~\lch uthcr lJ.). well :..1!> pcrpcndiculur h> the op1ic a'(h,. No\\' <tCC(Ifdlll_g tu the fc:uurc ntlnllxor-Frvc in ~cCthm I. l..lt\ E-r~t~ ;JOd 0-r.t} ''ill nmvc 1n the "iamL' dir!!c-liun hut '' ith diff~rcnt :>pt.:~.J, Su a.. th~~ pnK.'l'ed thrnugh tlw Uouhl) rcfracllnf' crysHlltht.> path <hOcn:nl.!c C8) a' ''1.!'11 :1' Jlh3\l' thffcrcncc

. 2,T ) ( t) = X A wall g.r:tduull)' ltll.!rca:.,c bctwecl'fl them ~"'' 111 order to ·-md mn th'-" :Huh~ llf po1.n ";thnn nl lfw u·,ult:u\1 hdd, we h., ,~· h,,;oul'!ulcr thc~upcrpu.. IIHm ''lthn~c IW«• '''"~· .... Let u'"-Oihukr tht: lunc \ Jfl.itinn uf Ihe i.:ln•tric·lid.J \CCinr ill .In)' arhllr.lf) f"lilrl(' pt'fp,~ntJkul.tr lu the

thrc4-·llon of pmp.tg:nion t'a~ Z-.1\hJ ;~~cmJin~· tn 1hr .:qn. Th1' ~.111 he: "rittl'.n :a... 'd)' IN O·n.t~ 1:. = ,\' =

t l _(f~l

"ilh (.: = 0)

en:-. (tm•

I C

Ill

I I 6RI ''hh:h t:oo n ~qut~uon 01 .an ..a~)'llllllClfh•.•tl dlip"~ ~\' hu .m) .LI'l'llr.u~ .... lui.! ~)f ph.I'IC: \fl lfcrt.:llCC (<5),1h~;; 4!1llt.:fg.:nl l!gfU rrtUlllhC c.fuuhl) rdruCliO~ CT)':O.IGJ WJLJ h. 111 .f.:.t'llt'ral Elll{m.-ct/1\· tudatt\c'd_ H.' Jht.' Ill' ut 1he n.•..,uh.uu l.'h."'l"lnc ildd q;l-'1111 • fo l '"llmo'c 111 un ~.·lllpuc:JI p;uh In 1n~.: "~.unc '~ J.) ·'' 11 we wu1L:d the c•ld e~l :1 ' 'retched ...rung un rhc t.:m:umLcr\·ucl' ol ,, nrcll." wr ;m elllpseJ. 1hcn eo11.:h pmnl Ol lh~ Stfill!! \\il l 1110\C Ill tt ~·m·ul;u lOT llf1 CJI IJHIC:lll

pmh,

S1wci:ol C:ISeS c I ) "hen Ji=nr.(whercn =U. 1.2. ·' \!h:',,

• 'HI

Jj - O.(th a-±1 lhcn 'hl· cqn

CI tlRl hccnmc"

[ ~,,

I I"

)'IX

.!..J' I•

:IJ

1- 1111b/a

ti.6C)J

\\ lud1 , ... uu cqu:.llion ett :1 '-lr.11~ht l1nr So h'ht•u (0 = lilT}, I he• rr.mlttUII h'<H'f'1t'll/

11{· plmlt' f'<}lttristtl. ( 1\ \Vth:n ('i:. (It + 1/l )n' ( tnr " -=.H. I ~ CIL) -)

t.:C'I\

('i = n.

"'Jil

;i = I Then the

t:yn CI Mtl hcc.:omc'

,.-;-

{ 1.70)

lntrrft'T('IIt"r, Dijfrm•tum mul/-111/fln '.'flftlltl

wlm:.h

,.,.,,rc.<s~m'

mt t'tfUtll;on of (I .rwltmt•trirul l'lltJIH: wl,·n (u T

th~ r~'uh:mt ''uvc

2 JQ

bJ TI1cn .abu

'''II he .:lhplu~:.l ly po1ari,cd in l1 ')lllllh~ltu.:nll) ,.,.">

But v. hen 8 =In +

1/~)Jr ;ltiO

u =b. Ihen 1hc Ct(n 11 .6H t bc'-umL"' fl 711

whu:h '' un cqu,JIIUn ut n l"U\.k. Sa lltt' n'Mtltunt uw•r willlk' t un,{ml\ polart H •'

'±•

-t -~ /{( ,.

-r-t+ '-

,, ': l

•

_J_ II

(."iJ!. l_l.i Re.'"ult11nt M-ah~ ur pnlari7,ution-. a nd din"ftiom ur pnluri-~:utiun (ur dirfrrenl \':thl\' ur {51 rur rc..,po ndinJ.:, to lu e hJ dut: ( 0 'lttpl•rp o ...itiun ur l\\(1 IIIUnl' po l~~ rin"fl

IIJ!ht

"it ..Ill.!' ttl pnJ;m,.JIIUfl .tmJ \hft"t:lnm ur fl'!JIJ.rt .,olJIIUI llll JtlkH'III \ o~ ltJt: ttl phJ~· thff\'rrncL· (b) utrrc-~p,nding to (o =II iu Ctlru. I 1"19. 1 70. I 711 arc 'hll\\'11 m the I ll ~· I '-41 N~m oh.'l:\lldiO!! tn tht: '-=011\CIIIicm. \\hcu tin: liJllll tht: ..:lcc lri~ \<C~hll ll•l.th.•., ••n ;t l.'th.UIIII~tcuLt• nt .t-.:tr~:lc 111 auttdt!~.!l.Y.t">C Jut:.. tHtl1 o~ ,J 11~ prt•J•·l-1!-t.lHIII 1-.lh -t l-~m:cw.m. th,·n the \\,1\'e ;, c.tllcd nghl Clr,·u1:trly puJ.m..,~·~J rRCPI hght, \\h\."t~ .1~ wht:n 11 \\II ml.iiC.Ii. 10 U. dod. \U-,c dlft.:~IIUII , th:ut It l!oo ~;tlh;-J .h left \"lrl"lll.u I~ rolurht.:d hgnt ( LCP). which urc ~ltm' n m tht· 1rit• I '-' 1

L l7 (,\)

Quarter Wave l'lalc and Half Wa ve [>Jail•

Quarl~r- \\':1\'l'

Pln1c

.\" ''-'C h:l\'c di\.CU\\Ctltn .theW\! ~clinn ~I '(t) thm \\hen otpl.ut ... f"Jiun...cllll~hl

v.11h pl;u1c of 'Obrutk·n oren> shown 1n the thg, U31, mckknt nonn:tll) on" UJII.IXI:tl tlouhJy rcrr:a~.-ttng i!ry!\Ht l (C:\h:Hc ur ~lloU1J'}, v.hH!,I! lllr:tdt!lll iaCC h:t\ been ~:u l parJIJcltnlt\> optic .uh. 11 ~plil~ up mlo E ;md O·m) The) will rn0\1.: .tll'mg ... arne lHcc;uon hu1 with dlffc::rcnt 'flCC:d,, Scl "'the lludn~.:'' tlf the duuhl~ rl.'rr.u:ung cry~tal anctc.a..c.!o t h~ path diffcreJh.:~ v.dl .b ph1t ...c J,rrcrl!n...:c w1ll mctc:t\\~ tx:twccn £-ny :md 0 -rny.

.L,

Noh· ((If IIJUII'ttCWtlf thkkntts.r (t ) of the- Jtmhl\' l't'}rm.·tiiiJ: ._.,,•.Hd/ ,,Jum tl~t• pulh tlifjt'll'JU'tt bt•lwtm E rtn· a, J 0 -I'U\' bt•CtJtttt'., }./4, tlu•Jt llwt /)/au i~ c.'allt·d a.s Quurlc'r H'tnt' plat!".

u,,, 1 = )J4 or 1:: )J..Hn,

Fm Pn ... ttt' ·~ ~.'f)'"t:tl Qu:utt - • t11,

Not

Nc{!;tl l\ l'

crp-t.tl

r;tlt..'il c.'- ~~~~~

ltd,:. AI~ or I

n,J

;;: ).14 (11 - II, I

F(lr" Jllhll l \~'"' I) \ lotlltlt: f.}U11r1/ \\II h ';t\\.hum lt£hl t A.::5N4 _\A). I -.0 onOX57 mm Aud l't't' ·' l'lt\11 1\ ~LT) \t,il lt~,· c-aklh'" llh ~nt.hum hght tl. ~X'-)3 t\ ).I , () U f(r.lnun

7~1

~., \\ i11·11 •• plolflt' pulm1,e,t lq:hl \\ tlh 11' pl.tth." ol' thr.uum uwluu:tlou :111~ arhllntl) olftt:lt.• j ~'''" rh.· 11)111· •• , ... ,, .. \fill\\ n in Ih,• h~ I I ,, I" IIU iJCOI11II ;uauan\'1 "':1\ l' pl.uc. upruuucc 11.11h •hllnciiL~ 1iJ 11 1c phJw thfltr;,ncc eli:; ITt:! I h<l>~«'ll f r;,y .md c1-r.ly. Uuc h~ IIll! ... ui~'IJ'tl\ll n'n u11hcm (Ut.'t:cnrUml_l tu Et.JO 1 (lX} 111 ~~.·n\.'ral

cmcr,t;~nl ht;ht \\ tJI ·~· f.lltp111..'i.lll\' p.,L.lfl"-~d. lltll h.'f ( =- 45 I (I.e. (I : . b. In tit\! 7U~ f'ntt'rl.'c'ltt ll;:ht 111///11 C·u( ulm-h J-',J(anwd m \lum u m ,.-,,. t I ~-II

l;,qn. I

1Rl tlalr-\\a• •l'larc Nnw fm a1mrtll'lllttr t.'udlh'H UJ ••/ O~t· ,/onhl\ n{m;.:mtg' r\' fMI hltC'II tl~«·r,alt tlttl~r.·un· l•t·fun·u F.-r,n· 1ilhl 0 w\· )./J, lflt•n tlwl J'lut,• , _., rttlf1-d '" /Ia/( 1HI\ • tdtllt

/t,.,.,,,.,

l·~'r f'I""HI "'-' ~·n -.1.1! ~hl,lfl/

Feu ~~~

N..:!!·''"~ dy~tJ il

.•Ink

In,

• Cu,

n, I I

-=--

1J!. t\f I =-

u,.J 1 :c

)./2 l "• - tl,,)

)J2. ur t = )J2tn,,

11,.1

whl.'n ,, J\t.nh' pnl;ul ..<''' h~fu " 11h 11"' l'l:ua: tlr ''IJ,r.:umn mclm~J ;It otn .m.:.:l~o.·

4.)· UllhC UJJIII•• lXI~ J~ -.hp\\ll Ill I he 1·1)!. ( J .~1) I'\ tnCidC'Ill llll :1

half \\U\t'J!I.&h,.',

11 pruc.lucc p;•lh &ltlll"rt.1U:C (A/~J , ,. p1t.1:-.1: 1hlfcrcncc («5;; Jt) bcl\\~cn /·. ~rJ} .unl O·r:l) Ou~;• '') !Ill• 'llflCI l~'"lllnnl'lthcllll.tt'l"llrdmg 10 Eqn 1.09) t'llll.'l }:l'llf lsl!lll u 1// ht• nt:nm l'lmu• Po/,nn,•tl, hut till' ~.hr(•~·unn of polttrl\tlllfl/t n[ sh, I 111/'llf ~mtrl!rm llglu "'"' b, ,-,,Wt d tlll'ouch va m cmupan wn It• Ott• thl't'c ,,.,, ,,, dhra1w11 of tm tdoo l .uw.n lt~:lu m ,fill\\ 11 m rJw 1-J.&:.- (I .1·11.

1.3K

Op1kal Acrh it) ~

l't•rltllll ' I"\ \In/ \ .nu/ /,,,uiJ \ hd\ l' lilt •lh~/tr-\ Itt IOI«ft· tftt· pfmtt' n{ /'~Ofttll \cllto •II

t~(lu:lu II\ 11 JUt\" ' 1hwugh t/, 111 I h,ll f'l'lJfWrl\ if t'll/lt•d Optintl \l tidt.' o•ld tltrJ.\t JIU'tlium\ mr ' ,nnl t ){'Ill lllfl '\;fit r IIU'Iflllm , Fur cxantplc \\h~u .J hn~afl\ t>ollm~l' d ll~lu h<Jm l'~""t>IM~JI.:~ thrt'll!!h ,,n Optically .acu,·c mt:dturn li~\! 'U!!.at M)lulion l hcu pl~uh,: ,,J jhtlo:nl...t1htrt rulllh,·~ 'I he ..tll)!lc of rttlation Jtructly Llcp('mh ,_m the: dblann· lfJ\~P•I.'d lhr,,uph lh(' ..,,,lultun 11:.. '"ell a:.. on the c.:uncenlmri,m••l ~Uf!ut :O.\lhtut} Whcu lttu,: ;•riJ· pt~lnn!t~cU h~lu prop:•~utin~ rtlon~ lhc: upt tc uxi:-- nl a quurl! I.: I) '10l \\ h1ch j,. aiM' optic;tll~ ;Kti\'1!. Ihi." pbnc or pnl:tri..:~Ui\'111 J!Cfl, !'Ot:lh•d Opuc~•l \ 1.:11\ t1)' c:m he 1!\phuoed m the fuJio wang way. In OpU<."ally .u:CtH• medium Ihe \ do~H~ 4!1 rtghH.~ I n.'uhuly l'tl l ~u ,,t•\1 li}!hl ( RCP) ., dLI r~.:rt:n1 II'\IIU <ho velt•cny ~f 1<11 <n<ulnrly !'<'lome~ hghl cLCP). lx!cnus.: M thc.r dlff<r<lll R.I. alun~ ri~hl htuut\·d d1 rt:t~l inn ,,,, :md :tlnng lclt hnnd~o:d dtre~hon t111t. Whf..'n the parllt.-ulur nu:dtutn ml:tlc, lh~ pl.uw '1j J)l)l::trisadon in Cl<~k '"'c thret:llftn theft 1ha1 nu:dnuu j, ..:;ailed k1gfu Jlmul,•tl ~·r IJ(1 Xtm·rmmorv (Wh('l'i.' > n, '· whcrcn.)> \\hen 11 furall'' ul umt-c.:lm:l..w t'>C I hen 1ha1 is C311cd IA'ft lunuh•ll ot /_at l'n•rotal(>n twhert n. > n 1t. Now ti Pl11nc polnn~o~.·d li,g:hl whrch '' •ncu.tcnt on Lhc oplicall) acllvc n1cdnun

1..1n 1~ r~'n l \c1.l mHII\\I'CIIl. ul.trl >· rulari,~d hgfu CRC'Potml LC'PI. \Vh~.·n tlll..''~lwn ~'P(ll"-lh:l,:. tlth~t:lctlurculurl} I"Uiurhcd h£!fll prnp.s~atc through an upti..:.tll~ .tL'th ,. "' uh Lhlfcrcna "l"''"d"' • •t p;llh dtfference n.. '"ell., .. ,, ph;t-.c d1fftm!lh.:c '~til ""'=''' ~,.•,·n lht.!m, uud th:u •.hncrcncc ''ill guc.. '"' tnt;r~a.. m~ 'ht~t.:lly '' llh !he

m~.·c.hnnt

L'\tnli.'

dt,liuh.:L' lrdHI"ied 1hm.1~h rhc mcdaum n' well a' \\llh the cnn,·~ntrmmn '" Lib.' ")IUIIIIO Stt uhlltl~lll'l) rnr ·' l ~."lflh.'Uiur lhu:lne~' ul ahe IIII:Jaum ·" \\CII ..... Itil the l'·•r1KUI.tr L•Htn·nlt.nmn uf !he 'olultun. p.lflkulm \ .tluc ,,f (dt.tW ,)t llcr~nLe "til ~·ttllll' llli'•I'IL''Jl'"''thlc ltJr .t nll:tliun uflhc pi.Uil' ul 111\..ttiCnll'l.lllL'IHtl.lrl~tl ~u111. ''hwh a..·wh' lrt"nlh,· rcctttnbtn:uinu nl' (R( 1)• uud tl.("l>) 1ipht \\ lwn tlw' wtll ~.·.mw uut tmm lh~ t)pth::• l l y ot\.'11\'(' ntl!dtum a .. un ~m~r~em h(';.tm.

J.39

El~ctrn-uptic Eff.,ct'

When <Ill r ~llt·1tJ i:~ 01Jllh~d :ICffl''t'" an (lJ~hC::t l mcdiiiiU, th~ ..h\tllhUIJI)n HI lh~; t.'kl'lltUJ' \\ tth111 th..: mcdtum Will gel.., dhturlx·tl <;u i.lw.: 1lu' apphcd bll~ld o.m hUIWJ'IL nh:·,.hum rn.t) bc(umc- an om~t(iHiropk Sn th~: pdl,nii.Jhllit) ;nnl ht•tn:t.• K.lut till' t1\!.'i.hUII1 dl:ll'lf.C .. :uH,\t l l'll J'I i t•rtll~ dttl!' IP 11t1: Uf'J'IIc-d 1-:·hdtl.uHt I IIIU\ hcctmlc .10 1\piiC:111y ttt.II\C m~t.hurn. \\'I11Ch '' J..n~'\\11 :t .. J II:Clr-t._C lf'lh.' l•l fl.!\·t Jltt• l l.'"llh ul 1(1h \'lt:\llll-Ufllll l!fiC\:1 11M~ UlthH.JIILL' Itt'\\ HJlll!.' ot\'-'' 1t11U ti.IIUiolll) d11Uhl~ t~fnJ£'1111~ t. l)\litlli"-c IKI)P ), m h•UML.~ .t tt.tiUJall.\ '"'''LI'l•pn. t ~ ...t.tllt~L' lfi.t.AS) inh: Jouhl) rcfr.lcting c-ry~totl h;. intn'lluung J IIC\" nplll J\1' l lt1 .. P'''i~'I1Y ul c.'h.\:lr1t ••pllt.: L"(fc c l ' ' \\itk•l) u ..~d 111 upll~r;aluh•dul.ltlll lw hhcr uplk' ·u utntunt~.:.unul hJ..c POC'Kf!.L ~htdu.l.llu r .111tl Kl.. KR mtk.IUI.Ilm lu lht.'!>l;nnc \\;1\ Ma~tnrw O!Uir· t'{/C't'l r~l\ullx the uplu.:al :J..JJ\ lty 111 MUnc mcdJUIIl lluc 1t1 the" ,tpplktttltlll nt ~l·liclJ Mn~nctn~optll.' cflc, I ,.., U'lcd m hmul.l\ ·, mntlul.t!ttf lnr lib.:r uplt~' ..:t'UllnuiL::Jh.m.

I A U r•huto-elaslicity lltt.' , ,. ·n tl~ ''' 111 J;!ITII<.·r l'C.·um' -.·tc ~,·,m he 'olu•hrtl ht tlw ( lpttL,tlt~·· l•llllfllt' \\hid! h ~"''"n ,, ... r!tt'lo·..!mthll\ When .1 duuh1) rL'tiiiLIII1l-' t.:l)'l ~tl h ptt-.·~d 111 h~.·H~c.•t-•rt tht.." '"•' t.:f(.,,c,J nKuh 1.1.'- dhCU\~cd \C' tton 'I 1"'11. the hcltl11f 'I""" a.."''"'''"''' h' .m tnh.•rl"'' "'"''c fl\ltlt.•rn ht.:c:au'c HI 1h~ 11h;,,,. dlflt..'lt.'th-'"" 1"'-!I\\~L'n cntcl~\'nl t~.tnb. Nuw '"lllt lllOII~tl;ll ' hh.\! cc-llulutJ. gla""· h.1J...\!II1c ch. ~~hl!n

rhc) JJt~· ht.:~ ftflltl 'tr.un du nut c\l11h1t the llWJlCII) ul Juuhlc rdt.t~llc•u But lhu\c '11.1tcn.d~ '-''- h1bi1the pn~pcny t1r dc,ublc n.'.lnu.:tion \\hen tht..'} 11n: '''"ICI.It:t.l lo \I.IJilt' lf1lCrn;tl 'lfC'""'('

Stt \\ht.•n \UCh :"tlfrlim:d m"tcrml I ~ pluc~d l't:l\\Ccn tV.dJ .... .._,..._~d nl\.:t,tl' olll i' nb..crvcJ. For "tr~·:--:.:-. t1l ttlffL·r~ntiW.'inl,, phtttn}!r•\('h' ,u the tOh~fil.'r'-' ll(C pattern (.111 be taken. Th\! ..trc.~ i-. n1.1.ximum "he1~ tJtc uu~.•t1l·r..:n~,.:..: po~th:m \\Ill bl.* do-.t•. Su thl' 'tr'-'" pn lduccd tn .t lx·..uu or m u. l;in.kr \~ h('n loaded <.:•w bt· C\UIU.Ih;c.J b~ thi.; mClhoU. Genr:n•lly u nuxh:l ot th~· gtl'dCr ru.ult: uf .1 tr •• thJ').ITelll Jlla:..lh. IU.Itcri:tl il-l pl.1ccd In ht.:I\1.-L'Cn the CI'H'I\l.'d ni"ul' ;md lntaf~.•ro:nt.:c pau~o•rn

llll'.n l~•:• dt'd

I he .. , r~ ~:-1.'!-. prodt.ll'\.'t.l :11 <.hffcn•nt pomh "'an ht• :maly1\'d :uu1

S1nce the h.:dll) l\ lll\', 'u thi~ "

estnn.u~J.

:!otf~~:-

nnd

Sll"o..~tn

reJ:tJion CLan he. csuma1cd hy 11u-. vpu~:t1

~:llletl a~ PlwtcJ·c/u,,lin'h·-

Qli ESTIO'IS 1:.\pl.tm \l.h,tl J\•., l'U llh.~.m b)

~·l:u I>J\1~111 ul

hj;JII! Ol'>llll,g.UI\11 bCC\\"''-'11 pvl,•rht.·d

lt)thl !mi,) unr \t\thi.'i l h)!hl

f>e\.lrd)(> lhl' ltJII\11U"CIU111 u( N1Ll.11 f'II"I'IU J.lld o,htl\\ htiY. ll ;Jd~ :1.-'> :J j\ill:tti \\'1 .tliJ

w• 1111 nnttly/.:1 1 1:..\pll•lll th< (~h!llu llll' IIHII 1

Jnuhle n:llllt:li\•11

<lm! the l;ltn•lnn;titlJI lhCHr) til IJU.lrln \J.,I\t"

111

cah:U\! ny ..t.tl

rl.t!C .tntlluJI \\';:t\C Jli:Uc

\ Cll\c- ,, dtt'kh'QI mcthn..l uf prnJt.h '"~ ~•l. •u,· j"MII>.~ri-.ctl h~hl It Wl1.11 J,, )llti till'.th h, [llaJiC )"'•lnJt'l(''l ht:llt. cllij'tllt-.JII} ulicl -:-n uil.trh l"'ll'l,ut~onJ l t ~· ht ! IX ~nh,• hoi\\ \UII wtiiJmKhtl.:l' Lu-:ul:uly jJ\tllln llcd ht:hl ;md dt,ungtmht'd 11 lh'llt un~•huo,c:..J lit;!hl • ' Wh.JI \\til lht~ <t.tli.' Ul l"'l:tn ..:tllllll ul thL' L'fth.'r')tt!IU hgltt when

.,l,

(ul

A bco.tnt \)I u r\'ul.u ly puJ,m,cd lil!ht

I !\ p. ~...~J

lluough

ljUilrtct ";1\t: pl.tll'

!AnY l'lmc llnl.tn,cd I

lh• ,..\ lx-um 11l pl.uu.: puluu'\C\1 l1;.:h1 '" l'·l''CJ lhf\~t~~h a quu11c1 \lioil\C Jlloih:

I \ m f-11pl~dlh pc1l..m\\.·LI t h. J ,\ h~.~~~~ ••li.·lhptl•.:.•lh r-•l.tri,~o.·4ll1;:ht ., p;,,"'CJ lhr~1u}!h " quartet\\ •H·c Jll.th: ( ,lm· l 11ln.: J1<tl:tn"'·d I hh t'lc.;un ,I Jll:mt• rot;&n\.4.'tlll)!111 I"' fl.t'o"'t'd thnmrh "~,u:m.:r \\',1\'(' plllll' ..udt th>ll 1h.: ' thl.thu n.. ••I !he• pliUh'J1HI.&rh..·i.l hi!IH h•llin~ un 1h.: quoul.:r ";1\t· pl.1h.:: 111.1b( .ut ~.m ;:k HI I~ drp..-~· \\llh the urttL ·"I" lr\m C'nul.trl' Jllll.lfi\l"ii)

ICI :\ n~hl-tlh;UIIul~ JKtlo~.• •'ctJ l"tC...uuu.. ~th:m ~~~~ .- "·~o~kuc- hll11 ""'"" ploo~l.. ' \nf l-411 Clf\'U1nrh f!oj\l.lfl"""'th

N f\p1.tin the rnm:rrlc Ill nllolli~\11 n l pl.ut\' n( JI'HI.ItiO,aJiltll h) un ''1\lll."all~ ;n·thc rucd1urn

IJJ:mc: ~ll.tJI'\I.tlll;!hl r •• , ..,·.. thh•u:h .lqll.tll/ rllll.: \\. 1111 Ullin:. oiAI' fMrulkllll tlh 1,1\.'\'' ( ••kul.th' lh" h,;,,,l 1lu~.·l..I1C'' h•r lhf: 1'1.11\! fur "'h1.:!1 cutcf~~nl ll\:.llll \\111 t... 111 J'IL,I1"'' po1L n-..·ol t-., ,r.,·UI.tth f'o'l,,rh ·ol f~l\l'l11 h ;JI 411 I "\~l '' I f..t I ,. ... (O~(Ju \I 11iwl

1.,

l "' ''l'· 11

lfl I· \pl.un ph,\&.t '-'IJ.'It'-'11\ :md u .. u ....•

d>~

~l·

"''-'"

7.!• 1

2 X-Rays 2. 1

Discuvl!ry of X-Rays

Ro111geo in ll't95 di~covercd X-rnys, -...hen h'" w::L' 'tudy111g 1he pht•nomcnon or ~hschar_gc through rMcficd ~as.es. He found 1h:u ''hen tht: pr!!!<>~url* 1111hc d1~h:try,c tulle 1.s rcduc~ w 0.()()1 mm or mert:uf) and nn -:lccLn..:o th ...~·hn rp:c 1!\ passed hcL\\ Ccn cnthodc nnd anode. tbc gl;'~' wnll bchnu.llhc l\tltlOdc- hC!!IIl:\ lO glow \\'tlh J p,o:em~h ~ydlo" colour Durinp d11' c~pcnmcm he .tl ..u nlhcrvctl lh:u :t flllll[C\..:.'COI '>C(CCll pl~cd dO\C to 1he \fl~h.;ug_e IUhc tfli\IIOUI.!J 10 rC11\.Uf1 num~em

e\'.:n rf the diS('h3rge 11.1bc was comrktcly "oHr.:d wuh n bl;1..:k 1hu:k paper. ,\ncr JNrfnun,ng. ol ~ene"i ot e-.:pC"nmcnt' l~<l1Hf!cn <'mH.:Iutlt•d 1h.11 when o hcam of la ..t rno,·in,g electrons sinkc!\ a 'illhd totf!!Cl ••m Ill\ 1S1hlc. lu~h l y J>CO(lr.thng rmlwtum '' pn.KhJc.:~,;d llct:;m~e t'f lhL"u unL.mn' 11 lhllUIC Kvlli~CO \.-ailed dtcsc titJiauon b X..ta)''!> Earl) j"' CSUgullon' nil he pcncrol prof>':J11C' ,,j the« In\ islhl(' l:l)!io in~lkatcd th:ll they nught lx ur I hi.' ,;unc l1itlnrt.' .l, \ i ..ihk :md uhr:t\ iolcr 1 hg1n. hUI ul vet} '-hf•n \\Uvc Jc.ugllt ( Ul - ltl ' uu1 I hl' I arM ~tlll'lllpl\ to n.oflcct. n:h:h.·t otml thfrt.u:t th..:m wctc, hu\\C\1.'1, un'u~~~~..,ful

In 11112. Pmf L:mc ~1l an mgcmnu' 1t k J "hh'h , nhctllht." r •·•hh:m lt1 a .. .:() t1loTI I1lc t.ulurt' 111ft..' Ikd m~. r-..:lr.t. l mt: lh!J r.u.;IIUn. ~11.... <1f X-r;1~' \\ ;" m~rdy dul! tn the t~lJUircrnl.'nl ul ~ JU••I'Cl 111\.'Jium \Vh.ll w~ts goc'tl ~n:JI c \lent H.: 'ug.gc,ldl

101 c•rtlumry utuJ c."\' cn uhm' WICI l tght \~·'"nut \lliWhll• fn1 X -ra~-. t•n otccount ul thc1r \)Hlr1 w:s' ~ length Btl1 mtrrnnl \I rut lttrt• oj ,.,.., '"'"' ,, ~llt/onn '-"fli'''t•ml\· ,,•finc:~J

mc•t/mm for X-rd\'$, \'Hilc' orJtnt~l' .\·rd,. lrcH \HII t /dl,f:tll.f bNWc."Cil Jfr11 rm whift• 1/tt' m•rrJ:~ dl\lmu·r ht'l\t'f:UI ulmtt\ m II w/uJ H ht>IU't'Cif f(} ami to·d nn. Sou f'I':''Mnl '-'"'' m 1 tl\ u , lnH.'I\ f'OCI.t•d thrn ,J;,neusimml xrmmg. u-hrrr tllimLdumft•t ulr.\ will m 1 tl\ ''fWf/"' ·'fJtlt't'--' wul mlf•,mtmtit· m wwn,nltttulm dutanr.• wt/1 uct U\ tipt•n 1111,. ;n llll'l't•-Jimt'IUWttal spatt<. £xpcnm~nts camcd ll\lt un this idc.u by Luut"" himself and t-'lhcr'. wen: ~ro\\ uccJ f(} ,\ umJ

" 'ith c~mttrkuh l t .:::uccc:s'. These were ruiJnwcd b) ollh.~r ri.!,C'.tfdt which proved that X-myscould bccO"cctivclyn:OC'-'tOO. rcFrnct~u. Jilfructcd. poluri-.cd ru1d S<:Oit<""'· S-t1111c:ofthcst.! phcnomennn cun becxplniru.'-t1 by thcclu,~tct~llhcol"' o f wave natun.! of X·r.t)'~ but ~omt:- can he c>.plaincd b) the qu;mtum nntur(' uf X·nl)'

2.2

Production of X-Rays

X-r~ys

are produced wh.!n ru ..t moving clccmm:- o;trilc u t..trgcl m:u~ri~1 l (If high

Lil&.;llh't'l'llll! / 1}1\ \IC\

.!..!..J

..th.llllll' \\ l!tght li,._e Lun~!>lcn t..-.·rllm "~lcuum~ ·1he b.t .. tt. n!4Utrcmcm' h•r X~ru),

puwhh.'llmt :u·e (I) a ..our'-'c nf clt'l'trons. (2) t..'ffc-.·th~ tnl'~ll' fN UL'l'.,..lt.•r:atlng th\."

nlnlcriub l)f ht!'!h .th~mi~: wl!ight. rlll·n.· a1c c.IIIIL'rcnt l) P"-'' uJ tkviccs for the prodUl:uon uf X·ray ... n.tntcl} (I) ~a' lUht:, t~l Cu·nhLigc 1uhc. (3) bt'.UUrun Thc'c :m: ba!-cd un the dlff~tl'UI lmr'CHloml '':'J.!C' tlt.J')<fiL'4,:twu uf h:::ChoiliUC in lhl· prnJultion Hf X·r:.t)' Ht..•tl! w~ ,uscus., lhc ('lu)lid~t.: luhc in th.:lllil

clcctl't'H h LlnJ

1.3

t."{l J.

hll'!;!~t

~uill•blt

Modern Cuulidgc Tuhe

I ht.• l1h~k1u l'Hlnflh'll"l,tl

hulh

(.'pt~ ld ~t> lulw I h t.: :!. 11 dii!M!!IICt..l h\ { "''hd}!.: 1~ "IJt.•h tl"cd l llr .tnd ll'll!dll.'.tiiHII I~''.clo.. h COO:!ol'oh ol .1 htt:hly C\ oiCII.lh:d haaJ gJa,,

ulllldlllln£

Jnti~.uhodc u1 •nllllc Flccllttn' un: p1udurccJ llmg"-11!11 lilumentary C.UhotJc /• whidl 1... hCUil"tl IU

.1 c.uht!tk and

thC1"11111liU\:011l) frl•111

o.1

ci1hc1 hy ., ... wr.sgt.• h:tth:ry ur h} u lnw \Ultag._. A.C. ,·urr~lll lm111 2.1 ~- llu:.sc ch:('lr()no, ut.: hk:u.\ttltlu Ih.: t.u ~.:t 1 \\ 1th lht.• la~lp or ol lllll)·~t.k llUJll C.)limJrical 'hit..""ld S \\hh.:h "llfrliUitJ, f kept >~I n ntr:!!·""c flt.llcnll,llto th1.· lll.uncnt 'lbc ckdrHn;o. •• n: :1-.=\-dcrnh:t.l tu \~1) h•t.!h m~.:;mi.Jt:, \:"~ lh'

;-.t~p-Jm\ n tr~msforntt:-r T .. f Rg.

'P(.'ctllUpm IU'·i- ol \chk.:tt~ ol h_gho Oy a 0 .\ pHh'Uii.l1 diffcn:ncc 11,1 ;1h11ttt ~0 I<> J(~l h vI ,1pplic..l i>ciWCCII I nno.l<( Al. hl~h IH. JlOI<IHI,II h ••Nniii<J frmtl II 'h'fl lip tmn .. fOIIIlCI ( I WhO~C Output i"' Cun\'t'lh'-d iulu rlm•l"t t.:urn:nt h~· lull \\ol\t'lt.'CIIficr Jnd U '\UIInbfl." filh.:r. The IUr~t.:l / 1..'111'11'1!- til ol..:t)(1J1CI hJud, ill

·••<I

'\lud1

.~ph.'\: . I..'

nu,

uf tunplen lll mPiybdenum

fltlrd Tht• f't't1111r.:m..·nh nf .mode

.ih'

llt~ h ~

.tlomic ''..:i~ht

to tcLhu.:-e h::trd X·r1-1y ..

mdtct.l tlw: lc) the ht•mh;tJ Jm~.<nt 1:1,1 tUtn'in~ c:kdnJih which cause Jl•t oJ hcut lli.,:h th-.:rm.tl t:t11lJUi.'ti,·H)-to c~ :J.WJ~ tht.: ~.;t:rh.'t.t.tcc.J h~:••t llil!h mching

ptmH-M1 1huL ill~ nm

11f

I h, ..u .:d l '' Jll•il ..~ .11 .1n .tn~ll! --t ).. to the- cl~diHfl' '' ··~till B\'lll" ., "' ,.,,, 1.! '•I hl':tt, t'('I'P'l'' hdp~ ((\ con\iucl h~a1 et ltctcn11v It, the 1!\h~t u:1l \'Hnhn;:

~o.·on,hh:hll

luh 01 'A.th:t ""doling !to~'h:m. \Jnd~1 th\! homh;,rdnu-nt ol llh· 1•• 1~d h~ .,,, m.ln\ clcclrttn". tm"~>..t Jncl.th willmciL 1l1,1t b wh)• mc1.1l' ill..(' lllll)!,ICn pl.!&lluum .tnd

'•

d=b

f.tt'~'llhC'r

Tub..: ~

ftite. 2.1

Cvppo.•t••\o.J

Coolida;:e tubt• for produttion uf X·ru)

u~cd 11." target nuucnal. wh1ch hav.: h&~th-mclltng p<lint~ high •UorniL:_ \\CI!;hl \\'hen (rL~I 010\'lllg ~Jc.x·lronl\ lnlm t:rilhodc

molybdenum. ctl.!. n.rc ,uld :tl\n hll\'C

.m: "m.Jden1)' ~tuppcc.l b~ the tun~'tcn tn~ct .!lituutcd mthcir potth. they c'pc:rie.ncc ·' (',lll\itler.,t'llc ncgativt :•ctdt~r.-tton, Such Ltuh.· ... 1y dc~dcr.-tcd charl!e .. r:'ldiatc cncl'};~' m th4.•1l1ml olt!lct.:trom~):!ncuc puhe' which ~·onsltUlC" X-rnyo.. Ht.'rc. one th•ns 'houiU be rem~mbcr\!d thr11 only li '-maJIJl>l.:rccntu~c uf the: ciCt;lflln Cncq;y 111 the target j, COD"\ ent-..1 inlo X-ruy,, \Vhile Ihe rc:~t '' di,~ip;ltcd u' h.;ul. Due: to thi' heal tnt=- rhc 111r~cl ,., he:th:d 11p (n nrdc1 ht ... 1\\' the 1.1r~t'l 11 •~ nnhl.mll~ ~,·nul~d

h>· cnhling. ~trr:n!!emcnl.

Coulrol of lmensil)' nod Qunllt~ lhc IOh!O~••> of X-ray~ depend, on 1hc numhcr ol clc:dmlh 'lrilm!!' t..hc t.trgc1 ·Ill,, numbe.r 1 ~ detcnnmcd b) the tempc:r:uurc (lf tht.:' electron cnutttnp: filnmem. "'hit.:h '' it...drproponiaml tuth..: h~mcr ••·um.•nl 1-l..:ncc h)' ~.:riiiH•llhn~ th..: filmncnt curn:nt '' Hh lhc help o( the rhc:<htill R. 1hcm1innK c-nu,..,itm o.nd h~n..;c mlcn,ily ol X-ra~., l.'illl h~ Cimlrollcd The qu;~ht,)' •·I X"T•I)'\ , ... lltt:•l'tlh:d 111 teflli" ctf 1h..:n pcuc.u;Hin~; pm..,cr whic-h i~ <.lcpcndcm no th~ putcnllal tll flcrcncc hci\\'Ccn !tlamt·nt:u) c:Jlh(Xfc .md lhc anOtl~ Gre;llcr thl.' .u:.:c:lcr.aLin~ ,.,,h:t!!C. highn th~: 'iJ'"t'd of lht.' 'lnk.in~ l'lc('lll lll\ :md '-'nn"""'tlll\'llll~, lllfllt.'J"'.'IIl'II !IIIH~ X-ta>' prc'(IUI.'Cd

h ,... \!lhi00\.&1") to refer to

tu~hl)

pcnctruttng X~nJ), ct.l! .. those Jk"'liC\sinl! h1~h

lrt:'lUt'll'-) 1...... hnnl X·my' ami tu tJw\o( lc...... pcnl'lmlln,g l l c .• ul It I\\ :1" \fliJ ~-t.t)\, Uh\'ivuo,J)· ~·Pnthlllt~LI

the

rn:c.lU~IIC)')

1-JUi:llll~' t\l ~Ul'lroUIII~ f'Un\Cr nf \.•f1J)'' CUll

h) varying the poh:nlial ,hffctc0\.1.' h.:t"•l'l.'ll co•thm.lt•

J'IC

.m~l

.mndc h "Ill be noticed l r.lJH ubtwc c.\pl:ut.aiiUn th:tl 111 C'uulu.l~c X-r•tY ruhc, 11 j.., ro-.,jbll.: to nchiC\'C s~p{lrtltl' <,.'Untrol of the ln(\,'fhlt\' .mel C)tlllht~ oj X~r;ty~ inJc~ndcru

uf eo.ch nlht:r.

2.-t Detection of X- Ra~~ >. r.t) '..r~· ~k~~~h:d h) ~unh: nllhl.'u pmJl~o"lh~ pl.th.'\, f hl production uf

nuornl!COI..'t.' 111

g.a'c" JnJ hJJ pcnclmlion lhrnug.h

2.5

Origin of

.ud, ..., ~ .I J udhHtldlplhlhi~I.JJiiH"' .:.:llaio \Uh .. Lant..:. (d ffllll"•ll1011 l-"~i

1n111tcr

X-Ray~

X ray' arc produced '"hen tugh speed elt!t:tron-. .stnkt' <o;omc m~1tcn:tl obJeCt ol h1gh aauuuc nmnber II'' fOund lhut ncarl~ 'J'J s•., ul the ~nct}!Y ll' the ~lcc 1 wo-.

goes

11110

lhe he~ling or lhe lurgel mnlerial. 11111) a lei' number or lnsl movmg

clt·C1mn:- pr«lucc. X-r;)y!) hy l.I(,JO~ thctr ~tnchc L·nctgy 10 the follow•ntt cwo woys: 2-5.1 Line Spectrum or Churaclcri.slic Spt·ct rum Some nf du: high \'eluc:ity ekctron' "IHI!i! pcn..:tr-:.uin$ Ihe uuerinr ~•f the atom<.; of thl: target material, lnoct mH the tighlly buund \! l ectron~ m lhc innrnllQ\1 ~o:hcll Hike K. L-shcll ctc.t of the atnm~. NO\\ the \;n~anciC'- w.:rc.atcd mt1y be filled up h)' the ch:C-tn•D' rrun'IIH.t;.hcr ~ hell, i.e. lughc1 l.;\'t;l elcccnmjunip lh 1111 up the r-ruah:d VO"L'llncic... Due to th i~ clcem-mil' lrnn"tl1lnD." thl! en c.~)' diffcrt:.ncc j'( nu.Jiutcd in the (onn o( x. ray ur very STnliJJ hut c.Jcftnitc W'd\IC f<::nglh'J (uncJ high frequency). Thc"C w:tv~ h:ngth' cun,litutc the line "IX:tlrum. which depcmh on

22li Engmrrnng Plty:crt .t the t.lt£CI s,._ lbCSC line .;,pcctf.l ;uc aho ..incc thGy arc cnmtng ''' J pnr1 1cui.Jr hilt: \)f the JUmp.s wkc.., phl\:c Irom' ah:JKC dl"clmn h"' "till~ k\ d whit:h ott~: 11fll UH1Ctll10''" I hen thal ekclronk tralt,lll\ltl produce, le'!o cncr~etil· ' i!i>ibJl' !i>pel'tr.t. F1gurc: ::!.2f'*•"'hu"' til.; ('il:~C \\ht:.n the h1gh ' docJty incident ckctmn lnoc~' oltL: t:kl'lrClll rnuu K \hdl. A':>. shnwn I ll Fig. 2.2(h) ;mJ ld tin.;; v;u.·anc~ inK 'hell i' mh..J U~l b~ nc.::uh~ l.':kt:HPI1 in thl" L-...hell r>unn(! IIW· jump .m x .r.. ~ r.rdtlllum '' rmllli.~tl wht''e lr~qucnq ' ' pnen hy the

('haraCit'thfiC a) lftt• rUdkrla( Of

~o:alkd ( lmntlft•nt/1( \fh.Yirt1. N<.m 1h.: 'Jlt.::CirOI, hcm:c 1h~ n:ull( \Vhl!n

.,n·

_v:, = 1t:,

~1.1 = ''''

.------.

•

-~-·>'( \

••

f~ ( • }}]' '

, '!

e.,.._ ._! • • •

.·----.

• •••

!.II

F.=·r-

-"~' f--

-- ~.-------,~.-.~-

" Slu ~ I P

\1 , ,

"..:"'-r-!-f--"L'T"

:'UIIIkli•V ' - -- ' - - ' - - ' - L - - - - - - - - --

~. '"

I< I

FiJ,t. l.l ( )ri~in u r c:hu r:u,-lt•ristk SI)4."Cirom Ku. Kp etc. due to elt"CI I'I'In jump rrnm hi~ h c r l<"\ ~l

whch: 1·. , '' lhc t:nct~) u~quued lu •..:move :)ll dt:clrou In''" 1!11; K·..,hdl ;tnd 1·.1 that rcquin:d tor L-:oohcll Since llus energy difiCrcncc ~~ comparuta,·dy YCr) larl!4.!· tht: X·ray .. ~.:nu111:.J h11Y( ,.C.:rJ Jorge .:nc.:rgy contcn1 and hen...:.: arc highl> penc~mung . nu, X-n1y r;~~,h:1t i nn corresponds tO K(, lin..: uf K.. ~nc' (f. h~•wcvcr. tlu; ''"cuney 111 K-sh<ll ts lilled up by an ~lemon from M->hcll. lh< X-my' emmcd W()uld he Slill mor.:. energ~tic :wd '\\'t'lulcJ Cfm~c<.tucntl)' fH)I)......:'~ ...1111 highe-r fn:c1ucncy bccausl".

1.:;

f X·l'fl\'

l ..o u\ p._11\

•c.:~ fM:l...,.

'" K·

,.r.sY

227

12 2)

b more 1h;u1 ..11~ 1 ::. I £11 f:1 I:: /if1 ThL' r.u.li.uhm \\ ith l'rcquen(y /~ t:mrc\J)Unch 1:.1' line 1ll "--~cnc .. l h~ ... :t:! rh) am.J rcn. 11te!-e K1,. K11 line~ Ml' lhe mu ..l nll~ns~ llnf'- in lhc X r:•y" "J1C<.'tnnn Sunil;lrl)'. when lhl' IIICI\icn1 clt.'CIHIII ~.:arne... s.omt:whnl lt'\~cr .tmuunl nf tnerg.~. lh,..n 11 unuwe\ the elecLrnn fmm L-\hdlouu.J "'m...cqucnllrtlll'HI~m l mm mh~r uuh~t urbit \tt)' M. N will prtxhn;c X-m~' ,,( fn:qucn..:) lmvcr lh.u1thJt Hf K--.crk'\. 111r~ trJn~i1ion' gi'l' ri\C.IO 1hc I .·,t:ric.\ 1\l

ol X-r.ly ... ~Jlt!Urum_ L.r-1-p 1.1 1hg .... ~ :!ih), trU.

Spccn.al iuu:.., nl M M'''~' .JP..' t.HIC:Q~)'·Ic\'cl d1.1~ram

'Ftg.

~.:!cl.

fUndu~o:cd til 1t ,jmibr W.t) ot~ ... hm\n 111 th~.· Sn the t'llm'(Wlt•ristit'i (.)/ r/r,· fmc l/H'<'/1;1 m

4lrruu,·urixm· 'P''t"lra W'('

l. It h::s~ dbcr~te 'iP\'CIFI.il lin\!, ol K-~erk~s. L--sl'rie.". etc. Thr t'lfl"'l:\' tftfft•n•nn• V~ 1- f.'A £, ur ..lf.-z =£A-£,, tltc.t/u• dmtml~lltlic· ufllu·J'tlllitu/nr 'IUilnial IUt'd UJ t1 Wf8t'l hr tht• X·l"(l,\ rubt•, '' hidJ Wt respml'>tblt·Jor thr {t·~qlit'llt.'"\ o{ K,., , A:.tt liuc. Sn tlrr$1' };,,. ~1',.,-,, of X m\'\' ur. t'lllh·d t Jtmm tr·1 i.\l;t• ·'l"'t/flt_ 1·11c,;c lrcqucnc1es will be dit lt.!l\.' ltl lor d11fcr.:m element . .t X-r.ty 'pcL't111 of difft.!rt'nt l'knwnh 31\: rounJ $imilur to c:J.ch oth~.·• All un.: h:n 10~ K. L.M 'c:nc" hut it w:L~ nolu.:cd by Mu~lcy thut thcfn·quurn('.t uj lmu fm t"\.'tn .lr-IU'-' Jmm t!J(# dt·m~fll oj l11glr(•r a/omit- mtmhn n ,s;:r~mer thtm thm pn•dm·nl h\· mr drmt'"' o/lown trunnh· nmnhe'l ~

II ~

round 1ht! rc-htLUin\tUp hci\\CCO [ri.!'<.JUCOC) nnd atomu: lllllllbcr a~

,7~1:-/J)

,, •"

wht:rc: i!i the uwmic

num~r

.tnt! h

th~ nud~:ar

scrccnmg con\ttml

2.5.2 l'onUnuuu.-. ~Ju.•ctnml 11u: cominuou' ~JlC\.trurn &'> cnultt:\1. "hen .1 h~ow Ju.,t mrwin~ c.~lcc-trun' JlCU~Lr.m: t.kcp into Ihe iniCI IHI l 1f th~ _.tlmn .tnJ ,uffcr tcpcatcd h)~\C: .. of e:ncrg> Juc tu 1hc divcnaon of thetr 1uth l rum nngtnal fMth. in lhc allrnctive Coulomb forcr.- fH~hl Of OUCit.:l U( l:trtWt 111lll11\ 11w, pmCl!\\ Ol luMng l'H~t~)' h) I:Jdialiun I~ c.· .tiled Brt•uuMmhllmx j hntk[ng-ur \hl\\ mg-dl')\\ n rm.hnhnn). 1111~ cnl!rg} upp~.u~ _.., J contillUliU> X fU)'.\ 'Jn:.trum The t.:t'Jillinuuu~ distribution ~h0\\'.!1 thai all \aluc' of energy IO.!o-..'ri:C~ are probabh:. whu:h lOO.!!Li1ut~ Lhe t·nmimwus spe<'srwn

Jf lh~ Striking ci.:<:IIOn h.L' i•' vd<lCiLy redu.;<>d from v "' r( (Fig. 2.31 1hcn 11, loss of encr~y b c ~ uu:- ~ me/!). Th1s must be equul to energy t•f 1ht· '\-ru) photon~ cnuucd • c "1'\o -~11c·II '"'~ t -I m <v-• u~->;; It{ m 13,....ttlvcl)' vc 2 '·n··e :1r~ \\ighTiu: high.:~t frequenl'y ol the ~mitted X-rays corre~ponds to th1s Cll$C, \\hen the I~enc .... u. h')"'C..'-cL) c:ctron •1s cunlple1dy smpped. a.c: .• uo :;; f) then 11 tho ){-r~ I .,h< · - mv:= hf, =l"ir/J., l".·c·=[J.J 12.3) cn\ly {'OSSCSS ~ .

ln.l\

•n

Whc:n un electron b accelerated by o. pott:ntinJ V. lbcn kiuclic cuert;_y J:;.

1I ,,, >-

i h)

l'liU•lliO!=

ll.J) :tml 12.4t

=r \

\\ C j;l.'l l ~"•nuu

=- ,. -\

12.51

Nuv. ,. ~ I flfl2 x Io u ('. ,. - ' ~ 1011 rnl~l'C ' ..·)(~-~~~ nr lighls ami '' -= 0.6:! >< 10 " toull!:-.:c. ~uh .. lltutwg lhc \'<JIUl: uf ,., It :wd t. A,,,, 11 b..:.:omc .. 11

1 ''

I~ •.JIMI I

I ~ljlioltlillr .2.(ll ~hoY. .. lhat l-,1ul'l h11 \.\Uihunulh '~'""' 11,, d•lC' nul d..:J)I.;nd upnu Ihe t.lr!'-l'l nmlcnuJ hu111 I\ ill\l'f'ICh prnpor1inn.tl "' thl· ..tppti..:d \Oha~'-· \ hct\\~o:L·n ....,tli,"lc mu.l unOOc 'fhu~ Ll11.' lhm·o,·lt'f'IW• "} ,·mumuom X·rtl) ,,,,,,.,,.,mr dtr' ' It <.:nn"'"'" ol conununus range ol frcqucm:n:s upto ma:<1mum trcquency /lffli, wfuch COIT~j)l)l)c(~ IV ..t..u.. thg 2.-lhl 1 h 1\ ohscrvcd from the Cllf\(:'\ (F•!! 2 ..J!-1) I hal there .~ i.l ,Juh or lhL' m:r\lmum inh·n~ily JXlMiion townrd' 1l1c 'hnncr \\ iiVl' 1c-ng1J1 s•dc a.s \11•h:1gc V incre::t...e~. ll1e hllell.~it~ pf conttnUl'U"' l'J>CCtnlm 1.. J ln:t.:ll) l'n 'P'tnwnal to thL· nto mu: muuhcr u l Ft)!.ur~

1 h~

m:•tcl'ial nt :1

~'()lli•I!Jn t .tpp h~d \O I I~l_g:c.

d•slnbullon (\1 X·tu)'·"' trom 3U l. V X r~'Y tube t..:Une lor UIO~\ICO CY,') 'hnw' th< ~:orltmuou' spcl.'tr·um ~~r X-ra}. " lwr~·~,, '"·un l"!'o for rno1} bdcnurn (Mo) L:lr£1.!l ' hm' l\\ o sharp l1ncs Au unO K11 at ;;pc.~cl fie \\ .t\' C kngtho;, !>UJlcnrnJ)n:,.cl.l url I he CUJ IIIIIUOUS l!.pCCtr\1111 Au. Kp line!'~ for tung:,tcn urc obtained ut 75 kV ,)pcr.uing \'O II il~\! . Thu!\ the "2AHU !'hows the

intcn sit~

\\ tlh mOI)htJCOnn (Mll) ,mJ tung::.tcn ( \ \ 'J t ~tr~l't. llt.:

"'1-

" --

€' ,.

( '-

•••

- 1-

I--

\(!!

I A..

·-

f- ..

·r-._ '

['\..

........

-- -

'--

-" Ill

"' l

~~-

" •

·- f 1-

f- ~

\Ok~ I

A..

'\L\

H i.\

II•-

" ~~ "'-- t-- 1--.... R ~

-·lh!

fi~.

2.4

:·!~"

•h

-o::

Ill

tut Cb:tr::H'h•rl,tit• SJH't'trurn: i b ) t"u n litiU OlL~ .Sf,t't'lrum " llh dlfft:rt•ul t-\('ilulion \Oitugt'

number t)l dmnu.:t-.:n"'t'' l1nc-. pn: ..cnt m lh ~ \ t .i) .. pcctlllm d~.!p.:ltd'- hulh un 1th.' ur th~ l.3 1 li.~l IUJlt.:rial :.100 I he !:.'\:CUOUI•Hl \,)huge . Figun: (2 4b I ..hU\\ ... thnl fur din'a crn :let'clcr:IIIOil \Uh.agc polcnllul X·r.l)''- produl:cd Ml! HI l;."ttnlmuuu' W;t\1.' ltngd1' .nul lh' )-,11111 j;, in,cr,t•ly ph1punlun.,Jw ·'I"Jllicd vnh.tl!l: h h;t-. J '~lluc I :!-UlU/V

U.illUh!

2.6 Moseley's Law In l l) l .~ I J Mo'Cit:) toumt m u rh111rhe chnr.tch:nMic X · ray !\J>C<.:t rum o f dirrcrt' lll an: rt:m:trkabl)" ~ unil.u to cuch other. a11 urc ha\'10~ K~. L·. ftl.. .,-,:1 1 1.!~ But then.• i s :t dlffl·r...·m·t' in lrt:qurm·y for c:tch ~~ric:-. . 11\..:!: fre<1uen~y o l hue ~ 111

dement~

\!Very scrh.::i produ~cd from 'an clcmcm ol fu~hcr :nom1c number. r!i. l):re~ncr lh:m th:a1 produced b) an c cm~nt uf luwcr uwnnc number. 11 1S due 10 lhe fnct th:n bind in~ energy of c i C"ctron~ ttocs on inc rc;t~tn)! as w~ irn:rc..~c the monm.: numh..:r,

'iO hll")!\.'r ;UUtHIIII nl f'llCI);) i!\ n·qUlrcd ht hherak !UI dct:IIUII rwm lht: /\,I nr M ,ht:JI u l lh.tl dcrn..:n' whose atotntl· numhcr i~ lar~ct Frc'-tucnq fur K Hue few ~:up(X't 1: = 29> 1:-. t'~ x 1 0'~ 111. wht!rt:;" th;u lur nmlyhdl.'mtm (• = -l:!) ~~ -l It• ~ HI'" li1 ·nlc tcl:ulnn'h't" hl't\H'~o.'n th1.· lh!(JUl'nc~ un\l :thutllt: mnntl<r h }!a\·~n ,.., ~h,,clc~ u~o

f•( l

hl- u1 ,/=of/

/Ji

whl·r..:/ '' 1hl" atnmu: numhcr anJ a""'' h ~trc ctm,t.tfll'i lnr ;tp.Ul acular '<'rie' hut ''II~ lrnm ont' M'n~"' In .molhcr. The ..:till\tam h " t'..!lh·d nudc·m q·n·t•nm,c: Jm·rm· f:m K. 'l'fiC:o. h =I and tt '' IM' tn}:! ln_flu:r \,lim:' h11 I \I wnl!"· :,o tJw ~ l c,wll·~

·. l.tw ''lllc.. thatlreqth..'Oc~ 11t •• 'J"k:d tal hoc- 111 the

duu"'"'co,ll ~:

'pc1.·trum '~'"c' chrc.;tly ""the squar~ ot lh~ :\hiOliC" numN!r (II the U.\IJ\.!l clcm~nt tFig . .25t.

/ f-i~.

! ..5

\"~1rJ-adun o( ~CJUllrt' I"UUI uf frt"<I Ut:'UCit'~ t ''IU~ll~ I"I~H

t,r/J

" 'ilh tJinmic numhn ti').

l'\d\.1

funn o l ~tn~lcy·, Lm '' ('

J= - = R, 17.

h)"'

[-:;-' I' tJJ IL

(1.M)

\\"here I< 1!\ 11u.: kydbcrg'~ COil:\ltJi\1 11 1, 111 :Ul.. lhc C fu·r~) l. . ,.ct, 1"'1\:.IY.ecfl whu::l1the tron.:.ilmn n ... ..:un.. and c lhc vdcx:Jl) 11t hght The ... hul'h!'l Wii\C kngth •md h•ghc ....l .:ncr,;y a:),t"IC~>Ill! \\ Hh ..t ~hell ~~ ca lled the ub,twplum etlgl' h 'm 't' lrng11l "ftluu ,\lu•Jl Th..: c.:Hrr~'pimdiu~ ~lh:..rgy will be ltbcr..tiCt.l wht:n out l'lt:clr(ln JUmp!- !'rom tnfinHtt (n = ....,) hllhal pan1cular \ helL S(1 lrt\IUCO~)

of •vah~crplion edge "

X-mrs

2-7

23 1

Compa rison Betwe<'n Bohr's Theory of Atomic Spectnt and ~loseley's La w

11 cnn he ..hm\'0 thul Mo~.,;lt.:y·~ l;t\v 1:-. ul J;Oud ;tga:Cnltllt wtdl I:Suhf'h llh;ory tur bvdrogcn nH,nt Mw•dt:)' generalised Bohr"s 1hcol) lnr :.til clcmcnh. One c:tn t:~mp;;rc lht" work or Bou .md Moseley in a quantit~Lh C' Wa). '4 ' IJl~ll it .. l~llt!lhen!\

tl<,tll thl!tr vt-:,,·~ ,.\<.:'-=Ntitllf' tv Bohr':.th~ory lh¢

lrequ~nc:y

f= II11Z'

ufthe ... ~.:tr.•l

l-+

[J.-

II J

f= /lc·{Z-1>) 2

rrJ

II j

lm..:~ ol

hydi'O!!en 1:-.

1 .]

\\hen: R) 'lht'l{' cc'lhL.. nl R11 :::. Nr and% in Bohr''>lhcory L.. rt.'J1ItiL'Cd h~ (/ h• iu Mo ..ell!~ ·.. law. Ntn\ 11 \'-t.' 11.'move tlflc nf the two K·!'.h!!llt.·lct:lrnll"t1f ;m clement 111 mtln11v. lhl' r~m:umn,g ''Iller clc..:1ron .. will be :mn•clcd ru I h..: rn.u:h:u' nc.H hy I he nuch.::n dtarg\! ll.t • ..t.\ lltthr J.<t~t.un"·d bul by :1 chnrg~ (~ - c ). On!.! tnJS lhmh. "ll r.:m.unmg K·ch.:-.:trnn ;l\ •...crcemrg Ihe: mater \::ICClfl)ll/'1 fwm th~ rull nudc~lf :aua·.u:lunl I hus '/I' J(.'.lnl lo. Mn!.dcy\ law l.'omcs out lObe I lor K ·..,1.:rh:~ wh11.:h j.., l"nllcd Ifill (.:ar lln'l'nwg j'arll.r. Su Mo~cl cy't. L aw i~ 111 ~uuc.l :tgi\.'Cm~ n l "''ilh Ot'lhr'~ tht::OI) t)( h"'drogen tUt'llll. From thl~ law Moseley fl rq pnwed thut it'' thl! ttl01111L numlx•r nnd not the atornic wciglll or an clcntc nl "hich «.lctt·nHtiiC'> ils ch:tmclt'listit'" ami p<hit1on 11\ the pcri<.>dic t:lble. l'r(lp~rties

2.!! II) I

of X-Rays

X·I·'Y" .u,• l'lcctronugcncric w .tVt"\

of very \lllBIJ y, ot\.'C length t•l the tH'dcr ttl

A. ~I

I _·\ Tht·y lr.t\'rl wuh vclocily Hf light .mJ an: mvi-.Jhlc ILt 1.:)1:'> I~) rhl') .m: \'t'r)' ~ncr~CtiC .md hig.hl) JJCill:lriltlll~, due tu \\hu:IJ thC:) Ci-IU J '·'" thrHugh 1.\'~llltl, f1ec:h. etr. 1.1•. hich nre opatlUl! to ordinury li!!hl I;;) l lndcr ' llll:lblc (.'Ondllion X-rny:. (.':m rcnccl , rcfm<.·c. irUl'rr~·rc. d iffrm.:t and !!Ct pc>lnri>~d

hkc tlrdinory ll~hl.

H) X·ra)'' nm umi'c thG

tS) 1'hq

~n\

thn:mgh which it p:,,;;:,.c-,

Ci.lll~t· fluon~~ccncc: in m:uty 'ubstancc.s.

(6) X·r.t;'- ha\'C tlc:>~LfU(Ihc dfcct o n living ti~~uc (7) Photo e l c~tric r:1Te<.:t b .lbO observed \Vit.h X-r.ty\ (X)

2.9

X-ray~

:arc not dc0t'CIC'd hy clcctnc or magnetic tieltls.

X-Ra) Diffraction and Bragg's Law

Th~ cry~t:Jl .\Lru"'tu~

can he studted by X· rny dtffrJC11ul\ nh:tlhl\.1. Di1Tra~1lon would depend upon lhc cry"it;ll t-lnu.:lurc ami un the wave length nf ltght. An

OJnical WilVe lc.ngllt ,;;uch as 5000 A. when supcrirnpo~c-d on'' cry~taL will !'.Caller ci:L\Iic;tlly by th~ individual J.lloms of the crystal. r~ult ordinnl)' optkitln.:Occtit)JL

IJut , .. hen X-ray r.u_lmllon PJ \~.<ave lcnlJ:lh IU' 11• ltr' em I!\ ua-Jdcm on IJiL' cry,t:JI "hn~e I;H I I~·..: .. ttn~tant r1.c .• the tJi,t:ult he tween t w<l moms 1'' fif tJh~ tlrdt<1 ol 10 to 10 " c •n. thrn '';..'~ length ..1f :\.4 ru~ ;md l;,mr~ consHmt hl:t:omc t.·•nnp.mahlc w c.·m.:h uthcr. '' ludl g•vc.., rl't' ht X -tll\' tlifjmrtltm X .. r,ay tli ffr.u,"1iC'llll" 'i~unl!' :" ordinar) diffrai.·uon which me:m .. - tftht· ob\lttf'/t• jf:'«! '·' t'otttf't.JtrtMt l f ttll tht• IHll'tl lt•m.:tlt r') r<u/ioumr, llu~,, tlrt\' cliwrt jtnm 111,on.xurt~l path ami tlt}jmt'lttm to~l'-' plm. t .\mn· the \WI\'(' /,•,.t.:tlr of X ra\' n 1 mnpurflhh: wuh thr lrrtrtlll, mw (/"umn ,,,. lntt'rpltmm·r tii\Wm' r• of the• ··n•,tu/. "' ultc n \' rtl\ ,\ " ' ' uu ,,/,-m onlla· ' ' \ \lu/ ,,m/tU , , thr-n the•.W.\'It'llltlllf llnmtg,•mt•m oj tht• 11WnH m t/11· t n .u allm•• ,·,/ui m rlur•t• dmwtHiom ad/1 m·s II\ 11 rlrr('f 4

tbm.-tl\'lfJIIfll l:TUWI.\,'.

wJr• .,, •HI'm'·

IIIII 1p/mmt' l dultNt c- at'l

+L\

Of'l

n' om o/J.\((tC'k mul

rm fiJit' tl ,JII, J ll.\'1 ltkt•

ortlumry

llll('flt ltWIIC: ' "

~I'IJIIIIX· /Jtu· In

11'/urll flt{Jmnum am m"-(' f'/(ll"t

W.L Ur::tgg prc,cnh.'tl :t 'nnph: cxplan!llum uj the X-ray \hUral'tu•n Irum

Lei

'"'l)')l.la1

\h "UJIIM.I!'o\:

X •••Y w;&H."

~uc

mcldc..·m 110 1hc l' fY"Utl u1

;ulglt• lJ.

where U 1s m\!a..,urcd fmm Cht" ay,lul plane and known U-'" '(jJanctnf nn~·l.: ' Cf l!! :!: 0). ln..:Jdcnl "- ~ ruy~ ~m_. .,pc:culurly rd kctcd (l.t.: • angh.: ul wcn.knl =omglc ~~~ ~e:fh.:-.:110111111 '(>111.._'11.-!d Ill afl \IIICCIIOII-.. ltumlht: par-allel l'hlllt:~ ul Olllllll'\ m 1hc CQ,loll \VhiLh ".u•.:luall) lfc:.ttc.J .L, X -1;1) diffrac1ion 1'/w mo;m J /jjt•tr•nn• hf'l'• t'''" n~Jit·cnm1 "' on/WtlA \ f·aurrm.f! il'Hir fltf(rucrum '' thm m ,/tJim('lum, mtcrp/onnrr tlt.'illln, ·;• , , . n r;,•ullamu dHituu r '' 1,•.v um.u blt• llltJmh, ,;r,·onhtJK trJ tltc. c.•tJn. (1. /UI. '"hh.:h,.. n\-u Lhl! ..::h< l<~r Ohhn:tr) r..:II~\:IU•n or '-,:;lth.:nn~. Suh.:C the fcfl'aCII\; u\dt.'\ 1tl lh~ \'1)'\l;tl l~ \cry n~·.uly CtJUotllu Ulltl)'. ''~ 'hc1r.- ,.., practu.::tll) nn hcnthnr dm· 1o r<fr;u,:uon , .. h~,·n X-r.ty-. arc cntc.ring nr lt:a\'111!_! llu.· cry ...wJ

•

...

(:)

\•J

~(~)~

-r~) /

--~ (:) " '

Fig. 2.1-.

- 8 - - 8f--8 X·m) dlll'r.u.·llctn \\hk h ohf:)

Brn~ 's

lnw

•

233

\ rm·.,

In (f)~'·'" then.: olu.' H'fl,un ri.IU~!\ \\h~t..:h Jr..~ f):HIILUI.nh 11\:h m dtlllll\'" tinct: (.hlllt.:II~Htn.tl 'P·h.:c .Uid lht' utmhuu..•d t.hlfl.h. IJorll,~.:.llll:nnr ,,j \: 1.1) .. fnnn the,..· p1 ..nc' l.tn I"· lr(".UCll ,1\ Jctlc-.uun tn:nu lh-.-M" pl.mc' l..Jt.:h ,u ... h pl.1.ttt; tdli:..:l' unh ..1 \~.'f) ,m ..tlllr.td l•n tH ahc tnlH.kru t.nti.uum .sud unl\ \\hen llle' rt.!O~~o.~cJ

X t.a~' J1\•rn f).n.alh:lp .m'"·' ltl .ahml' mh.•t rt-r~ uuhiUi~oll\ ""'· lh\.'.lll'l11} htUI1ll oat .m .Jn)!lc 0 lhJ! :! itJ llt.•Jt· v.c tr'"·ac ctJ,1K -.-.:.:aucnnr tn ¥.ht.,:h chc cllCII!' ul '< ra) '' 001 dt.tn~.:J. ''" rdln.uun dlr~o.ll\t· lhltr.n.tnl ""-'·"''' .th'

1 hu .. , the'"~ '1;~1 hcll.a\ l'' " ' d a•r~o.-..·-(.hnu:n,mn.U rc:flcf;llOn ~r.l1in~ "n.h X·r.t} ... 1 L"'l ":J''-" l.:npth t IU Itt IU • ... mi. "htlh '' t.;tunp.•r.thlc ¥.1th IJ.1t1 .. l" .._-nru.t.ant

ciCJ

~ ht IU •

,·nu

l't•:l,ad..:r pJr.aJI.:II.tlti\."'C' rl.t~' 'r.at:cd c/ ..p.an 11·1~. ~ f\), lh~ \ ·r.a\ r..d.t.aU~•n ,, Ul\:"hknl lfllh,~ pl.mc- ,,, tfh' p.~p..·r 11h' r.llh thllcu::lh:c hlf '·"' ldkd~d lmm .ldJ.h.·...·nt l'l.m~·... , 1lrmu l1~ !tn 118 • /J\'

=Zt/ "" 0

'Ah..:re tl" th~ fl.m~.•nv •• n~k Cun,tru~:II\C mtcr1crcm:c ,,f the ro~ehJIIVO trum 'Ul' l'''l\l"" pi.ICh!'\ 1"-\.llf\ \\ ht.•n lht• p.Uh titff~u·nn.• I' ..111 Ull\.'~r-JJ 11111h1pk t1 lll ~..I''-' l"·npth). .... 1h.11 ~~

ICh

I ~ ..\ 1.'1\. lor IJr"t urJcr. 'ccnnd ''rder m.t\lm.a fh1· 1\.'lutwn , .. l.ntmn "" /ll'm:.'t,' :\lthuu1h the t~fk(llnn lwiH cJ..:h J'l.lllc ... ,,~... uJJ.f_"ut onl) fHr n'rlllin \itiUC\ ttl H thr rcnccl hlll\ h\1111 ltll paralh.-1 pl;anc .. ollll.l up '" r'"''"' hi~ i \C .~ ,,,, tnp tdh:' h:dk.liltrat:h.!d hc.un Pm Olhl'r auplc .... thL· u~nl't...IIUil lrulll Llillcrcnt pl.llh."\ oil\' Ullt til piM\C illllllhcy \\ •llnnl n.•ml"ut(\.' Ur.l)!!t'' l.tw 1' II l'Url\\'lfllt'fll'l' HI lfll' ("k'IU'cli.'at~ ulthl' l:llltt't.' rill' Ju" th•l''- IIlii tdt"t IU the Ufht0~1.'11llll1 t•l otiPIIh tilt the ' ".1'1"' tl\,\l\'IJit'll with l!'.t~h l.UUt.'\.'" ~~IIU- 1h~ ~\llllflthllnm ttlllh· ''•'"'" t.l+.'h'f llllll'' the f+.'IU11\t lllh!U\11) \111111..' \iJ.II••U~ •nd~r"

"her.: It

'I""

ul ditlh.t\.llllll l11un

onl~ "''' +.\,1\~ h.·n~th dht.mn:O tl IH 1 ~,:m

2. 10

t:n-.:n ,1.'1 ul p.arulh!l plunc'

Brd~·,

rdkd1ou '-•.m '"-'-""111

~u \q; \.olllfHll u'«.' ' ... lhlc hrht ''"l +.' tntt'q'l~mnc•

Explanat iun of X- Kuy Dirfruc tiun

Br.a~~ · .. 1.J"-. !tf,lll

u).

"'II""-' \,tluJ lollhl.! rcfte\.Unl\ nt ••.uuw ''' 1~ tn(;tth:m

X-r:t) <I rum nne ul chc '""""'<~I< ul par.lllel<l) <wl plane<" hich 311' plmcu!Jrl~ n..::h an .l1nm... '"" ..urh rl.1nt\ .• ,..,. ''""' n In f•F f 2 71 hy dr~uhl<" hn~.·... \.;n\\ lhc mtl..~rplann+.'l

cJI,I:m+.'' tfl, dllh.•fl·nt tt•1 dtftl•f«.'nl ...cl' uf

J'l~m,•

unt.!nl<"cl t!tlrereml~

0 '"the tn<ed<nC X·r•y b<•m. ~.. J ond Q (I·~ 1 11 •hwld b< mat,·hcd "tth /, 10 , •• «,~.;~In ...llhl) Hr.J)!f ·, l;t\\

'lonr~hmmtllu·

A rdu

t~/

tH.nrlott{lh ,\ $./nl.uu:

'' tlun· dnnr'/1''""•11 c 1' ''"' ell u11 cJtbllrcJ0 UIIJd~ OJ rm tdt·m fl. ~~ rl/ nut m t:,tlll'fflll~ jhll'''"' I f, tl\f\ llu· /Jwtt•·:"' hn' tTqmrt·' •m .,n lllnH mt..lt" c·uflt,·tlu w, ,,,,.,, t.-· ,, uwh I.). muJ 0 11 u m·H·. .uun m !thln·lfl cwlrrr '"'"'·,•/rn.:th ''' •tn~<lt· flu· umul ml mttlu~ttl~ for.\ r,n d•JJnu tum uu·,/ m ,-n uu/ \Init. lutt' Btt~-:.: :, .tp('t. trrmlt.'t<r tr l>clfid mi thtt rcqmremt·nt.

""h ,/

""'"'Hi "'

FJ~.

2.7

X· r.t.\ di.ffr..c-Cinn frum dJrf~·fcll1 ~l' t or h\Uict· plane:~ fla, iu$: diJJerefllllturnk cmtet'lltr.aliun

2. 11

Bragg's Spe~trometer and U ill"e rent Metbods for X-Rar Difl'raction

A >Chcmouc dHigrnm ol Umgg ':\-ray spee<rornelcr ";hown '"Fig. 2.8 ., he.\ nay!\ IJOill a ubc collnnarcd mtu :11M1mW beam h)· ~l1t S l •mpingc on tht: cr)~H'I Con 1he mm lahlc. which ~•ct-.. "'a rlm::c dimcn.sion~l diffrnction gr:utng. "fhL>

nngular po:-.ltiOnfll the cr;. ,toll ~·.m hedl.mgedhy the rnt;.,tionnrlhetum , ,,bl~ ,,huul \rCrllcal n~1:0: p:'''lll!l lhrnut!h th ~.. ..·ntn: nuc.l 11'- n.uatwn 1.'-ttn he n.::u.l fmm th'-· .:m:ulttr :.~alt. A her tlt IIt~•~,. IhH1 th' \. "'Y~ ~n tcr itn h11111:111Pn dHll11b.!r 1>. whKh ,lh\urh:-. X lol)' -.In tnt I~ 1"11~ dc\lli;IHdt'r /· n:t..\Jh.i\ lht: 11\klhll~ of IUl\1-..ollmn m lhc c hamber ut 11 C>UI he t.:.:,au.I.:J h~ a phHtOJ:!r.!phtc lilm t1

The turn t:th1c and 1he Mm •If ol the 1\lni-,uuon chamber arc '\tl linl..cd togt'thcr c. the cr~ .. tal rot.llc~ thn1ugh an an~k tJ. the .Inn R. •. ~ . f011f\~lll(111 ch:.U llh!l" mHIU.' ... lhrough 28. Su tluring the ~canning or gi.Ulcing ,tnj;h.• 8m dirlet'\!'nt value.\. hc:nut "' alwoay.. diffracu.:d llll llthc inni1.•UU1n duuobcr ltmi ...almn I'Ht_,..,e~ tho:m_gh bc.anb :u Cl!nain ... h:li'J'IIY {!..:find nng.lco; 1l·rg. 2 '->J \ 1• /1 1, C 1 rcprc~cnt fi~t rudct X-ruy ..peclnam lmc. A:!. Ill.(~ fi ,r 2nt.l nrdcr Ang.lc:-. JIUI iuhm .. itic .. r:•tio u f the-:~ line~ arc -.aml" 111 nr,t and 2nd order A' \\C HKI\.'•t""' ~he: unh.:r. lrnmt;lt) \\til decrcJ"'~- 1 ht"n' .arc \C\ er::al mctht)(l"' h1r X-r.1y th:at " hen the tum t.ahlc. i

dtrfr.1~lWn

'1udy. 11\.'rCthe smnd.ard three mcthpJ, tire di,oeuv..~·d

o, I

I 0\" ~,

" Fi~.

2.Y

~"- -~ ~.~==--.

---':-"-~-1:'-:0---:'

lil

Chau.~e

.!S

1fl

1"1

-HI

of lonl<rollon currt'nt (/J "hh ghmcin~ nn~lr 0. Ptllk.'i showt'<l lhat nre. X·r.t) diO'r.adlun b: nt•turrin;:

o nl)" fur 1mr1icuh•r ''aluo

2.11.1

l.llue Method

In l.mn: ull'thod (FiA; . ,2.1(1~ u wu:lc- 1'\Mul !\ ' ' " ' " ' ' " ' ' \ m u/•1 mil ot .\ wn fl/ nmftlfUtllt.' nan•lt:tl~tll. The Cr)'lllul 'ckll ,,nJ ahffr.t• h thC' JJ ...~rclt• \~lhn•:. 'll ). tor whu:h uucrphmncr '~~p;u,:m); cf itnd glomcant: ~mgk (J '\ill l \ty Br<t~1' ·., law 1\ ..out.:a: i'" u..e.d tJtat gi\'ct.' a hc::mt u( X~ra)' met .1 wid~: r.mga.: ol \\~1\c length,_ A ptnholc arrange!mcnl prCldurc" J "ell cl11hmatc~.l hco1111 Fl;u film rc~.:dvc~ the diffrJ-:tcJ bc Jnl~. The difri"'JoCiiOn p:mcrn (00'-IS I~ t"\1 :-.!!ric~ of spot.... That r:mcm Will 'lhtm Ihi! ..y mrnt.!lr)' Ihe ~o;r~ ..tnl. t:ry ..l.tl ht'~ htur-ra.lt.I,IXI~ uf ...)'1111JlCifY r:ualld tulhe heam,then Laue p ~ncm \\ill "'how luur..t(,)d -.ynum.'ll)' (FiJ;:. 2 JUt

.,r

Ira

·J .: :.... ..

L Fi.:. 2.10 t..:uu: mea hod ror X-rAy diffraction

2.11.2 Rululing <.:~·stal Ml'lhod In J lH.ttin~ t ry~t.ll mcthltl u dn~:h ,.1_\WWI ;_, wuun/ almulu fi tt!iltt\1\ m tl ht'um oJ IIWtttJt•lrwmttlir X-rtl\'.\, fhc \'Urmtton in ttngle Obrings t.ltlfcn:nloiWmi~ fll.mc.., intU p()'iitHin (Or n:f1C(IIUI1. The hc.IIU l!o. tl1ffmch:l.J IHUII .t ~1\~0 t'f)~tal Jllunc wht!n m th~ cour"'c ol rnU111on fJ 'atl\fics thl! Bragg_\ lu'' Diltru~o:tcJ r.:~y" are rt.·~uulec.l nu ,, phutngmplm: illm mounlcd an a cychnthu.:al hultll:r !.'tmc~mrw wath :1 ruuumg 'JliiH.IIc l'r\\l:llnwunt. Z.l l ~' Pomdcr l\lcll111d In lhl· fltm C'r method 1Fif! ~ II) the incident uunmr hr,mttlli• ltHimllon \lrtA..t•\ a /Ill• lt-pml•h·rrtl 'lwnn.,·n ur .a Jindy gr.unt..'\1 pnl~cry\l.tllmc 'Jle'-1111\."11 ~unuun~\1

ln1t 1h111 w~t llctl '' apiiLtr~ tube. f'llt•tllnri/mtion ,,f,·rnwlfm• ,nrm,wun., H'l/1 JJ,. t'tutdt•m. '·• . nt•ml\' t'OIIItmunn. Thl! powder i~ method i~"> cnn,cnat•nl prl~,,,cl} hc\.·,au'e t1 ''"~lc: uy'1'1l i' nol rcquircJ which j, diffit.:uh lu ~ct and tt IS l:(t,11)

()iflr.tltcll r.1~~ gu mil 1m111 IIHh\ 11.JtUtl cry,.t.allucs. th;ll h11ppen 1t1 he uricmcd \\ llh pl.m\''- makmg on n~o·hlt..•nt :mgk' 0 wllh Ihe bc:un "hich 'ah,fh:~ th~ lJra~g ·, Cttlt.aiHUl. ~hlft::O\'.:r cudl M.'t \\all ~W··C out not ()nly lir\1 nrdcr hut ha~hl.!r \lhlc1 !\ ;ll\o Sntn: .all nnl'nltllll'0' .Ire C(ttmiJy likd) the rcncctcd my~ \\llllnnn a \-mu· \\ hl."tt" ·"i'lilll'!>. UJ) .tlmtt: thl..' tlirl..'ctiun t1fdtc lnc-iUent bc!omt uml v. ha,...c 'Cntl\ l'rtl\.;11 an1!k j .. 20 (nr that p~.nicular '5t'l uf plane~. Tht.• COill'' imcrccpt tht: Jilm In ;t 'l'ril'' ••f lUn('l'nlrk ring' 1Fig 2.11 ). when photopr:aphk film mnunll'tl m a C\ ltnclrictil c;uJit..'nt whi~ h j.,. conct:nlric \v ith powder crybtul 'lh:"CHih..'n

X·•·•t lilm

U th~ Ctt"

dl,toinc~.·-. bct'41..'l'D ... ~ mmctncal hnc-. un the ph~HH}:!r:tph .tr..: 1 1• 1._:. 1., (f-'j!! :!.I::!J nntl dh.m~:II.!J nr l.:)'lhnJricol film l ... tlu:n

'-1 48, 90 ,TD = 36(1•· lit = TCD 1.,

Fh:. 2.12 Caku1ation or in tnptnnn"r rfi'ihtnn•ltlt frnm th._. X-ruy diO'nu.:liun phulo.J.!n tJJh ufPo\\· d~r llt\'llttKl

Ilene<

KL 1

1 -

wh<'IC /; ~ 'iU /Jr/l

"iimil.&rly, 0:.: KL!. FJ = KL.\ ere tJ\intt 1h~'c 'Jluc" of Om Rr+lt!!!'' l.m.· cqu;Uit.tn (2. 101, tntCrJllanncr 'p:t\'tng dean he l'o&IL·ul;tt.:-&.1. ,,, 111 ' ' ':· fl, t'ur t.hrtcrNII \CI '11 l.ltli.:~ plane!'! m J pJnlt.::ular t.:ryStJI.

2.12 X

li.t~

Use~

of X-Ray Diffraction Patter ns

thllmdton patterns >l.n.! w 1dcl) u-.cd fur

I In t.h.'tl.:'rnunin_l;

mclullur~)· forth~ !itudy

~ In hK'ul inA,: a .. .1

th~o.·

th~.· micm~oph: '"u~tut~

wdl

folhm·in,; pui'J,n,..:-::

tlf nt.ltl~l 1n ""lith. rnr

t.~~ample..

of mcchanlcJ1 prupcrtt~s..

a .... dCICmlllhll~ lt:hthllll\h1J1 h~ I \\Cl:n

crptotl ln111cc ' ' Inch :tre nch in

dtflcr\:1\1 r~l:lnc~

Ill

' ItO Ill'

PKOII LEM S t '.th;ul.tl~ the "mjtlk!ol gl~m.Ju,;; ·''' ·k 1-11 wtu..lt ~ 1.:up1~1 lllh "' I :ri·N \ \\fll b,:o h.' ll ~:... l~d lnuu a'~w l ha\'illp Jltlmll: ,r:t<.·.n~ 11l I!"~ t\ \\.lt..ll •~ tlw: tu~t.c'1 mdt.•t t,f reOet:lt~lh th:u can he uh,en~~J \\llh du" r;•d1.1111111 '

'2t.l ~1n IJ .;:- rt-1. <,\f1Cftll=l.~,

\\'lH•n

Ct~o.·

n iK 11 ~ !o ln:lll~~l t h.;n It =

s,, IQr hli;ht~l vrdcr

211 = 11tl. '' = 2,11,. =

! " ..1.2~'\ CiJC) ,ll~~~o~, 1

- l '...1 U

Smcc rntt•uun t\ mean msle!<~ so htg.ht:!<-1 Ul dtr ttf Bragg ' ~ rc0cc1inn

~~ li ve .

2 An X·rn)' Hlbc 11pcmlC!" <'n 60 kV pote!nu"l dtfla~m·e 111e nun unum w:we l~ngth

,._,,~;,,.,., im.:

238

PlnJ.·i o

ot lh\' ~o ulmuuu, X r.l\ •~ luund tu he 0 l9 l A. As,umm~ all the ('lcctric ..:ner8~ '' ('o n v~ned •Ill~' X·ray~. ~ukul:alc the v~lu~ ufthc Pl;md. ·, CU1hllm1. Gm:u th.n Ch;.•rJ!t" of ck~,·rron

). m1n:.

I \I

h'=' Pl\1 1 · lf• xHl 1'' Alii ~ <&f)~- 111 1•1

'X 10" :- ft ~ttX )( Ill u J.S.

111 .1 c.:r\ ''·•I "'hh ~unplc t:ubU.'·!>trucrul't" rhc laui t::~·p:uttm ~l~ r j, '\ A wllh :1 cc:n<Jrn hi-am t'l monochn:)ln;uu: X •r.ly~ 11h: glt.mciUJl :llltzles fttr lht:o ( 110} rtu.e tn hr..t t~rJ~·r Hr.1p,p'o;. rdlet.~run ,_,. t~ ~· hnll t11c w:t\C kugth (11 th< m~o.· • dem '-r.sy heatH FwJ lhi! 11Ll\IIIIUI1111Jlkr .. pu,.o;ihlc I rom lhC\L' rhmt.'

.2J ..m tJ=n).

~.11

~ ... ~ ......uH 11 ~~: Ill. A, ..t: I.~'Jt' = rJ i) tiS ,\ ~ "2 ( SmH:,/n ; ~ rl ~ \ ,· 1'+ 1'+ 0 (hi M.o\lUH.Illl \<&JIJC i.-~1

"'u

;

.2_) ,!

0 =- I. then"=- ''!Nl

' I :: ,~IIUIII..It,~~.~. ' 'd1/.= 'l' ~x.\x ,~ -= .. I : ...' ,J.., .... 1 :!l)S :X , :!

.. ,

I lwrdnr~· 'Ill L' Jt.ldlu!l I" !11C.tlllll~k •\ \41JU~JU'.,I HrllCl h11

-l

f:if-.J t!!' .. l"dh:-.:111111 I"

('IIIII

.\ \ '"' tul'l\' up!.·r~th..·l' "II •ti()O \~llts Thl! .. hnnt:-!'1.• o,t.,t\'~ l.:n;:th ,,, tin• ·' r.

1•-:am 1.111 .. ~,n II r\).: l..

".tllt.:r~ 'Ullin

a l·hagg·\\ "('C'Cirurnt."lc:r h Ill hmnJ Ut.JI f~lf lfu.; ''nkr Hfilt{.. rellrcllon ,,~:.,·ur-. \\htn t h\~ J!IJJu..:rOf! un~fl: ,.. I4 I hllll th~.: fn~t prinuplc,t--;lkultuc the J)J.IIId .. ~ t.:unq.uu ht•m d11! .thm·c tbl.t Cit\ ~m 111~ 1111t'IJ11lnncr "Jl;ldR!! ,, :: 2.Jt I A. duu~c u( t•lf*t.•tmn = I (t ... II i ~ r \l.'h\\..h) ul ltslu-:: .:1- x 10' mfsct \\.1\4.' l l·n~lh 1h~ t1~1

241 ::-Ill

II.: L1~t)r(t "'

(} •

nA.

x W

1 "'

x 9 JUO x Jl) tn

1£) 1

l'l.u~rL ·" 0111 .. 1 - 11 • t1 :'~K :- W "' J s. S II \.·umpa.rtn!_!. the \\0\C' h:u.t:.lhl\ uf IWh nmnuc.hrumalit.":' X ~ r;a).\ hnt;:.;\1, 111~ ftlul\d th:u linr A ~h·e~ r. fi~t ord!'r Br:t~tfs f'(':flection maximum tu o ploncinp 1111~ 1 ~ :11 "\() tl'llh c 'mooth race ul n c ry"--.al. Ltne IJ ofknvwn wo\·,~ ICil!Hh ott) 'J7 A ~·\·c·~

u thmJ ordo::r rdlrctitut fiiJ.\.imum 0.1 ,, !!l.tncmp .m)!IC ~11 bl) "tth the nf the 'alllc cry~tJI l·mtl tht' v..;tve tcn£Lh ('I the lm<" A

Fnr l m~· A

'1J \ I ll

a:: )..A t·

ltl \Ill )(Y' ~

" -; , ..

'-JIPL' l~tl'L'

1 m hnt.: tJ ..n\111 l:.~.jn (~1

J:. 1 flt< ,,

w: vet

= l hh ..- ~ ~ .;m 1()'

\o 1rnm Eqo r II ). \ (t

u I Ml ,\

X·r.lY .. ,JI unl::n''"n """'-" 1.-nj!th ~~·\·"- tu ..t unl.·r lim~~ .. tl'll!o!dtun ;.U f!l.Uidt1}! ;mgll· ul 11 7 \\!lit •Ill) t'lilne.. tli ('u h.t\lnl~ I (• C' ..tn.•;.;tnn" r:md thf" w;n!o! lcnj!th o l thc ..e h·N)' althc l.ttttcc cunM.uu t\•r Cu h 3.6 15 ;-\.

.tr:t~ <,.,m(.:! l "t=AI'- 11-= 11

2J ..m-=nA. 2

·'

;,=. ~h13J\ .... I 'i11l

'' II

._Uli:C tf111 ;

o,Jil ~ +k!--41 '

[

rn~ r.ult..ttiun Irom iln X r.t\ hi...... ctpemletl ill (jf) ~ \' .UL' J tftt.h.IC'tl by il!o.Uilll '•' 1 ~I'Y"'t.a.l ur moi«•IM mo~s~ 74 (1 amJ d~R'"Y l '14) ~ Hl ~gtm·' Calculine tllthc ,.hon \\ll\'C tcnf!th nlth.:- ..rc~·1nun Irom the tube nnd fill ~htnt"mg nngle ICit l'i'"' Utllef tL'tle-t:W..m Crmn Lh~ puttCIIl•tf f'l•tll t'~ Ol lh~ U) '-laf fnt lh:U W:'IVCit'll!!'h (I)

f.l!nll

•t'l' ": ~~·

(Ill /':tl\\

"'he-re n1' the l;ala .:~ t..lfrt ,l.lUIIl tlu: numh\:1 ''' .tt~·m~ pcf un1t ":ell. m th\: IUI'I "'t .. ,\' th~ '' ''~uJt•• ' rt11111hl·r ~· llh· dcn'''Y ••I the , r. .;1.-l

l 'i. ot

7.S

I C.C cry'l-t;tl ..1• II

\ -

tl ;;.

IJI) ;

II:!~

ltl

'/L.~

·~ X

1-J.b

b.fl:'

mul

JUJI'l

u;CJ2~x

111

;/.:'\_I~ x 10

111

d = ul2

2-tl ..in 0 •

For Br.tf!{s.law 1 x 3 IJ

~ . TI1C

ln ,jo

n). .:;

.\.n11

0-; 0 2.J8 x 10

('.'n.:.lt

I+., x ~ ray frvm p.tll>tUtum JI'C' l ('flt('(..:J Ill tile fit!:t order from {I ~;enn trt Cl') sml :u the to lit'" ing glnncwg angle"· $,41" limn Lhl' ( I()(J) plane~ : 7 b.. fmm t I Wt pl:111c~ :111d 9.J • from i I l l) pl:un: ... ShotA hnw Ihi\ d:ttol coukl be uscc.l tu llcLctunn( the l)'p<' o( CUbic l.tllkc ~l nl\.lllrC po5SCS..\Ci.l h)' l hC cry~l.tl.

J:.,~giii('('Till}! Pl!\'.~k.f

140

1-rom l:h:tf:g'J- b\\, we lutve

2d ..-In 9 ~ n)~ = i. for''

r/1111

~ 1<

I) (JlJ.J

I' duu :

Ih/111

1/t/1111 1/t/11 ,.

:!_X 0

:::;

':I:

1]~1 ' dm ~

:!(

0 1()11

0 O•> 1J 0_D.!J O. l6] \

• I

•J

. -\ n X·!-')· >~naly•t., Ul o1 \:)~lo~.lr~ maloic wrth Uh.trhx.hh•lll.alli. X·r'" ... ,,, "inc kn~th U ~l'< ;\ Urug1,(s r~Jl c.•cuon .; WX' t\tul!ncd Jt :tn~lt" ol ta• tt,54')~ •hl 1) 15~ and (c) J, ('ufcul:ne 1k u'llcrplo.nner l-(l-"'IC:In11 u r the c ry'-1:11

QUESTI ONS E"-f'l.•m X·r.a)' diJfr.li.tiuu GiH' a 'horl.tn ~mut HI U!.ltl!!.' 'ltt.'4.111JIIk'ICI l)cdlh.:~ Lht' lummlc u..cJ. ~ Wh,JI ,., _.,..nltnUI•tJS und , h,.r,tcrcn ..tn'' >.. r.-p 'rt'-lnun'' ~\pl.wt11lC ir ur 1g11'1 :l. (II !-it.1IC .uu.l c:Aploun Mo..clcy':. lo~,.... l::.\f!l.;un 1h "'~mli\;,mt.:r litJ o ...c u~~ ht;'l\\ Moc:elcy C1Crhuot'J th~ ..:h;,r, l t'hm~tk X·r.a\ ~r\'dt"llnl Clfl !he lm~ J>.srnila.r 10 hue 'l>ectnt nf H r.thl~cn·lt lc utonf' .l me ~•mslle't gl:mc mg tmg.lc o l a hc.am ''' X·ruy~ tnctdclll un o ~·f) ..t:tl for wl'nth ri.'Oc.•LIU)f) , ...

oW<r\t'd

\\tlh J Bu~~-... ~pc•.:UHIIh~ler I\. 'L'O

n•.. ,,.~ ...,...... lhcn

mt:.ted h; .a ctn.un .:t.ns.le amlthe dc'ICt.:lllr '"lltt.ltcll h) a lnn-~.-•,rumlm~ an1•1e tn •>h~cn c t he 2 n~ mtl<:r r~nccr .,;(.) he.tm C\111 ul.ltt' the• ;mjtlc rhmuvh \' hil:h 1h.; ltct«Utr mu~l b.:- rormcd in ord"r '"' dctc:·n the ~nd t\rdl.'r •cfh.'<ll'III'I>C~m \"luUrm

2d Jo.lll

u, :: ).

Ill

'!d ~UI lh. = "!~ D11o~o n~

~~l

IZl by I I) "< gel

.,,n

0, 2 · ._.n-0-I :: , 'l-In

' \IU

V• :: ...

""' 8;: .; 0 3232. 8~

~ '1.10 · ' l 'II tJ, :: ._ ' =- I 8 M5

Wht:'n CJ)~<oh.tl rnouc.. rhn•uJ.!h an .•nt!tc U H~ H1 '= •I "~ rhcn •k..:h•,·tnr mt.•lc" rtuuu~h olll o~n~lc '!0 =- t9. 10' ro i.ktc...-t !nd ')hli.!t 5 When an clt•cuun ' "' trun!>£crn:tlm w~ att•tu hum the L·,hdl ,.._, t\ Shclllht' X rny:-o emiUctl h:n·~ 11 w:'' c l.:nt;Jil of 0 71'181\ Wh.ll j, t ht· llh)llll~ nurnhcr t)f Ihi' 1.'11(\fl\!

Sc;rccnmg cun,t:mt h

=- I

Rytlhcrg's Ct\m.lJnlH :: 1.097 x 10 '/n)

.'itJI11tiuu. FtcquC'ncy f

=f =Rc f:.- b):l "

( - 11

1 - -- )

f "I

X- 1'11\'S

. I ( I i'·h)·uAR 1-114

(: - ll'.

2-11

I 4 :),Rl

~' 1.()'17~ 10

b. 111C $JMCIM~ bc:lW\•Cn I~

rrandral rl:IOC\

In :t

Cl)'il:tl

Ol ~1:!("1 I" 2.1ti~(l A II ' '

Ht,l,!;l_: ... h.•ll<CIIIln ,,, ln11ti1 X'hn m~llll: heam or X ·f·IY' ocC~tf'- Ql .;.n ;mph~ f'lt IU' f<tl \\ h-..1 '' the '~ :nr lcnl!.lh ul Ihe X·ray... in A th, oi.l \l.hal.lllgle wuul!.l;, 2uJ \tfi.lc1 rcl1t:t.tiun (l\:cur 1 1 What i~ the 'hurtc~l wu' c: lcn~th thutl'".m bl.- t:IUJitcd by the ,.u.Jdcn ~lllJ)J' Hlg Lli (111 dcctrun \\hen II 'lnke ... II 'ln:Cn ur •• Tv. tulle Upc'rlllin~ a( IO.UOO V'l found

lh.ll "

lu .. l

llftll"f

(ul 1\1 '' ho.a1 p.d mu~t uu h ·r·•)' aut'c

OJll!ftth! Hl

!"rvdute X·nty~ wnh nuntmum

V.il\C len~1l1 (til A! (t11 Whal L\lhr.: rl1·"11iUIII\ fn:~. ,)1 X· l:i)' rn'X.Iu ..-cd Hl.tlu~· OJNr!Uing ,It

:!0 k\' ..

Uhm

l•u-·

=-!l!... A. =- ,-1. • t;'""' = ~"1!'

\ ' .:: -.!..!!._ = ~

,.;,"'

,\"""

X-rny.' l'mm 1.1 -.::(rt.;un ~o.oh:.h lr!fl!l.'l 1uhc ure ulmpu..c~o.l ''' 'lrunr K -~cne-. ~'' coh.th oiMll \\ l'olfr. K-lute .. ,Ju-.· '" =lhfltlrilu:-.. The \\;1\c lcnglh nfthc K~ l lnf"\ oUt' 1.185 A h.H Co~Jh and .2.21:iS A >.~nd J .~ ~7 Af01 li'lc unpurihC'-. Ia) U"•ngMu:.cle) .. !., ..... wkubatc LI\C ulunm: !Uitllbcl \'f ca..:h Ul th~ Lwo llllpUntiC"i. lbl WhtU t:leml!nl Lhcy·• HM ~ ·~n.:.. h = I 1n Mn..clcy"-. law. At No or ~o.•ob.Jit ~ 27)

~rc

i." . *

H 1/

I.: -\L

\;u

••I

\.'llh,lh

1. 1 = At. No '•I unJ>Onl)

i':

Nnw

At ~o uf u npuuty .J

...

• I ( 'j 4) =iii~ J I I t·=~

/.1 • 21! -

crunuum

oil

/ Ill

lh~ " ..~...urrlu.m

• Cupr'~·''

11 11!\ \ dll\llh,· ,1\~'I.JI!~ \\d\t' knrtlh ut A. •U~IO A. A1 ;() IM ,\ .md ll.r •tl 17•) ·\ .• ( VfhiUKI cJr \ r,,, CrK"I,~\ kH•J dJ<~gr.UU ttllbii~"C'II dH \\fut t" the k~N n h' f(''l, llfC'dh•.:'"'l~ the I ><tw- '·~~ \\ tu1 "tfK" "·'''' kn~thtll 1ht' I fduW'" ' d•ll .1 tnn "-<'\ d<\:ln-n •Uu\'l.lh<'lung:-Ct:u toll\!~f tn .tlUt·~.-. \\IUtt~ tbr: "hnrh·~ \ , .. , ".a\\." ll·n~th tt L'thtM l"uJu-.:1.' 1 t:Jj't' ,,, fUIIj.'\h"Q II>

!lit· l\ -.en.:' 11~.-r..:

12,.SflfJ

""- •;v=-,-'

11.·U~ _ ....n~,.,, U 17K "~ -<

I h•h. f\-,hcll Buk.Sm!o!

('ll<'flt\ ' ' /. 1 •

N~h:!

'"' •

" L (,Q"1,7l,· \

"~I

t{'

II INA J U UCJ,\ II I 7)o(J.

f if<. 2.1.\

).,1.1'"" II.:!IH ·\ ,

l~.nCr£1) ol A.,. rO&thaiiHII ; ·~·!~n· = W04S \'v

'\n L·\l1cl\ '':at l, =:: h'l(lC•.! 4 590J!'I;:. IOC'"tl·' c\' ). 111 ::

0 IN-1 ·\

Nrn\ M-Shdl ~~ "' 11Ju .. ,

")~) \'lltr)!y

r,, =-

l:.n.'t~)

ol I

1)1 1\tf ruditu1nn -;;.

-69flh:!

l l~U()/0_ 1 N4

l1i"l•J I t:\'

+ 6739 1 = -127 1 cV

l.tdt.ti iULJ::

1061J

~27 I

:: KJ., \ cV

; 69273 7-13 ,,

'·" Enc:rt)' lc.,.l."'llm!!-f; ul~ ' '' tun~..teo •~ 'h('lwO 10 htz (2. 1_\J (l-11 Umiling ~ ncr)!_) ul L".,~no '"" 1!1 ; 106 1 ~ rV Sn lt.·.~l ~nch.'\ C\lllt' the I .·'Crt(.--.. I" Jt)h 14 .:V. ILl

;.,

rct(Uih.'J IU

~I J{1 ,\

I~ I ~.,..,:; l!.l<K~IIXI ~ Ill'; 11.124 A II

"iu ..hl'"'''' u .I'· I.' len~ tit cntillt:~l j, 0 124 A loKlhlll•m fwm •• .\ hi~ tuhc upcUih.'d oil 80 ~ v IC\ mddcul lilt

n ...

,__1 ..,~~,• .,.,

hlllj;'lcn. \.,;"Ill~ th~ ~lli:r~) f~·\el' ul1 u n~M(!I\ uf p1uhle111 ( 10), fiuJ th~ nl.t:umum Luu:l u,· cll-:I~IC) "I lht.: dt..:lhlll!o llJCt.:lt.:d lrun1 K. 1- M ~-hell 111 c\

E1.--:- fi()tf62 cV £1

11-

-1061.1 cV ~27J 1..'\

1:.\1;;

l n1.t•llllflg' \.'le(ll\'11 .af\* f1.1\ Ill}! CO(' f)!)' ~J ktV hct.:.IUM! ( II OJ'I<!flllllll! "••II I~C' 'J11 I hi! K 1: lt(thc dC(twu cjt~ l cd ln•fu K ·~ hcll

Xii,IMKJ -lo'/(,(,2

• Xli.!KKI -:

bl~J86

lill>l4 ~

htJ.3l'th kl·V

Kl: n t elet.:tmnl!JCM..:J irnml\1-Shc!l=tlOOfitl

2271:777!'~e\

T77~UKc\'

1~\pl;-•n Ih.; ~t.11C:mcn1 ·\ t) "'"'I ""' .~ dHCt d1111Cn:.10fml r<:fh::..:hon ;:r;.~11n}; "11h \ rny" Why'' X ro~) d 1flr.acuon ~:ud 10 occur w.. :~ n a.c-ciden1 J I J What b th~ uupu o l tJit' t:ut.oll \VIJ \'clL· n~th ).,,1411 '! Why is ll un lllll"'-'rl!JUI due- llll phttiU UUIUfC HI .\·til}':-.~

\\by due .. thc.l·••u.ll.·tl!lhtu.: \:-r.ty :oop.!Cirum \ o.~ry m a ..p lt!IIUIU.: ""'}' lwm cll'mcut to dcuK:nl hu1 1hc 'pco.·uum m th~ \'i'iihle rnnl!C doc' Rl)t '

J 5. What nre d mnt& 1rri'11' X·rll) 'tlr ''" clc-m(nt•• ltow l'.Ul lht:) tll." U'14'd w dct~·mmh~ thl.! utonu..: null'bet ul 1.1U \'lc:.rncnl'/

3 Motion of the Charged Particle in Electric and Magnetic Field 3.1

lnlroducuon

Tltt,• Uh)lum uf :t ch•u g~tl potrhd~: t:, .11 k'1.:hal b) el..-ctm:. mug netic or gru\ ttallon:il 11dcb \Vhcn thi\ p.tnidc '"' -,ubJCCI~I..IIn cfcctri"· 1tt rn.:a~nCJh.. fidd~. 11 t'Xpc:m:ncc!tt il fnn:c. and hcn..~c i\ :ll~dcr.llt!d The lr.tje~.:wry c:.ut h~ t.lctc nnined prcci.;dy b) Ncwt1.1n\ law. pm\ltl&.'-' l h.ll tlu.• lclr~t:·· .t~..ung un the pantclc an.• kno"n Ttu ... pt'Hpcrr~ nt:JJ..c, u P''""~tblc w rn:1l..-.: r;l~olnuwn th:h.•ctm~ tn'Hllmcnt.., :md p~tnid.: :u:ccl~rmo r:;:. Chnrg< n( :1n clt:t:u·cm, h;p. hccn tuund h) numt.:rou.s e,;1x:rimcot!i. The dire\!t 11'1\!U:-.urcmcnl nf the ma,., m uf .m clc(tr,"tn ~anmJI b!; mad<: hut b) u.;1n~ the ciTccl "" nc~aliH~l) dtar~.:J clel.:ll'vn LIUt: ht ~ lcctnL and magn..:ti\.': field!., one ..::111 mea,;urc elm nuin (nt .111 electron, from which m~L'" o r nn c lcctrun t:;.~n hi: calculntct.J Th ., ~.-huptcr th'-4-'11"""-~" nJ().,t ~~r th\' ctt.M''i, by C(ln'iidcnn~ c hMf;\!d p;midc .L., clct11'\ln hut tt \\ •II h~· t'tJII.llly \':thd for other chnrgcd pnnich~~ like pruhm. ~·panu.:lc . clcutmn. etc .uu..l <tl..,o fnr tnom\Cd dlOJn'li.

3.2

Motion of Charged Particle in a Parallel Electric Field

,)r

(\m;.u.lcr an clt:clron "\llu;nt:d hel\~tt:...·n 1wn p:•ralld pbte..., l:tr~e ~urfilcc -.r~•~ ~tmlainctl in :ul C\ :tC\IiiiC:t.l t.:ll\'dUJI<" I Ftl! ' I). A difference or J>Oh!mial v j, Hpplit!d hccwcen the 1\nl pl!uc,,, 1hc dH!:1.·thm ul the l'h.•ctnc fteld helwt.•en lhe pl at~~ is oh \hown m Fig. ' l Thr: •h,1.1nre bdwt:t11 th~ twn p l,tte~ i~ tl. If tht, tli~tomcc tl l ' s mall t:vntpar.:d ,,, du: t.luncn~ inn' lilt.' plmc then the unifonn electric ticld bclwccn the phth!" i~

\ltl

(3. 1)

;uu.J hnco.. or force ;uc ptltnllng along n~~::tlivc A·:v.i' Electron.. ~•nnm~ from ch~ -v~ pl.at.: .nc Ullf'JCIC:d by ch~ +v~ plate und since there •~ no for<:e :Jiv ng the ,. ,uh.l ... dnct.::l 1u11 M> lh ~ clct.tr'on,.; l!mittcd fNtlll - vc plate nrc accclcrutcll ttktng \·dm~clion towards lhl! +ve plate:. The cJc,:t.riL rurcc .tct111g on lhc electnm ttf ch:ugc t' nmJ mU~l'o m il'o

0 lie nee,

"~ a rim

VIti

(J.3)

Mutwn ojt/1~ CluUJ.:i•d Jlunklf' m Electfl(' ami MllKIIttk' Fu•fd

245

- ·'

·.J---

' , FiJ:. J. l

(' hur~('d

prartl('lt• in puruiM t•l4.'t"lriC' Ot•ld

Thufo. the :Jcc.:clc t~ICIUO uf th1.• cJcl.'lrunfo ulong t-aXiS i(O CI.IO~l:\IH, (or;) p:.ntcul;ll vnlul!' vf V "'""' tl If lhc dt'(..llnn' ·tn~c lh~.: +Ve plolc with ;In \CIOCH) u, \\htch ·~ c:allctt u' tenmnal \·dm m then I he kmcltc energy T of the c ll"clmn will be T = 112 mu;"h•ch '' c4u••l

h•

\mrk done \\'. when:

=1 Mcc x Oisplttc<mcm =d · x ,, =,.viti x ,, =..,v

1151

1.1!

So the tcmun..tl , ducuy

F.qu.ttiltn tl~t •~l')fhl.'nl~ .t ucu tnllt l)f c.~,.,y or \\f('lllc.:.tllcJ 1hc ck"t:t ~o m Hth eV. Om· l'it•cttmr \'lilt i.\ dt'fim•d tu. tltl" ki11t'lit ttm'TN) uj tJ JHltlldt• tiHI\'111}: u l'har~;(' t• t ouf,,mb tl ltt/ arcrltrmc•tltllf'tJII[.:h a polt'tlftal tlifft•r,•m·t oJ' I \'olt

1 oV = 1.602 x I0 - 1" Joule

3.3

Motion of Elect•·on in Transverse Electric Field

J...c1 ll~ 'uppu~c lhdl nn ckCirull Clll~~

iii lhe r't,:gaon hc;:I\\1!CI1 IWO l'·ttallc l plotiC' b} ;,.1 Ji:-t:mcc rl Pig. (3.2). wilh nn initial \'clocuy (u 1 ) 10 +vc t··dire:ctlnn An untfom1 clcclnc ftch..l £, is gi\'Cn between t lws:~ 1wu pi:UC'.!-. tlu: lengah of Ihi! 11-:hJ 1Cf) is L. The i.lin~c •i on of the erectnc.: fi~Jd uJong -vc ,--a:u ... no other fkld~ existing in lh1s region. The molinn of the cha~ed pMucle under 1his 1rnn:wcrse field £• .:nn be ''tud1cd a~ follows: ~cp.uatcd

lmu:tJ \eltiCiiJ-:> ~,long'·,.,: directions nrc It,:

ul. -::r 0

"== 0

when 1 = 0

13.7)

- -- · - - - - - - - -•

.. Since: 1hcrc 1.;; no iCln.:l! along \ nntl :. !i;n \Clvcil ~ afoug : rcmnms .tero nnU

\'CIOCil) along ,\

::IXI!'I

tenl.un., t•. uncJ lh~ di,luncc l r.l\'CIIcd ulung' h)' till) urne

r·---- ~ l-=P,r 1-=lll•, _ But then: '' C<IO'\.Ianl dt:l~lu~ iiciJ otlunt! \ ~~t\i, "'' lh~.-·n: j, .1 cnn .. t\&nl ;li,·\:clcrntlon ,.·.t\i' :tntlthc ''c,t)(.U) .Jl dll) m·.Lanl of umt." t I\

:tkn'~

I I h.: clt:-.lam.:t: ficiJ rE r" [

\\' hcu

lra\'cll~d

= u, + tr

1' ,

;tlnnJ!

Ill

\'·Ol\1'

wuhm

thl·

upphcd clt-ctn~

:ul~ ~ '~~~= ~UJ ll

it•h.:l! u~1in~ Cln

thr ch.·dnm

\If ..:h.tugc

= 01 P .91

,._,_!!..' !0'•

h) atn: fum·

• U1

(3. 101

r itlunt= .,_,.·<lXI\ h.

~u.

( .1. 1 1 )

nlc~e

Ct411:11mns IOdiClllC lh::tt IU the l"('j.!lnn bei\\C~O lhC' plntC.S lht ei~CifOO 1S upward!-. \\'ith th~ \d(;cat)' \:on\IXlncnt u\ \'otrying frnm pdinttu pn1111. where.,, vdtx;ity cumpon.:ut ' '. rl.'milln' unchlln;!~tl m thl! ll'-'.._"a~c .,r th.: electron l\i.'twccn th~ pl:ue.... 1l1c rc ..uh.ant \cincH) \"Ill h~ actcl~rutetl

(3, 12)

'fhc p:tth

(t( lhC

panicl.: in the

l'IC..::IriC

licld willl

f\'trr;JX:i..:l 10

lhc

poml ()

io;

/'1/otirm

r~f lh(· Clror~;ctl

Particle m 1!/rt•tnr tmd MaqnC'tir J•tdtl

247

detcnnined by conlhiomg cquuuon~ (3.8) and <3. lnJ,ltte \on able 1 bcmp. cltnunatcd. ~n'i ' gi v..!!'

I \'=-u

•

1' ]

tJ )3)

ll~

\\Inch '\1\HW:t '""'tilt~ rmrndr 1110\'f~ itt,, J'fltr11m/u· path , ,,•. r~·,t:um IWIWN'tt th,. dwr~:nl {llaln Thl" ~n1t;ular tlcllectu.m n l tht: .:IC~II)lll lnuu llfigllhll ll;Hh proJu~.:d h~ the 1r.11'''"e.N:: de'-"tril.: field 111 ou1y ln!'tant of hmL" r ' ' l!l\l'll h~ tun

~~~ c-\ ' =--.--=-..m v. tim t•;

u v.,

0: - 1

(.l. l4l

Wh~u L " the- lt!ngtb 01 th~ plates whcr.: Lhc clcc~ru..: lieht '' ,g.h'cn then the lft~pl.uccnl..:nt

uf tho,! dCCfh)O due I(> 'r.:an:o.\ Cr,e clc.:~ttiC: ll\.•ld. :tlh:r lfU\o'~lhng kn~th ' L 1.c. ut the end pomt of lhc .:1pph~:tl dcCitl' fi\•ld {II'CJ ' ' <lht.uncd by u'tng cquauon~ (3.11) dnd (3.13) ct:-.

I :

I ( rl:.

Ill

)[ .~ f

t 1 I ~l

11 ·~ un ~4U>llii)O of .t pttmbola. !tV iL will m U\'c •n .a fMIJhulu. f1.UIL \11ct the cnJ ulth..: upplit:tl dc...:tnr iil"ld .trt:.ot, clccmm cmcr~c.., tillltuogcnlhtll~ tn Ill\' p.tr;;thnlu:

Jl:llh :u Ihe pninl

or eme-rgence (Sec Sccunn '7 J

lran~H·r~c l\lagnctic Jiit:ld tnluaJ ~f>C1.!c.l L' ~.·nt.:tulf •' unllt*rm trillh\ \'I:-\' molgn.:lt.: lidd >Sl'tin~ LI0\\0\\ .ml dlong: a.:\ I'-. 1.t' ('lt'r[k't1t.tn,ul.tr lu f'I>Jn~ ••I the P.SP'-'f • f't~ 3 JJ Since ITIU&!rtCIH.: ftdd i, pcrj"ICntli.:uh•r to anlll;.tl \~hK'II) l ' .md .,,, ht tl"i tWIIittll :at C\\:1y ithlouu. '"' nu work i.!\ done ~•n the dc:l·tn:Ha rlullmc.ut' th "-utcllc en~o•rg) '' IIJ "',t m~o:rl!-:.\1.! ;and ~u it~ '-pct:d r.:mo1i11' und'l.m,gcJ '' lthin lhl· m.tl:):nctk hdd The for~.: Jl.'llng on 1hc dec:tron due h' Lr.tnc;;\'Cffi' m;·~nctH.: fil.·hl ,...

3.-t

Mntinn nf Eledrnn in

L~·lu~ ... ,m..,ul..-1 ~~~~ d~..:trnn \\ tlh

/, : /Jt'Lt

Since 8, ;, L' .uc c~11titanl~ in mognnudc !\et 1... •~ cun,lunt in m.t~niHJdc and perpendicular In the dirc:C"tion nrmorion. Due hl lhi' l)'J>C t1( fun:c. ~ kl"tron will be C(111IIIIUUlt.,l}l dcOrcted 8,1\'CI\ by FlenUO£"lc-f1 hanc.l rule and nn,&IJy h~--uhs in mouon m a drculnr path wilh cons.tant speed wuhin 1hc lrunc;;ver'\,C ma.gneuc li~hl. For the d(m nw..rd magnetic field, tnlw~m\!nl of thl! <.'htuge<.l p:U11clc w1ll be c:IOI:l\'-'' i.)C. ,,-htreb it wdl be 411hCIOCI>.\\I\C for IIJ'IW<il'lllll:,gnctit.: field. hIS analogou< 111 the pl'(lblcn\ of rt mas.; tk'>ti w a rupc nnd twulcd tuuund wnh con~tnm $.pe~d. "1111s force which IS actu:t.lly th... tcn,inn in the fl'J'IC. rcmams eonsUllU in m:tynmuJe and i~ ulw:l}'S. di•ccwct mwords the cemre ol drclc. and so is normnl to the ntotion. which is known as ccrnnp.nal fore.::

2-18

Engmc•t•rinx p,,..,i(:.,

•

·--~o

•

h.:ohllt'i'... tt'~llfl

•

o, l',

•

~1.t,l-'llC"I IC f ll."IJ prrpcoJJ~ular II) p;lp!tfH

Chtl~('d

3.3

•

f.1g,~

•

pnttltll!' lo

lr1U1.~\erst•

)

n HIJ!IH'Iic• fit'ld

S111U tit~· Iran""''' ''' llM}!IICit\. lldtl when lhc electron uf ru:.t"' m '' llh" 1111! m cin.:ul.tJ l'oJLh ul r•• Utu' N \\ uh t.:••w,r.u1l '(1t:ctl t' fm, a r;ldt.ll.u.:'-dcl •.ltmn hl\\ .i1t.l' the t.:\.'nln: lhl'n lh~· ma~ncti~o: lnr..:c .11.:11nt! on ir iii

.:.. 1111 :/R

II I<>I

I .... ;;;;. &·v ; uw~ I R. [ R ;;-;;;;;; 8

i.e

t1 • 71

F.qutatt("•n 1 \ 17• ~hov., rh.tl '" the lrnnsvcr:-.c magneru; ficltl :1n dcc:twn "•11 men c m ••' 'n.-ulur p,uh nl rnJm, R A(tcr the mognctic field. the ele-ct.' ul L'Oll'Jt'"'" 'ml wngcnll.tll) In rhc .-n.· at the: ptllnl ol cntergcrKc. Frnm clJn n• "c r.tn r'"''

dm ::- u/RIJ

"•'11\.'h \.';111 h.,· u...c,l h.- det~rnunm~ tlu.: dm ratw ror ~.·l~ttmn If T '"' th1.! tunc pcnod 10 Ct'lllli11CI~ ,)nC rcvuhuion then

So T b imJ\!p..:nclent

j) f

v ttnd R. rhc r.:sonancc frt"qucm:y

I 3.5

= II/'= Bdittm

tliRl

Molinn or the Chnr~cd Particle in C rnssed Electric und Magnetic Fi eld nnd its Application (Cathode Ray Tube)

Con~iJcr

an l.'kctmn mm 10~

llh an initial vclocit) u entering in

J .. ro.,.wJ

clc,tlk 11nd nMgtlctil tichJ 'f he initi.1l tJin:ctitm o( ''clocit) ,,, tbc clc4.·tron '' !1lnng X·:""· clct'IIIC field E :tpplicd :tlong y. l11c dirccuun uf clcctnc lint.'-. HI rorcc .. ;dung the(- Y-a.\IS). Mugnctie field or nux dcnsny /J b upphcd ulong /.,

the dircclmn uf mttgneti(' lillcS uf r,ut.:c: 1:\ along(+ Z · ltl\i~).

th~

d rcle rC J)fC~Cnt~

1hc flf~u of uruhwni nllgnclic field (Fig. 3.4). A c:.crecn is t>lnc"-d nt ;l di:-.l:ln~:~ D (:: OSl from d1e: ccntl\! l•f clc~.:tric unc.lmu.gnclk fit.=ld. f

,. } - - - -->-

.\,

' I

WiJhiu 1hc'c cto,\td dcctrk ;uul nt:l~lu.:uc Odd· if tlh' "kdhm , .. m;nk to tr..t\ d .tlong .\' threcuon 1hcn tfuc Hl dl'clrk licld tllonl' u wtl1 dt!n.:ct UJm .tnJ~ ;•lung Y~;•~• .. fFI ~. 3.4 • Whcrca\ d ue 1~1 rn:tg_nl'IIC lldd ahmL· 11 w ill tll'tll't:t

dnwnword .lions Y-nxi.<..Aftcrcro~~lng the mup:neuc fidtlortlc~trk field cl(t.:mln \\Ill nnwc wngcruiall)· ht the: nrc ltl (l''>ml of emcr~t·n~.,. Su 11 S ,.., cln: ..,n~·~~~ (h1\itlon nf d.:ctron em t.he screen when t.he:re h no fidd. then due LU clcc1rk field otlunl! il will t.leOcct h) .m .unuunl SS1 upward .. tFi!!' J ..t). \Vhe:rc;l!. tJuc hi rnogneliC lield aiOnC: It WiiJ dcllcct by opp<:l~ill' dirccuon

rill

:tr1l0UIH SS1 dOWUWQrtl.

JU~I ill

lhC

Nuw if force acling un !he demon by clc~1ric and mogn~uc

lit:ld 'i.lnlU t 3nc-ou~ly ar.! $3.1fte. then there ,~,. ill not he .my tlcn\!(tinn ,,f thi! ~ ~ ~1.trun

beam Force artmg on lhc clcctrt'm due 1u electric field h Ee. Whcrea.._ furcc m.:tllll! due tom:a~ncli e tield i~ llt•t . l( lhc:,c twc1 (orcc:o. tlft!Ctluu1th~n SS 1 c- SS:. Sn then: will not be :any devbtit)l1 of the e leeuon from it .. oriJ!in:\1 p~•th. fnth~11 L"t1nditiun

I i'E=O.v I I.e. Bul

u = £18

whuc

t f l f\

IIH.'\\! lwo

1hc dblancc bl':l\\' l'Cn two plulc:~. untl V lht! vvlwgr.: .applictf h!!l\H~4:11 plutc~

I ,. : ''"'8J \\'hrnlhc clcciHUl t' nlo\ ll'l; 111 u l run"<:f'l" magnt!lic tichlthen 11 will lnrcubr pa1h Llt r.nlhh U. l 'hcu , ,, '!R [ t• ;

tf.l\l'l ;i

= R('t'

BR,•InJ

hnn11 .t I'>) nnt.l c\2Ut ""' ..:.:m ~ct I' :

V/t/8: IIRrlm

I ,/m= ':1 L ""- 'L.J

(.\.~11

whc.:11.: \ and .I me 1.-.ntnl>ll 'm' by fl't:(\fdmg lhr.: dd1cctlon qwf thl• tu;•gnt'h1lll~ll'r ncr.:diL·• .J u~: tu 1h'"· >tpplt n.ltn:t~n~llt: field. II c..·o.~n be culcul :ued Jrnm1hc- L'tJIIl11tnn

11 hm cp. when~ J/1, th l, hon7fl1Hnl \':nnlponCill o l c:ulil '!- 111UJ:!I1'-'IIi.' lu.•h.l H Fit? ~ 4 m the lollt"'WIO£. wo,y

~::mill.· ~:•kul;ttl't.llr•llll

_ /Jfx(}S

- ss.

0,,. '' '""'

\\h..:n: tli,l.tll~l' hct\\t,''\!·11 the cr.:nut n l lhc Ucflc~tlng plolh'' .UIJ 1hl· 'l:fccn R j, Ihe raJiu ... t•( nu\'~ttun: uf the t:UI"\'~tl p.nh tlu~ IH IIM!!Ill'lll' lic-IIJ . U/ 1' lhc tlJ,tulh. '-" het"c~r 1v.o mugn~:t' tt,cc.l tn ~pply llltt~ncliC field '\o,l'\'~o.'n linn!!

"truw..n 111 ~ttn 1,l ~~ J. lrlllll whcc.:h rim r:an ~"· det~nninl!d The' u...o:d In Thi'II1WII m~·tlh)d rtlf Oh~~l'llllU!! dm r.lllll tul \!h•t' llllll

3.(>

f!nn~o.IJ1Ic

, ...

Expcrimcnlal Set-up f(or T hnmson Method for Measuring elm Ratio for Elt drnn

Tht appnr.mh .:L•n~i''' llf .1 tlbchar~t ruhc tfi~. 3.5l enlled .:"11th<~d~ r~~~- 1uh~ ((" R T.l. C '' C::dt1uxk .uul A ill. anode. \\'hen ~~ high p .tl i!to .tpplicd hctwct:n c:n hud~ .ant.! anode. cathode ruy~ :&rc produced. Thc~l' r.1ys pa:-.!o ;thmg X ,t\1\ throu,gh mei.J.I dwphrugm' dcctfnrlt~ bc~1111 ' ' (lhl:uu~·d

mairu ~ mcd

,., nmllle f'IO teminl So. u fiul! JHlJntctl

This bc:un !olnkes the C.R.T

:,.cr~"'"

normally and

produces nuorc:-.ccth:c a1 :•;. P :1ntl (l.~te IWO l~;•r ullcl pl :uc~ ot lcntth L. bc1wccn wlm:h dc:t:tnc licld t:an hy n dist:lncc tl lnninlly when the re " no rlecmc unt.t m:I~UCII C lidO 1hcn lh: lluorcst:cnl spot will he at S. Now by applying c:lccmc J1eld ~•Inn~ Y :t\is, pencndicul:ir lo 1I1C lllollull uf the clc-.:lrtlll f;llon ~; X·ol\l'·•t. 11 dcnectwn ol dlc ' Po' ,"~<C,·un,, whach l:t dell..:i.:tCtl upward at~ •. :\..:xt by rJ.,, .ng

tx· upphcd. scparmcJ

lhc- C'.R T ht'l\\Ccu ,,.. ,,pole p1ecc' uf :1 m:•guca. ~~ downw;u•d ma~nch(' lu:IU \':UI be: <tpphcd ..tnmholncousl} nlong. Z~a:ti~. pcrpcndiculrtr lCl ahc 1nouon nl lhc d~c.:lrnn (X·a1ihJ. a' wc11 li5 pcrpc.mhcular to the direction ol chxtnc f'h:ld

~----------r ·\ II I ! • f

........

• \.- -

- ' l,:_ ==::I

J ll"

(

I'J\......-; - ' --

Fi~. 3.~

L " ~~~---

'llunl\:illn mel hod for

111fASUrin~ ~/m

1,--

rnlio rnr eh•ctron

t y .. tJXI!<} Thc dnnc!d 4:1rcular :Jtl!ot n.·pr~'enl'•· till' regmn ul unifHml magncuc lid d. n\c: dm,':CU~\11 VI dellf.'~·uon \\ill kc dm\ IIWCIJt.l Stnl.!c \.'W\.~Cd clcclric .uuJ

fidd.l\ ar~ JCIIU~ on th\.' ~k..·tmn ~anl ''multunc<'U"I). th~n their ..:l l.:et will cancel each other <lfltllhl' ~pttl \\Ill cnn\1.,' hnc"- H• ah un~in11l J10Mthln ,\ In tl1c~c condlliort\ ntlt~ l.olll C.:olh;;ul oUt.' l'im 1,,, m ttt dl!t.'ll 1•11 hy u .. mg t.'tf11 ' (3. I l)) .t.uLI 11.11). "ioh ohc heir uf cyn 1~ !!l nW!!Itl!lh..'

3. 7

Vertical Oct1ection l>uc to Eleclrk and Magndic Field on a Screen and St•nsith·ity

\Vh~n an ~ l cc:Hun a·dHtw inE "tth an111.1l ,-c Jocuy L~ 1 j1\: rpcndu:ularco the c:k~trh. fh.·ltJ ( /-.\ w \ '/,/), lhCII lhc \ t:r1h... tl \Jt.·O~·\ Ihill ~~~~ Ih.; '"'' ~n. \\ ludt 1:0. ,JI 3 Jt.\ I.IIIL:~ JJ rrum lhc CCIIIIC 0) uf th~ IIPJ'lil'd dl'l..'lflt.: fii!lt.l t.:'UR h~ cukuhth:d iu lhc follfl\\ in,g. wa~: Jl ~u.:~.:elcr.auug ;mudt! hlh.a~t.· " \ , lht•n th.... c nl.'l(!)' uf lht! l"il'Llmn UhJ\ in}! w11h nnlial \ 'Citl(.:l1yt• 1 frum tlh.- ~h.'Ct.'h.'t.Jllng un,tLit.: ''

i..:.

11,

From Fig. ~.5 we.• !1CI veni!:'talllc.ncclinn.

IWI

,. V L n1 d t', 9: c_!, : ....:_.;:_.:.!,._ e V L t•, t•, -::;;; d u~

Bccm.1s...:

r \' I u• .: -Iff -( 1 -tl, trnm• Et111- (3.lJ ))

t3 231

where (I rom 1~1~. 35) (.. ~ 1\!nglh or the plultt P. Q in C. R.T. whcr~ vollt•l!C ' ' h a pplied . t/ = di!\HIOCC bel \VCCiliWQ pl:tll' ' I ll (' ,f{, f . w here VCfl ical \'Oil age V IS apphcd I) OS= dbaam:c fro rn () 1u 1hc ,crrl!'n.

3.7. J

Verlicosl del11.·t'limt on lht· ~crecn al :1 distance I) f1'fnn tlw lht• pl'rpcnd icul:l r t•lectrh.~ lidd £._, t'

V L

I ~ D ""' B~ lJ - - - , m tl t'~

,. m d

ccnl r~

'"'

1o"l';

Eln tw.\lalt• t/(•J1t•c·ttmr .wn ,\ ilh ih·: It 1~ Ihe ddh:cl1un p~..:r un11;.tpplicd \'Oh.I~C. r.c. y

Il L

2 d\',

~\, 7.2

\ 'l'rtic-al deneclio n due t o perpt>nditula r nm ~nNir iuduclion II Fru111 ~'I "' n :!1) nnd (3 2.0), we !(l'l r~

'\'ow

m~\gncl ic

S.~, ~ I.}_S f.U I =lOS U/ II l'llm«' l'-=: , , ,

=\ ..-2c<\m1A

[ r ~ IJJJt

field of

[ ! '= f> B<'b

, (•i2-ml\

IIIU

]

I \.2~J

\\ h..•r( I> OS~ Jb l ilO'-'~ I rom .:c:ntrc 0 ~'>I thl! lll..zJ.'fh.:lh: 11..-Jd If' sal'l'n I ,- Ul -:: Jcn~lh uf t th,• otpplu.:d nm~h..:hc hdtl Mnxm•rmtllfrc: rll'flt'c·rwn sr.lls;ril'ity: II IS lhc.: ddlccuuu pl'r uml ma!!nclu.: mducuon )'

r;;;;-;

/ )/ •

- = f) L ,r.l2mV•1 =U- -m 8

Magnetic 11nd Electrostatic Focusing \Vt.: lm,·c aln::uly -.ccn th:u the motio n of the e hflfgl' p;.lrllclc!- c:.m bi.' ~.·tuuru lk il prop4:r ~ h::..:t rl t' nnd lll:l£ 1\Ctic fi!o!ld. So it ma) ,, l~o pos~ ibl c to fucu:. the divcr-grrlg ht.::ul l t)(ChMgC lliU'IicJQ. origul;.Hing_ rrvm thc ~Ource.:i. ·11\c.S\: oti'C C.."'-'llelth:.l fl"aturcs for ~omc ver)' impmt am SCICttlific cquiprnl:llh-. suC'h us \;uhfk.IC' ray osci llm.copc. Cyclotron. Mass s pcctroscop~. Elcclroo UHCm!-COJX'. etc. Now wt.~ \\'ill ~~ i~~u""' hnw clcci!USI:.IIic :1nd nmgnclQ::o1:11ic fCK.'U!""ing ~~ possibh: fur •..-lwrge pa ruclcs. l.\~·

3.8

Electrostatic Focusin~

In cll!ctro!ttauc focw'ling u seri\!~ of cyllnLitit.:al unod~!> t\~ B o.t increasing potential~ \'1· \ f~ a rL~ IS~ucd (\\bCre \', > V,). 8oth th~ .snudc.·, ..trc kept hi~hJ ) po\ltl\ c "tth r..:-..llCCl ro gnd G ;~ntJ cuthm.Jc umJ 'Cf!JI11t\"d b)~~ !UJ'- A high -CC(tltrcncnll:ll till!..' R j, rLeced in the f!:lp bCI\!JCt'll t\\H uno<.lcs A nnd B to gel the len'> 3ttt<.m The ~h:lJX! of the equipotential hnt.:l' onthl.' f..'ylnHI•·kal ~urf.ICt' ,)f unudc A tuhl fl "ill he \:UI"\'cd a.... ~hnwn hy full line!\ in Fi}:.. ].6f.lt 111..: clc:urk line~ offor~c ar~ .alw{1)' ,tctmg at rll!hl uu~lc... tdoltcd ~,:ur"c Fig.. 3.6a) to the C<.JUtpdknllallnu:~ TlH! rc,ull..ml dcctnc licld will be a_\. indu::utcd by the."! Uuth·d line\ Cl"'ig. 3 ()a) Tt•c cun.cd CtlUipc.>H:ntial phmcs form an ch~Cih'l\Wtic

k nl>. D1.1e 10 thl! ~ffc.~t..'l

frolll the source. s11y 0

f1f

whtch thl'" til\ l!r~ing be:un rtf ..:lc~llu l\'

3.C>a) l!cl.s Ui\'ertc\1 lrorn us ori,ganal pnth :.:a.nd pomt /. l 'hc dcctron ~uun.;c ·~ 0 ;.1nd lhc elcclrc)n'\ lmvc:l from •• CP'i~.

rocu.)scd ;al re&.wn A nf lo\\ p.)teruml \' 1 ut vch-.cu) r• 1 to,. rl!ginn IJ of h1gh potc-nunJ V1 unJ velo~.~uy u 1~ l!.nl!rgy ol the- panicle 10 r~.~g•on A 1.:-

tu\d lht11 ... Hllhc 1Cl!HII1 H '"

'' .. ''• l' ~ :• I f

t•J

,.,

t bl

Fit:. 3.6 (al Elt.•clrostuik

focu.dn ~t,:

(b) Oplk nl rncu..,.ing

'-'lit': :: ., ( \ 't IV: 1

Thi, j, i'-11llil.tr 11 t 1ht.: rcfr.u:lion uf ol bt.•oun uf liglu .u J COn\ t: \ 'PhCOliJI ,urf~cc. hom~~ r:1rr1 w •• dt.•no.,t.•r nh.:dwm <h~. ,,,fib •. 1 hu~.

\\hc-u 1hc l't.':uu '' lht\\~lflltg.

'' IH:n t.hvcr~rnJ; d~~U\'n bc;Ull nHl\ <.!s I rout l\'l\\ ,·r +\'~ puknh:.Jl artot en h1th~r +v,• pllh.'UII,tl ·1ll.'tl t1 ' ' c.l1'cncd IO\\,tnh the Lcnttotl (')(hilhm 1 c. l.!'1111g h• h.: ltxu,ctl Thi"' ..:;~u hi! mlllhcmrtlh:tllly ,hn\\11 "' h1lltm'

E\plunulion for t-Jectro.~uui r F'ncu!;"in~

L<:t L" <OII<id<r l'tg 3 7. where XY ho the C<fUif'(ltcnu.ol mtcr1:oce lo ~c R on Fog lN.t• hN\\l!l.'ll 0:{!11111 l.uul (( \\IHch urc ~tl lh4.'unil'unn dcdr•1'11.11n: +ve (XliCntt;..l \ ' 1 .1ml \ 'o \\hl'IC \ .,.> \ '1· ''I ~'h'

'' ,

' ,/ \

'a"m'

~~~~in,

'. ~'

j•··'"'"

L',:

fiJ'!,. J.7

E)(p(Qnru ton

or t-lerl rO'Iil n l iC fow..inc

F.J..:I!'Irum. 1110\t~S Wllh :1 V&!IOCily V1 in h.'!_UOil A and Wtlh t' Ill r~p.Hm IJ. t ar~ the an!!l~ nl tnt1dcncc und :m.g1~ vf rcir(tt:lum ot llk clc(!ti'nil t\t!lm on the IIH(rfncc .\'l. then \\I! con re~oh•c the \'CIOCH} l't und ~ · mw purulh:l :uu.l pcrpcndlc ul~lf t;;llOlfX.lOCIIIS lO the surface (t-=tg. 't 7). NO\\ ~~ un cqutJ')OtcnttOI 'url.t~c \0 thl! Jl.lralld vclocny componcnls u 1 :~in r ~mJ ll) ' '" r " all he l"qUal, th ere ~he-mid nol be any ..:hungc. So.

:tnd 1

t't

= Vz !olin r 0 .17)

i.e .. from equation t.l.27) it j.;; dc;rr thal wbcn \'1 > V1 rhcu I> r the-electron beam

Motinn

i~{ tltf'

('lmrxrd

l'arfldt•

m Elt•ctric mul Ma~:m•tit' /·ir/,1

255

will <hvcn IH"-:u·d ~ lfu• rwrmal. tmvards the ccntr.tl pchillon. At the ~;.amc tnm: .. inc..: i >' and ll~ > t'r · Ml the pt.'rpl!ndt<.'ulflr component tt, co~ r > u 1 co:- 1. w/ud; lllt'(llf\ dt•t lnm t1n1m U'i/11~~ m c t•lrratr.J a.\ \n•/1 ll.\ th\'t'l'tnl fl>H'cltll.\' tlh· nmtrol rmMIItJII. J.f'. ,t:omt: to lu· /tlt'W\t'cf Hht•n mm:iux Jmm lmH't {mtt·n twl urr•u hl hi~hc:r JX-"~IHiJI un:ol "I hi' I" -..uml•u 10 rclr.aCIIVII l-'~f h ~hl (FiJ;. 'llfll " 'hr<:h h th-: main lcarure nf electmsronrc focusmg The rocall('ni!lh l'l tlw C.'Plrcal h:ns 1'- lt~c<.l by the curvature o l lht..• len' tlur th ~ foc;tllcngth <'1 thl' ~o.'ll!\.tr••strau~ len--• t.:~m bl.! chnn~cd b~ hltcnng th~ rehsh\lo! Mt«:'

and 1101~nwil ' ''' lh~ ~ydondn,al '"""~~' tl and li Thts ktnd nl ek<lf<hl~li' focu,ing '' \\ ttk·1~ U'l.'d

3.9

111

cmfl,th

IU\

rn·dlloM:opt•

l\ h•J.:neloslatic F'ocu;inf:: and M11gnelk Lens

Lei 0 is tht: po:-uwn ol thi!' clcctmn m.,sdc 1hc uniform 11lO)!OC11' field o l llllctbll> li {Fig. 3.~;11 nul' 111~ "uh n "'l'fnt.: •l~ r• olong OfJ maktnt! on ttllgk lJ '' 1th H Vdoc it} «' c:111 he rc: ... ,:hetl,mo '"u c«~mponcnu. t' Cth 0 .•1,1ng ii :mJ t' '111 u pcrpcndJcular w ii. IJ th..·re '" unl) ' llll" ~nmponeml' 'to IJ 1hcn ele(.'Lmn '' 111 h,• J1l(U'IUg_ In ;. \'lh.'IIIM ~lfhll 4ll r.11.h11' f '\11.-'h thW mw

i.e •

f ' ''"

Nfl'' umc Fil:

' 'n Oft = HrP Mn

U((a~ .

t;i~~.·n h~

=- /lulm

tht: clc..:-trnn "' lnl''" m

"uh H'h'l:tl\ P

' u' g,,

comptct\" Circle n l r.1dtu .. '

liTrlr Mil tJ = '11trm/1Jn·

2nm /1,

1~-

Bu1 "hen the: .:J..·.. u· •n ("', ....~:,,c .. h• •lh 1h..: 'doc it) -.:ompunrm t: ,;n 0 .i' '•'-'-II v CO'- 0. 1)11.'11 it \\Ill ntll mtWl' m J t:ircufar p~tth. bullt will mmc in tt hdh:~tl path a' ~hO'-'n ut r1g ! '~ .. , ulong OX :ulLI pi1eh nf !hi! ht:li.\ 1/ = OH } 14ill ~ 11a· diSl3nCI! travcll~d hy th~ ..·tectmn p3rulfcl to lht" mragncuc held by the 11m..: 1 !)\) 1=&.'\'0'0)(1

= t• "" 112tr/8(e/m) I= '2Tr IIW cos (JfBf'.

E.xpl.anation ror Magn...rostatic Foeu,"'ing From cqu.uion t.l:18J il j.., ('lear Lh<Jt 1 ts llldepend!.!IH of 0. L' and 1. "u lhl.' dcclrons startml! from poiru 0 c:l111Ji, ~rpc in any tlircction. wHit diffl•rcnl "doc.'tlt.:.. but w i ll be foro~d 10 fO<:u' by Lhe uniform fiold 01 the point R tOR= I) ,,n.,, parhc ulur tuuc 11\1Cn1nlt UP p\·.;:, lhl.! dm.:clioo of ntl'•tion m the .,h,cJlcC nlthc m:tgnctir licld. 11m~ 1h~ magncllc fidd jtJ!ii:l nets :t.l\ a len~ hl brinH the tlhcrgcn1 electron bcanl inhJ .t rocu:-.. From Cqut~tion (3.29) it IS found thai focallc:ngtlt I (= OR• dcpcnd-'i. (10 P and co,; 8. But if VI!IOCily v i ~ large. di\'crgencl' 9:11 ~u will tx.- laq;c. bul cos 0 will l'C smaJl. So. again focal length I wi11 bl! consHuH ror ~·

' """

/" . y/....

.,"'

' '' •

" '

. '

'•

()

,,'• '\ '' ' ' I

'' '

~------

~II'

...

I I

.''

,''

/fj .

litpi

1.11

thl

l·'il!. 3.ti

.1\lagntlostulic foc.·usin:.:.

p:trllcular \':tlue: nf iJ. FH"·"I 1-:ngth OH = I \.'om hl' nltcn:J nnly hy ch•.mginJ? the n1:1gnctit.· im.luction H. II tlu- el~clmns m:tl..~ 1v.o or tltn,:l! tt'II~IIIQn before rc:lclatng R •hen ntvrc th:\n unc r!X'ul point wtll occur ;u d~:-.tances /, 2/. 31. et~. Thus till.' fol.'ttl length of tnngncuc Iento. can be ' 'ancd hy v~tryi11g. the ullt tiS•ty t)f the magncli~ tic.ld l 'jj ). which is not po~::.iblc for o ptical lens.

DtiTcn;nt 1yp\!s o l magncth: 11!11\ o1r~ po:-.,iltlc ... Bu-.ch.. fir-.1 fl" 'P"!--':d that :1 mm·utttf••rm ma1;JtCI1l fit:hl ;tltliiJ:t the a:\ I'- ot a :-.hon solenoid ab~) h:t' thl! JlhlfX:t1h:.., nr::~ lll:lf;OCik len' Ill Fat: ("\ KM \IJ "lht• <.,cecum ha\'ill¥ -.un 10111 :o.IHcldctl cOli ol dectnlma~rt~l \\ hh .. rMJTn\\ _g.tp 1n lhc tumt u l u nng p .tllt.l tf rcprc:-....:nt tht· ~up~ :H (hJmclm:.dl~ "PP""ilc J'k•,itiun,, .uul there I' .t o,lrlln~ IIMJ!IlCih: hclll tttfO'):!o lhl' ~up wh1ch ,......ymmetrtCt\1 nhoul tht• uxis Ul of thc ch:ctr''""'~nctt~ cnil \rrJngemcrU '' m •• J~ 111 .... u..:h •• Wa) liM I () j, "ttlUrt'i.' uf ~·lt•l'lrun "hh. h ,,,.. h"tt.'U\I!"d 1u 1h~ pmnt J dut: w n~ott;nt:tlL' l..:rb I Fi_g _ 3 RhJ. 11tt.:: fl"l'o~l h:n~tll ,,, nl.lgnl'tic IL'n' i\ ut ''r) "'mtlll nakr ul frw ~~~~ I ht'l i'l th~ n:qmrnl t.-lllf.·n,t hu J;clling l;u~~ m.sgmfi ~~,;,tliun in T/n tnm ~\firmMUflr, \\-hco: .111 mttll.,t.' ~md \Cl) lo,,t ml)\ mg b,:am ot ~r.·lco,:uun-. .uc fncu-..cd ~mtl mnm1y magn~llt. len-. lucu-.hl~ \) -.tem i~ u;;cd. Petal 'ut Elecmm M•cro:.cop¢ ond mngncuc: len<:<-.. olr< dt'>\.'u.;.,.~d 10 !oCCIIOil 4.12

3.10

Cathode

Ra~

Oscillnsc(lllC (C.R.O.I

One nt thC' rmpor1nm 11pplic~•tion ot the dcnro~lalic lOcu ~mp: .m,J OJulmn ul llll" L:hlJl!-:d fl;Jrlh.-k\ in ~k.;rn.: anJ/I)f lll;lf!11t'lir liciJ i~ c;Uh\:w.Jt: r.a~ ,h.nlln"np~: flu.._

m.t:llloscop~ I "' !U1l" 11f Th~

lllU\1 1111ponan1 UlO]\ lur lhl'

U~\'d •\plltl'rU

dc~tront~ cm:ull:. ~md

tm tnndi'rn ck~mHm.''· C K.O. 1:.:1 delli.'~ th;lt .,IJ,>\l:-o U' hl dl\fJiiJ~ th\! .unt)lllut.k lll dcllt u.:al '•t:rMJ, Whether Ihe>' ht \ nlla!!t' m -.:UIIt.'l\1, the:y t•an he dt,pla) ..:d prunaril) ,,, a funltum 11f 11rnc un C.R.O. 'c:rccn_II dq:.,.:.rtd-. on tlu: OUI\'Cnwntul.ln dt·t. tmn hc.un. \\ hKh \\ill h~ vi,lblc h~ .tiiO\\ lnJJ 1h~: lll.·onn cu ilnJ'IIUf!t: "".a phu·phc•t .. urfuLc.. It ~h!llrun ht:.;.ttll j, dcOcctccltn l..'tthet ,,j 1,._., ,mh<1J-:!tl0;,1ax~·" X un,l Y, th..: htmmuu' \fWl can h.: u-.cd tn crcatl..' IW4Hh11Wtbli'Oi1l dtsplayf-. Afon1= >..-,t\h, "'i'k-~t j .. d~Otd~J ~11 a con~~tt nl r.u~: rcl.tiii1J1 hl um~. "her\!11~ 11 Inn~ ) ••• ~"-~~~ l!o dcOI!Ch!,ltn rl',J1\UI\t: IU .mtnput 'lunuhh 'u.:h ,,, \'OIL:sgc l11i' p10c..IUL'l'' llml.!·lkpt:ndl!nt \Oinatiun of lhc inpu( \Ohl-l_t!t:. \\llll:h '' ,.\!'t:' nnpunnnl l'ur th· ,k,lt;n .ult! dt•\ dnpmcnt ul dc~~lrnnu.: \:In mt 3.10.1 Comaructiclll of C .K.O. Con ..truL'llon and "-+1rl111g tll C R.O ar'l!' 'hO\\U in 1-=tg ~ ')(JI unJ lkJ. lh-.• l:ltetron heam i'- ~\!nl!r.\t~.:IJ from .. conventio nal heated cath<x.l~ ..urtounth:d h\ the <:Ontml gnd Gn~ " m.uul.u!'h~tJ ill nc~nli\C: po1t!1Hiul \\' r I r,tlluKft: tu '.:I \I.' focu~ing. cffco. Afrt:r 1!rid. the fi t-st .tcrclc.r:lling anode and fcK'u' clt"t.'IJ'tKk folllm

,,·hich pn1\ iOl' dc~.:trlJ~t.IIIL focu.-.ing. :s-. wdl :l$ fas t accclcralmf \ 'Ui tJpt:. l:k) und ahc t'octt"ng_ eJed1r«, rh.: decuun hcnm p:.sc;c~ abrough 1wo \'COll':.tl tldlel'IIPII

plates IY-plulesl. Th< beam at thiS point

nollully r<><:used. The beam Will be

furl hi! I' focused .u h.-:nkl1t!i'tiOrl w prO\ adc- :1 fill.: Sj)()L J\11cr vcn~t.:oL1 tl\'nccuun the bc:om pa.\$CS throu!!h n ~can ex pan~ion lens {focus clement) ch:ttmcrcu-;c!- the runuum bcmn bcOOmg ln lh..: \ crtkul phme Tim~ beam b. Ihen dellcch:d h~ 1wo hori,oma1 pl;,uc .. {X -J'II:uc~J :"tncl p:~..;:sco; 1hrough :.1no•her clccrron lt>ch "'tuch prO\'Idcs addiuonal lt;X'u.;,mg ihc beam 1~ aa:cclermed 10 the 110~11 vciPt;Hy hy 11 quadrupole sc:~n c;o.p:m,uullcn~. whtch prm 1dc.-. not only on lllCI'c~t'>C 111 electron 'doc1ty, but udds to lht: !'Can nnglc without d&storLing or dcfocu ~mg thc dcctnm (,cam. Nmv 1he elccrron bearn nu('linge.;, on rhe C.R.O. ~c_. een '\ hu~·h " coated Wllh 0 1oycr or nuon:s.ccm m:ucriaL pho.;;phor

t)u.klro~p.,le "-""

I \P!lii,I-Hn I.Crl\

•

V~nl-c.tl

llt.•rkt;r,un

l l..•tl"-lh"l

flf.o! .-..l \ \ I

1-.l.n~-,

""',""-.

lfljfllllfll.ll

IXXt

~h)!h• "••lll1¥l'' .\u:~Jt'UIIIIIII

"""

E:h.'\:lllll.k

Fist. J.91uo

l nlnnnl t' UiliJlftiH'nh or t '.R.O.

h=:= - - - I ~1 mNil"

llml

\I-

"·

It• II (j,ojt

~tto.l

.u•·«

~ I \''a den''"'

Qu,wlro~p•IC'

qoan e:<p:u'"'"" l.::n~

FiQ. 3.9 Ib) \\'or~lnn !)N>e• du"' ur C:.IUl.

rho""'"""' ol hghogown olf ~l oho phosphor ..-rocn ..tcpcnJ< on ohc amoum Ul cncrt=Y tha1 1s 1mnsrcm:d to pho~ph,-,, b) the dcctmo hc:un h u a tn.'t o~~:ll loM:nfk" II 1:-. dt'.'lrahk In tJCt:t:lcruh: ah, .:lc( Jwn bcum In 1hc j1ft:"utc:.L amt-lUnt pt').S~ih l c. \\lull' ou the! uthcr h:uu.l a g~h:r t= k~lrnn hc~am \CIO\:Il) Will mn"c il mun. tfil licullw locu~;o the team So UHIIII IHtrpo\e m tht' cun ..tns~tnm (l l good C R.t) '' 11tc uwtchmg IH-"lWt:en «h\'M: twu. t·tf'\1 th< electron bt"am is ~•t·c-el~r:u~d. then il'I<Cu~cd :and 1hen deflec1cd 3ntl. ~lftl!-1 !h!ncclion 1 ~ hu the.t :ln:dcnated "' lht' dc:o,tf('J fi unl \~·lncily.

{

.l. HU Workin~ C.R.O. 1 he h~.ttl uf ch~ '''"'ilht\~.:upc i~ tht! cmhodc ruy 1Uh\.' IC. R: I.). If u stc~td~ p.J .• 1 c .. I) C , ..,ll.t~t.· '' .tllplh!U to X-pl..th:~ Fi!! J 9th) till' b~;uu '' t.Jcnct.rcd ~•ltlll,l! X :t~P.. II lh\.· u.~ \Oit..tgc j, ttpphctl \0 Y-r)l .tl~~ the hejUf1 \\iiJ tJcllcd !thmt: y. ,1, 1.., Th..: ~,.h.~nmrc hr:I\\Ct.'ll th~· centre :mtlthc new pulrl.llum nl the "'IX)(;, prt1pt)J1ttmal u• the D C '•lhu~c applied Hut in,lc4Ja.l ,,, I> \ ,, .t tac~. tf :.n J.c. H\lt,t!o!\.' t:>. .tppllt.:d o n lh~ \l!rth.:..tl ~okl1~d 11lt! pl., , ~, . then the :.put ... r ltghl ~~ dr;,awu uut ;'' ,1. \(t ltc.al Ime otml ~~~~ length ,,f the lwt: 1~ jimfk)rlitltla)l,, tht.~ fH!I\uHUn~ \.lhn! •tl A(' \(lh~~t~ Fnr dl,pl..i\'111l! t'\:tCI W:.l\'~ fonn lhe A (.' ' '!!O;tl on lhc C.R.O \trCCU.

hurilt'lll <~l deO~..:'tion

'hould ~ ~ync hrom7ed wuh lhe V\!rll~al mpuL. 'ucb 1hat lwn11•ntal \ldlt~tion stans m th\! same poam •11 lh.: mpu1 vcrU<>al "iagnal 1:-IJ.! J HUb) \\h¢r..: the 1u1c p<.mo<l 7 tlf lht:. ....weep vol111gc I~ C<tunl to or 1:-. !'!4)1llC nlulupk ut thi." llnlC j)Criod of the A r !\l~O:tl on the \l'rlH.:<•I plate;,. hll llu, II .. ~ nchrllrtl/lll,g nr mg~cnn.g c in:u11 h U!-Cd ;,, 'he'"" 111 f1~ '\')(b) T lu' c.' tft:lll l 1' the Imfr-. h(t\1.~cn lf·c \'CrltClll 111pU1 and Lhe honl<•m~ll Hml" htLIOC genen•h'l' \ crlkl.tl (li.•nct>~inn :,)~I em

T lw IIIIH:tum nf lht.· \'trucul ddlccl1on '' r.dh~r ... tr.u)!hl h•n' ar\1: 11 mu't prm td\.' Jll ••mphf1cU ~•l!nal to :t proper lc,·cl lhat "1 !1 p1m ltk .a u'uul \ldlc~..-ll\111 ul rhc ch.'.:lmn ~;un "11ho.11 imruc.hu;mp <Ill} .tpp•CCtolhk t.li\Hcrtum into lhc '>·'tc.:"rn ll1L" nn.Jct ulmnpl n catton 111 :t "emc:..l 'tdc .u.llu'tl·d h) .tlh.•nutor. \nh ,/dl\ lo.ih1l't '' mthc commr n 1 ·2·~ "'C<.tu~.:nc..:. S:ty lnr c>;:nuplt.• I !. "\Hh IU. 211. iU 111 V t.'ll

per n:nunwt'!r

llnri.wntul dcllcttion sy~tl'm It •~ the.' }!I:Ul'r..J purrH~:tl! of tn\bl C.R.O. tu llctlc.:"t 111.: ..,wn hMJI.OOI..iJIY .11 11 t:c.m,tunt IJh.' rduti' c lo time. 'duch t:'l. 1lftcn rdt·•r~d tu ,1., lmc.u "''t.•cp . Ssu~o.T Ihi.! , o il .tt!(' •"!."~ .n ftl .. , l u•ritun l .tiJ>I.u~ .. '" u'cd h' ' " ~t.·p tlh dcdnmt~.sm 11dn,., thl' -.~.:reen. 11 1:>~ c. .allctl.l' "" l!.l"l> \ ohaJ:!c. The ht1rilonhtl d l'Ot:dhlfl ,)' .. l\"111 <.:t.•ll'''" 111 lllllt' h.t ...: gcner.ttur. .o~ tnggcrclrcui t. :md a hoiiiVIIt,ll.uuplih~l (Fi)! ),'Jlh) llll' tllll\.' ht!"l' gl'ru..~rawr or !-W~~p !!I!IICI'niVI ~<•ntml~ the rat~ at wh1ch 1he be .Jill " \i,:{IIIOCll ,)l' fl l\'\ tht.~ o.;.crelo!n of I he C.R 0 :mtl •s lldJU'Il.'" rn'tn the l m iH p:mcl hy udJmlm~ umcltll\'. lll\lh The tng_t~tr cin·1uL. .. cn!-urc' thnt the hurizoniUI '"c.'Cp !\l:J.n ' ;ulhc :'l:tlnl' po1nroi Lhc \'C nlc!lllnpul ~1 gn.1l .l' Ill I ·,!! 1. I U(h • l1le hcmtunt.:ll

•unphilcr ~ ~ .. uml:•r t l) vcr~ic••l

:\tl tplifier

I hm· ltn)C ~cnc1"11tur The

<l\\t!'~p geocrntur u~~

llu: chargm~ dtar.lLlcrio-tl( ul ,, Glpoll'U\lf ( 'tu gcm:1.1IL'

hn~.ar nM~ llmt: 'oh:lt,C' tn feed lhe horiJ.unt.JI amplilicr f~l!tuc .'\ IOt :1 ) ' h" " .. .1 l.':tp:u.:iHcr ..:;tp:lCII,II'ICC C tlcing l,.'hul'gcd rrum :ll'.'Oihtanl t.:UITt.'.nt 'OUfCt!. J he r;tlt..!

,,r

..,, vvh.agc nM.! h Ch:mgc or ' 'c•l(ugc 1 Time '" C

ll1u.;, lhCrt!: 1:0. !I gruduaf lllCrca..~ of \'Uhagc m.:rO~~ C, when thC Critical \'Oitog.: b. rcach~:d. the cnpacltor returned ht tcru \'ullage tlUIC~I y by d1'\Chut g1 n~ thmugh

Working proC'tdurt l:lf time

FIJl. ·'·IH l:ll

b n~c

gtncrnlor

" '

-----1 :, s\A, ttr \ nho~~-..· lllfl burw lft.WII \ \ I

pl,riC'll

rhr lrunst!<oh•l (ht• 3 IOhL So rhc el ~..:lwlh tu'c d~llec rcd lincarl) w 1th li me 111 tlh; horll.onraJ chrccuun lllf J lime r. Th-:n rhc bcum return;,. It) it' \.lar11nj!. ptmu O~ll_!. l iObt on th~ \.dl!cn \'cry qutd..ly. ns tlu: sawtooth \'t)ll::egc rapu.Jl~· r.. ll!\ tu i1;,. initml \'nlue: a1 rh,· ~·n"l l,f .::1ch pcmH.I. llcc:m~

the r:JlC <lf tncrctt.St: ()f voila~.: 1n cnpolCtfor <=•10 b4:: \'anl.'d by ndjusun~

~ 11hcr ~urrcnr

I t•l ~.11)a~u.m~e C. ~u rhc ~weep roue

(IUih'

pcnut.l 7) ~0111 he

\.'ontrutlt."(l The 'wcxpgcnecmror or timc/b.a~ lillob follows the ~me 1 -2~5 ~qucnn· a' Ill I he- \' Cri iCal "')':O.IC:Ill, '" tJ. I . 0.2. 05 IllS, I(), 20, 50 JniCtoSC(: C(C. ptr Clll Tile.' rclaLion,lup he:twcco the sw~cp gcncramr and 1hc u iggcr pulse. which lt.:prc:-~111 lin: ...lint: pnnH H( the mput WOl\'C J'prm ·~shown Ill Hg J w.tl). II a :-tnu.so1dul \'(lh~•!!t: t:- lmJnco;~cd .t<:ro... '\ the '..:11acn.J dcnccuon plntcl\ 1~T• tlwn. 'llnuhom~ml~ly. lhc '"C''-'1> \'c>hu~\' 1s unprc~t·d across the hnn..-omnl dcnccunn pbtC!\ (XXl1hruu~h line ba.)C lfCHemwr 11lC.._:musoid;•l voiUitft:. wtuch ll!"clf wouhl ,ghc n~c 10 a vcntc:tl line. " ill now be 'prcad ou1 and will appcaf :l' a 'llinusoidnl

i\lollOilU{t/1(' rhur~f'"ll cru~.:c

..:qu:al

\lf1

Pmtil'lr in Elt:t Ilk rmJ r\lrJ}tlft'tif• Fir/d

C R.O 'itT.:~n. I he p!Hl..:'nl \\ Ill ~PJlC:If <.:Wti<Jilary (..Uiy If the l1111\"

ur ;, ot

'nu~

mulhl)lc uf. Ihe

11m~

Ior one

<~ d('

Lhc \\'ll\'1.: on

~61

r, . . Lhc

VCTIIC:11 plutc.., hI' lhcn 11CCl'!'l\:.tlj' lh.IIITC4UCnt:y ui..,\\C'Cp 4-:ITnnl b.: ol\lj11"1t:tllu ')IIChronil\t! \\Hh 1h· Jn.'l)UCilC~ o l l1ppht:4.1 tnpu1 '1!!11lll

J. I U.J l ise.< ol' ('.R.O. C R 0 t.) u'ctl.1' n h'''l h•r fh!o;J)l:,y of Ihe ".i\ dHnth .t' \H•II .,., hu mo..~~ i n~ 11111n) l.inJ, nl mca-.urcrnt:nll(Uid.l) .mJ ahnl'''·•~..:..:urntd) It h 0111 p.rniLUI.ul~ .1 \('r~ ~ILI.:ur.uL· mc.t.,Jmng tn"'tnnm:n1 bull\~.,, uw.,l \\lha~:unl) .m ••fiPIP\IIIItU\! .1111.1 \tuii.:L mc.twrcnu.'nl 1.. fCl(Uin:d (l, t!l'ttll \';tl u~ lie~ in it'\ ~:r.. :lllht) .uul appliL-:.thiluy 10 rth;'i.I\Ur~ •• \\ H.li.' l'liUl;l.' uf A.C and n.r \ Hhd_gc. A\ .t li:\1 lll .. tHIItlc..'.lll, It , .. Ultl'll rct&utr~~o.I Wnh:., ... mc rolto~.glo! whose rrcttuen~y :unl m.,~nmu.l\! .u.: h·t~n~ unknn" n In 1111: I{ o·.. 111Ul'>t C0111111UU "''"le uf U~i.l£-C ut tlh:a~llllll!= tunc \' .I()'IUj;

'lt!ll.lh, the unLn;'"·ll ,ij:!ntll l' apph~d to the 'cnicul ( ,., ..., pl;tl~' .mJ 01111111: ha\r: w lhl' huriton1.11 t.\' \J pl.ltt:!>. In tim. nhtth.• uf up.:1;1tiun tit..- J, ..rl•t}' un 1lu: C.R 0 ,c.·r;•cn i .. in the rnnn c.•C11 gwph with tlntplitullc uf lllc.• unl...mm.n ll-l!!llal HJI til;: \\!nlc.:ttl a\i.., ;uhltttnt on th~ hCintontal tl\1'-. rlt.: I\\U ha-.il n~·;t .. UH'ntcnt... \llll' t:an UUI"'-(' with(' R.O. olh: Ull\J)IitUlk um.l 11111c \llllhl"t ~·thc-r tnc-'.u-urcml"nh urc b.l:!>Cd on tht:'c l\\ u mr:a.wrcm..:nb Su th~.: fulltn\ inl:' Jl.l.f.Jllh:tcr-. ~,;an be mc<L,urctl h) C.R 0 ,m;; ·" lnlh"''

.,JI

J.lfl..l. l

I 1

Mt•n., urn.rnl11/ ,\.("./JJ.C. \ 'oltag1· C.Ro..... u ''')h;~~c-rnca,unng dcvJct• . Slllt.'~o.• ,-olla.t..: .... '"'\'" n .....UI ;1111plumk4.•n C.R.O. !>Crccn fm .\.C. :-.i~nal ulon~ Vcr1il'~' l axb tl;i!!. lll l. wluch ..::au hit! l.'4'11lmllc.al b) \ uh ..hh' "'-n(lb Sl• ampluude ul unkthl\\ 11 \ ( '~~h~t~l" '"

\mtlh'Wdc (\'J = \mp. x l'c"'lflsltlil•. 1\tlflb po$1lion =em. \ 'ltm-=-

\~Its

(J.J(}aJ

In . _••t,t.' \-•1 O.C ,,,,hJyc. 1hc d1qancl! bciWel'n 1he 0\}l(ll ""-''"h' .an,l Jll!:r 1hc; U t \ ''lt·i!!~ >lflpllt:J I • (lhl('Hlfllnn:tl Hllht" tlpph,·c,l \'Hit:t~;_l' ' ' h1•.:h I ,II n •'lllllr•'H"•'l'""' ,,,lt.Jtll\ ~twh

FIJ;. 3. 11

3./0.3.1

~ t ca,o. u l'~mtnl

of .-\mplllttdc

Mrtutlfr.' lllt!lll nf Fn•qurllt'J

(,, 1 C.R.O b aho ..-:•nmnonly u~cd for Oblltt11111B drt .lppro:-.un.&lc m~u,urcnleut ')I

fn.-:c.lul!llt.::) t!~~i.tl1l iu circuit IC~l .uuJ f:wll di:t1;no'i' :tpp l i<.:.uion~ Time pcnnd for a p;1n1cul:..r Signal can be measured on C.R.O ...crt..-cn :Jionl:! hontuUial :t"\i' lFi~ 3. 11•. whu.:h c:m be cmnrullcd hy timc/(h\'. knuh. 1.1: h~ unlc hn.'c p.cner.uor

HC.Ih.:c hmc Jk l tud of un~lhl\\ u

lime period

(1') ;;. Di!olan~c

~1g11.1 l "

.:l.l·

between

IWO ~uccc~M\'C

cycle' x Tuuc bJ'!!-C knr1b

Jlo,iJ ion ;;. ~m 'eckm = 'c'--

r/1 ~n1c !lllcJII.III\ c Wll} oll'''IIJ.! \

puuem...

111C'C Jrt:-

trr ,;,·rr.

1<.0

rrodut:C:\1 h~

11::..

O ..IUbl

u• uu:a!l-\ln: frc<JI.h.'IK'Y ~~ It• gt.•ru.·mt..: LI\MIJUU!\

U'>IOt;

C.R.O. In X·t nlddc. \\h~!rt•1llh:'

C<.\11 h~

P·''' the llllt(·h·•'l". nnJ ·•Prl~ ·• ~"""" rc:fcrcm:c frcqu.:ncy "-111U!oomJ.o..~l "''ffl>~l ,hr~CII) 10 Wtll"•ll ( rl phil" olflllolfl 1111~1111\Vfl fn:l(ll,fi C)' J < \IIIU\01~.11 'l~llollhl che h-.)riiOnl:al (X 1 piJtc-... Thl!' r.:,ul11ng Li...,ajma.. p;tncnl fi~ 3.12ol. on tht.• ...ue-en dcrcncJ ... 1.10 the (re~.tucnt.:~ r.tllttoll\"o <>ignal-.. P:mcrn '"all he ..c.1hlc ""I}

when Ih.: trcquena:y r'-IUO ~.,1 twt' 'i,gn.th j, tt whole numbc:r. Su -aead) rMncrn ~o..m be \'lbt:uucJ h) adJlhllllg I he rt>fcr~n\,;c f1\!qucnc)' ttnd lh~n un~m,wn IJc:4u~nl.'~ can be C~1 fcui.11~J J('"'Cirdin~ hl the p.tttcm. ac"·orJ111g_ tt• hg ' 11.1 l•ll'\1 K.111u

ntllt1 for Jlu: paniculur ulll,uncJ

I\~ \ I

f~taUCilC)'

/ ........

__..

)

()

\j ~

)

•HJ

IJS

IHli'

f'h.• ~ 1111--r~n.:..•

Fie.•1.1 ~(:d

l .i....,ajnu!\ PHih·rn

.1. /fJ..l..l \lett.wrc•mt"llt uf l'ha\t'·dif/<'rc•uc(' tu)Whc:u '''" 'mu,~•id.tl" ,1\·c lmm 'IIU'tcd 111 d1ffcr<rnume. thcu .:t piL'l-< dllkrr:tt4C: ur ph:t'\C ''''fl \\ill t:tlm~· hctwc.:u the Ill cFit:. l. I 2b). which j, c-.:prt~_\CJ in ~m1' o l tll!gr~.•c: . Phu.;c ~lu ll betwc('n t \\"tl a.t· sii!nols of .~mmc amplttutlc. same ln:qu.:m:)

Fig . •I.IZ \ bl

Jilg. 3.12 \<)

can be mc.1:surcd. Wilh duul 'rnce- C.K.O. when l\q• a.\'. :-.ign:ll wnh :1 phtt.:,t.' th ll crcncc (~)arc apphcJ 10 twn \hff..:r.:nl (;hann~ l H the hori£tlllfOJI dt"IOIO\.'C h~l\\~culht': ..:unc ptunh fll lh..: ' '"' \\,1\cfnnn~ fmm lhl' Fi1;. :\. 12h j, (i n mnq r". lhL·n ph:t~· JilfL"rcnn· hct\\L"t.:ll Lhcm will fx

1'/wsc </rift

= ¢ = (I(/') JM <leJirt'c'

(3•.11ic)

\\ hl!n r-= 1 nnc pcno.J of l hc \\"" \! (b) Pho.sc !-lttfl bcJwct•n iWfl a..:_ "il!!-11111" can he cakuluh:d ahu hy Ll,~.IJHU'

p:mcrn (F'1g 3. 12:a). by u'in~ (" R 0. HI \" )'mod~: When (\\U 'IUll'ntdal 'lgu:tl wllh s.;_m h.' umpliLUdc :md "i;UHl' flc~Jtti.'Ot:)' but wult :t ph:.'c t.h tfcu.:nc~ lO) :lfc urph,··J ltl 1hc X :md Ypi;I(C-t, nr X- r plntiCI' thl" plol nhl:uned jo;; 10 ge.ncrnl clltp)loe u:;. ~ hown 111 Fig. 3.12a . .t i 2C'. Jl X unt.l } a.c.mpot ~1gnab a~ ~.1\·.:n U!t \ 'a .- \'

"1111 rtil

\1\ - \''"' (WI t- ())

nl~.~n at t n. V\ e I I,\-\·~ l -..an¢ Nflw from 1hc F1g •.U1,·. '' ht:n \ r _;._ 0. \ '" =-II

Hence hy c•tu;llmg ;thm.,.· 1\\il.;qu:-ttluth hu \\·, \ ' 'lfl

\\C

gl:t

¢ : h

,,n o =hi\

Plm,\ t•tlifferl'm:t : ~.!:

, ; ,· '

(hi\ 'J

(3 ..10tl)

..-\ :.a ~JlCCiuJ case. wh:n !J-= \', t h~n phtht: stunt> =- 9U 1Jrd Ll!oSnJOU ... J)tmt:m. 1 111 ht. 3.1 ::!.1. which '' u cud~ 1 c. It ;- \ t ~0\\

unc c:m c-akuttlt'

ph••~l"

diflcn.'RC.:l" bcl\\\'('11 .an)' twu

''!!n.tJ,

''Y ob!>Crvin~ L" ..;IJIIU' p;llh!tn

3.11

Cyclotl'on

:a.~;, ''"U~Mtd;l l

\\hs!u (' R n "un X-)' mtk.lc

I h,· nmgncln: rc::Mlll(lflCC .u.-u:kr.•IPI 1•r l·~~ )~tiH•n '' lh..: Uhhl I.Ululth of ;,!J o.~c..:clc-r.~wr.. which tu.:cknnl·, ..:h..tr)!cd JMrttd..:.. tu .t~ tu~h u 'aluc .t~ tU Me\

which arc bumogcnccuo, 111 cncr!J:) Jntf

cmcr~c

._. ... a

p~mall~ l ~.un

Thc'c h1~hl)

cnergcliC pal'tklc!~ can he c.hr\'(;'11) uo,cd a .. JU\>tc... lile 10 .t nuclear re~Lclion. The cyclotron COOSISt~ OJ tWO n:u 5C:IniC..'trt.'ular mcml h<lXC~. c;llled ·tt~.·c~ · ~,r

IJ'.s ~cuusc of Lhc1r ~ hope. Thcs..: hollow chamber:; ho.\'c thc-1r d1omcm...· edgb pamlkl and )hghtly ~pamh:J rmm cm:h utln.·• (l•lg 3 13). A ~uurcc ur I~IU:) 1.:. luculcd oeu1 the m1d·po ul1 ul 1hc !lilf! hc1 ween lhc Jce$. T he dc:es (Ire connected

10 1he 1cm1inal<of a radio frequency oscillmor. So 111!11 n high frequency nlicmnting poh:nlial of sc\eral m1llion cycle~ per sl.."~.~oncJ j, .appli,·~ ~rwr:cn rhr: ~Ct''J \\.hich acl a~ dcclrodc.,., In lhis '':l). ahc pmcnuul hc:1wcen th.: de~:" •s u~;~clc lO tther rnpodly and lho eleclnr field on lhe gop" dtrecled firstlowards un" dee ond lh•n Inward~ lhc ,.a her '111..: de(--:, ;m.! .:ndn.,cd W1llun but llbUI;tl\!d Irom ;, larg~r met.tl ho~ Cf,ntaining gas :.tl low prc.' "urc und Ihe whole appar::tLU!- j, placed between Ihe pt)Jco, C1r .1 'trong dl!tlmm.t~OCI whic,;h pnwidt: ~~ IH.lpnclk lichJ rJCr)lt!llt.fic.:ubr 10 lhC rt ~uu~ of lhc dl'C'- EIN'ItlC liclll "''-itlc dee.~ lo, /ern beCalL'C nf electnc;ll .-,hicldmg When ~m ifln wilh a po~ilave <"hMgc f/1'- ~1111 U cL1 frlml the -.our~c. il 1~

3ccelcraoed hy the electrk

r.~Jd

between the dee. oow:ords the de;, which i<

lu\.•~~UIIl

pumj)

l hRI

'"'!!·Ill\,; ~•I

j, ~1unlform 111:tgn"·1il 11l·IJ U aumg .tt IIJJ.hl •Icc.<>, the ivn lnt'-'CJ.., rn :.. ..:rn.:ui.Jt p.tth "1th1n the t.l~o.•t• gtvcu h~ frnm t:t..jO. 0. 17) a.,

that w .. ldlll S1111.'l" lht:n•

.m~lc... h'l lh~ pl.u11• u( 1111'

of r:uJw, ' 1•

rr = 1111..' 1/Bq '' hf.'n: m h th(' tml'" t~r the.- iun. 8 the- )lrcngt.h oft he m:1gnt'tk JidJ, :tnt.l ul 'l'k:Ctl uf lhc it1n While till ion i-.. tn....idC' llte dec. ab.... peed -..tu~' t.:t.•n,l..tt11, hut ufll!t tlc'4:rtb1Ug :1 !ooc.'lltu.:1rclc 1hruugh lht: di.."C, the 1u11r.::tcht:' the g>~r. wh~r~ 11 i-. :tgntn

,ubjC{'ICIJI(llhe .1ppll1d Jllllentml dillcrencc. Now ~''lltplctt:

.r 1he umc IJkcn b) the ron 11>

the :-.t:ll11..:1rdc 1s C'IUJI lu the time tAbcn by th~ "":ill:.tw 1u ~.- h.ut~t" tl'l JXtlunty, th..:n till' wu '' llg:tin ucc\\h:nth,:J l l)wurJs the til h\!:r Jc~.· \\ ith .mmcrcu'l"ll 'Pt:Cd U-z. h Lhl'll IUI.)\'t:~ ill a semicircle wilh IM!!Cf rad111~ 1': rhu\ by W.Jjll)l.lllll! 11tc.:: o,:,.dllathm frcqut'ocy and ~tn!ngth of the magncLk lleJJ. lltl' dt:trgl'd pani~.. lc" a l \\ ay' keep in pha'c.: \Vith tbc clnmgc~ of elcclric field polariul!s and 1hc-n tht• speed ot the ion ~01.!~ on incr.:asi ng :b il 1:. moving from one lfct~ ht thl! nlhcr 111 .1 ...l'uuctn;h.: ol lu~c1 tuu.l larger rndilb Each time the ion~ uos.. the ~~p. d1c) rct.·dvc nn atfdilimual kick. so 1hc cnc~)' will SICadll)' lncn:J.'C uulill it will rcuch th\!: pcnpht:ry olthc dec. Now Lhcy c:m be brou!!h ou1 of1hc- l."h:unhcr .itld t•an be

llm:cll) :as hig_ily energetic panicle.; in the caully u l nuclc:u rc:tctums .md in the pnxlm:uon nr rodin nudit.Je«; Ourin~ thi' fOUltlon angulur \'docil\ uf tbc 1011 "dl1crn:uu l'>;imc

11 ,.:tJ

1r '=-

nh.: nl~l.lmltUUl COC:fl!,)' fnllu..-.~n~

w.,,

uf thc iun

L'/r

=ffqlm

pw~ I U\:ccJ h) :.1cydullllli 1.,:0111 he" calcuJ:ucd tn lhc

Due 10 csrcular mutu•n nlthe itln trom ~qn. (3.11• we get UtJl' ..: mt•:.IH llqH

!'~--

'" \\ht:rc R i .. 1hc

r:;tdiu"~>

at \\hich the- pJ.niclcs h:.l\C the m••chmL· When .m 1011 h.h b~en acceler:Jied by p.d. V, then cn~rgy i .. tf\

.Su the

cnl"r~y

"='

1/2 IIW

of tht ou1g:<nng p~•ntcle frum L"yclouun

rh,• \ llhh.' (lithe nm~ncli C field "~>l rl:"l1j;lh lo:JIHIUI he «.'hll\CO :trhHflldl} hut dt.:pt;lldt., on tht: frcqu.:ncy of th!!- otpp h ~J alt.:rna t m~ \·nih•!!~ Hl the Ul!c. anll mu~t b«.· \.' lh•\1."11 :O.\l ;t' tn gi \'I! rc:-.HmHlt:IC Ft,r n·.\tmam c. /Itt lmw /oJwn hy m1 wn. wllh 1111 m•a:ular 'rim tl.\ w. ro dt:M r tht! a wm11 ;,r/;· '' rlllm tht' f/n• "'"'' ht' t•tJtml (a half tlw /tiiW p~nw/1' of tMdllutum o{ ''''' rtpplu•J A C fldd. llmt j,

;;, .:. ttF/"1..

trt"

rr:.

( ·: lU

=tt/rt

(1111•)

Due ttl 1hi' rc.MIIl:tnce. cyd('mm ;, .rhn ~.tii~J .t:-. M~•gn("IIL Rc..,on.U1cc Accclcnunr. U11ltt.H rt· somuKc \It// occm; tilt• an•t•lc•rauon f'IYN"I'H m ndotnm wi/l.m'l'· .\o tJm· l't:'WII(JIII't' jrrqNt'llt'Y (It}

r,\

rlrt' um,-t mtJmrttmtpnwmr •tN m

r·ydulrtm

l·rom cqn. 43.3 1aj we sc~ lotio\\ tng thong<: f I ) ·n\c cn cfg)' ;)(;(lUII'Cd hy Ihe r~llllde IS lil(.lt.~pcndcrlt uf the \ ,.,hagc npplkd. \Vh~n the \Ohugc is small. it mnl'-·" l.srp.c numOCr of fUm' hl rcoKh the p:nph.:r~ It i" lhc pmpcny or the cyclotrnn to Jccc:lcnuc ~hnrgc:d punu;k..; 10 n:kUi\'cl~ hi~h C!m:r~y hy me;tn~ v( ~Jil.all ;;,pplit?tl vuh:.,~e. (2) Jl i~ ul!'.o obsN·.,·ed that ror .>ami! .,.alue of magnetic held tH). if the r.tthu' of lh~ dl!:c-~ i~ J ouhJed. energy ut lhc 1nn wall ht incrc:.r!<.Cd b) four limcl'>. t]~ The c m·rgy ocquircd b) 1Jn· pMhdt' l!; tn\'Crwly proJ"lrtw;•l luah nlil"' So for m r•l\'1\'C pnnick-. h~c: u-rMucle:. h• th~•· mngn..:th: Cldd ... Jrcn~th i-. nc~c~~31'}'.

So fur .tccelcr.llln£ di(fere nl parltclc.Lhffl!renl1)*pc llrr.mgcmcnl j, llt.:L'l:,sar~ .

Mass-Spect roscop" lJ'-l!, ul M.L'' 'Jll"Ctro~"'OJll'!-. J;lll mu' mf• nuun cJivi,jnn ... Fur a,:~urnh.' dch!nnm,,u,,n ul .11\'fi~H' 111!1..,,~.._ lh..:n: " lh< high pr<d~son Mrt,_,.s,,.., ''"-:mph .uul fur lhl' .t<c.ural\.' c.:mnrMn ...on ul td.lh\c h<llnpk Jhundan~:c' nl ~tithlt: t·kmen" Then• ~~ Mtt\\ ,,,.... IWIIff lt"t

lltt" +\~ '"'"of ch:•rgc: h.p cmcrgu1g flt..HH tht• t:>. lt 'Ill \)1 th~ 100 -.;our..:~:. 111.1) hll\'t.' ..hlku.·nt CllCI,!;) t.l!!p..:IIJIUg upon lhl! type! nl th,~ \-{nun.· :u1d :1 rotngt· 111 ma,,fo!, \II l'''hlJ)C' f~ I J rn· ....:nl 1 he Tnt!!\~ :'ipcCifl"h~npe nliJ'I h~o.· .a hk In focu .. '""'HI lllc: ':1111\.' uu_,, :u th~ '''"'h,: phtcc: tm Ihi.! (lt:h't.:lor i l" C'i1hcr phut0£,1~1ptu1. rl.u~ Ill l.'h:~.ui~.:.ll dl'tl'dllr h i\ vit:tllhi.tl lh( in\.lr111nt:lll , ... (ap;•hk Ill lt~o~.-u'm!! inn, ul ,liffcrt'nl cncrgll''- h·clucity rocusmgt :md dtlfcn.'fU dirccllt.•n ,,J rnounn \"£MCt.' ftk.'tJI•IIlg t ~lllht: -t:trnl! pomt ur fine tm llh: tJ.:tt:(.'tor. tllh coanban.11 •uu ••I dmrblt·f~~ muu: ' 'a char;.tctcra..,llc uf all rhl!' ~~~ ' '"~lrum~nll\ hu111 ,.., not pn..... ihlc to +h.hlt.'\C gu,..J hll'U\111.1,! lor .J wade- r:mgc nf ionlt ..:n"~•g•~~ ami thn:~o.·lmn .. Hcrt• \~C '"'II th ...,,;u'' til A~ un .unll.2) Uai.nbndge m:t\' ~pe..:lm~r ... ph

.3.12

A~lnn·Mass Sp~ctroj(raph

h'l' t.h~l.ul~·J ~·nutr<- •' olrhr 1'\'IOJ>IC m:tss..:~ ;\ ..wn ,,J.,.~... ,~nc\1 01 m~t'' "~":tCl"~gro•ph m ltJIY. I h~ ..t.:hcmJII~ dt.J!!furn for lhl.! Aston m.~... s-~pc\.lfn~n• tlh • ~ ••~ ,h,•wn 111 11,1.!. ' IJ Po,unc ra)~ rmmlhc .suurt.:~ are m;Hk (H lhrl•Ugh I\\U \CI) lhln par.1lld ... tu ....\,, .\-:. Tha' fine cnllim:ucd beam contlltnll\1_: p:u ucll!~ ut '' 1dc range.· nf ,,,.,, ... tilL'''' 'UhJCl.'lcd h• perpendicular clcctn c ticld 1:1 m;um.unt:d hl"l\lt~\!n ihc plali,'" /-'C-t 1 und /'t l. lluc to pcrp<'n~hr:ular t:h:"l·tm.· lieliJ p<lSHI\'~o' wns ntH f~nl\ ~oldk..:t hv un angle iJ h~\\ unh ncg~u l 'C pl:ak tnu .~r~ ·''"' c.h'J)\;'''-'\1 hy .tn i:lll;!k· JO. rh~· -~ llt ht.--cnu"ic 1hc amount of dl'lh:l'llnn '''II h~o· !!n·.a1 ~r for lht•

fl''"

1.. '...111\C

H'll'

\\Inch'' h;.l\'mg 'muller \'cloclly. lhllfllhc p;u1u:lc!\ h:nmg h1_ghcr

\d1'1.11~· )un.~o• 'fii:JII L"J \CittcJI)' p:ultclt!\ att: 'HIYIUf.! luH).!t.'l IIIUt,; Ill lin,_• ~o'k(lll'

fh,· JJ\crp:l.!lll hto.~rn ,., flU\\ hmtLed h~ pn.,..,tnp lhfltUf_!flo,IJl /~ ..,nJ ~fllt'l ... mtn .• f"-'rpl·mtH.'tll:tr ma~_:n~o'll~ fic1d H~ mdic:ltcd 1-'t}" cuclc rerrt:n~ho..'Uiur tn 1hc rfjiRI.' Ill lh~ r-J~r. lllh nlol{:flCIIC field B: IS ot ... u~h Mgn tholl 11 hc.·nd... llw hcam m t1lhrct.: lhl0 npp<hltC tn rhat cau).cd by clcctru.- held/:._ It w&ll u_goun uor onl~ Jdh:.,:llh..: IX!<1m 111 oppo~ih: dm:cunn by an 1.1ngk ~l1ul ab\' m.,t..e 11 hl ,·•m\~o·rg..: I•~·IJ

Mvtiou 11} rltr

Clwrxt•(/l~attidt•

in f.'lt·C'ttu· tmrl Mtu:.llt'll<' Firld

267

111C' <~i:IO\\ ly mo\'ing iun' hcing

dencctcd more thon tJtc faMcr ont:s. b) ~In :m~lc The p:'!th uf tht: .. ru\\ -moving mn.s. lhcfl.!fore. imcr~ec:t thn~e: of thl' (;t,te:r IfiLl\ Jilt: tum. ;11 pnlnt L. Thu~ 1f the IO~tnnncm '" prupcrl) lk\I):.Tlc~l. lUll' h;.~\ IOJ: ,,.utl~o: '•llu ..· or q/M l,ut -ih!!htl> u.tru..:nt encqucs ~...an be broug.ht H-l a 'm~le ln~u .. •11 /.on ,1 phomgrJphu: plate. other 1011" \\llh daflcr..-111 vnlue- tllq/M .u\' hmugtu IU ~ fucu .. til t.fiflcrcnt Jlllllll\ on the phvtOg_J.lphic pl:ttc.. So the i",lhlf'C-' nr Ih..: ,,Uih: ~kmcm wluch urc htt\'lllfl 'nml' c h:ugc tJ hm d tl t"erem .unmtL' mn\M'' M "til fo..:u~ <U dlfkrt:nt ~lint " on th.: ph c'hl~n•phu.: plate. Since 1h~ ann,. hann~ ,:1111~ \'~h"' ul rJIM bur nl ~~~~hll) dtlfcrcnl \duclly arc hrnughl lu lu~u' "' .1 pmnt, lll'nt.·~ 1hi' 111~1hnJ '"' cnllcd vchk'll) fnt'U'i:iJtg method. AL'IUitlh for .1 p.ulicubr \'ah1c' ui 'tiM 1ht.• f,teuo;. '' u hn~ not ;a po1nt 'l11U). tor dllkn:n1 \':.tllll" nl q/M. J>hLllugraphtc rt<t:tln.hnt! will be: \CIIC' (I( hoe' 'unilar lu upll~:otl hue:

1Jt)

"J'C'-'ITUIII Due ,,. lim~ \.lllltlanty lhC ..cne.... o l hne.!: ror dtlterem

\'liUl"

ol q!M.

'' called Mn.:t-..-spccln.tm ~nt.J Ihe appar:uus a~ nn ~·h,,~ ..~~trogf";)flh I he ma ..-..'lt(!~ttum ut p.:.nnao.uflll' 'ihu"n 10 Fi.g. 1 11. Gc 72.. Gc 7J etc The rdoll\1.: :lhUndllOL'-1." t"'lf lhC h1•ln('l'l."\ j, ffi\!,l'Urc~o.J frum th~ dcn-;iiiC'\ nl tht: phnlo~rnrhk tm<tg\'' lht>) pmdm. cd

Cunditlun f•,r rncu,inl!

r;K:U\101! l'DU be JcrhcU a_, lolhl\\\ L~t 1h i.'t'll'l<h.•r .ll~·•un u' ~t nllp ul 1un-. ha\'ing 'anu: '"lue tlf 111M hut mn, in)! \\llh Lllrh!rcnt '.:li~• uc ... Ll."t R .tnd t/J h.: the: mean .mglc or dC\'irtu(m b> 1hc clct.:lrl~ ;1nd rn:c~nclK flchh ul,l tlf1 he lh..: tfi'P~~wn angle dm; lO c.:1..:clllt- l1clJ .uul r/lJ)

111..: nmLiililm (,!1 ..ucll \ch-.:it~

he the cnm•crt:,cncc Jn~lt· tlu~ m mat:neuc field II S j, Lh~: linear tli,piJ~:~mt:nl of the inn' .mtl L i\ Lltt: length''' tht•ir r~llllm tlw du..:lm- tidll tF1p '\ 1.! I then. Q; S!L

.\' = I·~.

ql!

2Mu· qE,

=M·' =v·

So. S = .!. -'1-1:. ' L' ;- J 11.Ul 2 Mt•·

Sn fl= C x q/ Mu'] whercQ' - Jl /2) < 1:

(11'

XI]

U.J4)

SJmilarly 1( .\~ i.; the hnear c1tl\pfacl!mt:IH rtnd C .... thl.' len!!th u11hc mal!:nCiir field chen.

~·- ll, ql' ' . - ~ Mt•

fltll

I .. Elcctru: held dtocl

i!rr>

cancelled hy

ln:Jf!llCIIC

iicld

Clft."('l. '"

I C.,

~u.

R;:;ql --

Mr.•

( un<l/) on~

''hen~

r I> :

- N I

:!I

·J nr

tfcfWndin!! •m th e .. 11'1!11g1fl lUtd cli'\tnhlllli m the c:Jn·tr'Ufield .... Nm' thc rnll! uf change ul angular tfl , pl!r"ll11l ''.r.t. \l'h~o<.:ll\ tn ele-ctric ftl•IU:-. i ... fro111 Eq <3 - ~~JJ LUO\ I i11lt ...

,lllll tn;.l~ll~ t h.

.md thai in magnetic field ~~ from l:.qn . <3.-'0J

':,~: =-( AI:.~, ) =_II dO _

ti<P 0 II -- <P

Sn 1.~1

U'i '\Upposc the ckcLric and magttl'liC licld!\ :tcts

:t~

ir they conccntntll'

ill

0 ;md R rcS(X'CL•vdy. From thl! poml f I the beam bcg.an~ en d i\'Crt_!«.: and from the puun R clivcrgcn1 hcafnl'o hcg•n 1n convc•yc. :md le t OH = u :ulcl RL =''·\\'here L i:-; the focus.

Nuw af n1ag:n~lic licld 1s not present. 1hcn ahe dispcr~ion~ l>rOt.iuc\!d hy \!h.:cark fidel ttl u llil\tnnc< f(l + /1) i' ~1\'tn b)' It)+ h) d8. A~ lht' c.h\'erg~nre i<: c:mcelcd h) mugnclk fj~JJ .h..hn~ •• t R. ~o th31the proup of bcouns are broul!hlto a focus at L u1 a ,_IJ,tuMcc /; frnru R Sn th!o! condition nl ft•CU"~IO~ ' ' ~1\'cn h~ Ill+

hJ ,fO ~ bd~

ta e hllh: dl/>ltln: MW: I + olh

T lu:. . 1:-. the t:l.jthUtt•n til., ..u.usht luu: OL drnwn from 0 muling un un}:k ~0 t.lt.'\iu.t~d by the electric tidd tFig_ J.l.SJ Frvm blU (:'L\X) unc can lmtl Lht! m~•' t ronvemcnt po~ition nf the photo~rJplm_ pl.tlL' ro rec.:orJ the focu .. of tlu..• ~.·on\'t'f£CIIt lxtlm.;., When r>:: .J8, h::" i..;. nR ~ Rl

''i1l11he tJin.>t·liun '''tin; hc.uu

fnml Eqn t33N). "t thot)>»llion. <n) at poim G ""<~'~'

photo~rnphtc p l.ll~

can

be pl.tccc.l. un abe hue OL. '\ILh thJt UN::: NO N I!<. the fool of 1hc pt.!tJlCildl~.;uh u drown from R on lh~ hnc 01. AI D. 9 j, hein}! cqu3lto 46 air> ir>hown in Fi!! :\. 14. whil'h ~.·an be 1~1lcn 41$. u pi.nrU t•l rcicrl!ncc. The

photvgr.1plm: p1at~ C('llHIHIIfl!! nl rcf..orl.'m·~· (,'"'II not tmh n.•cdvc th~ trnce of the "Cict'fl!ll !!Wilfl of H)I\S n f the same \ol1uc t\l q/,\1, bul ubo be an ftair lt'CUS rt,r mn-. of dtffl!h~nt \'t1lu~" ul (t/M mer l r.UI!!t:" rJ 1g. ~' 15).

th"

po1m

:\,13 Bain Brid~:e's Mass Spectrograph Titc 'ch~.·ua,llh. JJdfr.tm ul Bu1n hnd~c":-. nm'~+"''Pl'i..'lrogmph '" ,,, <th\l\\11 lfl Fig '

I (l, tM,

.I ...(lUll.;:

rw .. llt \

1.'

lofl\. til' dtotl'f:l' q. !>iiU.Ih!tl "'"'* 1\ lC lhC' ,Jit sI· Thl.'

• ••

-:- ~

.....:.__ s

,.,

---

. . - \'t:h"'-il~ ""'"''h~

b Plrur<

..-i~.

3. 16

Unin-Brld.:t•'' ma."S !-. (Jl'ctru~r.Jilh

itHl' und\."r 'tut.ly p~~ 1hrough the ' ' h"Sl :1nd Sl,111d nuwl! Llm\n HIIO the c lectn..: t1dtl (E\J hci \\CCII l\Ht pl;llc,'- P 1 nod 11 2. In lhal ICP,Ul!l thcrt.: i" ;&1\{1 UHti_:nclu,; licllluf imJuca cnn ~~- doucd :tn::t, t>erpcmJa ..·ular w Ihe rtllt>er. Thu' th~ ltm' eruct in a J't"~Wn uf t:n.~s$td ti\."Clfl~ nnd nl.Jg,lclh. ficl\h, .ml11l lur~c .ILHn!! h) hnth

lidll' nJI thl" it)ll-.

Ul\

t.'\IU,tl then

thw.c ion)!. whm.c veh)Lil)'• t :: L J I(. onl~ lhl!'} p.l''- unclt..'\Hilcdl~· throu:h lhi' rt.•gmu, but iun~ \\tth utiH.'f \'clocitlt.:.., 111!.! ''*'PJlt'tJ h)' the ..;Jit ,.,. 1huo;, allth~ inn"'' hkh -.!merge from S; hi\\'C Ihe sum~\ d~ll) t•. Thh n:gton ut ~.:n'~"'~ll field j, C~clled II ul'lodl\' Mlntor Below s;, the IIlii .. cnll:r ... regiOn or oHIOibC:I m.tg.n!!Lh: fi\."M R •. rcrpcmficulal lt I tht." p:tpi..!1 but whh nu l'IC'4.:ln\. f1ch.l Ill"!'\! IOih ll'lfl\ !o! in .t dn.:ul.t.r pi.ith of r.tdiu' R 'uch rholt i.e

J1•qt• = A/r•!IR

[ i

M = !!:._qR = H H',l_/1 I'

--- --

R ·,....M

,\.,_,..,unlnlg c.4ual ch:qtc" un c:1c.h ion, ~mcc II ;md r: art.: ,;un~ lnr ;1llum~ '\U mtl"'\.l"~ uf the ion' ._z·c: prupmuonJIIrl the raJ11 nt 1heir patti, ..:;o ahe l(lll\ t1r

tht:

~hftnl!nl l'•ulopt:'

un.: t..Hn\·crgcd 111 diffcrrnl pmnh on lhc plwlt,p:raplm: pb.tc t•f rhc i"'ttlupc' j, 111(';l'•tm•d frnm lhl• dt•n,illl''> uf lilt.: phuw~t.tptllL amag~' rhc_y pru~.hh.:cLI I-1~Uh.' .~I~ -h~.-•w' th~ 111•"" 'l'lt.'~.- IIU111 ,,r j;~rriMUIUtn, GE 70, Gt." 12. Gl· ~~- Gt.• 74. GL· 'h

Ttw 'dt:th·.:

~thuntl.tm;.,•

I'ROULEMS I.

\n U·p:u1tCk \.'ll lcn; 111 ti i iHITW)gCneOU~ rn.i£11~'11\.' IICM rcr--pendiCular II) II' \CIOCIIy.

n~ an}1ulllr mnmtmmn or n·11;amde ''nnw I 1 ~ · IU l! kp m.!/'L''-' ·n,c mducuon ~11 1Ua£nCtk lidcJt..: n_c)25 \Vh/m! t..:mJ 1-(J· 1tl lhl" p;1rtadc Cii\Cn lJloll Ihi." llla)." "' U•p<:Utlde _;; h.t!g )C If) ,, .. ~ umJ t:h.u~c ••I IL rnntdc c ' ~ < Cuulumb

w ,..

J\ np_uf.u II'Omcmum

=L c

llfl .. u

• 1..-n ~ I o-!J' kf!. mJ/..('\' ... /u

\\hen; u =- 3.U£u·.ar "d~lly = ulr • 8 qhn 8 mngrc."tu: mdut•tt~n • 0.025 Whim.: fJ: Ch.1l]:!C uf O·JM111dC:: ).11>' t() Ht (' m = rna~,. nt cqurhcle = 6.M< X to • · l.f h•V

=- I rt X It) 1"' r

= ~h.1ulefl1 -~1

H\C:Il l ~l

MtJIItm o(llu ('hur,twd Pm tidt .., Elt'4:lrit.• cmd /1/tJJ.:Ilt'tit' Fitld ;\n_!;ult~r fl\t~nh•nlmn : L: I

; ! "'

w :: 1.33 x IU .!.! kV rw'/~,.CC

I 11A IH".:.:

111

.1.5

··•

X~.~ X I__Q

t.,f\t( vlfl;~

wmt\ x w 1" J ~ ·~~>7.'7 c\' 2-. hn ..1 9~h.nnm t!l It l; m r.k.im' Md fn.'ll tll l"l(llC1l11:1l llrphctl ''I ~X"' IU II.t., ''"'·•in 1h~ ,,.Juc 111 111Judml1 nl m:~n.:t11. hdd h_lf \)o l"; hrt\111111 ' olt(d~·• .nrun "' 7

t'fltiHil'l >~nil ll.:nn: ~,;.tkuhtl~ lhe 11111' \~nt: l ~) u l l h ~ J~~rkr.ttt'll pruhtn\. rn1h1U.!>

=- l.(,7

Ill l" 1-.jt. d1M~~

rr\)ll\R~ = I

h cqUL'IICY of tlSl'IIIUliUU :

b X

,,,,

ICI

\1,,..., \!I

Cuul,,mh

so 1 _r.m

tJ = .! /fll mht )o lll~ \- I (J7 I t\ X IU ,..

R • .! • 1 lol...: 138 : I)()..$[\

lo(

w ...

l tJ I

11 = fi'JUt<i wh/rn~

=r t _ !0 •KJ.l5)' 11.6 • 10 1 '-~151 •

Z:..t67,.,l0 •.

l r \ ' = J.C• >. J0 111 J

f'-=- (l 07~'1-N .., 10 11 Jm1lc ~ II OJX " 10' e\

·' · t.tlt\11 Cfcil.llllll U\l.dl!f\lh!ll h> 11 (lOf('llllul t lt ff 1d I(IC)I} \ llll'i C'llh-h ott m :hl iUU!.IC\ mlu •• umft•nu nu~ n~t n: ltciJ lll Uldu~:U••Jl 1 1(I'< 10 WhJm· 1- ,,,1 11 Ih.: r.1 hlt.. col tlw ~J«tr••n 11'il0it"t:U,ll) '" tbe m~,pn"H~ lleld 'II) Tt"k~ •mgubr lll"nll.'nltun nl the t lcl'tmn

~1.1\' 1)1 dcdrun • 1J_I "' tU " k~ Chat'.!C ''' dC\·unn = 1 () '< 10-IY C'ouJornh llut.• tu dw Jl 11 \ dcclnm

t'l

occ:ch:Jatcll

Ill l)ue ttl tmn,.\CN: ma~nclll: tidt.l IJ d ectJuu uiO\l'"' HI u lllt.u1.u po~th uf ra..Lu\ k

Su mu1JH. =- lll"\ wh~r.:- IJ =

llli.igl!<.'th.

flciJ = I.IY v lU 1 Wt-1/m:

m = rn:.o;.q-.1 cl~~:uon-=- 9. 1 x W " ~g

\': p.t.J. ; JOOO \llll ,_. • ~.:h.lfl!i!' ol cle~.;tmu -=- I .6 x lU

l•mm f I J ' '

= , !r:VIm ::

1 '' ("

1~ .752 x til" m/~-.;

fl - ),1 x IU

X IS.752 .-.Ill"; tWC.2 x 1{1. • I.(•" IU ,.,

t. ·~~.,.

l(t ' 01 ::o

H'H'•~nn

= mR w = mR 1,'1/o( - m1•R-:-- I ~Q'l~ .I)Jl x 10 ~, L~ m!/~t~

... An dcdJtln

111(1\fUJ;

hrm"ltll.tlh wuh a \ducil) n t I 7

\\'On;at untltl(ffi d~.·. Int. twhltll \ lA

IU'"

\l!IL~fn('f(;(

tf)~ m/\4.'\: ~I'IICI'

o11.1IR}! duv.l)\\dllt'lo

ltn~l

Ill,; \~ltt .. ~l th,rl.~~~•n..:ut ul til• d\.:\lh•n m lh..: clcc..tm.: Jtdl.l.tl .a tum· Yolh·n '" IMrvnnt:,l J,,r a..·('mo...•nt i' ''"' FtnJ .tbo th<: maa;nuud~ luhl dtr..·~.·thm ••I llw ma~llt.'IH. lu:ltl r~ttun~d h• lll'Uiruhtc lht .. \CIIrcal d t-.rtlac-cmcnt

Ch;t.l}:o,' nl dn:rrun ~ I h >< W ''t ~·h1':-. 1•1 ..:kdw11 = '' I x I (I ' 1 ..._~ t· :

I '1

'.4 ..

tn tuht•.._

tn 1 \/m

=•·

l")i,1an ~.·c u-..,,.:l!cti:.Jun~

:... 1U

= 0 17ft X IH

y.,..\1 .. 1'\~ the rtmc (I 17t. x 10 • <;;CC 1'

\ = 11.2 ,,,,. fi

..,~

lrlf =

I (\K IIJ

1 "

--,-.-,-1( Jll'A\( ,,

If: .. 11~'-''i'\T

l(t 11'xt0

IOJ = 0.5')78 )( 101" tn/'('o, ..

17flX 10-)~=9::(, .. 10 tm

'I'""

l h\." tklko...·tt••n nlth~.· ~Ju,- 111 d\'t.:lno, ncult.alu..:tl .,, lla.J.}'lh.'tu.: ltcltJ "' h..:u d~

lidJ ''

\11,(1,

m flu~ -.·.u, t

: R ,.,.,. J; : f_ , /t

H • ;--' x In'-;;.!,., W' :;;:(1(.1(}2Wh/m:l 1 x Ill lllol}'111hhk ttl olllllltt•llm.a~m:ll\.. IteM j ~ fUKl2 Wb/m· IUhl itJ. tiH'C'di\>P \\ tlll'l( rcrptndi~;uh" '~' tl~;XIrl\. hdd ·'' w~ll as ~rprnd~rul:.r 10 the muu,•n ''' th"· dcclron Sm~~ l~rtl..:ul d..:l."tn..: l1dd J._, 1-. "..:Un!t duwn"A :udJ., M' B: \\Ill h..· "P"'·••·d 1 5 . l11c r.nJm, ul .t ::~dnltun ,Jn" j, I m .unJ Ihe .J)lplictltU;tl)llCiic lu:ltl •~ U 'i Wt'm1

h j, ~~ ~ 1H .u4dCt.lh' pruhUl' C.tkul,u..: lht: fn:c1 tlf u:.dllltlin~t \llh.t~e u~o...'llt.:tl 111 n11uru:un rc\flm111\.'~ .u:cclcmtmn \\'tun IS the m-;unwm cn~r~;,y Utllum:•l tn the JHi!IVn Ul

£'\'

\1.1" ,,f Jlhilun ~ I h7 r Ill ' 1 l..~ ('ltai!!C .,, J110l1111 Ri.':-(.lnano...·~

,, X I 0 , ..

fr-.•,p.ao...'l1') = 11 ::.

,, =

fltJ~Itm

U5 )( I (,A 10 1" 2 X 1 IJ X I 67 )1. t0·11

n • HI

10" Ill= 7.6.' Mll1

\ l.nunum cuc:rt::• nf IIFUI• •U ::-£: lrq;k!J~m

til,,

J·

I I h ~ I ll

(1J

II,!)

~" l b7Y I 0~

u I'Ht1 X IU

II I

II I Ji'7.: 1n• ~V.: I I ~1 f\k\ f.( Jl.&ltldt \1. .lh dk&I#,C t~ )( It) t• i.ttUIP.l\~ .1nJ IIIJ~\ h. h.\ )( lfl 1f t lhj«I('J ''"'' .. luhu,·n.t tnaj!l'k·clc: HeM''' I "\\ l\.'1n 1 "llh \tlucll~ 1 :h~ UrtuJ, t.at Culc."'UI..U: lbt 1\JI~o-~ ttD l..l'lc J"'f1l..:k •ttl ( :iJ,ul..slC 1~ I~Uiodl~ lin~ an.l tw-n.. ~ :rrV~~run..:r ltn.ltk'l1ol-~

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I l•~t ul\h~

X '

2wU I I : J.!f/l/ m/q =- - -\. 1 ""711~

1·-:~tJI,."fll.

IU • \,!,. Ill 1...,

f\.C\1\ )(

x tn "''' u '1•111' 1ft• II

'=1fT= I

\11-{1

7. In .a '-~duuun the IJ~o.~UCDI. of the ()S('illlll(lf '' 11 • HI U1 lo~h:akubtc lh<' lltn .Jtn,lh' /loo~t ,.h,,h \ \,lull•lQ ,.,1) ~\iU.t\ lht' tc-.c"""'"'"' h..- 1•11•fnn fH C"olkul.alc lhl• t: lk'Tl,l ttl II•· l'ftll••fl tt..-,uu d t.bc r-.Ml1u.. t.•llho t. \dnCIHII ... II 'i Ill 1\; l , ..t...ul;dl" th.: cnC'f!:,:O tuf the u '••rttt.k.Gt'cnthct.:hMgcur tt ll.i.Jh..l~ •2X I t.x lfl 1" ( . ,....... , ,., 0 r .• nu;k hhi" l( ki:.

w .:·

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1 "

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111'1

R•• c fl 7~~~ Wblm'

4fli~7)~ t 1.6>' 10 1 r· .U\11 2~ 1 .67~

Ill

IK75 )( JO 1' J 7 J.! \1cV

,, /l•

= lxq. ""'·

• I.S7) '.'b/nr

Ill ~· t.~

ch:•r~e 11r u-p.mu:k = ! x I h., 10 1'' m" = 111:.13:- HI C1 f}IUhd,: = 6,(H4 -< W ~ 1 ~g

q,.

II~

II '>71)

>-l

I!I ,. ) fU S)'

('8 _. 107~~·

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ft. A nu'cll ht>;utttfll'L

tii'loCI'I

1h.tl. cLtrft' ul l"'co.:unn :: I ,h

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m I+ \

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Itt\

:; \

·,J

lltJ \ "'

R =- I II \

~~~ t 'I

- 11 ll'i

I II.OS

1 '-' (t•l~ 'I~

.. 10

n ,. 2f)IX)(')

I (• X 10

1' 1

Ill

=.., S x Ill

!>11 lht: hnc.u ~potr.JIIu n hcl\\ I!Cn llh·na ~HI nmunon b.•un \I:Jr)' \\ .\ll ,lft\"1 lr,H ~· hill~ "~>I!Ulh."lf\: U fo.l l

r••lh

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Elc~trun., .u:•.:eh.:ratc:~l

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·"

., \ 1': ~ ,., l'i~.

3.17

ei~LtrU\t .ti i C f1..11.u.Mug

cffh:1. at nJl.lk(':' !Ill <mi=IC I S~ \\ tlh the nunn.tl It, the p.d 1\\:t\~cc:n theM": l\1.0 tc:t:wn

m h.:rr.K!c

,,f the ..~ 1\\U rqpon. Find lhc

\·, :. ::wn v I ;:;(!()'ll I

;45'

t·~ a-1

"nt wa1

1 \' \ 1

Sin~:c the .:ncr¥.)

lll

det.taun •~ 1~ un· .. ; .:\"

s~,

,. , : -=, :2c)o ~ .. m .J:'i

..j\~, =- 17 l2 \Oit.., $,, lht r.d

bl!t~-.·c:n lh~!~ lWO

C'CJ:hln h

\' 1 ; "-l").')X

\ :

li)tl \'Hib

IU. A 4:haf¥~ll \\,llcrUrop '" JU..'l flL~.JIUI~ lll.J utuiVJtu d~t'lflt.. I kid o(250 Vhn ..inJ tlll: \:h;u~c em il Given th.tt

R.uhu\ ul the drup .;; W Ht Dcn'll) ut wutl."r • IU' l..t:fm' Wbcntht: duu;::cd \\Uitt dfup •~ JW ..t lh-•.thu,: 10th(,;' dtl.ln-. ti<'ld then the: \'-flghl nf'thc " '-'ICr drop'' Ct11.1Mtt.!r-1ul.,n('('cl h~ tit.~ lnrl.!c acaang ••n il .bu.• II.) clc..:tric l tchJ

"' Nm\

1- IU:J~:\ '-''

Un:

\\,;tit::

,,r

1111: ;

"'v~-1

llrop

l.!t

.:}r.lltl

)(

'i' •

l>cR:c-11~

Thu' "'~t~ht ''' 11'1~ \L,It~r dl\l('l

"'J.I = Sv 111 b;tll.ll1\.:t' wut.hlttlU.

4ntln

m~: ~ 1nll0 "t' 4(=

O.IM

, II) ' ..

'l.~

·'

)li

IU ,...y g;;;;;; tl >. 2511 1

trJ ~I('

11. A 'm~le i<uu~ Gc .1tum cnh.'r"' .a U.unbmJ~c l)la:-..' "'-IK'~U<•~•.at>h \\Jih "WIO!.:II) S x tO' mh.• C:at~.·ulot~ lhc rndu ,,, lh~ p1uh.; toll~'"'~'l hy l"-0 mu'1 :shund!lnt '"ntuJlC-"' "r m:.""-.c"' 11 :md 7-& "hcu 1he nt.t,t!llt!th: nu, tlcn.,tl)' ,, n 1 wwm' Cnkul.llt.' .:tl~lthe l mt.•~u 'ep;J.rutlun t.ll lhc lml' .. uu phuto~raphu.: !'late (ur thow I\1.0 i~OIOpt~

'' • 5 x l(t~ m~ 8: Ol Wl\/nf M r-= ~'l:t'!\ ul .. m••lt luultt•t.l nt '", ~ M n :: i2 ~ I n nLu

~tluan

.,?! I u·':-r J.g

f).U..),.

'' r!:: ll9~ll \f t<;1'

'I(

1U ,_kg

li-

= lkt·

\( ,~t·

kr - 1 2-'4~ x IU m H,, = I

24~

U r:

~If

H •

~--·

N..

\1 .,:

R,! ll,,=f17hm

7,_-,,

R,.

\u\' lhii.'IHk"•ll "-'f'tfJIUm uf l\\U line.. on phuhl~·rnphk fll.lh'l\ 2tR

R.,...)

nun lit

l l. lu " ( H I kn~lh ••I 11-...: "l'l)h..:d tna~netJc field" 40 t.:n•••"'"J11h~.: ·''''·the d.,•.,f'kl' 111 lhC' "'11.·,•n hull\ fk' t'n'll ul lfk" m.tgnelt\:. litld h U l.u ( ,,J,ul,lt~o.•111~ llu\ llcrt,ll) /1 r...·.lull~·,lll• ph.Ju.-: .at.l-.·ll"'uvn,,f I ~ouhm It~ ~~.h...:utl .,u.,k '''''·'~~ i .. wno h•h

taO!-~,,.

'·''//"'"'

' _,, .

1/.;;;[)/8 ;.,"

1•'\Uil./1:0:\ +U!:-0:\•1"'" Ill 11n

~m~

111

I-,-

~ ·J l x.IH V l.bx Ill

IIIH

• II l~~ X (j(j~

u • hC. '' •

,, , ''

1H •· "lt/tn!

tJ. \ndc.tnonh ..k~-l.'l~r.lltr:dlhmu~bllpiJ u l) or,U\HII .. 11u,~:l~'\.ln•ni,Uije...1~101H.t tJ.IU\\lT'l:ci"IUi. fid.JI'tnlilll.uJb) lbrapplu.·,tUI.lOU( :.ht~h IU .. f\-UJ tlf ~.illd pl.ih.'lo uf lnt ..lh II h 111 .u. II uu .qvrt. \ ~ t\ pU...C-'d o111 '\llun .&Jl.Ullrumlht: c.:rnlft'Pl d11..· <lf'rltal dn u~ hdJ '''" ".dndolk f.t1 "'"'""-It) '" 11-..~ d:, tn-.. n-.;,xhmg lhL" fk-kl thJ --.-xct..c ..ttc'IH Juc- ··~·~CJnj! rtC'kl fd FanaJ \t"lt \.lh .MIMnn.l "'' ddln.1Jnr IM-kfhf• .m•k ul '-":H"'\.U•fl.. It") tklla..'"tiC'IH un !he: ...._-,a;:n iJnJ Ill drtla:bun 'oCINH\ll\ fi:oo/,u,,,

> I'

ro~l I', • \ .. ~ ~. • 7 20 X IU'" tn/~

"' I·.· \

~ ~lh.,.,

·'

thJ "' =.!... -'

tt. I •. •

u I • ,, '

tJI l.&nH=

' 1•

1c.-1, •/h.• ,. th

, I

111

J x toe

tJ eLm •

nn m

t: 11

I:~HV. \';2IJV /•llhm c/:-. I ..:m f) ;;; "'0nnl

m/-.cc~

w•· m/-,« ~:: :n J7 1',

QliESTIONS IJc ..(flbc the con..tmdtun.

2 (it\c the

\Hll~ lfl!!

t.:OII"'-CUC1i{tn. \\(ll l..llli!

.Uid u"' ul C R 0

:tn,l thcnt) o l lll.:)·dutrun Ohuuu.ut l'\l,n:,,n)u

(nr the cnt.:lt) tlllht• p.trr.dc' ..:mtrgm~ tfl"~m 1>~:'4.nhc lhc ~.'ftt:d Ill lllol}!OClU,

Jfdlf, ttll

•' ~n-h•imt•

o* IIIII\ 111:,! \.lt.U~i,;

J'·111h,Jc ( il\c oil\~

\tilt:'

1t!)(l l u.~.ll iun

.l. l.k~rtb<

ul tim. d tn:t th...• :lf\.'1.:1 l'r .l

~~~n~tt:"ubr ..·l~~.·tt,.;

lie lei \'n the m,,,,f\n ,,, ~;ho• rt~cd hne;JI tll-Jko.;;tlllll 'lltuw tliU1 lhl' ~mrttL <"nt:~)' ttl tht' pilrltllr 111 1t t ~rlttlmnl' tmlrpt'mk"nl 11f tJu: ('l:mu:JC~ l).:n•e IIW: IIJlJ'UlJ1J1Uh.' I U IIUU!a lolf

\ nlt.~gc .1JJphcd

1 1\tt d<Xtrnn bc,ml P."'c" thhtll)!h .1 m1tl!ttCIK ftdt.l 11! :! 10 Wbflu· .md .111 ckt..IU~ fidd J ·l x 10~ , /m. bvth <'I~Hn~ .. unull.meuu'h .tt lhc , ,uuc ~xnnt If the

Jl.llh tlf the du.;tmn h'tu;u n ) uuJI."\IIIh:d ..:;at\uluh: lht: :-.f"Ct:..J t•t •he di.XIh•ll'· It lh ~ d~o"' lnt: li d\.11~ rcru~,".:d. \\ ht:n ""'11 No rmliu~ ,,f Ihe -.•lt\.'Wln·.., p;.,1h·1 m:IJ.Ux 10' 1 ~£ • .-: l,n)c,_ 10 '''C 7. t\n Eli.oc:tron u nc:ed:~rutcd throu!!h ~ P•'•cnual ,hueu!n c~ J)U ' ''''''· Tlu' eh:o('ltun , .. lnJCl'te.d tlllll u ununrmlrJn(vc:r"C ch:cnu: hl'ld . pwducet.ll'ly t he applu;auon ul .W mil. lu a pan nt par.illd pl.ah:' 111 kn~lh ltl t.:m t".ilt'UiiiiC' 1hc t.kfdt:ti\llt J•wdu-:ca.l in 1lic d«Uon path 1lu..: llt U olfl\\l.' f ..C ck~.:tm: lldd em .J ..t: IC('11 Jll.u.:clf ,11 ~() llU <t~p.Ut from •he ..:cnm.· til upplu!tl dcolrio liclll ~ O..· ..cu lx: the pnnciph: u l dc\·tw:.Wii~o .wd WoJ~Ut:llJM.aUt. h 'lt.t.l'-lllt;. lk;.-.nlx lhCII <~pphcuUQn an ~omc uhtl \lln.:•ll IJ l>hc u '~ ,.\,tn• :uu.l Hamhmtg•• tnt!"'" "I'C'dru~tuph Wh.11 ' ' lht· lhf,' tU \C h ~ il y o.elet. h,r m mil<~..\ ~o-pr(lm}!r.!ph W Oo,_•tahlc: ion1:locd Cic At~1 111 enter' m all::u nhml~t' tnu)' "f'I\:Lth•£r.trh \\ llh \dOl"'IY n '\ )( to' nl /'t(:(. C":1lct1haU; lhC l!l4.illl" 11r th._: JUt h.. '!U 1.1 11tJ (ic ff, " hen Ih.: ma~t..:lt~ 111tl11~·1utn '" H.01 Wtl11W II An ch."\:lwn ~lth hvu /uniJl "0.:11' 11~ ll, '"' lujcdeJ 1\dmi.JI h.t ;.~n ~~ t~.•.,• tn~o· fidd .n

nr (;._:

thl!' Y-ditXOC:II\'\Il ~el

ur bi!- 1 \\C~·n tWU p;u.tllo.!l ~·mnlUC hlf JliUI~''· ( "ah:uiUII! \l.ll lll.'ltl

a.:.-."C.'IJ.ruuon u,, the 11110'11 uuM.•t.lhe \COI~.tl •dill..' II~ 11. lh•·lt~o•l1c..:taun Upn.khtt·t•d tn dcdmn p~h an~ltt' \Crtu.:.tJ dt,rl.1\'(lnl.hl \ I! tf cncr~y t l( IM:CcicrJI<' prmnn in l)dlltrun "" I (I MeV .uuJ H•llagl! .taJplJcd hct\\.el'n tht Jcc) t3- t(IO(I \Olt". t!Jco huv. l!la..Q\ rot.allon .t pmh1n v.tll rn;1J..c hi .u:hit."\1.! lhi' CllCI'g) ·l1\ "-'U1llC lhoU pruluth ;U~ JU"I 11 \lhx.IUi.:t:~ In IU.(I dC\."' Cit\'en ma'~ o l pmh,n • l 67" HI !'t 1..~ .1nd ch:~rJ!... I flY. W 1'' c

•wluu,.,,

l.n tl.tal \Ch.-..:U} :: t' 1

f'm;tl \G l11oCI1) r l'nu\

(J) II Illl CI C'i) 'l

mu1: ~ t.JU 11:

I m ..l l:ncrt:)

V,i~· ltj

1,\•.

X lU ,-. )( H)t)U · ·

~·

•

..,_ :

If•• Ill"

t uu•n,..

= I .H 1\k \

=~ - UNKI 1H

t·,~....

IOI.lt•f

l!n...n

~Ut:!

t•,

,;! l't

fh u,), 101ul nurnbtt t\l wtJIH'II I t.l••nc h~ P MtUI1 tu !1Cht1.1\ •= \dtM:11} 32 lillie> fnmt one dl!c- to otha:r

Sl'l number (If n>t.lllt~nAic.: hl .1-.:h1<VC I MeV ~.·n~·•ln 1..: ...

''nw• frolll 1•1 i•.

i, • lh

4 Quantum P hysics and Schrodinger Wave Equation Q UANT UM PHYSI CS ~. 1

Int roduction

11lc mouon ol a

p:lrllcl~ \\h1cll

<·nn be ob,\Cf\'C'd Uircctl\' u1

thu1u~h

mJctchCOJX.'

·;m !'leo t..'X.Jll:mh.'d h) cJ;'"''ca1 m.:..:hamcs but in the- ca'ie or Jtmm~ p:mtdt' like ..:ll!t:tmn. J'TOWn da~:.li:ul mcchan 1 ~S fa1led m do St.), ,\(Cnrtllng tod.,.,.,,\·••t mc~.:htiOlC!'!o, the r.tdra11on ofall, .. m c lcn!.!.th' '" COI11Jnuou' lrnrn hydrflt:cn mom \\hcrca.;; c.'peruncntally It ~~ Clh~~.·ncd th111 tht' 'l>l'\:trum 01 hydm!!t.·n auun l"l m ' ''L' oJ d J.;crclc tquamizetl) set of l•nc:s .liH.IIIll'rc: ~111: ~.hrfcr~m 'Cll\.':. h~-.· Lymcn ~t:rh:', i;(~Jirucr !'Cries, e tc. l11us classtral UlCOI')' hukd 1u txplain tht! d1"<!r~h: ~jl\."...:lrum or h~ J mgc11 ~•lorn. whu.:hcnn heexpl~••ned b' 'luanl••n• 1hcory. ~.2

Q uantum Theor·~· or Radiation

Vuamum 1hcnry nl r;1d1a11on wa~ h rs1 proposed hy Ma\ I'Lmd m 1901 m dHm~o.·;,·ft~ln \\ 11h lilt.' I m.d Jllthal io u .. ~o.•mittcO 1rom a hlm:k bodv I '"''\!Ill ~\h:ndcJ 1h1:o.. 10 I •m.; to ,~,\·er o~ll iJ\.hntH>Ih m c l udtn~ hgh1 ray!'., )'ra) ~. ch. Th\! :o..lud) crl lfl\.' n:thm: ~)I r.nlmlmn "·'-l' unganally mudc 10 connc:l'tlon \\ 11h 1hc n.uun· o l hght uud lu•" 11 ll.a\l."llc,l lnm ouc poull h) ;wulh.:r In 'h' ~ t:nmu;t.:llon. ' cwwn Ph""~pt•«:d CufJ'U\.~Ubr llu.:••ry IOw~ud~ Ihe t!Utl or l71h CCIIIIIry, ......~,;unhng (II wlnth hl!hl C(lll'l"'' ot mmut: l:l!Oiol mcw1ng elas11c parucle:-. nf ~mJ11 n1.1s..' \7;tlled oa:\. urpust•lc' Hu1th\.' phcl cUill\!1l8t)f 10tcrfe1ent.:e, thffntt:lmn. pufm1'ah'm t:Cc.: l'ouhl nfll he '-"\pl.tincd ••n the b;.c,IS of corpuscular thCOI) . So at "u.' 'upCr!<lh~ad ctJ hy

I Itt)'~"'''''""" I henry nl h[thl. where il i• con<1der lhollighllr.IVCI' m lho lnnn in .1 h~·pulhc l lt:~ilnh.:dium called ··IItrr 1-luy}:;ctl''\ \\ot\~ th..:~n ~ nf light

~,r \\,1\l''

' ttt.:Ct''-'1Ull) C"\pl.ttnl'd !h e phcnnnlt!llJ (}( intcrfcrt!llCC. lhffr.a~.4110 1L JllJIMI\.UIU10, Th1' tlleur) \\'!." ful uwcil Ill I g(-.4 h} M!I :CWCII'~ ch.·clrunmgru.:l lCIhem)'· But

t."lt.'

.. u l l ~crt:nn Hth..•r c,,,._.runcntul tact:t. t.".g. phuto-electn~ effect. Cnmptum effect. cmi~o;;ion

.mJ .lb-..tHTHk•n HI light t•lc. which coultJ nnt he L...\pl:mh:~llllllh,• ha~i-. ''' .tt-..1\c mcnllmh:d thu•ric... that gave hinh ll"l tl1e 4u<tntum 1ltcu1~ 11f 1i~ln

Thl' Quunlization Enl'r J,:y In 1901 ~h•x Plnncl v.hih.~ ::.tui..lym!! bluck b<x.ly rndhtttOib. Jmd .:omc to the

..:onclu!-!ion 1hm tht.! ttb:'l..- ,rptiUn ur cnu~"'llHI c._tf thcrnml energy, ... IWI :t cvntinuou!'llfOCC!)'i. a' lik.: "Itt'''"' til henry hut t :t~e... pl;tce Jn dhcrctc :mlounl.s.. He :.h~urucd th~t nmncr " '"mpu...:d uf "' large number nf o'c1113lln~ partH.:Ic~. c•rch l.IO 'ibr;tll! willt :. dtar.u.:h·ri,lll' t rt."tlucnl'} While accnrdmg to lht.• cl,,,,,.:.a1 1h.:w~

the p~Lnkh.•' can h .l\l' .my \',Jiuc nl fr~c.1ucnt"y No" lhC'-C .uomk {hdl l.tmro. m.l) not .;mit 01 atNnh ouly .unount of crh.'r}!y tr. but onl)• ccruun nmnunt of crh:rg•c .. du·, ,cn frnru a ..,ct. *"-'lnu.·cl h)'

'"'u"'"

[!C~ ,/,I'. n =- I. 2. l.

14 II

when: n 1~ the 4lhtn1Uit numhcr II th~ Pl.tnck·s COibHtnl. fir,lllmc lflln'l(lm.:cli 111 phy~ic,,

and \'the frcqucnC} o( O'iC!II.ttOf Thus w~ c;111 SJty lh: ~:ncrgy ul ;m awmu.: U'iCilbtor " l~ Ultntut:tl :.md thili tltl.' 101eger " 1:- cnlle\llh~ qum1mm nmubt1r In ca~c ol hJf)!C·M.'Itlc o.;.~,·,lknor, !!U,:h ~·~ n !!Wingmg ~ndulum. l'Ur dad~ t:'<pcncncc '"t!JlC'I' (hat u P'-'mlulum ~:an thCtllute with nn) rea'\ntl:-thlc lul.tl cucrgy and urn only w 1h 'otnc Ui...cn:te l!'ncrgh:s 11th h: lxc;m:,c trk11on c.tu'~' Ihe pendulum umplhut.Je to llr·\.'~1). ~(.l th~ Clll!r'g)' Jl)t....;!p:tltd in ,I fk-"1 fcCil)' cnntHUJOU\ wny and not m JUmp.. <\(lually JUIIlP' .trc: thf!re. lull the~ arc!' JU!.t 1uu ..m~tll lnt u' to dctcd (.!Jr .mlm'l Jltnu, mu.H m:n. t ll'ttll ..-Jas:rit'fll th,·on· m tilt· 1111111 ,,,

Jur,-:c quam11m numhrr. ''''•·n n -; c-t Ft)llowm!! Pl:lll(~·, 1<k01 m 1 90~ hn,h:tn ah1.1 'luanl ill.'d the r:u.Jmnt .:lh.'fl!~ uf light h) pH,tul.ttiul! tkn h 1 Light enc1g~ '' 11111 cuu11t:d (nnlinuu:-..1)' btu ltttcmuincntl). h>· tndi\·a.. hll· J ITlOUI of i.adtunt cni.'~Y whu:h 1~ C'<~lletl a> '<tunmn'. (•i)

l11¢'c

JIIWitlft.S

t~u.mtu

1 ... ,cl in .. p.i-.:~ 111 lht: fonn ol bundle...

~1r p:.td;.ct~

'ailed

\\htcb ~.tn") ~ d.:finHc .mwunl uf t.:ncr~) The cut.:l~) \!.larned h)' \.".tdt

phlHUn j, g.t \'CII h~

whcrl!

h the ln..·.qucn.·, uJ r;•chauun

Oh,·iousl) !he rholun' or qunmn of high frc<lll~ncy y-my. X-ray. h>'< l:~r~< umuunl nl' ctwtt~ y,Ju·n·~"lo" frc,,u~n4.:~ pht,lon or rudi(, w~avc... huw t.'Oillllar~h d~

lcsJ- amount of cnl'1}t)

4.3

Photo-E lectric EN'ec t

Photo-clcctnt: t'ffccta~.m c:\.unpl\· of u ruthauon maucr interaCliOO. The emJ:,:>tun nr electron-; trom u metal ...urrm:c. whl"ll ch:<.:lrc'>m;•gm:lic radiatnm ,._, l!l(;l(lcfll upon 11. " c.~allcd "t#uro rlnttrc- ''mtuirm'' rtnJ lhe effect •~ coiled "()/mw· rlr<·tric tif,.cl' The cmiucd elecrron~ .tre called "'plwr,..d~unnu'. The !Nnu theof) afpliotu dt•nnc 1)/ft• tt.t l)u_, qufJnmm tlt~Of)', whcrr qtumlf:r<l ammm1 of tnrrgy (ln•J i{ ahwrbrd b\' the mr-tul \utfm:t• fmm mcidl'lrl pJunnn, mul J.:il't ' \ 4

nw: Ut Jlu· ~miHIOII oj 1f1r J'lmtwdt·ctrmr<r

This phcnulll~nou \.a~ tin..t ulhcn.cd hy Hcr11.. \\hen uhra\'illlctllght faJh un z.inc plate. Arter\\ ardl\ R.A Milliken ill\e.\liJ:!nlcd ( Jt>68- l iJ53 J the dfe..:l "uh .number of .tlk..tli mctab fWCr .1 '-'ide r.angc O( light rrequencJc., .and WU..~ gh1(!R thr Noool Prl>" In 1'113.

or J'hoto-clec tric Effccl 1(1 SIUdy tlhOI<>"'Iennc <fl e<:l. Li~ht v loll~ on :1 mc1~ l ~ud ;tC'(" t and rt the frcqt ct.:HC} I' Jngh l.}nnngh. lhe

E>:J)Crim~nt::tl Vcrlfie~.IIIOn

Fl~llre 4.1 <hows the t)piCal arparaiUS used

of I R"4.( UCIH:y

h ~ lu '' 111 '-'JCCI clcc lft)n~. from tht: .;.urfacc II we sc1 up n o;;uuablc poh:ruml thffcrcm:c: V between met:tl 'urfacc I . •md the cnllcctor C. \\t! c:m t.:tJ!ICCI 1he\e ph~'to41!ICC 1ron:o. u.~ we c:.1ll lhern. tln\1 rnL!a"urc llh.'m as u ph\"\IU-<Iectnc current ' I"'

Wim"'"'

'l IL

·j +~- -- . l.q::hl

~ f v

lo' l~ .

4.1 lhpt:rJnwotul ' t."H.tp tor ltllutv•t'lntrlc 1.'fft'('l

Fagur.: -t2(;~) shows.ch~.· phdlP·t:urr~.•nt .,,., u 1um:11un ~\I pnh:ntHtl dllt<renc:e V \/ 1:,. +w :wd lotrgc cnuugh, ah~· Jlhnto dc~11 1c rurr,:nl reo1ch~.s :1 \:Oll~l:mt 'i.aluJ'iHion \'aluc, J.l \\ hu.:h all pbmo·~.-· kctmns cjct:H:J fmm f: ou1d 8Cl ('tllkCI!!d h y C. If we r.:dut.·c \'to t.Cn' :unl thl'n n:v~·~~ ll, the pllntt1-cli!<.'lru.· current ~0\!S ru,u '"'u1cd1:11cly drop to ~m. "c"·~u ..e thl.! "·lc.:trctn..; cm~rgc- from cmiucr £ wi1h llllll•fr.ro vclucillc•. ' cme ur them will rcuch lhr culkclur even thungh lhc r)ul!:mi:sl dtffcr~ncc OpJ>O\C\ lh~ir lt)llliun. H\\\\'C:\ c.r if WI.'" maJ.a.· thL' n-vcp..e potcntml d1lfcrct"K:e Large enough. IIH.:n lht!n~ wiH he u Vi1luc Co11lcd V0 , the \tfJppiuJ: polt'llllill. :u which Photcrl'lectric c urrent J'1, drop~ 1o Jc:m (F'ig. ·L2:t). ·n-i, potcmial dirt'erence multiplied b) thr e lectronic chargl! r. gi'-t:.'i th~ maximum kinetk t.:llcrgy K mn, of 1hc. IH(Ji!oo( cncrgt•tic cminttl phl'"lh1clcctrnn. \Vc ...t:.: tholl

ntc following Fif!~. (~.1:1 ~

b. C)

Cha.JaCICri"-tll'.~ Of ('JhOIO·CICCifiC Cnli'\<;IOfl

i' Observed fmm

Jt ,hows th.11 .h~ !-lOf'piOg poti.!nlml

\ 11

(F1g. 4 ,2;t) :md A'JN,.1c.: mti.:J)':n<.lt>nl

vf rhc intcn .. k) llf lhl! •ncu.knt hghl I 2 Stoppmg po1tnllal " dtffcrcru fur llll:idcnl liJ::ht u r chficrcnt f rl'lJUl'OC'I("'t 11 hu.:rt!a.\c:.. m ln.'l JUcncy of mc1llcmlight t v) mcn:ol'c' fF•£- .a 1tn Hcut..x m:nimum (lll.'r):!) A,.... , ul phnlt,~lct.trun.\- .thn mcrl.'.:t~" \\lith lrc\lucnq of anCI<h.·m n.dr.. uon. but ll as llhh.:P<mknt of lnten~ll)' uf I"Jdr;UH11) /. 3 Phollt-1.'1c«.·trl~ ~.·urrctu tn.:r~.·a..,~.; .. , 1, 1nt-:rhtl) •'( li~ht I mt"H'·''-C' f h~ -l !~• fnr a ~1\1!11 fr.:qucnq. hu1 .th\:.tY' then: '' n ,ulut.tltun ll1ut

\111Urntinn ,,,lur " lughcr 1f intrO\il) ;, ~

hi~hcr rfi~

4.2aJ

PhUIU•t:lcl.:tn~; ~'"'"'inn j, imt.ull.mt:iHt.. Th~ limel.tg lll't\li!L'O tum111g 4'11 I hi.! \() U I~C \llf,HJi.Uinn :IIIli CIII1S'IHI1 uf )Jht1UH:J\:CI((,ll1\ I 'I \l.'f)' '-101111.

lc~i$ lhan Ill ' ~c-.·

-·

',.

\ I ~

t ',"' \ '1

SliJ11I11110n CUr1'1.'111

" ,.

'• Ib) Fl~.

-1.2

IJJO'ertnl

e:hur:-u·terb;lic.~

or pbOIO-tlectrle emission

j '

________________'"'/

,' t

... S F·c,r .1 ~1\ ~n ...urf.JL~ uf ~mint.·• I \( , t.lf cu.liauun. caiJW

Ihen: c ,, .. , .. 01 \.l.'n.un 1111111ruurn lrcqucnc~

l.hrt~\hnhJ lfC(IUl'lll.:~. \~ hu.:h j, th Ilt'rt.:nt

It •r di rrcr.:nt

llll'Htl' CF•);! ..;J ..·J, When 11u.· mctt.lenl treqt~tr.•n..:y tll hgh11 .. not t:t.JUaltn l ll ~m:. IJ.:r 1hun that of lhr~-.h•'l\1 lh~ttucnq \'n· then lh\'ll' \\ allunl he om) plhlh• l'llll'l'liun. H th>e' nnt m.• ttcr whal '' the lmcn ... it) ul hgh1 6 'rh~ r..tll! at which pht,h")!.!lcctmn .. an.- cmallcU tnm11t~ ~:ur1.M.'1! ... mdc-pcndcm ol 1t~ tcntt'k!r:uu~. 'in the pht.lll~h·ctwn' .:lh.·~·t '' cnllr.:l! diiT~r~m ln,tn th..• th..:rmmnic cmi(saon.

-1.4

Einst~in's

Photo-Electric E4uation

;\~,.._,,,JIU~

hJ the l.JU:tntUJII them~ fl l r •• dJ.almn .1 l~· •• m nl r.uh.•lum nl lf<:(IU\."111..) \ utn"'l'h of photon CiH.:h of cncq.!) E;;. Jn· ,\~.:"·ordu1~ "' Eilhlitlll who ,;:n.: an C~pl11011 tion nl f1hllllH:Ict:Lm; cltt:CI 1H 1\J(}:'\ hy U\ing J.>IJn:tcJ..', liU:ullum lhcor)', th.u wlwu nulwtimt J'ol.t,t vu u mNol mrfm 1·, tlw ('ltotou m tit,• lwmn (,\ ,·nmpiNI'I\ fll'~rtriJrtl hv llll decmm i11 the.· tWtltreJ £. rltut photon m llrt' uu·ttlt•llt rmh'arwu tmt mil\ gil'l' a part o) Itis f·' llt'l):\ w the t'let'lfolt hw pan oJ til~ r:"llt'rf{\' of thr all"'""''' plwtrm i\' ""·d by tlrt• rlr·t·tmu If• lwnmw l"rP~ ;1\..Jf {mm tilt' mrtnl Htrfnct'. rh~ hulmlt t t'l'c.'f'J:.~ wifl "l'l"'llr d .\ 1 rllt'llr t•tll11}:,\ oj tltt· rmtgoing plwto· t4t+t'lltm. Th!tl K E. or lhc.! phOtHd&:t.:lnm \dll be m;l\imum fur lh~ ~~''' t1ghtl) boumJ cle..:trtlll. 11u.• em.'tg\' rctJlW~·Jito mti!t• }"''' tlu· J,•mt ngluh bt~und 4'/p~·tr. m {mm tltr ml'lnl wrjiiCf ts Ntlh·d ·w(1rl: Jiuu tuut' o/thr mnnlt c,!)J (Fig. ~.2e}. II l oti

dlfkren1 lor dlffercn< nl<tal. Jic,lCc if u J'lwtrm of t:nerg) /1\' cnnh electron' from m:•ximum K..li.. K,tla\ :- In ml'~'·". then \~c i.:~1n '~ riti!;

[F= l /2mv~1;u -+ cp I

mctul 'urlucc \\ ith

14..,)

11u ... j, ~IIUWn ~.h •Enl-;h,::in ·., Ct(U,JIInu· \\ hich t.'Xpl.un photu-ch:tlrk t::Occt Hen!'

lh..: \\'()rk run~.: linn of the 111CWI. Since fP ;, ,, COI\\I!If11, tor th~ 111~1111, so lhL're ,, u tmmmum fr"•qucncy c31Jcd (FI~. ·L2-e) tlln·slmld /rt'qllrnn V11(cp =/n•1,) nt r:u.Ji;lluln, t'tclou \\hich no photo emission fn:.un lhl." mctl11 'urf•.n;e ' " fh>:o.,th1c Su 1/) I~

\!~lu:Hil)ll (J

3t cun he wnlh!u a:-.

... .

IJ r ~ ·

, ., J

r-1. 1!

F.tn\l~in ... C4U.Uhtn \!XIl l,ttll:; JlllhCcbara..:l('fhiiC" II..' ,Itllrc\ •'11h\! l)h\UU·~IC~o.ln~

ciTed .. ,,, lulltm' I I he od"'U\C cqmllifll't 'how" lhtulhc m;u:intulll K F uf the dcurun cuulh.·d fnnn 1h.: ,,uf:tcc .ult1 'hO\\ tlw 'll'l,rlng polcntia1 \.'11 .1K,u.~, ~ 1 \ r,), dCJ')Cilth UJ)IIU the lrcqucncy nf the r.Jdi:UJon~ nm un lhe inlc.n-.tl)' (11 rJdt:lt•un lhg." 4.:!:1, hJ_ :! Wht'n th~ tnt\!n..,Hy of the mctdcnt rmti:aiHttt t\ uu:rc:l(,ctJ, lhl! munhcr ut plhlhltl' rc.tchtnp the "url~u· ah~• i nrrca~c~. I km..~: tht• phi!hl-t:l~.:~o.·tnl· ~.·mn·nt lllCr\.';1'-C' \\llh the iJll\!11\ll)' of nulinltnn (hg . .J.~.IH "\. "l'tt'-' u~l~a''-' uf .t phuw clt-cm'lll from .t 'urf.Jn• lki)Cnlf, upon tht: dl ..utu.:: that .s pho wn hum the incident beam hitting Lltl'c..•h:nrnn Jnll ..upply tlw lll'Cl',,J.f\ ~:ner~s tt..t ,., ...~pe arum the meta) !!-Urface. Sn lh.:- ~:tni ,,a~..m '' in't~tnt.un..:uu .. --1 II j , :o.t.!cn from ClfUUtion (4.-l.lhat if''< \'n Hht~'ilh•IJ fn:atw:nl.'yt. no phntn clcc.:tt' •u t:.ut be lrl.'r. 'n no phOlo cmb!!-.iou Irom lhL' "t•rfw.:c '' (X'"''thk \\hut~.·, .:r he: thl" nth'IL'>tl\' e1l th.: n1t.hn110n O..;•tz.· 4.2c). 5. Sinn." in different m~•tcrittl'!> the clcc.:trun!!o .trc houml to the 'url.u.:c wtth 4

l.hlfl·t ~ IU l'ttergy. '\(•the

('Ocrgy fC£iUar('d lO Ire(' tht!

~h:c unn,

wtll h.: lllffel'l'fll

f(1r

dtllo:r..:JU lth..' l:tl' fll:u b why th~.,• threshold lrcqucncy t \',,I t'- dtfl\:r\.'111 tM dtllt.:rl.'nl IUCI.th (l tf:!. •l.2.:!). (l \\c hun! ( 1/~) m(J~, ::: Km,_, eVt,. \\hen: v,. '' 1h~ -.wpptn~ pmcnu.al 4

•·\'u= llv - /1\',,

l l tU!I

h\!ncl." lhl.' piN 01 r t·'41 \'crsu~

~·•:oo :t

!'OirJ1gh1 hnt.• 11h!

I I 41 ~ .!\.'),

\'-hll.'h ''

~hffrn.·nt

tur

Ll1ffCI"CUl tni.IICfloll!,

"-5 Compton Effect \ompwn l."licct e:umple ot l'i. ~lllO T her

lltn h~.·rc the rttdmllon should be

mterocuon nf rJdtauon WILh m;,uer nf very !ugh ln:qucn<:) or low wu\·~· hmt:lh lh~

rc{twn. :-.a) X ·r'J) {'lr Y· ro.ty, olhcrwt$c 11 will no1 be pwmmcnt. ln l tJ2 .' Cumpt\m ut"l'i'l'nt•d l lm1 whc1 u munocn'l'r[!CIIc ~ana oi 1ul!h lrCliU~n~.·y rath"'""' "'') X Ill) 01 J4"'Y '' ~t:Oith.:rcd hy a ~ub-.t ance. then 'he 'io:otucrcd nJCtialtOth cont.un r::tdi::tiU)I\ nf t\\£1 Cl)ll\p<)llClli~I\C' havinp ~:tme freqllCOC), ':tO\C '"-:'"1\C length t).) nnd flthcr h"'vmg lower (requcncy and h1ghcr \'-;n•c lengLh A' The chang.: of wuvc lcnl!lh vf th..: ~:ll~Hc-r..:cl r:uJi:lliOn h. culled CnmpMn d1i[t und t h~ dfe~:t I' ...-~tiled Compton rj/~cr. II j, Purely a quaJlhnn cltc\:t C nrnptnn -,hill nnly dclll:l1tl.., un lltt: an1:-h: Rat wlidtth~o: ~caucrcd b..:.:utb ouc nh'\1!1\t:J. nut ~m the \\OS\~.·Icn,gth nf the incident rudtnLion nor on the ~caucnng mah:ri:.th. A,..·t.:unling w Compwn. the phcnomcnun nr -.c:mcrinJ; ,, due to t1a'-" cl,l\lk l.:lilltstun hc-1\\I!L'Il rw~1 p:truclcs, rhe photon ~'r lnC'tdcnt r.u.hnllon am.llhc d.:.:trnn

284

Em:mtc•ritl~ P/1\'HC,{

of the '~illh.:rcr ~'hc:n the ancidcnt ph,lton o r cm·r~} /:' = l1v cullhJc._ wilh the the ~lttcrcr. '' htch 1... ;ts-.umcU (0 Jt be rc~l, II SI\'C.. '><HliC of Ito, electrun energy w th:lt clectwu, 1.c tlu; HICidcnt photon lv~~>cs some energ) a nd h~nc,•

erncr~co,. '' tth tuw'-·r c n\·rgy ,. • = In•' snu.:e , •• < v so).'> A ssnce

\' -=

ExprcJ•~ion for Coml>hm Shin \Vh\!11 t\ l';lltttft• n\H\C \\ llh .1 \'l~l\k;.l l ) H \\hUh 1~ \ 0IHparabfc lo \'Clnctlyol h£!hl t . then r.:huh·s,tiL m;':-.' .:•lfh.'Cihlll h~tllltrctl .•c~tird ing iu Ein~tc tn u'

where m11 = n.~,_l ma'" d the Jlttnlcle NPw l.'ncrgy frum E111 ...tcm's. rulat1on

I. "hen: Nn" fnr photon I h:ru.·c

re~.

~ I "' ~ "'f

II\

.........- - . . -•.

=- \ p-f' - + "'•i C'

uw : momentum m0 -= 0 ,.. ~ pf·

nm''

nnd rnomcmum

,--~

Jn•

"" 1t fl =,=;.

Fil!ur.: •Ll shnw~ th.11 ,, pho11.m o f cncro~y /1\' and momentum /n•k wuh \\ ;w.: len£1h i. co lltdc~ \\ nh :m dc~tmn wh1ch ,.., uuualy at ~1. No"· 1f m 11 is the rc.''l mns~ of th&: c)c¢tron. l1u:n rt~,, -:ncrgy i' m1 ~:! Since the electron 1-: 111itiuly at re~l so its momentum "~till be t.~h).

No\\. aftl".f Cl1lli5mn rh~l'-lm ,, ~l"Ullcn:cl ill .mangle 0 with lnCJ\!dSCt.l wavc l cn~th fi.c.:. Wllh res.., I.!Ol'f~~· ,.._., .. l rcqucnq ,,, ond the Ck \;tron OW\'C' off \\llh vclocil}' v ~~ .tn :tH~·Il! (f. :t• 'ho" n in Fig 4 '\. Thu" tht- m•'mcmum ltl lhl· A~

c lcclr<m Ulh:r collt,11•11 ,.., Jlr

::. mu =

Ncm rt:s<'l\ ing thl!' hn~nr mHtncntum ut th~ phott.'n and ch~c tn1n :JIClng. :and m nghl .Ulglc 10 Ihe mdd~nl<ilr~cMn OX ~nd ;opplying lhc principal()[ COil>Cfl'alion ul linear mumcnlum "~ ~cl /u• •

'Nhich we

mc~tfilicU

hv ~

~-cos0+ p COS I'J

a., ~·/',- l'O'- If' ~ hv C'{ '; Stn

hv' co,_ 0

= ltv' Mil 0

)

i. .. A ,. < \' l'htltillll

~------------{~

\ f lcr c~·lll <o.l ~'fl

f'is:. ·Ll OunJ)fon 6hirt N<m h) ''lu;:mng :111c ·•dthng we gel •.:_;'~,.:-= (}, V)! + (/i \•"l!

l hL•

l.'lh.'lg~ (/n

In •

lu~l

hy phowu m

2(/n•)(}n•~) CH'\ (J ~;olh' l (•n

w 1th

~.-·h' ''"~~'

c:k4.'lron u' K.E Thus 1\..1:::.. nl the el~l:tmn - hv - Jn·' Ilene,· ltllitl .:ncrg) P rccnJI c:lcclmn I;: KJ:. + Rc~l m:t." cnc1gy::; (hv

h\•' ) + m11 r :

and aiJ>o tolal t.:rh:l'p) ul lhc c.lectton fronl Eqn. (4.(,) r~--..,

/:a , , !',7«--

--,-, + m1;c

I knee. b) cqu.lling .-., "~ two cqu:llion.s. we get

un ' quunng '' ~ gcs {J;r·~ + m 1~i'"J

:(/IV -

/n•~) l

+ 2 C/tV- /Jv') III(Jf''J + m1~t'..l

14.7)

,. l'atncd hy

(

,.. ,. I

I )

--~ I I

- t.''-'' Bl

m,1f ·

~~ cI - ~n... 9! mut'

C.h(/1

whh:h l,!, the cxpr~S..\1011 lor ('mufl/1111 ,/uft hom lhc t:xprc~..-•on (-Ll}) H '' dc.trl~ round l h:u CCllllfllOO ,fuh dcpc.·rl(h. fUll) on .tnglc or ~c:nucrmg H; nOI 1\11 the

indd1:n1 \\:we lcn!!th nor em 'c:tu~rinJ; m:ucrial. Ff(llll 1hc :tbovc C'\:Pn!'''on "'l! h:tvc ~en thlu for tJ;;; yn·~. C'·'"'l'lnn Sh1 h ..l). =- hlm,.J', whtch IS ('ailed Compton wm ,. lnr,;th. \\'tHd1 lor ~u1 ck·,.-tnm c1! 0:\1 mat.\ m, 1 1 ~ cqu\tl Ht 0.024 A l·or ~oucnn~ .lll ~le II =- I XU~ c.,mph•n ,(ul( \i. \\Ill be gi'C:IICSI, anti .... i!l \t:ll ~) 0 OJK A. '' hu:h ''called llr'ttrl "" C•.lllt,ion. I he mcidcm phlllon bdn~ rc\ l.':f't.'d an dir('~;tlc ,H

l{e~.-rding t'om1non Shift I lllc 1.':>-.pre...,iou nt C'1nlp1ull Shill h)r hqJhcr rn::qucnc)' radultton [L' We h:t\\.'

Sonu.• Import not Points

. m.,,. "

'' v..' =- - - n co' th No\v II 1hc incuJ..:u1 ,,,.Jimum , ..

~en

,.r hm cr fn.~tJUl•ncy 11.:g.Hm ':.t). in \'t-..thlc "'

t:uJiu (rl!IJtll.'lt~~ r.tltJ.!C, \.lolh.!re ). j, \Cry Jarg~: Compar e hi_\)._ 10 thnl c.;N.~ ),':A. 1-- »~ i. .s~~ Comphm df~cl 1~ m. ,j~mfn:ant in ,m;h ~·'''-'" In

Olicf0\\,1\1.', ),. fll)

l•r

y-r;'~ .J). ' "' ~;~lmp ;u;thl~ 11• ),, '() lt!IIIJ'h\11

,j~n11"i.:um 1\Mml~· lnt h1~h'r tn.·\ltt<!n~o. \ r:•~IIJm,n. 2. S~.-·\.tlfHII~ . Ihe Coiiii/Ufilt C'/Jn I " tmrrh

' tuft

j, 111c1l'-Uiabh·

:uu.t

qumrlum t•j{al, u.. "

u·t ~

, n.

J). - , 0 , 'll il~.--;tUIHtt hr e\J"'I.uucJ un 1111.:. ha.c.i~ of das..-.icul ph)'ic'. ~o:xperifll('III.OI Vt.'rifiraliOII or Cnmptun £ff('('l In \omphm C\Jlcttnt~nl. .t tX'am ,,J X tuy' '' ith shtarply detine\1 \\IJSC 1\!0}!Ih A fa ll' on til~ ldrpcl T ..l' 1h'•''" an Fi:; . ..t.l(u). For Hlriuu:-. ungh; of .-.coJIIcnu~ 0.

the jotcn,it}' ••I thL· -.caucn:d X 4 r.t~ ' '" nh.:.t:.un:t.l .1~ n luncti,1n l)f w.tvclt!ngth Fi}tUf~

..JAlbt shtm~ I!Jl" C't)lllph•lfo;; cxpt·rirncntal rc,ulL Pur mOI)hi.Jcnun A".,· lim· fU. 7fl8 A). lh~ "'" .: kngth of the lfH.I(Iifit:d fine tlhwn l!d :u ')i) '' :•s 0 730 J\ llu" g•v~s. .li. = ).' - ). : 0.022 A. \\hu::h IS Ul agreement wuh 1hc th~!cmntc~ll vttluc 0.0:!"" i\. h!!ur..:- 4.-HhJ show~ the wn\·c h:ngth o:pcc1ra (ll p1H,WM ~cuncrcc.t ut vanou ... ~·nglc from·' ~rophu..: scnttcrcr.

11tc ~rt llcnng of photon ;mJ f.1J~CtJOn ol c(c('tmn ate .. unultancQu~ pr,)l.;c~:,. n:rifl.:d h) f::h 'II'C Jnt.l Gci!!CI'. who "Ct up two lom ~<;;uion countL·rs \'l'l')' cln"c 10gethcr One countCI' ~u' "!n,.mn~ 10 electron.'\ whtlc the other one w:ts sensmvc w .\-rnys. The larg_e number ()I MntUIHmcvu~ rcsJ)On"C-!« m the two cotJntcr showell th:lt the (li'(W..'cs::- o f sc:mcring of photon and recoll ol eleclron arc This ~~

stmu ltam:vu~.

Qucmlum l'h,•.Hn mul Sthradmgrl'

)

\\'(1\'<'

t:qumion

287

f:)

Or;a.plutc loti

I '

0 -; -l ,

' " \ ~ LL~ .I\ );

H ~ Cl '

I •

a .,..,

H ;;

•

Fiat. "·"

!hi

1-:xpcrimrnta l ..d UJ) nnd ro.ulb' for Lomptun shlf'1 rur difftrent ~cuttc ring ungle 0.

Explnnatlon of Unmndifit-d \\:H'•:h.on~fh in Cdtnphm F:ffccl rh~ pn::-\!'lli.'C. of th~ pea,k 111 "'~· -l.4(ht ll!l whtdl the w:wc l..:nt;lh (.!(~~ 1101 c hange \) 11 scattering. can bt.! explained Ui<o fo ll ow~; This j'X!Jk rcsuhs from the

collbion rn:twecn

photO n~ and

the (;)cclron that.

m~lcad o f ~in~

neoarb rrcc. (lr"

tightly blJuml in ~n ionic cur~ in th~ 'cnnerins targcl. During photon ..:ollision

.UU~

F.ngmc·c·ttnx /'h·Hn

thot1 ~·und '-'kc.:111111 twha\t.!'~ like a very h~!U\'} ire-: di..'t:lfc'll Tlw. '' ~(,":&ll~t.: Ih.,. CPIIi,h10 hi'lwc~·n lhL'III lllliO.:I he C.'Hil'\ldCr~cJ :1'1 IJkin~ ("'IJt:C bCI\\\'Cn th\! IIICitJ~,•nt

phcunn ;'n~o.l the ..·nur..: ollr•m uJ hc.•vy ma''

nw.. would g;n·e ..lA =

dl'\.'IICIIU,

j-1'' ( I jl

tl4

M1• >> m lm'''' ol nco.1rh lh·e

'J.)

~()~

o•. Su lht..• ( WliJllllll \IIIli

lur

1i}!llllV houmt clc..:~rnn h Jnlm~.lc;;ur~•hl> \tn,lll t;;11 Uuru)v. ~,·nlll ... lilfl "''m'-' phnt\'"' h> 1h~.· dl·dmn-... whid1.1r~ rc:ntiCIC'tl fn:..•• rhc'\.' ph• .ton' .m: 't.tHci~,•,J \\ 1th 1111 ~li lied '' U\'f"h.•1gth i.'. wh~rc<~' '-0111~ phutun' !!Cl ,._::aut.•• ·•Ill• '111 dl'Ctr~'n" \\lm.:h a1..: llt;tuly h.tmHJ u-. tth.' lllh,'kll'. lhc""' pht~ton ... r1o.·m:un ,,udl.Jrl!!~J 11.1 "' 1111.: \\ ,1\·c h:n~l h, \\hhh g_Oi\1.! n~c to 111c unnhKIIII\!d ~"':·'"' iu l af: (-t -'h•

.th' ...~,;••ucrcd

\'\ a\'c Nnturc nl' Particle and Wa ve·l'articlc Dualil~ n.ll';.t HI \'-o.t\c nnuuc! ol p:1nicle c:tme iif\.t fr(un tht..• nh,t'l\"tlfinn nt Ju.tl n~uure- ofckctroma~ncw: mdiation. In imcrfcrl!nt..'C, (.Jilfro~ctiun ..:xr~ruu.:tu. 1:u.liittlun hc-IM,·n hle \\ ·" .... "h..::rl'·" 10 Ph<tlO·ch:-.:tm: dTccl. t't1mpton t:tl"c-d. hl.t~:J.. .. hud~ t.ltli;tlu111 11 hch;nc~ .• , p.trt kk' ()f\:fmr~t. rJJjutiou-..:.umolt..·,hibitlt' panu.:lc .tncl \\lt\'1! llrOj)t.'lttt!"- .,hnuii!Ulcoudv Rill due tu thi, du:tl pl'np ·rt\ tl o..c.· cm' th:tl 1111.: w,t\'-' th~on :mJ ~ant{' l ~ tht•ory nr~t t.'t'ltnj"'k1T1«!n1M\ 1£' ~;, ·h t\lh~r Sa~ lur ~\.uurl~. t'\J')Crtmt:nt.llly it 1~ H!t'>· dtfficull to uhscn c tnh'l h' h'tl'"~~ t'llcd "•th 1u~h l n..'lflll'llC~ )1-ruy ...... u:.. \\U\C' t.ll"'cnptmn llf }'-m}·' hclnm~: -. "''' phthahh.: ;H

4.C\

Ill~

1111.''\,.' ltct~tll!lll.;h.'' (r.:ttllt:lll'~ p1ohahl~

Phutmlnr rurudc 1Jc,,;np11lln \\UUill ht.• 111111 u.Uur;!llur lngh \\11crl'~l' if thl' fwcru..:-nc> h I~"' th"" \\:1\ n.uurl' j, illoh." SIJJI lh..: ,Ju:ll no111.1re t•t r;ulmllull \\"~1.~> fHII .::NI~ ..1u.. J'!~o: d . hi.!t..';tU'\j,' 111

phfHon

lhc ..tJlfMt~nlly cuulrouhCh11) ·•~pc~·a... t,IJ

•h1

lhr: l\\t~

n.•lur.:'

\ \\•1\C I' \~i..l l n.•J hy ll' ll) ff~'JUI.'Ill')~ t1J \\JH' Jl.'11~1h I \1 ph;ti,,C Ht \\an• \'C:hk:'H>· t·H :nnphlut.l~ mull~, 1111cn"lt~' 1\lt\n.'•l\'t.'t 11 w,,,c '-Jm:~ul-. 1•UI .and '""·1.·ur••l.'' .1 rd.ill\..:ly l.u.gc tl'f!,h•n t'l 'Jl·•~o:~. \ p.lrli• k '' ..,~~.·.,;•l•t:t..l h) f I I'"·'" f~) 'Citl\:11~ ' ' 111 ·nh·nluau .uul 1; 1 cnt·r~)· ~1ull'\!\c,'r .1 p;11 111: lc ~~~UI)It~\ .1 Jcftnlh.. 1111... 1'1111 Ill 'IKKC .11111 hl'llL:l' i1 j, \ 1.'1) "\nlUJI

Inn~\\

ol llw uho.c. 1l h r.llhcr t.hlfi!.'ult h) u..:ccrH 1hc ~tmlltcll n!! rdc;1!- rh.u fl '\\,.1\l~· ~\ htch il\ !\j>rCad Olll H\'Cf 'J>~It..'C ;tOlJ ;.JI\H ,, p.trlldc' \\ J~tt,:h '' h'f.·alw..·J ;u ~•Jllllllll!l )lop;n.:c. Uut 1Jn:- ;tn:cpl.nKc '' C)lo,CJirl;tl. tt nn~,.· ...;tt,,f:u:wril~ c'\phun' Th~· l c'uh llf C\)ICJICIItCIIt' , "h1ch 4..':111 he- ['CII(IIIIlCLI \' flh I :nlmtHlfl ul \llltcrcm mn!!e ol IN'qucnc1cs. lrnm Vet) h igh 10 low v:1h•"' We h.1Vl." .llrcotdy lCtn Ill ~cellon 4.5 thnl lhc w.. \c ;llh.l p.111h."lt! mtwr~.· "'' phnlnn' urc n.:l.ll.:d h) ah~.· ~qua t mn H :ci) l".h.h ..Hhln

h :: h\• i : fW

I'= !!J:. , = .!.!., A ... t = vA..)

\\ht:r~

II h

lh~:

Pland(,

145.11

~..+on:HunL

In Lhc'c cquut1on' l.,. 5 I) and

(~.5.2).

.uhl 11\0IIl t:OIIIIft ( fH o( phi)!Or1 :lppcar 0 11

l\VO pun ide M...: rau.mw•c .... cn(fl!) ( /J

lc(t. \VhcfC:fiS 1\\'0

\\ ~1\'C

like t.tu:ulliLit,:)lo,

Qmmtum

Pll\'\li \

and St:hrihlmg,.r Wm t• t.fjltrlfron

2R9

r(equc.rh.:-y ( \')and Wot\'C length{).. ~ ~lJ1J'k:31 \In r1ght. These 1\\t) C'-flltttinn.~ .:xpr"•'~'~ the fl-hl'IH1H1Cna ut w.I•'C pllnlclctiLJulil) uf nu.linlllmt(UHnl;ll.~ phntun Sorncl nn('~o phl11CII1 hdla\ C' ,,\ p..niclc with cncrg) E Jill! mtunr.:nlmn f1 untl 'lnlk!tian~ .. <l' woa\C wilh fn:ttucncy v ;1m.l wn"c lcn!!lh J..

Hypothesi~ .1ntl panicle~ :trc the on I) t\\iO 111(ttlc,.lhrnuc.h \\ lm:h c nt:Jf!) ~tm pn,pa ~ru ..· in n;llull'. Smcc nalUJc 1.!1> ~ymmi."HK, 'u m:mt:r.1nd \\aq':.. mu'' ~ ,ymmcm\.'" If r.uhuuon di:..J>f:tyl" \\.ave like. a.~ ,,eu,.., p:mu:k hk~ JlnlJlerliCS, mnu~r can ol.!>o t..h,pl,ty f)ilfUCit.! hke. II.S well a.s wnv~ Itt\(' Slf'-'P\.!nJ\.''· On lh\.' b~hl'> nt IIus argUI11l'OI , dc-HmJ!hC put forw.trtl h1~ byrx:HhCSI ' ••' ,,,.,;, lc1 wlrmc• ,•C'/a, tl\ r.s t tml[utmbl, w•· tl1r ''-~lor".' ofllg/11 ('(lu rthilw u "'"'" IIJ..t" fi(O[Jc ' t'llr., ami thr '''ln't>lt>u,t:Jit a[lilt" u·m c nJ ,\'odm~tl "i1h JUU'Jidt' of IIUI:i.\ 'm ' mm·inl-!. with l'rlot it_r P f momemum 1, = mu J <·(m hr r.tpruscd tl'i

4.7

de-Broglic"s

\\ ';1vt'~

rhc...:...: W3\C\ 3,\.\0Ci.tted wilh p:tnidn 3rc l:allcd :.1' Mmu~r Hm n .tnt.llhc \\ iTV\~ ll.:ng1h a,!. dt·-/Jroglir•:'i h al'l" lt•ngrh d<·~8roglit''S \-\':n•eltn~1h of an Eh•('lrno \Vhen an eh:cuon u ac..:elcr.:~t~d h~ ·• p ~o.l c l..:~lmn

rV = 1/2 nm

[ ),:/tlmt1 h)'

\ then 1h( ~IIU.'IH; cncr~) o( lht.•

'llh'l-tituting the ' 'ltluc of h.

2. \Vnvc number·

= , ~mt\_.

=lt!,~mr\ ~ 1!.~5/, \'A ~tntl

14 ll1

= 1/A =

2n,.F -m

'\ \\'o.I\'C Velocity· The W:J\t: vdOCII) I •' Hf Ihe ck~.·tmn

\1.~1\·c

t:<tH bt.· found by lh1.·

ph''"'" nnnlugy £ = IJ\' 1•

=c!\ .

=1•\' :::: /1

.?ml'\1 h ..

h ::!m

:. lrom equuuon 4 II ;.1 =

So W"vc vciOCIIY of electron

=U = vA = -2mh ,.,I•.

;. = _,,_ 1m).

2:mr\'] .J1-, 1

(~ .12)

1l~nct. the''·'"'' w \k. aly ut cl~.:ct rou i ' not coru.t.u1t. a_, A. i.e. \'CuHclcr~um~ \ OIIat:d ch.m~c-". waH \ci~)Ctl) ''Ill ;tlso chun!!C.

4.8

Davisson and Germer Expcrimcnl

I lc\.HUil

\\,J\\.'

lcngLh frn m thl' dc·Broglic', hypmht:'i"' 1,

A('~

_ 12 2~ _ 1 "~ A ·-- ·

' 100

v. h11..-l1 1' o l the l'lrllcr o f tl1c mt~rplancr .Jbtan.:c sn the «..: ry!\ttal. Tim• l~1ct 'ug,gc:'l-' lh~u II jt; J'ktl..;;ihJ.: ((l 10;h~'''" t~ cx.i~h!ll i.:\.' Of dectron \\ :t\ I!" with the help of l'b:lmn diffrucuon. l'l) u.. lll!! ">''1al ~s diiTrncrion gr::uinJ! :1-: it wa<; used for X r.tys

b.L..~d on lhl'" ldCu WU.) pcrrumlcd b) o.• \'bM'In ''"'' Gcnnl.'r Ill 1917 Hc,·tmu-. cnuuct.l b;, ·' h<:~ltcd llkuncnLand m;elcratcd through n p.d \ '(l(h. cmct~t.· fr\nn lhc dre~mu ~un with cncr~y t"Vand an· allo,wd 10 ''''l..c.· ,, "''IIJ!I'-' ( ·ryst~l vt n1cJ.cl (hg. -15 •· These elecrruns. acung hkc: a '''3\'c. '"'ere Jillf;lt..lcd ufl m a ccnam prcfcm.:d (.hn:'-'llnn u~ g1vcn hy 8 rogJ;.',(.itiTra,·uun l:tw ft•r X r:1y~. 1~. L\(X'Illlh~lll

I hi;' ...;uuc ;~,;J dec1ruu ltcntn can hi! \lciCCiet.l hy the elt:c1ron Oc.lct:h" "h1ch coul,t ht~ ru1.ucd ;.lft"'IUthl the mckl·l crysml 1hmulrh a large nng lc From CtJII.IIhlll\ (-t Ill ;md t-l 13lH ISd~Hr 4htu torn f!J''Cn ucccl.:mtm~ \'UII:t~c \. tlu..• m;t\IJOUIO tnlcn'll\ ul lht· '"::ll ll!rcd ~ am will ~htl\\ 10 tJ [M!1H.'ulnr dir~cliPn Thu.,, lhl' clt:a:tr,m •kiCL 1nr }) lht•n l'nn be 'i.Cl 111 nny desired nngk .2(.) 1h.ou .tllm" Ihe l nti.'INI) nl 1 l~ ~n ncrc.J llcam h1 be mca<rO;un..-d fc,r \'lmnu' v;,lut~ ol lhc ;u,:n·l~·niiHIJ;! pnwnt1.tl \ h~urc -4 tll;11 't"'"' llll' l:unou' n,..,ull u( Oavi,~un (icruu:• l''I"'ITt'n~eut \ •IWI~t'h .~..-~m,·rcd '"'~Ill 111 clcc1run '' obwf\c.tt ~1110= 5tt Jor ~ - ... J \1llh

\lftJ'I..- !lk.-k.cl C')"!.t:l-1 Fi~.

4.5

l~ \pu1 nt <'I110I

set U&) fo r

Onvlss4) n-(ie rru ~r

t'XJK'rinu•nl

Quu lit ~ttiv~ 1~ \:plonntion

The ~,i,.,tcnC( .-,j lh< pc:tk m lhc lllll'rt'lt) of the ~callcr~c.l elct·t ron beam ' Jww .. ~JUlllil ollJ \'l'IY th~ \'fll chty \)I de~Br,)~l i!!';o. hypdt hc\1~. Bccau ..i! 11 i!<o .lnah•gou-. hi dtc X ·n•y diffrucliun h) u cry~wl Juc to ron~tructivc mtcrfl"renrc of \\',1 \'C!<o dillrach.· d b\ pcnvcJu: ml.lllf.CillCill o l o.1l0m'

the pttnc:!r. of the

cr~~t.t l

eowmllu• PtJifmm•tiiH ll'l'tll;ng t•lt.•unm m fUirtt<'lr\, Pnrt1d1•~ will IJt• rt'}l«-cU•tl f1\ tht• til(lUIIt· pltlfl(_\ f'lll tltc'\' t'liiiiWI ;,•tllifJU iJUl'11t'rt.'lfCC'. t>lff\ h 'JII't'S filii in t l'f/t'l'c •

Quunliluli-e

E~r•lunulion

Thu' l h(' ' ll t •lll! hcam ~lf l'k~m'll' (lH 2~-- 5(1' 1111d \ ' :: 5o4 \'Oil~) i~ .;caucreJ llue 10 U!> W:J\e lilc prO(l<:fl) trnmthe awmk p J;:uW!'- in lhc Nitkd Cl).~>I,JIIJ~• g t (,h, l h'll' lnnn l.;1g. -tNh) 11 "dc:-•r lh:tt 1hc sc:mcnn~ pl(mc.:- in \he ,·rv..t~ll nl\•

tndudcd ~· :mgl~ (~:: 25 ) to the mr surf;~cc ot the c-ryMal. ConstruCII\"1.! Ulttrtcr\!n~.-c will nccur \\ht!n it \\'Ill ,.,11~1 ) 8 1':tg_g', lnY. cc.tuatinn ( ..J 13), 1.e .. 1tl " " 8-= nA

N\m gl:m~ l ll}! .mglc 0 911 :!5 -. ('tS0 fmm f ig. J.6~ hl. .md tl-; I J ,10 .,-., l l llfll P•t! · -1 b(h). where IJ = llllt>rultllfiU.: t.J1'-t.mcc l nr Ni Cf) '-lal :-2.15 x 10 111 1u .uuJ ~~ :- 1S' frnm Fi!! ·I (Jfhl

"',.,

·~

r, '

!< I

-· ~

...__

•

--·

....._

-,-... '

rb• f1J.:. -1.6 U~ ) Vnrlatlon M !'<'AIItl'\-d elc..-tt ron nuenbt·r "ilh ~atming aJ1~k~ tb) Ell"t'11'QU d.irfrucllnn flt.~ urrinA rrom lui Lice plime ur Nil'-kcl cryst:tl

I kn~~. 11\h.:rJ, IUnl'r

,1!:-.l.anc~

tf::: /)Si ll

,/of lht: :-.C.III ~ I·inl_! Jl la sh;.~ w1ll he

t!J=- ~. 1 5

X 1(} 111

\in25

=U.t)()(J X 10 IU H1

rh~ !!h111cang ttn~lt U 1:-. ClS ~ 3..\ ~"'"'''~ 10 Fig. ~.hrhJ ~nliJI\. h> '''"lg Urug:g\ lwmul.t w~ h:r~..: lor hr!itl nrJ..:r d1flr;u:tinn

21/ '"' (J ~ I

X ).

).,.... =2 >< II.'J(~J >< Th~ Jhcnr~li~HI I.IIIIC'

\ ult-. fntm t:quatiun

~..1

IU 1"

Y ""

= I M t\

(4 I ~ 1

r Je·Fim~ lic\ "·"~fur ··h'cunn.u IIJ'Cnlllll!l \Ullage ),J II ) I \

..i,: I~.;~" IJ>7 A

15)

'.1\.j

The clo<:.c :tE!rccrncm be. tween ahc t:xpl'rirm.~IH al and lhL·oretic;ll ,-~tlucs show" th:u c l t!~tr('IJ\!\ ha\1! wnvc 11-:c n.nurl! and u \))llfirnb ahc dc·Hro~lte :-. hy1xnhe,1s ol

4.11

Properties of Matter\-\ aves and buw the)' Differ from Suund and Light Wa ve'

~1ttll~l w:nc::-. ;tr\! n~al h.:r\!IC\:Imrua~n..:hr \\:1\c.., h~c

hghl \\;tw ... uur lil..c .,uunJ \\IHch l'klp:s!t:U..: lhmugh the 111\.'dM due In 1hc v:,ri:uum nf JlfeS!>Urt.: . h " ·' nt.:\\ l) pt: nf wan: called pilut \\'JH''· in th..: )ol' fl'-t: that thl'~' pilot or guidl.' the IH..tlll'r p.u lu.- ll' 1'111p1.'r i~ ~ ~r umttl'T u ;t\ ~" ,;snd hn\\ thl') ~..hffcr Imm the u'mtl \\·:1\'L''

\\01\1.:!\, \\tWill d l ~\.' U\" nO\\

I l;or de· liro~li~·, ~ave lc:nglh A Ill 2md' l lc:ncc. h1r,;cr thl.! mn~:; flf Ihe \ 1• .,hnl11!r I he\\ o~\·~ lcnglb 3\sOC-ialcd " 1th i1 nP1 ~.·nn,Uin l 1 rh~ phoi.,_C 4'1( \HPC \1.!10\·11~ ol rnolltt:r \\,:i\'C 1-.. l = \' 4 'em rn:lth!T p.tnide nr l:uger nccelcn.Hng h'lll.lgr

1:.:

= lr\'

trmn phown ~mnlog) J.C

\' : 1111

~"'

A ; hlum :. \\U\'C \'CIOdt)'

lJ = v). = mt.J.fl, 11/mt•

-= ,.J/t•

u o f the pnniC'Ic cannot e"ccetl the \'Cit>en~· of H!!IH r•. so u •~ that Ih.. - w;w..: 'N iotaly o l the nl<Jll¢r \\':l\4.' f U) ,.., rlhn¢ thun lhc Vl!lt'l\!11~

Siau:c th..-: 'J\I.!Cd l'1wwu~

.,r I1)1IU. ,.. htch b \!4\ntradtctory "i1h the pt.~~ tulml!.... of ~ fA."Ct.ll th~''r~ n t Nltl11\'tly

3. 1 he v~;,·lni,:ll)' n l l•t:dll '' con,t:nu. whereas. that nf matl~r '"~tv..: Cl/) I!'! nm '-'on,l.tnl ... mcc 11 depend..- on \'CilX'HY ~ u) of mut~n ol partJdc ..$ L1gh1 VJC\\'l"d a'\ curpu'\dC U l po.uudc ha' :111 t'(ICI~) uml a.-.~ucsated m,L,!'!

11 .;an he located p11.!Ci..cly at any pni111 Only difference het\\ ccn rhe light vic\\cd pnnacle of mmh~r I!\ that. the rt•st nm-.~ nf hght phuwn m11 =- 0, \o il ICC. It I~ IHO"'IIg \'o'llh :1 \'dUCII~ uf hght t.'. Yo h1ch I\. nol :<-0 for 01hC:r u~ p;\Mu.~ k and o•her

mauer particles. 5. If the wave lcngtb of lhc m..tHt:.r wn\'c h Iurge. i.e lrctjiii!Jlt:)' i .. s tnall, I he n

{!mm11u11 Phutn ami Sclrri~tlin.s:N· \Vm·C" Equmwu

293

'"'wave Ltc ...cnpuun •~ mun: probable. it :tpp.::u ~ Jil..e :-t w:wc. Btu irtht.:: ,,,~,v~lcntnh 1, -.nwll. fk((UCil~} 1 ~ larcc then H hduvro;;. like~~ pnrw.:lt! ;uu.l ~~, Jr.muJc n~IHIIL' will b<.· Ill ill'~ prtlh.thlc. :-.\}' f(ir t!~ol l11()1c. r-r:.l) anti r· par1 1C'1t.•. 6 Qu.uuurn tnc4;:h:um:o.1l.} lht: \',ln~tbh: tluanlll\' \\hlch churm,: lt..:ll!'i~!-. Ih.: ilMHI.!a w-a\e. b. c~llcd '""'' t: fum.:.uon t VtJ h cun be n:prc\Cmed at c.hst:.uJcc' at a lllnt." 1 a~ trfl '· 11:::.-\ Th~

-.tn "'!rru!T

, /AJ

pruhahilit) ur 11m.linp the pan ide ;,, pumt t.lJ at tillll.'

I j,

propomon..&l

Ill I ~~~-

Thi"i wa''-' functh•n ••f m.llh.'l ''~'I.' \\-ill \!U~ 1t1 -.p~•c..: and tilfll'. hkl' th~o.· ''urialinn t)l ch:clt\lnhtt:nclk lidll fur hl!.ht wuvc pi'Opll~~tion und variouion ,~f priO"'~un; in tht: ml.'dium fut '\\tunJ ,,.._,._. propJJ!•ttiOtt 7. The W!JVC 'clouty til Jll<llh..·r "..._, '-' ' ' nl!<.d gl\ ~~~ hy U =It/1m}.. (Eqtt "' 12 I ll .,hem'' 1h.11 \1.-.t\c •, ·cluc:il~ dcp..~cld' irt\t.'r~cl ~ tm Wa\c lcngJ h A. C\Cil II thl' p:Lnich! js mo\ mg. tn vm:uum I tw••~ 4\Jih.' thfferrnt bcha' lOur frum thai ~•• ltg.ht. \\luch rnOh!~ \\ tlh !-.<~111~ \th)dl~ • 1\!~urdh.:$~ of \\u\~ lcn!;!th. S. Maller \\-..&\·1: ..) nnl J ph)'H:al phl'Oflntt.:nun II t~ rather <I ,_,mbctlll «prc:-.cnt:11IOII L•t "h.tt we lmm .tbuut the p;trudc Su u h .:••lle:J a \\otH' 11( pn:)h!lhilil)

4.10

Hciscnbl·rg', l lnccrlainty Principle

The to:ttn\'Cpt

th.: dnnl

pdTth.lt.: .mtl ";t'\'(' n<~IUh- lll m;llh·r l~otd<o lo itn 1n1JlfHIIml

rc,;,uiL Accurdlllt-' tu d:t ....u.::tlmc...·h;uul,, :t pJni.. lt.· ha~ :1 Jli'MIIon ;tnd mnmcntum

\vhkh

L·~m ..

in pnnrip1t:.N" lll·tcnnincd with .my t.l.:,trcd .u;cur:tcy. Btll ·' \'·""'

lllo

l:ll.lcndcd lhftUJ~huut !l l t.'~IHfl til 'fiJL't.', .ltH.J thl..! ltk.J.IIOil 111 Ull e ll.'llWII,lt1tl,.idl..!n!'J

.. , a w:wc. \4.'.-.:m .. hi rn·..-...cnl 'Hnl\!' ,hun:ult). Tht: C.flh: ...tlnn ;m ..c ... ; If ;m "'kCIWil h d\!:--... nhcU "''m\!11111\."' ~•" ~'·''"'' \IIUh:liHh.""> •'' fi.IOI~It:. I' 11 fM~~1hh: h• 1-.JlU\\

t:hXIICif\ I ·Ill "l'·l~t' .tl 'CIIHl' ~1\\."U UI\I,I01' 1 lfu; ;u1'"''1 ht I hi._ tiUC"IIClfl I' gtnm h) J lt.'l'l..'llh~o.-·1~., U111.Cr1i:UIII) ('llllll:!plc Whtl:h \l3lt:\ 111.11 f/11 fJO\Ilimt mul momt'tltiml ot' '' J'1ll Hf /,- i tiiiUtlf ht· tl1 l,.nnlm:tl \iuwltmrnm ,/\ tt irh Jugh;_•_u un uwn • ln :a Hl!lllu.:mutlt!<~llurlll H ~hit\.'' th:lt t'\.!Clh

\\h!.:rl'

olfl

_j_,

..lp

.Jt

jJ:.' '<:"

prvchu;l U! 1111\\'fWirUjt;, in tJ).;-:...tm!IUl,'lll t'\f t\\t' \1 ~tri:thlt;~. Ill 1'"1"illflll (.:_\.\') tll1d IUtUllCUIUI"'l (.\fll t\1 II\ the litnC (...\tl :mel L~flCf'g) (.l/£) lllU!'l be allt",l!-.1

i.e:,

!Itt!

of the- or<.lt'r or II t= I./2m \\h..·rl.' II" the Pl:mL'Irro.\ Clii1St:ml Hcru ...h '. J..\ p arc: Ihe: etrors m the tlcacrmin£trion \,f po~ttmn ,u\d momentum . .J.£ ::tnd ..ll ar~ 1he t!rmr!\ in dclcrmimttion u l ..:t.:~y .JJllltiml~ h means tholl if pl•:-.rtionlb mc.t:-.un.:<.l ttCCtJrut~h (I.e.!. ~h I'~ \ Ct) \' Cr) !-IOU Ill then lllt:;-'i:U I Clllcnl Ui 1110ffit."IIIUIH hL"'~olHllC'

/th\1 and \tee \C"'~' Smul:trly if u 'Y~lelll r..:m:un' m :• p:tnlculnr ,I;Jtc ol nH.•ttun nnt IOII)!t:r than :• umc ..11. 'h~n ener~y ur 1hc ;;ysl\~111 111 'h:n q;:u\! IS unecnam by :u lea."' 1h1.· a111ount . _:\1·: = III.JJ :ncl vice \t.:Nu. corresponding!) m:uxtu.ue h) 31 IL>a..\1 the .unoum ..lp

4.11

V~rifkation

4.11.1 )'-Ray

of Heisenberg J'rinciplc

~licrost"pe

Ext>crirncrll

Th~· 111\!;uung t)f lhc Ulh.:crl.tlr\1) princl)>k \'iJn he

lll u,mucJ hy .ut ldi!aliN~oJ C'onsiUc1 the fullowang ..mcmpl H-• ntcu!\ul'c ... unult:mcnu'l) the f'4''illun .md momcnlum ul .tn eh.:ctron '' 11h ;m 1111jgumry mil:rL''r~·~ u l \Vry lugh IC"Mh 111g power It hu:. heen "hown m ,._ .tvc ~~pri~.:~ 1h:111hc lmut n/rr.w1/111um

c~p-:ruu c nl

~~1 ;a lllt,·r~•:-.\.',1)~ I'\ ~.1\~ll ol)}(ln.l\iJUah:ly h~

)J~ " " "

j \ •

~0\\ r~·wlt·mt: t>Oht'l (R.P.• ;, proptlrlt\ill:tl R. P t)f Mi\.·nl ..(.;Oj)t.:

14. 16:.\ to -

1- .

!_ "' IIA .~ . l (>b) .1< \\hcre \ t 1\ the di'\t:wcc hl;"l'-'~t:n 1wo ll\1111h \\hu.·h ..::.mju-,t lll: n: ,ol\t.'d by the rntcro,t:opc.l ;, thc \\OH! length of1lu! hglu u ...cd , urul A,, chc hull :m!!ll: o l the ll'n'( 11'-i.'d (h[! 4.7:u 1hcn J..\' 1, lhi! un-:<namt~ an tth: d~h:munmwn th~,.· Thu!t,

o::

,-,r

dc<:tt'w\: t<1 nl:lkc h "' 'nmll ;h (1Chl:.1hlc, l ht: \~il\'ch: ng_Lh (A,) U\~d hl 1llummate the electron mu~t he , ·c ry 'mall a.c.... t:llht.:.r X r.t) nr ')4rny nm-.l ht· u~~d Ncm tJ1c pt.lMUon of llll l'kc.:truu ~.Ill h~.· flll.:il,Ut'Ctl "11h ,, micl n-.cc'l~· nnl)' i( .11 l~.l'-1 UJ~ pholii'UI j, \ICfl.:c-ICtl rrnm II"' inllt.~IIJih.'..:li(111 1111Udu.· mkn''"n!X'1\-. .1 rc~ull tll elm. tlhpluccmcnt, the l'unmhtHiun ht 1hc X -L'Unlt>uncm t.l r the munh:IHUlll wJIIIX! unc.:crt:tin Sim·e tht.! ..c:1lh:recl phntfln t'Un t:ntcr tlw rnicro~co~ an~\'-hL'rl.! \\llhu\ lht! ang ll' A. 11m.:.. th1.• unu.:nauH~ w 1l1!! \ c~lmp~m..:m of nmmcniUm ,,r dcct ron j..., I'H\IIH1U

th~

.Jp 1 = ,n'\iriA Th~n:hm:.

thl' pnwJur1 o l the

pchl11un .mc.l nlnmcntum

( f1"ii n A) =- 1.p ..mA= uncc:namll~

ur :111 etc,tron ,.. ).

J\ Jp, =-~sin A .l ~

I I('IICL'

\\ Judt '" lhC

UllCCflflllll)'

~1 -.1nA

111 Lht' ' 'muh:mc:tHI\

ml.'~l ,tii1.'111CUI'

~hi A ..;an..-\ = 11

• .Jp, = lr 2: /r

r rul(.'apll!

Sinl!.l~ Slit Oiffrn~tion Method Lc L U!> c'•n!>lder the ei!XLron beam wllh n•omcntum Jl lnudemnn tJH.~ .. Itt of wrdth ..l\' 1r ..ly '' c.:umprablc Hl t h~.: wave lt.·nglh oflhc cl~,.·ctrun bc~Hn, then the clcc.:tra art' ''Ill ditfrutt uccurdang ld sing!~ sht daffrncuon pan~rn and fonu a t:cntrul ma~tmum M11 aml l \\t~ ~\!CUrl(bry 1ninanlil :11 P1 :md / ' 2 lf1g. 4 .7h ~. At.'\:mdmg h ) Ihe J, rtr:rttion

J . IU

theory the

lir:!~l

order dtffraction minima condrhnn from equatio n ( I .SUl i:.. .J\' (;ut 8 =

1.1!•

..l)

= Alsm 8

'"'hue ..l\ = unccrtaint" in position of the clec1ron btfort bciug dltTrdctcd. wh1ch nrl.'

hu,·ing momentum I' only along X·..t,is.

.J I

•• ,,, ,.

--1 --

' ' .."'

·~

"'-.. 0

I I(•. ~ 1' '"ill tl

-- (;,

- -r

..."

..., ~

.., fig. 4.7

\tnOcalft.n of' fltiwn~ UfW"f11•1nl~ prinripJP b' ••• y.na' t'\.pt'rirn~nl: 1IH 'inRk ...t11 dinrvcr1on mttbod

Notw h\·lnr~ c.llffrul lll''ln cloctrons havt.~ IUI11tlt.'nlum ,, on!) ulunr "< ;lXII\ hut .tiler t.hlfro•t. llun 1hcy Ml' h"''"!t momentum dlon~ V .t"" .. J,u_ NtlW tluc In d1ffr..w..·atnn "hen tht.•\ ..i.rt fonmn~ firM onkr -..c4:ondaf) mmun., .&1 P 1 ~uW / 1 Ihen lhe oomptll'k'n& ot mo~nlum along Y-.t"' '' I' ''" 8 •.mJ I' ~m fJ Stl th"· un~-:r1onnt~ 111 mon*ultln1 110

., ,,

..h .Jp, ~ "iln ~8 "'>.

""IJ ~ llr ( wh~rc h

\\h~e;h phi\C'\ UnC'CftaiOI) pnOCIJllt

4.12

Electron Microscope

i\u dcf.:lrnn lllU,T'"'":~I)ll: m pTIIKipk '' "trnilar In .1n opuc:..l ouc m,CPI)C lu

qpuc:tl nHcrn"·up~ \ Nhh.· 11~111 '' UM.·d omd fcx·u,:o.in,; '' done h) 'uitnblc npl H.11 len !'I-t:' Whcn.:a.'l 1n :m d~:t.' ll tlt1 uau.:ro'\\.'Clj)t: :1 h.:;un nl d~c-tmn"' '' U\Cd m pt.u.:c

uf tlrdin:try light anti rot-'U'''ng l~o done l1y dl!L'Irn\l ;1tk und ch.a:tm magncllr fidd~. I 1k ~ :u\ " Piu!ill nu~nh~llpc 1h purpo\C •~ uho to mag.nif) c:nn~mtl) mmutc oh)cCt'\. Bu1 111a~nafpn¥ pU\\Cf ' ' nhJ~ thun 20U tunc~ !!fC31cr than that of op1ic:.~l rnicnJ.'ICU("-=· ..11mc tim"'' 11 '' lH" lime' grc:Hcr ,,r m~n-c nte Umu t!/IL'Wimiml jnr llf!IH:JI IIlll'l l)\l'f)PL' I (. lht: hnc:lr 'cp:tnll inn ht:l\\ t.'i!n two du~e;.>l "hJc,·t-. "hh:h -:un h.: r~'t1h(,.•d hy .lx. th:~ord mg to cqutith>n t ·l l6aJ and i FojL 4 7a l. " .\ ,

1./~:o.HI \

1.1 ]U, t n.\~).11/~N_,\,

whcr~.· Jl 'Ill A 1:-. l h~ nunll'nl· al oiJ)I.'I Iur~ (N.A.) and ). ~ ). 0 /)1, wh~.~u p r:o- the rdmcli\'1: 111dcx r•f tht nu.:dturu. ,i, 1 lh~ '"·'vt· length rn l:u.:uum A" 1h~ \l.;t\~o'

lcng1h in Tit!!

ml',,h um

~J I

l l1\lth•mg f'lll\tt flf

lht.• IIII CW\~U IJIC

I\ II.'Clpll~:tl (If •.1..\, I,C

lht: r\.'..,()lliU!!

prt•I')Urtntrllil h) th\· wa\'c length o i Mtfr:dl,u• lnr i llunlln:llll,l! lhl' ''hjt'l.:l 1111\kl ' tully rhu ... lu~:lrer mfl,t:ttifintti,, mrd

1)0\\'<.•r n l otn Hblrumcrtl '' IU\\'hcl\

()11 , ....~·d

flf-' afttmnc t/ /1\ utt/HIII}t \HJio'c'.\ tJj .\Jtatli•r lnl l t ' ft·n}:lll At.:con.lin1_! tu Jc .. Rrn~li"··, h)f14•llh.'\l!>. f.L.. l mmm~ L'ltttrnn' \\hkh hciU\1.'

f r' HJfHIIX JlfiiH'I • till

h~c ;, \\ ill~! w ith t:}..tn·m~h ....hnH ""•"..: l~.·ngth (S 1 A), c;m h.: UM!ll ln'-h:.td 111 h ~ l u h111r1Jerh• ~1.·1 IH!!1lcf lli!I!!Uifit:allo!l llt~ d+:ll!1np•ncntuf ck·c:trnn mtcrn~cnrc Wlt'- t.a~cll un th!! 1.11.1 lh.u .m ~kc1r''" ucccll~r:th.':d t.hmu!!.h JH"'Iemtal dif(ercnt:c \' \,,IJ, i' u-.."lol'i;Jh.'J \\ 11h \\,l\C lcn~Jh-..• .t == CI'1.251, V ) ,.\ Wtwn \ : (~).t)()U \ ~ ~ IH ., (.'JH ~ H 0'\ A. \t,hich ,... IU< I1111C\ .. nmlh:r

unllnnry

comr.tri:,,,n Hl ••r'lll.:t11 h~ht. Oh\ 1ott:.l). thcn:f\il"t' u wall £,1\'~ much ~r~~Ltcr rc..,uh inf pu"' l'r d11d IIMl!lllh•· ·"'"'' PI llw 11n kr " ' IUU,UUU 1ttliC\ l!r~·;u,·r th;m lllJll u l nJlCit:.ll U\ILilN;II''k' HuL ' \ 111 !hi.' l'lt..'\:u-uu tnh."n•-.nltk' a.... nu1ll~1 tl..m lh..u \Ji t1plll;il miU0'-4-:UflC ll~ lhlng 11\.lg:nctlt.: lcn~t:\ Ckl'lf\)n lxam ~o.'J.n h"· rocu ...ed, j11._1 ,L, .t lt!n._, f't\:"""'' ltghl ,,, \\ C h:tvc di-..c.:U'"-t!li in ~C~HUn' .lX .md '"' rn

;, ... c h:\!IHl'-l.u ic

:uu.lmagncu~. llli-'11'1 11~

In an

opU ~;~ I mic l'm~•tlC.

uhjc-.:1\ h:tl tll,t'

diameter 1.:-..c; than 200U A CJili\O' he rc~\•lv¢U. whcr~ .. m ttn \!leccron nucr~\.S\:OPI.' ~l\'in~ ptlw.:a·•, lOA.\\ Inch'' 2(Xl rim\!.\ IUtlfC th.m 1Jun un oplh:al11111.'n~npc Rc~olutiun ilt'1hi\. t•n~r J)l:nuih- t•h-..~n .11hnh in 1hc r-:ul~'-' of nw•h.:cu1nr dimcn,iml'

t•r

Construdion Prind1J1e of F.kt.:r ruu ~licroscope Magnc1k dcc1ron mit•ro,coJll~ ~JI lr:m,mb.,iml type whidt j.., u~cd w1dcl) "'U' ti r-..1 buill b) Ru'!'k3 in I 'JJ~I , Af1er thai o;cvernlmuth l tc:uton~ were done and very h1gh de£rce ol perlectton h:ts t-een n:~H:het.J 10 nu,dl'I'O d~-. r~n Figure 4 ,8( n) ;md (b) ,give 1h1.· ~h..:m~uu.: t:hng rnms Of d~!C I J'Oil nuCroSCHilC und t)j)IICUl prOJCCltOn m1 Cto~COJ')C, fC-~pcC II \'\!Iy.

MagnctK kn\C~ arl.' u"cd "' 1hc cJ,;~mm rn• cru~copt.' An det.:llfln nu\:r"\C"P"' ".._......,... nu;tll)':. l'CI)' large modified C;tlhudt r:l) 1uhc. where mt:tg•lclu: lcn~('s ;arc u~d ·1h(• f uncllons: oi rhr \•UrtOU.!' Jl:lnlO man chxunn

rnic-rosCOJ>C t:, S.lrnilar In lhos-.~ or ~111 t.lpt i(.' ill micro:--copc. An ..: l~.·..:tron gun CUiil-. clcclrons whtch Qrc ac-..:l.! l ~.!ntt~.:d hy r><Hcmi:st of ahout 60 kV. The rm c r\i~~.·n~

Qn.cmwm Pfly.rh l tuul Sthrbdlngt·r Wm·r F.qttation

2t>1

. <"_ \ ~

-)I\ _ ,_

Sf~i.'>.:III\Cil

·1 -

~f,

- - - -·

\; 7\ __

ClhjC(II~I.' len~ - -•

)

I '

, l'h•*l~•nphl.. pJ;ll~ I .II

Ih i

cnclt;,cd 111 .1ugul tnclal fr:m u: :uul high dc:!_!,n:~ •'F vat:uum 1.. : nwmt:.Hih.'..l \O..IIh ~t hi~h 'P~cd thl lUSIUII pump. M:tgn¢ti<:' conden~r lens M 1 concenu·mc, the hl.:.un of dlX:trUil'i on lhl· nhjccl sped men X which is (0 he magnified. SlllnC nr Ihe ci··~Htll" in the he-ane. \\lu~o.h \trike tlw vh,lt.:Cl an: MoppcJ Oth..:~ ~caucrcd h) th~ ohJn.l 1mvcr~c LO rhc mag ncti.:- ubjeuhL' kn~ M 1. which m~L.~~ the clcctn:m~ h>lh\'l:r,gc «>!bat !he ftr>l m•gmfi~d tmagc i; fonncd. After that third magnctoc Jl"'l"<hlr len~ M , foc u~t:~ :a 1\lll:tll ~cct ion of thl' magn.Hicd bcmn cil h<.~r in a\ Jewing .;c r-.·~n. usual!) mad¢ 01 o lluort!sccnt mJtt.!rio.l or on a suitable ph mograph i~,;. phat..: fm .a pcnn:llh!nl t\:CC1tt.J. 111' ugmn flll~t>ibk 10 enlarge the phologn1piD. -lto5 timt::,. withom IO))S or dct.tils. which g i\'C."i piCHifi.':S of ithout 500.000 01" more tiJUt!l, larger than the ~pccuncn. The mcthOO cf fOCU!\in~ orclcclron beam con.sisls; or ahcl'ing lhl! IIIICihil) of thl! nl:aFnl!lil.! field in the <.'c.1il or dectromag nctic l~ns until :1sharp lnl~!:l! is "c~n on the sct·een. In tm rlrcmm fWCm.ft'opr niMef'l'r.r lodkin~ lllllu~ .H'It' t n, M't".\ north~ magmfirtl olljr~·t bulthr maxuifitt d slwdow oftlu· ubj(~Ct. In <tc.lduion to the higl1cr degree o f m~gnificntion power. 1hcrc is a noll1cr advan1agc. Uuc: 10 1he grcaLdc:pth of Inc us o l de:clron... one gets nmgniJicmion in three dimensiOn:\.

Us<'~ uf fl ed ron Mkwstopc An c lccm)n micrf"~'iC<lJ'L' ha;;. a

\1 ~tricl)' nf u;.c:=" iu n1cclidnc, intlu"-lr>'• crys1a1 '-lrucwrc. :m:llys.t.:: ot funt'llt•n ... ol micro-orgamsm'. t•tc . due w he;: ht,gh Ot'lkr o f li.'SU(\• in~ puwer ttJHJ m<.·r..:-u., ..·d l.lrpth uf fo<.'US. In :m electron mkro~c opc. the objc,·t i, dl.':,troycd by electron bornb.trt1me.:m One of the method or 0\ c-rcmning thb. Jiffkuhy j, tu \Oak lhC l(.pl!'dmcu in ol ,o)ution flf osmium ,,Jib. ,o th:~.t e\en tf the objec-t bum' due to ~lectron bombardmt•nt, a min~:r~tl \kt•ktm1 I' ~ull ldt fur t.lb!\l.'f\': J.tion. Study of tc.:-;lil\! l!hct'l, p~rilic:.~tiun uf !uh t tt:'~ltin~ tlll.\, Ct)fTI()(hll iur1 pf r~tpcr .mtl p<.tinb. tcstint: thl' 'urfaLc uf "'Yillh..:ti(.· dtemi~.: ..d pla:-tics ck . .trc dt)Jh~ u~in£ m1 electron micro~cope. lu the lich.l or 11\lUi~o.·in.: JIIU p;tt_h.~lng~ . IIO,r,' l l f .m ..:lt:I.'IIC~Il mkro,cupc i:-. Slf!OIIicant. S!udy o r t.liff\!l'i'.lll LYI>t:::. ol h!INC I in umJ \ lfU;.C!- C:tll ht:! done irt IIIUl'h greater det:ul wilh Lh< help ol clcmon microscope h1 lhc swdy ul CT)\t.d .. um.:turc umtl)'""· clcc,;I HIII mu;.roscnp,.: 1:- U~l!'tl. \\>ith the help or electron Jiffl~tC iion unit Ill .uldllhUI HI the main inc;.tntment This. ~rnltls one Ul g_c1 t1 pmern ol the mom 11' a '\~f o l ~.~oncemric ctrclc.~, l't•om 'uch p:tltt.!rn tht~ ron!i:lltuem awm~ '" the m.u..:nal t.•an he dt.·t~rm•n~d !\o th:u cryslal !'tlrucwr..: c:.n he idcnufi.:d .md ;sn.tl y;,..:d.

11mgnifkation. gl'cal

An dec:trnn 1), : cmlln..,"4;1 tu ,, ..p)l~n~lll b." ul ,11:-.m~lcr 1U

m c. "••lc;ul.uc th<"

minimum unC"enauuy m ns \tluczt> Ma.v..

nr dcn run

., I X Ill II'-.!!

Ptllh.~ .. 0,:(!lh 1;1flt = ''·~l5

((I II

J.••·,,;

~r.;! lt

Here .1., : W " m Thu>

J.i' ~

hiLl•

6·625 x 10 "

2Xl. l~ X J O•

1.055 x

to ··•· k~nllscc

p; mu Thcrdorc. nuiumum

unt:ctt.LUU~ 111 \dU..:at~ • ~

2. P"md the KJ;:.. :wd velocity u t pmton :i-...-.<ICt.il!!d \\ ilh dc· Brogtlc·!- w:•vclcng th of 0 .2:i65

A U 1VC1 th:tt

Mru.~ uf prulun ~ l fi7 x W tl 1;.~

( •h:uttc of l)rnt<--'W'I = I h x W PlanC"k:'~ Ctm .. lallt de-Broglie'~

=(1.625 x 1(1 u

J.!\~c

W;)\'Cfcngth of proton h

), =l!Jp =llfmt• i.aU!~M t\- 01~h~" II) 11 m

'" = l 607 ;.; IU ,,

lr.~

(•25 ~

J -....·e.

It- h tt:

1•/m). =

10 u

tt b~.·\ ~~

t•=LUM7~:

;. IH -

!a. I) :'~•" ~

I h7 "' 1fl -

I ~.SI

IU'nlf.,..:.:.=

lfi '"

~m/'<!.,

K 1:. ,,f rr•,•or .;... 1/2 mp : = 112

1 h7 ..... HI ='~ Ill'<~ n

tn',~

Ill ' J

: l60.()1)

= lO<Jx 111'\.•\ = 1 .: \ J

WILtl '"lhr "J'clt:nl•lh c1l J tx-.nn 111 neulntu .. tu\111£ I l 1 :lll cncr!!}' U02:l t>\'"1 I:!J >U1 cii.'Cirrm:md pholon ca;,.h ha\1.' ·• w;a\.;-kmh ••I 2, \. whullltl.' tht u 11\Qilh:nhuu .mt.lrll l't~y·•

K E. nl ueul.fe•u :. f1 H2o'; • I h 'a.. Ill 1~ I .: IIIII • Ill

:!.IS'\ ..: W m.•

h hl..' ..:::.....I 11 j l.b7l•)( Ill x.! JS~x

1(1

llf 111 e , SOl'i \

:. ' = ~.6'S

X Ill 4 I \II 2x 1n w -

~I)

,!!

VciUI.'H\ u dCI..'UUU :

Hnt.'r_f!y ol

~le;.:lmn

= I

ll. I t IJ 1

lilt* • :

33 11

./. I ll

1(1 II

iI f't'

m·'·' X

.< 3 I>)K 1.6 X 10 IU

II)''

= l7,(._..h c\ '

12)

Encf~)'

ol ..,h,,u}n 1,. 1- = In•-= ~ _ h.b2:'i X I 0 u X ~ ). ! X ltl 111

=9.•n'.) .. 10 tt> J F.:: h .l lt,q

;o;

lfJ 1 eV

K I()'

I••

.a \ ..-tuf'!.•<"d r:uud..- .a.:..:d~.-'T.Unl h) t."'\IU.II ht Uff~(! \

3 r d td .2tl l \ h.i... .l !.k-Rhloj!ll<' ~~\(" I<."R~Ih Ftnd 1M m.;..., tll thh (\,'lntc:IC' aftl.l,.a~ •h•,h r-artkk '" 11'1

=I n

t 'b.U}!t" nl lht' f'-'m,it,· l'l.m..~,

,,lfl..Lm1 :::- h ,~_.;;

lll IU N

tn u J ........

•

When ttr p.tr1K:IC' ,, .-.:, dC""rat.:li h\

\ 'then

•

,·\ :: , m4'', ,.,,. - , ~mr\

Iii-

). • ldmt

({){)2~ X

' -

:!.);\:\' lluh, 111.1 •

111, 'md

"Ish,

x m.u~u~ x HI

j\H11.1•· ...

'""'''"

t'.el.. u1.ah." 1h..- Jc Hfni!Jk

"' 1'

10 l~ J

u, " 1u -,. '

m- 16)( .. 111 ..., • 1 hK

'*"'<"kngth ell

~no

\..)!.. ll~:lll·..:

11 ' ' ..

rk'tntun \\h<t\,(" c:nC*tf\ ., I c\'

\to~'" ul l'k"U1n'11 a I tt'7tt • IH ~ l.~: h.uf'" e11 dc-ctn"llfl s.. I '• "~~ Ill •• C l'l.ur. 1 ·, mn ..l.ln1 ~ '' t.~! • 111 14 J \.L"\"

IIH

~ ;. I ,, " IU 1 Jnuk

~~ .

: !

1 n ,., W , .•

lh~f••lll

,,: • I 1Jo4)'•

,. • n :1\f. h

111\ t•; I lK

l tl' n\1-.(t

1· "\pl.~tn "h~ C'l«tran ~.mnu4 <""\1~ tn dK" mkku' t•l

'"',.,tJ,nt h' ~~ u"cn.." ' rnn"rk -'• ~· "h\'l.:" •.b - Ull-;..Cil.Jill~ tn

f.llhth

lfl 11 m

the- p.,-,..Uirtn Ol

r.1fW.:k

\p-=- u n\.~l1.aml~ m 1b mmntnmm

\HPI"-'"1o.' 1h;tl lh!o! \!'l:~tl'lll1 ,;nn <,Ill)' in llh· nud ,·u~ I h..- un..:\.'rl.unl~ h m th.: P•"lhnn ul un <lc..:uun ... ft'U~hl )- I he ,..runt.• ,., 1hc ~ll arnc1cr v i the nu ..:ku ... \\ lu~h i• ur lh\' md\•r ur ~ x IH H m ·1hun

.Jf•

- 1•'.11 = I !l545 >< IU " " n' x 10 2 X J() I'

Fnuu the unltn.umy tn the: momcnwm. il ior.. f'\l~!<libk lil get n rough c...umau: 4)r -."flt!r)!y or •Ill dcclmn Ill Ihe nudeus Rclilll\ I 'ill!..: tollnulo mu .., be u'\CJ hcC~I"U(!(' 1h~ dl."t..UHn rumc:' u:ry rapid!) in lht nud~:u,, ;" .,..,11 he ....c:cn •"'"' lmm tb: V-\!11 kuowrt l:Jn-.t~ •u·1'> 1\"',LhVI"tllt.. rclultvn we 1-.UI)\\ f.

=: u/r ·' ::

r ~

Rc(!l M ••~ f'.nNll} :

~ If!\'~

\\hen the \'ttlncil) uf the l):lflit'lt ,, very IHJ!,h lht'n the ~h.lnfc" WIJh h'h\\:l l)

m~o,o;;.ul

the r:mu:k \\ Ill

OJ\

111

''hn1:

.. lllttl -

•=''="·.:.·=~

··h- ~·~h

Ill= l n!h~ ~J I p.u'tn:l!! Wllh \'d,)CU) I'

m,, • 1

re~1

m;, ...... tJf the JMMIC'I-: uf Ught

~ '~ludty

Tht•rcftut·

' 1: - ,..:'.::"!!"':..·=~

Nu" 1f '' I'•

"'"ume\S 'h+ll

.Jp .. p. then

,, o.s

10 :u

,~:.. : = <O.~ x

onJ

w -:o'J.!: o · 1n.. ,.:

c:!_1~x IU.!'J

.. Su

Y.C

\.oHI ltt:~k..: l l h~!

w ' . rh ~n

2mJ ll!nll, 1.C'....

£!• 2._25

I~ • 1.5 X 10 1 ~ Jnu1r

1.5xi!J " Ut

E . 1x

1 "

w" ~v

/;· = 10 MoV 'llu•~ Q~;or.,;utdJflb 10 1h1s tc~uu.

Q t ree clecltl>O l.:(ollluH:d \Hllun ill)pa~o:C' •D ,-.mull as 1he nurltu'= ~l<'ll ld h:w( 10 h~\'C' lane1ic ti\Cr~~· ul ihl' ~lrder of W \ •leV :1nd :1 \C:ItX'I1}' wemrrthaH 0 999 e But cApcrim~.·uU.tUy lho l.'lccuoncnoned by rudtOIJCU\'(' m~c1d1 hJlVc lk'\'tr b<-eu fouod to h.,,.c Lmcoe c n l'r~il':'S ~teuter th.'tu :~hou1 4 MeV HI ul lh:n (Ht!cr. ~lm.:h '' \tn:tllcJ lh:.u chc cakulalc.J \'a1uc lrmn tht· UII\.'Ct1:\lmy prm..:•rlc hax!d nn PrniUII<Icctn,n h)'fl'-llhc-;i,, AhhHuGh tim a •kulalhm 1:. .. ruu~h om~. hut \IIlli far I"C-'iUh "i arc ob~>un~d frnm more rii;ornu~ calculataon' UI'Hl

in ''tew of

tu,~;e

diSCr(pn.nc)' 11

~t: m!i

lmpwbabh: that nude•

c~1n

contain frcoe

i!l.:dnllh II ........ ,;'i)Mid\o·r lh~~ 111\CCtl•IIAIY «"l!lt10 11 _\ ' ,, ~It IA"'h:ad u r /:. lhcn 'el<l\"lly t'~ltk" 'fl•l'l -~\ 1ll come liO MeV, \\'hJch '·" ~·C•)' 1nuch h1gsL'' llum cxpcruncmaJ \ .JIUc \.1. luch ptH\C' ~ l cLLmn canmu !>.l.t> 111 nudeu'

7 C11kul.ttt IX ·br• •;!.•L''\ '' J\'clc:ngth a_,'-('K: I.lli!'t.l "1lh h~IIU\\ 10}; p.'ntd~::o. .Jmt .. mnntcnh on the rc ... ult 01 ~Iii<-;.''' hll mu;f,)l! l~nb \N\'C'IImg wuh \ CI<KU) SO u lf~ (11) M.a.., ••I h IU ~~ k;l, fr.wclltnt: "''h ''dr<il~ 1.1 x Ur' ~,nf, 4 1 (II m.: (,fl lltu.-ru~;UI\ =: f~l v: W ' " 11J e (~I X lfl Q l p .tnd 1 su 111• "-• munwmum /'- ,,., ·• X v If)--'> J;.l! mf, _Pit :::.

6.625 •, Ill u ..,. I tS ;. In ·._ J .S);, 10 ,,

111

Cotmnt ,6: In fu~ l.,,,,. lur ,, n.um;al p;trtu:lc ''I 60 nm:-m~ru nlnM ", 0.·-hw,tu~·, \\11\C '' "~' 'lll••lt "h''"l. '' bc>\•ni.l t.•Ur pcr..'tpCion Uuc lu lhollll ' ' m•t I.IPJ!·LI~nl1nr \J:uh Ill" "a'dcu~lh '' ..amt· ,,.., tl1.1t ttl IUU ~c' A lot) phntuu c;,,.cu thalli ~ h.b:l x IU " J.s, , "\ ;.. H) mi... '~ f h • Ill 1 ,m--- 11 I "~~ IU ' 1 ~!l.l!ntr~y ol phuh'n-== 1:. =- IIIUk""'.: IIlii

S CukuWil" t.m.·ttl t'lll'JJ!' nl 1m d n trun who"l' Dc•bl-o}!lk',

• I ll' h:.

\'!

h,. IU

~\\.' lt;m:lh til "

I : Jw: 1~1

'·

f-\hHhtll = ), = b.b.l X JO 1.i X J X !0> :I11,.,Hf

l .b X I (I

~~~ Dc-h1nJ!h~· .. ''·'"c h~n,\lh t"ll c:"

clc.:1rnn -: A.: .J!._ • 12 41 x Ill I: n1 m~'

QUESTIONS Sl.tle .md 1.''\llhun ll-.:1"cnbcrg'., unl·cruum) prhlliple Oeuw the \"'\f'IC\'11'11 h•j liC· IhH!! III:-... \\.IH lcnt:lh Ul 111.11fCI' " '.1\C.

I')C"'-.'Ohc: lhC J),l\I'•'IUI'I-(i cnner C:\pcrimenl for lhc COOJ'irmUIUIIl Ul \\41\\' U,UUI'C Of dt4.-IU10

3. Hu" m ••n~r ".1\·c" thflc1 IIHm h~ht ,mJ Mll.ilh.l '' nvc~, Gt' <" Jlflercncc •lUI)' l>to\'C th::11 ~k.:1m1 eJJ'IM•)t exi+,l 1ft nudcuo,; of :.n 111om (i,, en r-;ulnh nt 111um .... 10 _1J m.

Cah:ubh: d1c tk·flrop hc wuw~leJl~th 01 a proron ~hO\C ~10C11..: trk' f~) j., cqu.-..1 h ' thr teo;! 4.-'llCI'£} Ill ~m d ~t:ln'm \l,l"-" nl pmlun 1... IR3ft time ... ~u:.1trr than !hal •tl !111 el t:,~IOlM- GiH!II tlllll

V~lochy oJ lith I = J x 1U" m/s, Mn<.:s of clc~cron : 11. 1 x I n \I kg 11 f'lon ck 's \.'Oft!ot. ull • h 62 x H1 J sec

' lfll'~

\I I >. W

1 x43 x20 11 J! IR:I6

fl 6:! J( 10 .f.j ., I .. ~j) ••., l}l16 )( 9.l) X IH"

~a-I.OOx 10 ,_.-:OOI)f')4x 10 lilm

fl. Wnt..: oJ\'''" Eu·~h:m·~ cttuatavu tur phO I CH~ l cLirn: t lf~.·~ t . Wh.u ~~ llu.;-.h,,JJ

tre..lu~n~.·y ·' 1 St;llt:

llcN·uhetf~ unc:cn.ulll'' IJIW\.'Ij)le

lind illu~tnne n b\ :m C>.J)I:Iuucnt un

chlfraL:Hcm :111 ..t "'"!11..: '"' R \Vh~ i' ,m<k..-tn•n mirro,C'il)'IC' Ml fJIH\Crfu l thlm ur,fimu) mkru,.~upe'' C"t•tupah· \\'tlsl..HI}! rrmoplc l"-'tWt'cn ck•:ttuu .u1d optical miLfo~eupc" '' 11h lhJ.f!rum CJ, (\uuruh! tht' nnnimum um;<"nuint) 111 I he lucatit)n of :' nuL"~ t')f 2 rm. llltl\ mr

,,.,,h ·• -.I"C.:d

I 5 nil> .and lmi\Ullliill uncerwint)

rnr,vinc_! ''a1h .1 :-pc<.·~ I' fc•• h~tth ''

olll

dedJ•IU u f!.ti'IJdc'! , , II.L ''·''~'}

)(l(-!Uu)n ('of Oil! ci~,:IJ<'In

E:ttlhuu your.tll'o\\1:1 h:r

t•xpcnnu~m:•l ,·v~~.lcru:c.

II .-\n ek«.ttPn

the

,,ru.s " I011 m/._, g11.'tM thntth~ unctJ1111111)' an the nwmt·nlUIU

llHt'h>'"OJ'! \I.J'-

tn••-.k hy

u~ln.g

..,_hon

~1\1111! !dl'\,tul

""''1! length vi ek"lf''"" hi

pnwutc tngh r.·.;.duuun n~cn 1:-. It pus .. Jble U) mal..c a pruwn nucro!>copc and u llClltr.llt uu,·ru~ope'' E'<pl:un y _ our :m~w~.:.r in c:1ch co<.c. .. II ;1n clcc•mn •· lncnhwd m 'Jl:'Cc. ii!O nulmcmum t'Ccom~' unc:~n :110 II 11 ,.. lu~:~th ....:d

u11im.:.

Jl:\

cnCfi!} become,, unccm1ln"' Explain 1hi' \t.ucmcm

Wh~ ... ll.'"\4ll\'il1}! I)U\\CI til •.m dcclJ(IU 11111.'1ff';(.'OJK" I u~ lllliC'> highc.J tb.m lh.ll ul

1-1.

llrt upliC.II mi'-:rU~t1JlC ! f~:\flloUil \l. ji!J prupt!r tn:lt!Jcm.lticnl t!Xflr~!<>.,jUII. I( the r.m•dc$ list"d h(:Jo,, 11rc have same energ-y. wh•ch ho> the shone:-~ 1

\\ 11' c

length· dcctmn, tl•p!"lr1tcl(', ncutrnn m proton! 15 A prot•tn :mJ el«uon have the '-lame speed, which h,Jf; the lnnJ;!cr w.tvc IL't1~1h i 16. Why i' th~ \\;t\' (' l'latUIC l\f IH3lh:f IHJllllOrt' 3J)J)~U CIU 111 OUr tl..uly ob~CI\attur.-~ (1/hm· ~111~.: in u.1r ..tail)' oh:.t:rv1uiun mas..-. ofdlt' portidc.' i~ 't'JY lnr}:.c m L"Umpari'-4lll tu t:let:lrttn nr prmun mn"-'· '" ll..:-Rmttlit.'<ti V.ll\'1.! lcn.glh Y.ill nnne n:ry 'mull. ll·~s- 1h,m ~lhlllll~ .;i;o<.·. \\htdl '' ~')\lnd our pcrcc.pllCIIl \U it h,..._ no• h<'t.urn~· ttpp~ltlll in ®r d.uly htc, • n t-'ind th<' uncerutwuy in rhc lucaut.m ol :1 p:\rticlc. 10 1enn$ <•f the. de- Brog~t:·, w:m.: lenl!lh ~ o,;o 1h:u rhc unN:mumy '" II!'. w:locity io;. cctuld 10 115 vclociry i;<;,c,::IL

·~

I· \Jdam Cmnph1U co·l·~ l \\.llh

t'J. Ounn~

~l l~.tl dl:lj;r:uu

rhllll,_l-t'ICliH111 \.'\llh~lttll,

COIIIj)IIJII ~lull ... JtJurnl hJ bt.: ().(JI! .\ If "'"'c

kn}:lh ol 'he itll.ukut phulf>ll "U,OS A, finJ nul Ih..• llllj,'lc ltt:h\ .:en I he Jm:·cti,1 11 nl mot~nn l.,l lh\ 't.:alh.!r~tl phul~'" ;md ut 1hc rl.'-.:t'tl

\'k\'lrtlll

SCIIR()I>INGER WAVE EQUATION'' -1. B

The \\ave Function

l'ttc d ..~... Bul~hc·., rcbtltm hctWct.:lllllonlcutumuu;l \\;1\~r..' h·n~ 1 l 1 wlui.:h"' L.nown ~\p..·ram~lll:tll) to be \'UII" tor holb phocnn:-. .a.nd nthcr lu_;:h \'dV~o'll\ I)Jtticlc", \Uf!!!L'h. lh:1l II mighl ~ lhl,,lhllo! hi U"l' llllll'l'lllr.th"\l hlllh,hl'"" ul ~\:1\1.:' t11

dl..'\4.'rihc fucUJi/t!ti Jli"lr1idc:+o of ll!atiCt ~UlCI CIIHifU ;Iof nldtatmn. Ill 1110\ Ill~ p.tt1 1Ck -.: .:au h~: \ IL'\\'l'tl,h :1 \\ ·'"~ .md on~: c;m mca:+oun• 11' lLl\t' lt-'llL•th ~ml Ihe 'luc ..linn '': \\h:tll' th ..• qu~m11h' \\hns.e v:trt~umn m 11111c und o:r.l\. .,• m:t"-c· ·1p thh \\'a'~:' Tt• II\ uur idt:o\S \\.; !+oh.tll t'OI1~ul.:r .1 \\,&\\! luudwu IJII t 1). th.tl dqt.,:ch l \ Hn 'P:H.'l' cn·P rclinalc~ 1 .. ~. omd l lllh! 1. In lht• cot'c uf \\.t\·.:, tm n ..u\•tdwd 'trill!!. lh~r..· \\:1\.:' lmh,·ttun 1(1( 1. /J r\'pn.:~l!IH!\ lh~.: tr.ul,\'t:t'c Lh"rll,tll'nu.:nt l ttl tin.· ..,,rill}!. f••r \4Hnn.l \\;t\t• it ti.!J)It..'i.CIU"th~ diffcrnUi.1l pn:-..,lllc 'V' .md fm tl-.·l."k.,.tltitn.a~m,:rh.: ,., ,I\\" 11 rl'prc,cnt the declriC' rield \'I!Ctor 1; •md nupnNil' fidtl \ l'dm 1f Sci fnr m:u1,·r c:, rc:p~scn un~ lhe panu.·h!::o ,,.,.. c:m .tl..;(' H\ l l'lk,lu~;.·c m th..• '•tnw w:ty tlw ''·''"~ lunCtlt>ll !p'l L 1). S;Jy a ~<lnductk•n ~lc~.:lltiO '' JU0\'11\,p lhiOUJ.!h "'OI)J>cl ,., HI." ur .111 dc. .·uon III•J\ mg ;tb<.•ut lht: uucku' 111 ;:, hydm!!\.'fl ~tnm_ ,., hat~' c:r he th ...• '"'~I,C. , , II t' ~UIJU liu· wm·r {imt'lmll VI(' I, = II jnf C'l OT J•mm Ill vmu• om/

w., ..

(llf , 1'1'1'\ mHnm oj 11'111'. U't'

tn/1 c·nmt• Io ~Hmt nflulumt tlw hl'lr,ll'll'lll n/lht•

J'IU'tldc•,

\ I~ fUCullllflll l<lr J CC"llh. Crlll':tll"<l btandt Ul

\\,1\ l'"'

\\ hn. h \\'-" 'half ~.tit .t '\\ :1\ \.'

p;tl·~ •t' ' ' ,,, .. hown 111 ht!.

11.J. wht:rc IJI(,, rll"" plllllt.',J ilJ!•IHhl ' ln1 ,, Jl.trlll'u1ur !Hill I rh.: ;I\ \.' l.t~~ \\ .1\·c kOJ:!lh i. <JIHJ :Jppnt\1111.11~' l'.\h."II,IOil \}j thl.' p,u,-1."''1 1-. ,l\ .hn\\ n m hg -l 9 Tim qu~mll1) V'f\.1). j, ;, ...,umt:~l tu h;t\l'lhr~c ha,t~o: p141J)l'.t1h:' ~"''. 11 n111 utll'ljl'rt' u·.tll llwlj. ' " Ilml rt f'mr mrmml_(m llw •111/rm·Ium '''fWI/1111'111 /mgc fiiiiWKIIIIIUf<.' W/tf•f't' flk (ICIIII•'f1· Of t•fu•IIUI M /14t•f, I•• b~', muf

S\'\.'t'OJ. II I,\

,,,,If ('hrw/wn·. \ml

hmJ

~'I(.\, r} tln1-rtlw.\ tlw lwltmtotu

1' ' " .Wl ~t~

I'~" ftt

f,· or

J'hiJ/rU/, unt tlu- t~tlli \IWnl ch \lfilmtum uf 11 mmrlw1 of HHfl fJutmla

.t.l.t

Phy~ical S i~:nilicance

nf Wa ve Function

When ch.:~ttluu.tg_lh.!ln. "~t \C tr.l\ t:h lhh>ugh licL: " f'-'Lc dh·n .b.:t:ohhn;; In M.&\\\cll" .. l."tllldlmn the niTJngcn·cnl t-11 L'lcclric ;md m.agnt.:tll" tichh lhitl l Ufll"., 111 "'IMlC .md wm· ;md 11lt' 1a1c per uml IIICtl tJf which. cncrg~ j.., tniii'JXIIIt.:tl h~ 1hc \\11\'1..'.. I ' pruJ)unh•nal tot:=-. ,.,Ita~ I:.' I~ the t~tnpl ituck of l"kLlriL ndtl \t:t..tur In 1h~ 'arne: \\J.~ \\hen .J photon iqnuvmg with lhl' 'pct.•t! ul l i~lll thc:u. JCc.:ordm~ 1u Eirl .. tCrn. Ihe tdh: of ~twrg~ tr.tn)+fcrr-ctl i"' l'mporttonul to lhl! U\ ~rat=c nunthcr nl phcunn JlL'r un1t vnlumc nf th·; heun1. wh.:rc c.tdt phtllon h hu\'ill~ an \.'11.:'1":,!) /1\' Ncm fmmthc ..,;onnc~t um llclwccn \\'1.1\'C uruJ p11111clc pu;aur...: tlf rml11t1uu1, \\.1.:. Gill ....ay ah:rt the ~u;tf'..: of the dl!ctric fiL•Id imcn~it} is :t direct m~:.n,ure of 1hc =1\·cr.I~C' d t.'fl'll)' tlf photun.

~-~ _f_ I

~urm:tlisation

-----~

cundition:

Ntm rf tp(x./1 i~~o the mnpllludc t'l lhl! 11MUn \\~1\'t: .H .U1) puml 111 'Jl:lCL' 1hcu dt\! p:lfiH.'IC dl.'ll"ll) <If th I( fXIHII 111:1)' hi.' l.ll..L'II . I .. runpnnJt)llC'c.lltl ty'~ t. / } nu ... y?( l, o h 1hc measure ol ·h~: p:sntdc d~n'u~ . f\I ;Po lSorn :,uggct-lt:d n nt.!w idC'~ tlbmll lhC' phy,j(.·ul 'lgllliH.tlllt.'( nf ltl t, 0 \\l11d1 1' i!l'IIC ioiJI~ iU:t.:CjU~d U()W·ol. tloi}'~ -\f.Ct"lhllJ; to Mn\ Rnrn. 11 ..sr m·.Lult t ,, ruc_,,.,urt.'.mL"nt '' m;u.Jc. to locrllc the p.1nu.:lc .c,~oci:ucd \\ tl h lhc "·''c lum.:tu•n If/Ct . /l thcu ,,,. t•mlmf,,lttl l1t \ , 1) tb.. tlttll tluo pm ut'lt• u 11/ ht· ,,,u,J tit d '·o-otdimw· \ uml \ +- th 1\ f'h'.tJ rl\

a:.

'I' 1,\, IJVII\, IJ (/,, 2

PI\ tlcJ, -1 "'' \ 111 d .\

"hen:

'/'*(I, tl I '

tit-.: i;UIHJ'IC\ (tHIJUt;.oth• H I

•4 I'll

1,!11 \, IJ. ~CaU'\L: ip'(l, II I' l:Oil1plt:\

111 ~cncral hut plnh;ll'tlll} IHU'~-1 he r~.al .tnd nnn·ncg;lll\'~

I knee.

/'(\,II.::

~II\ I)

=1'1 1

l \ , l)tjll \,II

'"enlied the •pmbohduy dc•u.f;l., ·• '' hl(h " tht" prob,•b•IH) ut ht\."oUmg I he po.~rlld~ I"'' umt tntervul .uumtl l f Ul 1h.: t·il\1" In three tluncn,imml cas.c pnlh:•lulny dcn,uy ,.., t\nllcn .,.., /'If. II=

'I'

(I riVIIf rt=l ytlr 11 1·

1111~ rnc~uh that /'(r.l )th ,/,.<I~= f'(t, tltft•. ' ' w b..: the prob:cbilil) o r 11nt.lin~ 3 p!lniclc in i1s \ olunlc \!lcmcm ,/., ,,~ ,f. = dt' nbout us pt'Hnl r at ttm-: t. rrobability uf rindin!! lhc partu.:k ..um.,;whcrc 111 lhe rc1=um nut<.l be unny. \\htch give-s the ct;nJ•ttun

J.~IVJ(r,ql

dt•= l

wh1ch IP(r. t) muM .suusry. llu~ contlluo n •~ cnllcd ,,>r~t~nlumum rmufttifln nnd W~IVC or Vl( r. / ) wluch ~ilh'Jfic:-. ''· .... C:JIIcd uo rmnli.wtl U'IIIT f,wdttU) .

••

4.1 5

Dc,•elopmen t or Wave Equation

Au'l~rc1i np

HI th:~Bitlglic'-.. tht.!llry. a panicle ul m:''' m i' .• Jw:t\' a-.,oduh.'d \\'1lh

b\'' A.- IIIli J.L If rh~ I'M nKft• hiJ\. \\ ~1\C proN'IIIt: ... , .... II I~ \.~1\pC~I\:ll th;ll lhL'l~ ~huuld h.: ~~tlllC h0r1 ol \Vtl\ C" C\lUalittO, \\ h1-.:h tlc,~o.·nhc' lhl' hdta\ I\UJr ol thL" p.tnsdr Earh..:t \\C ha\'c tla\Cuv..cd th:11 V'' l, ' · • 11 ''the v. ,,, '-' funi.'IIUII '' hu:h 1tprc~cul!\ the w;'' c Ui,pl;h.'4'11WIIt ••I th1.· pantcle \\ ho!\\! (U ol \\ .1\ \' \\ hl''" ",1\ 1: lcni!lh 1' !!1\'Cn ~ .,_

ttnlm:lh: ... om:

f.\,

~It\\ \h' r~

It.-

"·pu-.lanl

v. :• ilt tim~:'·

''''h: till" twn .:tau;llrun' I

hl!lf~

!' t - Jw: f'

= ht'omcl p

... 11/). m '''rnh

,1r uoncr-~.•1

''' lnlhm·,

!!). :::

J..n = ItA

'' h.:n: { =-

_;r A

'r. -A

I t ~ II

t-1.2:!t

(2H\'):. /)\\,

-ff

\\ ha~o.• l

llr. L'iJIICc.lfn-tl/kiJ-:11111111 \'f't'IIJI' .lfli.J H j,

C!llll'IJ on~u/nr

/rc'f/flt'U('\

nf thl'

\\:1\ ,•

A Ultl' tlltll~o.'fl"hmoll \\ .1\t" luuch 4111 lJII '· 11. th;tt n·ph:"o4.':tlh il p.trtll.·l"· nl complctL'l) tm<lt:ft'IIIUncd pu:-.llumlrn\ cUing in du.: pu,tll\"t.: \ ·"lu c\.'1 um. "11h IU\"1.'1"<1)' "-mm n 11U1111t:nlumf' and K L. /:'. \\Uuld tht"n be cxpcd&:c.J w hJ\\" ''"""til Ll1c fnllu" lnp ft,IOi'- ur "1llh.' Un~;ur t•nmhin.uinn n( th~m. ;t .. it j, fi\Cil d-''"''C~IIl) lnr lh~:

.. nlnuun

tit

\l.''"l'lf,.

~qutJtlon for

k und IJ

VII r , If=,\ co< !1<1 - u·l) =II'"' 2" (

vrr, , n- h111!h

~111./1= ~«'"'

.u () rhc

wll=.hlllltr[;, =At>'

,.,]

(l \/)

Ph•b~

\'Ciocat~

'ci\'~·H)

~~\'/) 1

Velocity ;md Group Vdocit y ot pn.>pagauon of the wn'c 1-s culh:d u~

pha..~

\do.._,,, u1 won.·

;,md "::,htlWII by

I"''

T_]

It 1~ th~ \do~ II) \\Jlh '' lm .·h t.hc phw"c: of 1hc "a'c m ''"' ch lh~ ~. IU)

.,..,>

crc:,t

.j2.11

0 1 J lrtm~h

The dc~Rrof:.lu:·~ m;mcr w:wcs can he dc~crihcd a.._ !I <.'\llll'Cmr.ucd bunch oJ w;,n· p;ackct' nr wuve ~n,up. w d!!.sc:nbl: lhc lor~•h,ed p;m,~..·lc~ ol munc1 f Fl~. 1. 10) ;mll quantu of r;ldtnfllul. as ioll<ms Irom d111 r.• ~ 11nn C\(>Cnmenl.., h~t· I hu-~~ ul-[)u''""an unci Gc:rm~..·r und uf Thom"c.•n :-Jo" the quc~nun '' Wht.•lhC:f lhC \\it H.' t!n•up ur WfiVC pac"-CI [fU\'t:h \\ 11h lhC H1thndlll.ll WOI\ l" \'eft •<.:II) w1.) or not" \\';1\t''• ;1'

A ltcm.uc 6.."Uil1<.U'm.ti \ t: ~uh..l dc,ll'ul.!tl\e intcrfcrco.:c ~)(Ihe twu mdt l aduo.~l ''~t\'c.'' ljf11 ~ . 1) pmducl!'( a 'lowly moving cttwJnr}C Of ~roup (u p;tckc.~l uf ..:~ Sll\Wo 1\ an hg. -LIn. 111c \ ehlClt)' Ql the-\\ U\ c ro.h.~k\!1 1:- t.:allcc.llhc.• J!hmp

w1(.t. /) ~md

\\ ,,\ ·*'

\clonl' W •· ''ludt ~~ J!l\'c.•n ~·'

\~hi.' I

./u I' the llifh.rcn..:c nr .m~u l:u (ICliUC IIl!~ h\.'1\~'..:l'll

dJ. 1h..:- \hlh:rl.'n~c ut IU\ll':lJ!au,m ' 'ti.:tor i'k:IWCI.'Il

~/1

:mol 'JI ;111tl

'"'''"!' IP! ~ln\1 \'1-.

ILD4-/ \ (\ (\ (\ vv\TVVV If\ Q 1\ 1\ f\ f\ f\ 1\

\\.;i\ 1.'"'

vv v v v v

II·••

f\[:vi\Jtfif; J!h:. -I. ttl 1'\~m

foOrtmUJun uf Wi.l\t' llUCkt't rNnll tlUitlbt'r n( iudi\ ichJlll \\il\l''

I - IM and 1}

-e

ltk, fmm whac h

~ntllp \dtl\.ll~. l:ncrt:~ .utd llhnhl"lltllllt .JtC

llh' , ..11m· ,,, ' '

tlh'

.tbtl rd::ncd b~

,,.·

L :::: 1 -W

WI.! ~.111 \.!~tl!,:ul:u<

~md

I' = ;m·

='J"'= "'·:=f!... = "~ =l' dkmmm

t .C,

\ciOCil) = !';midi.' \docity, whic:h ~.uncfuJc, th.tl d,· . nm~lii·\ t•r \fli\'C"' pu.·kt:t ltm I Itt• wmlt" 1'r/o('ll't' m 1lt1• f,tU7idt• Fhml 1hc: tci:\11\'Hih: ~.:qu.IHO n Jl!'>o Y..: can -.:t,Ul!.! tn th ~ -..unc ~,,ndu-.1\111 A1.aaH'dllig ht I IICUI) ,,j 11:.lati vity;

l~cn~.:

(imur

h·at·c 1/fWift

=Jl!f'J

+ m 1~t·""

l1ll"rcfc ,rc C'

= ,/u dk

f :::

But du tl~

k •

11'

/nr

r·

= 1111.2

//It

It/..

= mr ~ l' - ,/h•ltf).

1.1.' gtaUJ' l't•ltJfll\' r l' o:l "' lht• .Hmtc•

fUll It I It' II""'' lh (I ',

(1.\

Whc~~.::t" ph•*'l.' \l"lt.lC.' I} rP,,Illr "·"'..: '"'IH1:il~ ,., ll I!r~

'.' J:._ : (

fm : II){ l, 11

i.e

111 '

.::;

VI'

\\ 111" h !'>htl\H lh,JI lhl"

phoh\."

till

mr•

It!. ~

= I'It

Ill(') "

h'lllCII} l11 fill pnr1 h.UJ.Ir lll:IUL"t \\ ol\ l' tl 1 ,. I' IUPtC 1

l h;m lht• \dn..:u~ ol lit:ltl Hut J<:~nuhnt! ''' ltw 1h~~•'f) nf rdaii\H~ nu punidc "•Ill lr.lh.'l .11 ,, ..pc~c.J uwn: th~o.·n r th~: ' 11t'"''l 111 h!!hl llcn ..·c ph,,,,. '-l.'h.lCH) nr \,,,,,. \Chldty fP,,) hr" l't' 1L'It1lhnt IH tlh.' ..ps.-cd ol the p:an1ch.• I hit\ \r~, /ua 110 t•ltntr ul \t;:mfkmh't. hum .aho\c inlorm.atum \\\! h.a\'~· "'CI.!I11huttlh.' "·"·~ \'1.!1~11) ur phli"''C: \C:Indly lt·,.• h grc:.th:.r th:m pJI1t~.:lc- 'clncit~ c a' \\dl J\ murc th.Ul t tht• \dncity of

li,ght.ll due~ n,u ml".1111h.11dt!-Bruglu.~·, W:t\·l' £L't ~IW:J} ln'llllhe parlldt." In ftu.'l the t'llllll' u·uw•Jmd..<"l h c the purlldt• nt,,d n,ll·,•l'> u·ttll ::n•ur l'f'f,,rrn (t• 11 ),

11/11clt tv Will<' rt.r prtntcl~ l'<'lllf'll\'

w J. wh~rca;. llldtviduol 1\itv~scmposing the

"~'\'. poi~J..cl, lff.l\~1 \\llh Ihe \\, IVC h:lu~o.tl~ lt"tl whu:h '' •hlh·t..:ut lu·un ghHtJ) \l'h,ut~ r•K.

~-17

Gmup

,.:j\"'-ll~ (1'.-l

i ... thl

'\JIIh" ;n p.1r11dc \du..:n~ ll'l

Schriidingcr W:tvc E!JU:tlion (l'ime Dependent )

In 1'>26 En\ m Schrtkhnp..:r in..-plrcd h>

Jc~ Rt\,,.:lic ·.., ..:-onccpt. dcri\ L-d ,, rl'.markahl)

,u....~c.·,.,full) theory on '' OJ'-C rnc, hanu.:' II!-LX'IItral lc:uure b. ;tlltHcrcnll:-11 equation um' J.nu\\ n :1\ Sdmxlmg.,.,- t'IJf'l'ltmt, '' luch gun:nl' the \':armuvn ul ":1\ ~ functmn ~fin :-flUte and ume. whJch dcM:ribc:- the bch:l\'tour of pnrudc 10r :a wrdc tJI 1uuhlcm'> HI lh..:. Atnn ~il.: liclt.l

r:ul~C

Dr:twtn)! unalug;. \'-llh d., ..... il;,ll v...l\t: -.:qu.tsmn t· 1.2'\J. :. ......ncmtcd "11 h .1 ll~c p:u Uo.- I ~: ~;,u t I'H: rcprc\t!ntctl h)

f/1 H,IJ=t\t

wht!rl'

•• 0

Wt: ·'''-Uint.'

llu.• "'H"'

( ' ll

tpl '· 11 ~ ~h'!tpl.11.·~·mclll .tt IIIII\' 1111 ·• cli,tl.llh.:t: ~ lmm ongiu

\ =.uuph111dc t.\C tu ••xinuuu t.H .. pl:.u.:"•rn~:nt fn11n tht: nn·.m fll1"-iilun ). ='-' h.•ngth .1\ ..-

t.·., h~qu~Jh.'\" ut \ tbl.ttlun

i\ .:o.

o.nJ:!.ul.tr Irl'qu cn~~ ul the won c

I H." .thll\ l'

C4.fU,ttlt•ll

I\\ tee we

=~nv

~r.:l

~It ' "/ (I I) '=[) .;, ' .

,f'ljll 1 I)+

,,, ,

ir \\c

-A = /j

f!hlj l.s~JIWn \ -.:LlHr

Jllr..:r..:ulmlm~

Now

., ;r

J. -=

l.uu,ttlt.t lltl: ITinluto ut clcctmn. th~:n the :tbo\c ct.ru:t11tm cout 1'.:

aJJphct.ltn the t .. IJn.qn~ "·') I he: h•t.tl enl'rg) of the

~ Jc~.trnn h

L -= K L. f- P.L .:.. 111uw: + \'

or Nt.t\\

""' = lm, IE

length''

tiL•-BruJ!Ih.'\. \\,1\C

A= llc•u..:c cttll.tti••n d

''" -,- :

'" i

- ""-- , - , ::!:m( I! - V 1

\)t,:~( .t,Jt.:l l

\lilhiiiUIIIi~ ,, ..: _rr ./' ••dltl\ c t'<lli~IIIVII ·;

tJ I

f/1 .,\,I) + ~H , t11 trL th. ,

ti:W(l.t)

d'i'

mc•

~1< 1 h..•,'t1111t'" j

NIH\ h)

\ ')

-J.Jrt\'llt::

,..

; (/.

,, I/;

,.- -T,rI ll

H 1 111-

r)V/

rl,t

I')

l)l.•!:UIIH.: ....

'I' (.<. II = 0

and

- = r ·· l#

-p:. - l-,l - tl ih

Thu .... 1n one dimentional h-=- 1h

c<.~~c

.fl.- j;; t1 difh:rl.!rHi.tl opcrawr ror energy L' unJ h

a ,.:.d.tr quunti1y.

H 101

rll

I'=

Is tl t.ll llt.!rcnunJ

opt.!ratvr. lor Jlll)nh:tum ,-,, dnO 1:\ ., ~...:~lt'lf quantity. (4.3 1)

\\·._·Oil\\ :t.,.._Uillt.' 1h:lllhl:\ C(Jl.I:IIIUil hold\ j!lJ(KI..:h'H when JltliCIIHUI ~ncrj;)' 1Cnn

\ '' a luncuon ol \ und 1. Thu:-. w~ hll\'C' - h' i!'•p(.l,l) 1- __,-

.__-_,_,_

Ll,!IIJI(t.fl:ll/

i!~l( '· ,,

"'i

_:U.:.;l:...'____

33J

l'ht' l"" lh\! S• ltriidl'lll!.<'rt;,m· rh't'rntlt'ltl \\:t\' t'l.'t(UOUnn. lor lhe unc thmcntto nnl Jn thr~.·e dimcmioli:tl c:h~ Sl'lubdmt:t~r 111111 th'f1~Wllt>lll ''·'''-' Ct.lll~tUuu t.~:ul

c:.L'~-

bt• ll10l.hl11:d ;IS

t, '

-,-t·

lf'C I t •+ l(l,l )!p(,.,Jl~dl

riVtlr. )

Wht'fl.'

If/( I. I) ,.. tpLt.

1'.

::.II

,,1,1)=- \'1\. \,:.t) nnnnnh~a1i1m

l 'ww llh•

cund111un

t-l.~O)

J'(, , l)tfv=

l\C

J..nu\~

th;JI (4.2!1)

I 'lf(r, /11 dt• =I

NO\\ h'r all physac:tlly 0!.:\!l~,·u:ahll· pft)bh:m-. lhc \\.t\l' funcUt)ll 1,\f(l, n ~huuld be nurnmll'\l'd and wdl ht·huvL·d II "hould fnll n\\ th.: tullnwang \'(JIIdllmm•

I Ill"' wavl! funcuon VJ(r.ll mu:-.1 be hnhc. 'lngk

p~rtlcul:n. w11l

lfl(r, 1)

~ 11llmllc

,J!;I(r.ll

""'~--

-l

:md

0!1" r - '

va lu~d Jnd ~«l11Unuous. In

~. 01herw1-:C: lhl.! lnltgr.al

norm~thsmwn

\\ all 001 he

nHISl be lin11e. SIIU!II! •

\'UIUI.!d

J-'/'

JID'~thlL~

and ('00ll llUOU~.

(r,

I) t;l(r. t)lfl1

11I

Qurmlum l'hr.\ic.' tmd St ltd'idm$!er Wtl\'t' F.qunlwtt If Lhe nhove conditions me 001 'ati!<lfici.J, the CX~CtHUitOn value

''cchu

ttr oa p;m~~..·~~: {r) =-

or lhC J>OSI1100

yr•tr. t) f!JI(r, tul\ ' will nnt he fin1 tc anti .. in~lc

vrtlucd, tlu.·y may be o!h,urJ Su Jlu:~ wun•Jtm( 11u11

ljl(t;

111"-fl

bt 1n~// lk•hfwed

tor filii'"-"~"'"' pmb/.·,;,s.

.us

Schroding~r (Time

Schrlklitt~CI um~ t.lep:mlcm

Ind ependent) Wave Equation (STIE)

\\tl\'t.' Cl!U3ll00

(.t31)

I!\

0 rundamem:.11 cquauon

wo1\'C machanics. but lr()rnthe pmcucal pmnl CJf v1cw '-<)rnctirn c~ we ha\'C ll' he con1:crncd wtth :a ''m1:h:r l!tJumion. wh1ch as c;~llcd S(hfiJdmJ.:~r tlll/f! mdept·ndc•llf w~n· c cquauon In case when 1hc P.E \'(r) " no1 dcpcndcnl on umc. then we need .\'dtrihliux('f wm• mdl'fJt'ndrm u'll\1' e'tnatum ISTIE), whtch .;:1 0 be wriucn !IS

ll 1

- - - \"' ' f/llt ,tl + \ ' (r 1 yt(t.fl

r) =tli il'!l(r, - ,-ul

(~ . 35)

The solution o( tht> above l!4U;tl•un c.:.m be wn111.:n in :1 ~ep:t1·ab lc form a~ V'l' I) "' Vllt'l <pill

where

'Jf(f) I~ a

hnu.:llnn o l 'p;t\,;C \'an ,1hlc

J 01\l)' nnd q)(tJ I!\ 3 funCliOO OfUinC

\'Mioble (f) unl) \'~ l{l(r. I) :~= fll(rl q>lt)

Hence,

<1'1'

if,

and

(r, tl

r)<pc 1l

= ljf(l)~

h)' 'ub:..t1tu1u1g the~ ul l.!qu.uwn H.35l "C" g\!1

h· • -- tpll ' V· 2m

ou(rt + \ ' (rt yr(rt tplt) T

Otp( IJ =til ljf(r) ~ ,

Div1J 1n~ throu$!,hOUI b~ IJIIO q)(/J W\! get

_II_ [ :."' \-; l/llr) + Vtr! y/(r)'] V' fJ

- 111

= rpi(lt), iJ~(t) ( 11

(4 •.1?1

Thelen hnnd ;ode ot oqunnon H.37J

1> only dependent \lf r, thc 'I'""""""""'"· wltcrc.as tit~ ragltt ltnnd ,ld~ or cqunuon (4.37 1b only dependent on time variuhle

1. ~o b)

tl1c: mcthoJ ur :-cpuntlilm \ll "anuhlc. bnlh MtJe" \\~II be c,,~u:.lto the smne \\ c ...·-an t:<~ll ..... /;.'. Then 1he equ<~tion for tp{t) is rcad1ly

'cpnru11<~n cun'1 ~n1, \.\'hich

lntcgr;ucd 10 gi vt."

(4.38)'

hy ,,.h"'lllutln~ ctiUtlllon N.JS) o n ..:-quntim\ •4.17) lht~ equatio n of lj/(rl becomes

[

:I Vl +

l'(d] l/l(r) =/!IJI(rl

(4.)'))

J 12

l£ngblet•ring Phy.tks

T tus ~~called SchrOdinger time tndt•t>t•ndc•m n~''<' Eqtwtirm (ST/ EJ. h :\ sohui,ln tp(rJ dc1cmltnCd 1hc spn.ccdcpcndi1nce o i IJI(r. I) lhrough the Schn.>clingl7r time dcpcnJ cnl (4.3·~) wave equation as

'I'V· t) = 'l'{r}P ''"' ~.1 9

Eigcn Value Equati on

The Schrikfingcr 1nnc indcpcndcn1 c.q u:tlion (STIE) (·Ll9) can be wlith!l\ :t~

t-iA i J \\h.:rc II

•~ du:

Numifwnian opc.·rator;

[X v:. 2m

\1(

rl]·

Hp~.-·~;uc., on

1hc

funclion tp(d. T h..: effect Mchc Hamiltonian OJ')Cr~&hll (N) til\ ";1\'C func:tio1l is 10 n.:pruducc lht: ~umc fum::tion IJI(r) muhiplicd by a constant £ . S:uch ~Ill cqu:tlinn i~ t~tlle<.l ;Ul Eigrn \'<sllte Equati011. Th~! function tp ( '') on whrch !ol::nntlh'lninn Opcr:um (H) ~1c 1s i' caJJt:<.l an Eigen frmctimJ of th~ OJ>crator. and the c:onstant L' with which the Elgcn funcl ion ~CUi mulliplicd is called nn •·J~u:nr \tafur". Ph y~ i ea l

Cc-,m.:-e1>1 of EiJ;:en V;tlue Eqmttion rho SchrO<Jingertimc indcpcndem w:.veequntl<>n 14.~9) .md 11, 'olu1wn 'l'l r J oro 1.!:-."cnli:tlly similnrh'l thl! l in~ indl!l~•lUcul w-.v.;cqmtllnn vi clu~~ic>ll wuvc mcuion ;uu.l l iS~olutionN. Jn cla'isica: wave. cc11ain freque ncies r&ri~e JHtlur nlly Ill lhc C(lursc uf lhcir \Oitlfiom•. Nu\\' sint:-c 1:. = hv. ;n h'lH't' mrrlwnit·\ t't'lltllll purtlt:ulur t'lwr,gh•,\ will un.\f' 1wtumlh·. This i~·

('(1/1(1(/

"tJU(uui.mriorr oj

t·m·t:-:\· ' fllld tlrt,\'('

(mrtit·ulttf allawe,/ \'tllues t.{ euc~rg ie.t fll'f ' 111 /u• Mt/t.l u,\ dmrtwtrn\t;c·.v ,,. Jlmp,·r ,,. "t•(t:<'tt Wlluc.\ ( /:.J" Carr.•sJJtmdiug to t'tJrh (JI/owcd c.•i}:t'n wlim• f.. t/w,-r' tS rmh• t~m• {um:titm 'If( r) ubwint't/a,'i .W1/utitm t~(S'/'1E t'tttratitm (-1. Jt) 1. 77,;,, fimninn 'I'(t') t\ t altt•d U.\ i luuut 1r1 i~·tin fum:thm m· "l'igttn fmwltou" On!.! shoulll clL•arly remember the difrerence between dlc e•gt.•n funchon \ll(r) unO tlw wnvc flrnc,;linn Vl(r, 1). 71u.• wal't' (tmt'limr l\' yt(r, 1) = 'l'(rk '''"

u·hose J'ptn-t• df•pt•mlanet• pan is dewnninrd by 1lu• Pigt•n fimnion Y'l ,.,. Ju~t :,~...- the w~1vc- func tion lJI(r. f) musl be well bch:lvcd. bgcn Iunction f/l(r) mustolso be well behaved. Since 'I'll'. t) = 'l'( r)c •Ed>, then fullcllon !jllr', t) wi l l misbehave ir I.JI(r) misbeh ave~. 1'hus.

( l) cigcn function Vl(r) tl1 U$t bt.: fi nitt.:, !'i nglc valued and cotHi mJQU.\t. (2)

i)~~r)

Above

I WC)

mur-:t be noitc,

SiOI;!I~ V~tlucc.t :tnd t;t)fUinunu-..

conditions should he fu lfilled for

~II

physic:1l problems

that

cx.pectahon valut:s of the posuion vector ( r ) will b~ fitlll\!, o;:•ngll! v:llucd. :tnd

ctmsha:.tnt, they should nos be nbsurd.

Qunmum Pllyt;n anti SdJrOdmxl·r Wavr Equminu

4.20

3 1J

Stationary Stale

In ,, panrculnr .;:t:ue 1f the

prob~tbilicy d1MrH1tUivn f unctivu

Plr. r) = V''(r, r)

~t lr.

Independent Of llt'OC, thtfl the :-.IOIC ot the !\y-.tcm IS C.JifCd Mftrlfmary .flalt'. Now if the pantc1c !JUlY be dcscribcJ by JU~l one or lhl· WttVC function 'Jf...(r. I) wi1h energy clgcn value £ ,.. then

TIIcll the prob1bili1)' d is tribuuoo ror the particle i'(r, I)

1-h:m:c:

= yt'(r. I) yt(r . II

l'{ r , l )= 'If~ (d

'I'•

(4.42)

whtch i.s tnckpcndcmofrimc orc!ilkd .H atimwf)·. 111l'rc forc. th~.: rd!&tiYl" probabiluy of finding thl" particle. c.loc-!1. not depend vntimc In thh.t.:::t_}C', lhl" pnniclc i$ ~aid 10 be in ~) ~\'llllionnn· srm~ or t•sa:t-u swu• of the r)('ltemial \Itt)

-1.21 Applications of Sch rodinger Time (STIR)

Independent E<tuation ~.21.1

l'artidt in u One Vim<nslunal llux: One dimensionul infinite rectangular potMlinl well ConMdcr a particle: 11-3) dcctron. u r fTI Ob.S , \\'hkh can mO\'fO: rrccl) in tt one lhrncn~i4)1lill b('>, ur length /_ 11tc pr.tcot1ul enctg}' j V) oll I he tln110UI of 1h1! htl)( j.., 7c.ro btu u.\ 1he cltctron cannot e!\c-npc from the ho\. ,.,the irnpenet:rnblc wall ui t.he box ' ' n:prcsl'llted by a potcntiJJ V = oo. No'' thl' particle: ;..- u-;,1pped in ahc rct:iun 0 < '< 1,. of•hc X·:,xh. 1l1i' rl!giun h culled purcttli;tl well, :t' 'hc-,wn 111 Fog. 4.11 \J). l'(.r) = U for U ~ r 'ZZ

oo for

< () ;;md f > L

Ill the prL'l\clll c;,•-,e \o•e have I (I ~olve STIE fot the regauo 0 < .r < /,. where V = 0. Hence. we get fro m equation (4.39)

where k =-

A ~uitubl .: solution of ;1bove SchrOdmgt.•r cquauon lp'(.l') : A

-"!c..

V 11·

•~

, ju b + R cos /a

(4 ..14)

31-t

Engineering Plry!iit:S

l =-

\ : U

.... u

1•1

(b)

-~-~

fi~.

4.ll !D) lnflnh ~ 1~\!ntlnl wtU ~ th• Wo\f: runclion 'fl'J rorflrsl two f.'ic,en runC'Iions

in inOnite potr nli:tl well; (l"l Pmlmhilit) dcm.it~ t\jl(x)l1 in lnrinile pulcntiul \\f.'-11

The

b<.mndt~ry

I ¥'(.<)

2. '!'(.<)

condi1U,)11:> ;m."

=() :u ' =IJ =() :11

X= /.

By applyml! thc>c lwn boundary conditions 0;; A 0

~in

cqualion 14.4·1) we gel

0 + ll co' 0. i.e B = 0

=1l ~in kl..

whh.:h t;ivc:' kL

(lf

Et11r:u i n~ equal ion.;

LIJ (•i.-23) :md (•S ..i5). we )!CI 1 1

2m£_!..!..!!. ,,

=11/C, (4 4~)

315

Qwmmm /'h \•.fiC\ mul Sdrrlldingl'r Wt''''' F.qumlrm

(4.4(>)

when~

n ; I. 2. 1 . , Ihe prindrt:ll quamum nun1hch. 11m. equauon ~how~ thnt the pnn1cle in the one d1mcn~uonal bux. nr 1n u nne dmh.:nMonal inlimt~ J"'C)h:ntwl well. cannmlusvc :any nrbitmry l!ll eiJ:~y. llui ltruppcd pnnu:lc t:Mt nnly ha\1! d i...crctc cnrr~ic..' gi"cn by

25£, - - - - - - £,

~;,

16£,

91:.' ,

_ t.,

41i,

r:,

£,

II :

(2mL,_ )

£: £, = "''-• ,' 1•' = 9/· 1

_ _ _ _ _ _ 1! = 0 fig . ... ll

Dl~crctl

cnrrto lr,-tls fo r a pariich.• bound in

nnc:-dimcn.'3 innal

innnite pot ~n tiaJ wdl

und 'o on. u... shu" 1110 Fig. ~.J 2. Thu!\ the energy of the p:tnJdc '"an Iinne \~·ell I!\ f{UUIJIUN/ Sine.:-.· llw p~1111d'-' ~:an c:a.•M cmly 111 dlscrere levels. 1he erlt.:fgy thar 1:-. c:nllllcd Of :ib!\Ofbctl by the p:~niclc can also ha\'c some ccnain discrete values, corres-ponding to the diflcrcnce m cncrg)' kvcls. This spccialily of 1rnnsiliun cnl!f!!.Y '"' OJl C \lf the mo)',l ~trH~in g f..:nturc:'\ of ntomk physic~. £ 1• li: . .. e1c-. nre called lhl!

ena~;.1 r•crn

ltt/un.

rnc lowes• possible energy is c1 " ( 2m!.· tr'h~ ). nv1 £cro.

nc:cordu1g 10 '~'rtvc n1cchanic:-. or qu:lmum mcchnnic.s Th1s 1S called "t_t•m pouu

is the lo\\ CY~I energy Lhru the particle have if it is hound m a on" box of "'ridth L The panicle cannol have :~.cro kinc(ic e nergy. bl..x:aus~ fnJrn Hcit-cnbcrg um:crlainty principle. lin; 'nu.::erwimy m lX.lSiuon of Ihi! 11'!1ppcd parliclc inn bo;..Js .b; = L. hence t.\p a.s well as \l~locity 1h~ p;u11CIC ;.md lht.:Jr l1uc.tu: energy ~ou1n111 be lcm Figure 4. 11 (b\ •how> ~1c plot of Vl~r). for lirst two ctg<n linction' of Ihe panicle in rhc inlinilc wcll nnd Fig. 4 ll (c) >hOW> the corre>p<mding probabili1y dcn>ity (/'(r, tll IIJI(r)l' , 1.c. ~•c probabiluy uf finding the pan1clc in a box. l!l)ctgy'. it

djmcn~ion.DI

3 10

£nxureamg P/n•Jrrs

In rhe mode of l.)'>CIII:mon wnh " -= I. the probut,rlity dcn$11)' 1~ lughest at .< = L/2 ond the sm~llest next to the walls. In 11 = 2 mode, pwbahiltty dcll>ily ;, nitnrmurl r Ol .r= /,/2 nnd rnox,.irnum til l/4 und 3L/4 a~ shown in Fi~. ·1.1 J(c). ~nrc hori7ontnl :-.mught lrnc ~hows lhc cla."rcul .:xpccuurnn va l u~ for Lhc probnbility dcnsuy. In c:a!'c of coruplc1dy free particle "~:ty. elec,ron m a mcml. n posses:-:.es lhe ~mcuc energy £.:. 112 mv 1• Thi.· de Brot:hc')l, wa\·e; l..:ng1h .r.).StlCUtiCd with l.hc 1 1 ' ,tbewuvenumber i'>J!IV~n lwk= [f Now.comhirllng£= "' v: pantcleis~= IIIL' ' /o 2 .utd A== )J_ with wa\'C number k, \I.C gel ltU-'

llctwc

lc=

11r

, ! ~:!

2111

!4.471

The ..thovc t:quution :-.how~ a conunuou" p;u.th.,lil. rdruion~hip ht.·•wcen F: .and k. fur .t free p;utk1c. ~ay for ;m declron m ..t. mclal. u... ~hown 111 Ftg. 4 l"3 11us nrc:tn.,,ji,r/fl't:' tmflicll•tlrf t'IIU}l\1tlilftrtlmwu, i\ t•nnlimwu.,., n ht'Tt'tl,\' for bmmd pnrtidr flw '-'lfc•rc:r i\' qumm.rcJ lh we h.wc ~~n \!~1tlit"r in Hi! -1.12. Thic; can be t:'(phuncd 111 the follownlg wuy. F"or bound p:miclc in a ore ditUCihtiwl:al no, or widlh /.... when.: L h.... :t definilc but small vnlue. ahc cn-!rgy lc\ ch rmm F.qn (·1.-lhJ 11~ <:hown in Fig. -t 12 ore widely 'P"C"d· But ror free pun tdc I ~ ""· 'O from cqutttlon (4.~61 UlC !\fl.u.:mg of \!lll!rgy lc\'el.:; be~Ohh.'"' tnflrulc'iianall) ""'·'" Su lhey .tJ)IlCM ;:alm0$1

, _,,

like J continuous llpectnun waLh encr!!y - , - . ••~ -<hown an Pig. ·tl3.

Fig. "'·U

0 Con1inuoe.s tncrgy di.b1 ribtllion (or a rrc..~ pnrticl<'

Quomum Physic\ cmd StlrdH/fn~rr Wm·c E:quotirm

4.21.2

Harrier 1)tnm~linJ.!:

Kecton~ulnr

or bcigbt v,

317

finite potential harrier or

Lc:t \l!'t t:Qt\l\tder a p:lrtlcle tfrmn ol benrn of monn·ene.r~ttic punicle~l. incident fnuu tJn·_left on the rectangular li.nltc potcnti.tl (Fif. 4.14al. ll1c finite potcnli:.tl is dc>cribcd by IILI)

II( I)=

\1,

\1(.1! =II

R~{!.ton· l

For,<O

F'm 0 S

Rcj(ion-11

S: /.

Rc)\ion-1II

hH I>L

when:: B j, the cn.:rgyof th.: inc-idem p:trtielc fmm lt:ft un the rcct~lngular potcntbl burrier.

Ktof!Jun II

Reg1M·III \'( 1J =

Rei;J<»l I

\ ~1

' 1 - -• r

T -· I

\.T.t) =(I

•••

L -- I

(h)

t-1~.

-1.14

Harrier lunnelllna

ClnssicnJI)' if£> Vo. lht parlu.: le can ~n ter region~ II fmm region~ I. hut ib encrg)' wriJ be slowcxl down tn u value(£- \10 ) and it will travel with velocity r.-.·-~

=\12<li -

Vo)

The pttrticlc is thus trnnsmincd mto Rgion· ll,

But if t:"'< Vo. the panicle ..:;annot trnn;.,mil to tJu: region· II. duc- 111 potcml,,l

Vo > £ h will be then rcnct:ted h:tc~

10 r~gion·l .tgain without lu~ of ~peed Quantum mcchun:cully/wave meeh9nlcully v.e: cun tre::urh1s probll.!m nict!ly nn~J :1 IHUJnr tj1W.n1Um surprise awni1s for us. if we t.~on$i<.lcr u more reaJhaie case

31 S

Engilwt•l in}.: l'h\•.tir.,·

nf it WCII Ol luntc depth. inStead of infinite depth aS it W:tS diSCUSSt:d Jn 5CCtioo 4.2 1 I Ouuntum rncth:.uticul rc,ult is obtained by solving STIE ft'Jr 1he pnniclc in rcpion I and II. n~ 'hown in Fl~t .a. l·l In n:~mn I. l'(.t'

=0. Hence, STIE hccomc.'\ M Cqn. (4.•J3) o1 vtl,X I + -1m/,- 1{/(.tl = 0 <h.

,, 2

'" The '11h11ion ul

cqu;UIIIII {-'AX)

reg10n

j~;,

'Jitf r) ~Ar 1l 1 ' +

Br 1la•

\\'hel l! tltt! fir'\ I IC11U I'\ I hi! I IICOIIUil~ W;t\<C rtiO\'ing uJung ( +VC) f dirccl ion wherc::b 'Ccoml term i:\ the n.•flel.'tcll w:H'C' moving ~~long (-v.:) t dirc.t:IUln. Equation C4A9} ;, an '"clllaun~ Sin<' wnv~ as >hown in rog•on-1 In Fig. (4. 141>}. In l <~aon ll, V!1J; 1., 11<-nco, SllE Etcn. (4.39} hocomc'

il~v11.11 2m - - , - + - , ( t - V0 ) V'l-'1 =0 Jt-

cH-

;)~VI(\1 .::__~,:..:

cl...-

whcrL"

2m(£- V0 )

+ k • 'I'L<l ~ 0 ' 1·1.5111

It~

S<llution ul •quat~<>n 1~ ..'01 " ~p 11 t ~)

•

Cast 1: When f.>\ u· 1.. ~ = t,Vnf") :u\d their

Jcn\:1111.'~ mu~ t

commnn for hoth Hc ucc

2mc li

1h~

.. fr•

= Ct•'4:-'

v., • 1~ real. ~o the c1gcn . fun~tuln \lf1(') .uul

he (;onlmuous ut the

tl.:g•ons

1111( q I, .. n ~ yt11• \) I, ... 0

;nuJ

l'hcrelore

I HD=C I nnd

or by cornhining abo\'C

t\\f'

(45 1)

cquntions. we get

bound~' ::

0. \\luch b

Quamum Pll\'siCJ am/ Sdtrlhlill);~:r \Vm·(' l~'(fuuticm

t1 =

Ji =(A 1 -

1'1tu...

Now

the.~

C[ \~ 1k,

C[\~,k,

31~ (4.52)

k,)

({,+k,)

pmbublllly or rene.clion or reflccuon cocfficu:-m IS

R _ Rcnec<ed prob:ability nux = B' llu \\he~ t ' IS

lncidcru prvbabi1it}

nux=- A• -\t•

the \'elocuy of mcommg p:tn1cle m rct:ion I IJ"B

R = --

Ncl\\.

A•A

I-

I+

-., =A·

(k , - k,J' .. lk 1 +{ , ) •

f E - Vo v £

(4.53)

J£ -6 "''

Sulc-c the mc1Jcnt p::1rtzdc gets either n:nec:ted ur tmnsnuued . Sf' th< pn1b:1h1ht)' nf rcflcclion plus probnb1liLy of lran:mu:sS•<-m i\ c.c.amtl h) uruty.

R+T =I

I1: F. \'u

Cu~·c· n: 1:. < l'u ('J::..,Mcull) \\C havcnlrcndy ~en that If£< Vn. lhCil lhc rmriK"-: ~,-;1111\UI trn.m.millftd to 1hc region 11. 11 '-'Ill be rcOcch:d bitck .again Ill rugum I No tmn\mi,.,ion b pos.<iblo. But 11()\1.' lllltllllUm mechanical treatment of IJwt r rohlcm will giv.: diffc:.•ft!nt n:>ull. wluoh os dcscr 1><<1 "'follows. TI>I< ;, Ihe 11<au1y oflbe quamum mechanical 1rcatmcm.

When t:: <

1~.

lhen

ali un imagmary quaJlJty. Sny k: = ir. where r •' real . Thcn;fofe ~ol uuon in rc.g1on II will be (4.55)

Thi' is an cxponcmiully dumped wave a.< •hown In Pig. (4.14b) Al<huugh ~ampcd hut the t:Jgcn runt::tion IJfu(X) has pcnClr.UC-iJ intO the d:l\.\iC:JIJy forbidden region II. Till! rrob:Jblh ty density In region-If ls ~1\'CO by 1'11:

yrj,(x) •flu(.<l: C• C•''"

(4 .56)

This dccr~a"'c' rapidly with mc:rta)\intt ' il\ ~hown in l.;ig. (.S.I..Ih) in n:gion-11 , but there- Js: :s linitc rrobahil ity uf tindin~_: lhe pan ide in rcg.ion II. n,,, u m f., t'lNJJp/t•tf'fV b iJJJOSS{b/t• It) /lit(/ tflf' II. u ht•n F < \ ~~~ Pt'll('trathm w !Itt" c/(IS,tit'<lll\' fm·/Jultlnt t't'J:lOn is one v_ftlr~ mo...t jfriiJIIJ.: jf:an;n· o{wul·~ meclwt1it"s Ot'tltumtwn lttt•clumh·"· ·r hc \'alue olrhc lr.tJNni.;s•on cn--cffu: icol ( 1') is. "cry sem-.1tivc l('l 'he tllid.uc'i~ .tnd ht.:ittlll of l hl! h:1rri¢1 :tnd l(l l ht: f~ICIOI J.:. I he \Va\'C IH,Jn'lhCr. Now for 11w. caJ'c wJ·cn J..., =- i1 ,

l'oJIIrtUI W t/tt• dtU\I'caf fl'l Uft. 1\'/Jt'll' il

flllrticlt• in r(·,~inn

und rcncc1iun Co-efficient

BB• R= -= 1 t\1\*

Thus 1hc tnt'lf.lcnl p:anicll! h ai\\·JY~ r&:O-:cacd. ln ugr~·-:men1 wath clo'"'lc.ll l'\.'":-.ull But we sec aJ;.~IIn f1·um tLJUltllun (.:I ~2).

a.c Thi.S ffit!::tn~ C-lhC a tnphHtfh: ul

the

lf:l llSillltted \Vli\'C 10 regiOilvJI "

IIIII /CI'll

unles:- rand hence 1~ 1 ' ' inlinnc from equatoon (4.501. w Ihere 1sn linllc prob..h>lill

of fi,l dlt)!'! tht: fK111 u;:lc 10 1hc c:l:a~ ..u:ally for h td dcn u!~ 100 ' > 0 fo( lin& IC jMlll'nlml barncr Th1~ "callr t..l bar nt•t rumlt:tlmg phenomena Th u~ in wave mcch:mic~ m <lu;mtum mc,·han& r' th!.!rc j, a lnmc chance that lhc clc:c:tron ctm pc:nclr.llc lhc h:nric1 ;uHI c:umim.h: il, mminn 1U the riglu ~ts ~hown in Fi!!, 4. 1 ·~h In n~gion .l l l V(t) = 0 , '~nne u' 1n r~gmn-1. So 1he ~CIIutlon of STU.:. 10 r~g.Hm-

111 woll he

of'""''' lyfl< ·"

111

'"gonn· l l l~c E<Jil. HA~l 1~.57)

i.e.

'l'wl.l) •~ al'o <.,~._.·, 11:1tnr) but v.nh !-il11:tllcr amplitude a' "hown in Fig lll

l~hl

i<. DISo ~('I dr;~wn lh.&t oil c.:u:h "oundary t \'=nand,\'= I.,, I,JII.\') ~nd ci!J!Iclt hc:tt\111~ t:on1muou'\ Proh;:1htli1~ dcn,ll)' m r~~tnn-1 11 will Ill.:

1' 111 IJ•D ~ 0 111is me~ms th:111hc lnc•dcm p;u ltcle wuh £ < V0 has rinitc probahl ity to tunneled 1hrough the rcctangulm b~uncr potcnw11 and arrh,cd m region Ill o~ u rn..'>C porhclc. With ~mall cr :tpphtudc Thu.:; we have 0\Ccn llxu il 1hc n:cmnguJar h:arncr potential had o tin it~ hc1~h l . yt(r) 1s not zero nn 1hc the other s1dc or the bamcr. Wh1ch mean" the p;trlldt'

could tunnel 1hrough th~ cl:";ic:~lly excluded rc!!iuu :<nd cume uu1 un 1he mhcr "de. \\ hu:h " calle-d lht - /mn ,., JU'm'twlhH,-· and pr.lcticnll) thl~ can clc.ul) 1 expl:,in the ~\orkmg ~·<'rdllion ot tunncJ dmdc ~nd f1·dcc:l)' fw m li! Jt -1.21.2.1 (X.</ccll)" 11tl' pmctic:tl c:campk •tf lhi.; IUnncl cO"L":ct I!' ob~l·n·cd in the u dr,·n.' uf t I·''~ nuc.:lcu)\, which lht:n ~CI' t.'OU\'Cfl~tl intu tlmrium 1" nuclcu~. Tile K r uf the vu1guing tt-r-,:~ nidc '' ·l.t9 MeV. whcrcr" i1 ovcrcume..~ lhe elec tru~tutic hurncr 4

p01en1inl heigh! ol ~ M<V. due 10 lhe nl!rnctivc force of lhc nuclcu; nf mdtu< R (Fig_. 4 I5). which i)) m• pn~:->1hlc. In e:<plain by cli1~~~ca1 m ech:t nlC~. 11tl! \'Cry

~21

Qumrrtmt Pln·.ric's ami Sc:hrmlmgcr Wm·r EIJumw"

~u~: le.u r.:~dm~

well lnLIWtl problem or a-decay can bl: t"X:pb.ined on1)' by \\.tv.: mcch,mical borrit•r tmme/lhrf! pfrtii(JIII~'"(l . AccOrdjng Ill \\':l\'c nlCChnni c~ CiJ;,l!l1 runCitOil is. oscillo.wry w1thin uttractivc po1C~ntint. within nucleus (0 < r < Hl a\ in fig . (4 I ~) llu.:n ~:<ftO t'"'lllally dccayulg in rhc hnrricrre~ton li/u(.\1 :u1d al!rttn oscillntorv Vm'' I outside •he nucleus aflcr pcnctmlaon. wilh ~muller amplitude. t;~ 1( .\J

~hown

./.21.2.1

Tunnel diodf:'

Currcnl no\~ lUit.ICI ~m.t11 inrw,trd bm~cooduion II\ ltmnd tlimlt- is nbo pm•Mblc, whtch c:m 3l~o be cxp!atncd by thh bllrTJttr prtlf"tratimr pht!IIOIIIt'llntl. In ltlnnd d1odc. h1!:1Vtly ~.JopcJ tH) pc.: se1mconducu)r i:i scp:uated by hc~v1 ly doped tHypc scmiconducmr h) a \ Cf) thin depletion ltlycr us '\hown in Fig. 4.16. F~:nm len.· I c,, is loc;Hl-d m:.~dc r .u fur /Hype !n31cria1 and in~idc V.B. rw fH)'J)C uuueual \Vh:IIC\1!1 he 1hc lcmpcraturc. Ihe Ferml levels (£11, nnd 1:. 1 , , \\ 1111ml" up in che Qbsenc:e of c\ternul Vtlltage. fhcn:forc tunneli ng can Ia~.: pl~cc ''her.: lhe: 1\vo band ~ overlap 10 1hc1r cncrg~ ranges. \Vhcn n small forw11rd bau.o; 1~ applied . the electron, can LUnnclcd through the hamer potential. frmn lha; C H llf n-~•dc 1o VB nf I"'~ ide. In 1hc. h<~mc:r dcplecion regiun. eke aron euc.t~} r£) ' ' lc~~ Ihun 1hc b!trl'l,·r polcnlr:ll height ( V0), o( finn~ \'ttlue, a~ ~hown 111 Ftg (-L 161

£,.,.

C"R

1.,,

"· L

•

VJ1 ' : I

·-~"'-:.

V.ll.

FiJ,!. 4.1(t Thnnt'l diodr-.

the CIC~ttuth do 1)01 ha\ e \'OUu~h \'IH.'f~) tc~ t)\ (reO~ the p01Cflll:ll lhC)' rem.~un lr.tppetl tn the lf+~ttk, unc.h!l \CI) 'mall rctf"\\ard bt.t~

5,1 \:l.t\"i,;.t11)

t'i.trrtcr

-.tt

.,:un~hu.-n

But quntum m:kh.:mtcall) ei~"'U\'"' Cdn ~ tunl\4!'lnl thrvu~h the boctont the: ( 8 on the ,,_,,de n..~on tnto ttl<: "ttmtloir c~rs> \I .st.: .stthc tn1-. ulthc \' H ut t•·,ttk r<rtun In a 'nml.ar ""a) holc~c.J.n be tunndcJ 1n the 'lflJl'O'llc dire~11on 0tu' UO~r 'm~11 h)r'\\ dtJ haa.' l,:"\Uldlllt"'O t:Urtcnt llu" 10 tilt- tunnel tltode c.:!UI be ,.,rt.uncd '{lloHnum mt.•t::h.oulacall). "htt:h '' uul 1"'-,'"ht...· t·1;.e,,u.·:•11} Th~: ele,tron t'l~cn lun~tu.m '' t':ooCIII:no')' an the n-rC:J:IOn. H '' C\P'meniiJII) d,~, .J) ang m the h;mu.•r h·~u'ln ~uu.l otg.m1 hc'nmc~ o~tlllillun .titer pcnctrnuon \\llh smaller amj",htutlt: ul 1hc ntlu:r "d\! c..1f the bnrrin. 1c '" f'•r\'_ptnn. JU't .... in 1--i g .. J 15 ' I unnl·hnl1 t:um:m ;, tl.'t\1 when thcr~ " lltl ·'1'11ht•t.t 'nlhtgt•, .. me~ 1 , ,, ;md f 1 P "''U Itt llucdup With tnt.•rc:J.\t" of l onvnnl hm,, lttltlleltnJ.! 'uf'fl'llt \\ •II uu.:n.•01,e Out upw ct.•t t;lln v;aluc. (lfl('r llttll n.,·turwcml l'oltal!f: i,, l"c'rc•mw(/ tlliHirfmc.: rtYhe.,, WIH tiU'It" 1.\ 110 m•mlublt :ttult',\ mt tilt" ti/Jfltl\11• J't41t r.t' tm 11 \Uir. In rn ~,1

t.,.,

tltutr I ha' flrtl(ter1) ot tunnel tliodc make' at uwtul •.-. Jn olUlfllllicr, ~•n o'~ all.ttor Ill U\ lt ' ' " itdl Thu .. I he currcm thrnutth tlu..• tunnel c.lttkJt!" l~tn be rapatU~ IUrn~d 1.111 i•rnU h) t:llfttnlUtng the hcagtn uf tlw h.anh.'r put,·nu~•l 1 ~o.· b) \;&l)tn~

new.

th~o.• .:'t'-"rn.;d h~tP• \·nho•ge Tht\ can~ don.:" nh J \I! I) sh,)n r~'p.,.n-.c ume of 1h~ c•rJ.:r ••I IU 11 'e"''ntl ,_, ••:.llhc tS~u..:c" \Utlo~hk hlf" .tpph,J.IIttn\ whc.re \P..~ ''' r.;-.run"-' '' l.fllil:al Thu. acuon nt.t.) be ciillcd •'" w.udung. v.htch J\ h.t,c~.t nn llmnrlhn~

fl'"'"''''""

QUF.'HIONS (,1\\"' M;u,·Born·, un:rrtttiltJon ot "d\'C lunuu.•u ! , h>-1>tun the flh y~tc-ul in1~rpH:t:&tivn u( "'IH'C futlWtlll h:\tll,un \\h1n '' lllCtlnt b:V nMm"h'ullo,."'~n ot wow~ runcuon"! l·,rd.un L"t~.:n tunchnn..: :uhJ \.'tgcn \ "oth~ ·

\t.lh' tlw lntUifPIHt'tll. N

S~.:hrtt\lhli!-~1 "ll\\'

IU111.·Uun amldl'tl\l.'hllll' imll'P<!IU,lcml

'-lhtudlnt!n cqu.utun lor a p.11lJck UIH\'1111! ltl.t hnnt puenll.tl \ '\ \\ h.tl hc.:.-U...'\1 h.trm:t •uunelhn{' I""Aptun lum~hhi"' uprr..ct~'" "tlh "-:.tl di.tprnm

5 Laser, Holography and Fiber Optics LASER 5.1 Introd uction-laser J3onnciplc of laser (bght nmpltlic.atmn by •;lmmltalcd cmt:,Mun uf r;nlt;,atiOil) •~ 'iiiTUinr to M(I.W.'r (MH.:rowave Alllphfi(.;.ntaun h) Slnnulmcd Emi"'\tOn). The liglu emiued from a c,l,wcmumal light -.uurcc h :'\t:ild lo be incoherent hecnu~e the r:ldiauon emlttt:d Irom JJ{fcrcnl atllnls d\1 nHt 111 gcncr..1l. bc~sr ;111y deflmtt· ph:,~e re l ~tion.,.h i p with c~t<:h nlhcr. On lht: uther hHII<.l, th~ light emiu~d from n laser hns n very high degree or ~<>horency ~nd IS olmuM perfectly pnr.ollcl to coteh other. The lh~;ory olla\Cr w~1~ p1\lf1'-l~·d 111 I t>.~~ hy T()\\ ne~ :ttH.J Sch:.1wlow 111 U.S.A TI1c firliit l:tscr W!L~ f:thric~ted by Muiman 10 I iJ6U. In lase-r Lhc fuml:tmcnHal proc~')..\C-.. ur inh:r.tttiun ;arc ·'' fu11ow,,

5.1.1

Absurplion ur Rndittliun

We know lh31 light ;, absorbed or ~mlllCII by panoclc> during !heir monsiLion from tlllC cn~rh')' h::vcl to .mulhcr In ~cnt.a.tl .11 nonnal t..nndltinn all the utom" arc "itumcd 1n the ~ruund s 1atc C/:.' 11 (Fig_5. 1u) TI1U,. whe n lhc: cn.:rgy ltv=

is .!iUJ>plicJ fmm OUl\idt: in the (tt\'UUruhlt: COildltiOrl. lht! tllOIII WiJI nhM,rb th;lt energy(£::- £ 1) ;~ud gu IU the uppt•r eucrgy \lotH!£~. n1is- procc~~ h.

0:! - £!}

c.dlcd t~b.\urptwll uftadi.tltwn (Fig. 5. 1u). II Olt)te energy 1~ !.Upplicd from OUL*;idc. uiiHn c mt nb~OI'b niClrc !!netgy :uHI gt) hl upp..:o:r energy ~I Oh! £,. £~. ciC.

5.1.2

Ernis~iou

or Rm.JJ.utioo

Atoms which arc i n the excited s talt! :llw::t y~ try to comr down to the ground SHUt.~

by cmiumg the cxtn1 energy. m form of l.!mi!--5-iun of rm.tiatil-.n. Atom.~> can t:mit r.u.liation in two w:tys:

5.1.2. 1 Spvnttmcou$ £ missio" of Radilltiou Consider Fig. 5.1(b) where the ::uom miunlly •s in lhc cxcucd Mate £ 2 • ll may !<-pomancously emit energy "''I = /:.'! £ 1 and come dL''"Il 10 i!<HHC £1 Now 1hc: photon~ h:wtns e nergy lt\•1 -=- £'!- £ 1 nrc cm•ned in nll J:>OS'tble d1recuons nnd 111 random phases. i.e.. theemmcd hghtts hoghly incoherent m 1hc case ur sponlancuns crn1s.~ion . lf the atom initiully as in cxcttcd $lntc £ 1 • then It w1ll emit energy /J\'2 =

,.. .,.-------.""·---" -; ~-

,,_.

1,-----------h, _________________

e,-----.--1--t---In'= F.,~ 1:: -

1,---e---4-- -·

E , - - - ' - - - ' - - ' - - -(:al

f, ------,.---c, -----,--11---

. ,.:T

F,-"e---~-------Ihi

Flg. 5.1

(o) Ahsorpllon or rndlatio n; ( h) S pollbllll'Ot.t$ e.m l~ iun or rudiulion

l:l I· 1hy .;punlnncou' c rui "1un ''' it 11111y cltlll lrv1 = l:."'.a- 1!1• when Ohlin\\ til <.:omc dm\10 (wrn c.\"- ilcd 't;lli! f.a 10 h.'J . lllU' thc~c O:: fXUlHmcuw;ly cmlnci,l pluuuu~ ~1rc· (I) nv1 tnotHx:hrom:tttc. bec:m~· they arc ha' ing diffc:rem energy Jtv1• ~tc {2) hi!!hl\ 111Ct1hcrl!nt. I)L-c~tu\fo! lhcy ar.-:: emitted :u nmdom phrt-.e (3) nm un~dircct ionul. bccru"c they are e mitted in tlliiXhsihlc llirccliurh r4) ' 0 ~111illt:d CllCPJ)'/Unit !Jri:.J h \'Cry lc, ~. £xampf&: o( ~pl111HlOCOU11. ~lllj,,HlO .m: ~unlight. onlin.tlj light frum uwant.l~ccnt lamp. tuhc. etc.

"''>

5.1.2.2 Stimulated J£missit1n vf Radiation and Lasing Actio11 In stimuhtlcd crni ~lon. ttoMiti<>n of .Jtorn fr<)tn high!.!r excited :-.late to lm~ cr '!~ late h ~trictl y n:strictcd between two energy levels. Out of th:tt the higher cnCtl?Y lc\'el j, ~;cncr.J.II ) "memswb l~ " . which b. having Iunger life tim.: ( 3 x 1 I 0 sec}, 111 l!ompm·i.snrl 10 01 ilin :u·y ~l31C ruH.t lftUISil ion from mt>taswbh• J'WW l\' tower swte 1s noa:tUIOm::nieally possible. according to quantum rnechanicnl selection rule. So ~ptlnt;.tncous c.nis~iou fwm meta~t ...blc st:de i:o. 1101 po~~iblc.. l l~rc utom:o. .:m: initit.:tl ly at the c:\cill'd mctnM~tblc state£~ (Flg. 5.2). Now if n photon hilVtnl! "' '\pcC1fic cnl.!r"J,;Y /rv = t :J - c·, C()Jiidcs wrth the ex<.~Hcd ;11om in mcut'Jt.lhle '-ll ntl' £:.then tlu~ collisiOn can rorc..- orMimulatc rhc :uom to drop into lhe Jo"·cr level 1-.~1 Ouc 10 tim. transitilm ~~ 114:~>\' phmon of cncrgy '"' = 1::"! - E 1 will be cmmcd. tn :rdduion1o 1hc me idem pholUn having the !'lame enl!r~.Y· Til is IYfN' af t•mt.·u·wn i\ t allt•ll \fttuulmcJ t•muswu bcnw,,·r it is stimutmcd In· tlu· im·h/cm plwum rllc ll\0:0.1 IIUJlOntUH JlOUtl ahoul '\Umutaled CllliSMOil I) LhUI the CUlll lcd ph01011 1s cxncrly identical to the incident ph01o n as regard.:: energy, d irection nf lr"".J\'cl. ph a.;.c.• and 'l:IIC or polan ~U I Oil. Cl<.." No\V \VC ha\1CIWO ldl'nLic~t l photons '\l~H1mg

Uu,.t, /-lofoxruph\' twtl p;r,,., Optio

r ---

M:a1~1iU~e o.tult'

~'·"

/ ,/ Jw ;;;;

125

B, 1-;,

L - - --h- - - -J-- - - Fi~o:-

S.Z Sfinm luled emission or rudh.Uion

ItOfU Ulll' phtJIOO uf ~C'IL'CICd frequency \1• Jf Lhcs~ lWU photon!- l."uutd be mzuJc to en~. 5.2) coll ide with more cxded moms in level 2. lh~n we "uuh.l gclmulupk vf h.lc•l liCaJ pholvn' ~' 4, 8. J6, and ~o ou Such ptt1Ct\~ uf lncrl':l,in!! 1hc number or photons is Indeed possible in laser. which IS taiJcd IHsing tu·tirm. · n1U \ photon~

cmiltcll hy ~limulat~d cJni~~icio

111

ln.scr ;lfc:

tl) mono<:hrommic because all are havmtt same <ner£,)' IH'. 12i lul!hly coherent becau~ lhl.!n: b a p:u'ht' ulur lime diffL"rcncc hclwcen 1\\''l CCIIJ i~ lttO.

13) lughly unidirccl!Onal otherwise they" 1II be >toppc'\l by l:t>crtubc (Fi~ 5.3 ). t·U 1he cmiucd .:ncrtty/unil are:a is Wr) high No" in urdcr to get lrt:,.,IO£- nction. lhc folio" 10~ urc

I A larl,!c numbe r ot cx""ued

atom~

..:s~cnW1 I:

an level 2.

2. Phuton~ :s-hould not he lost to an Oilprcclllblc extent by nh~orpuon m nloms

in Lhc lower c.ncrgy tc\'cl E1 or in any mbcr \'-'ay.

5.2

Popul ation Inve rsion an d

In g~ncrnl

th\!

Purnpi n~:

numbe r of moms 10 the ground

st~Hc

1S ~rcml!r lh•an the-

num~r 01

:elums 111 the cxclll.-d 'tAl~. !:Jut 111 onJer lu g~l lot..'llng m.· t1un. '''' rcquu.;tllhal we rnu:.t hav.: Iurge number o f mom~ 111 lhc cxotcd ~tn tc 1h:1n 10 the !!round or lnwcr .\l,1lC Thus tor ~umu i ;Jicd emissiOn 10 take pln\:c, we rnu'l nrllh\:t<lll)' m~n:.H~ the pc>pul:tlhm Of the tilOnt ~ 111

higher t!UCI'g)' C:l:lll!. T1w~ is l!Cilll!d

ilS J)CIJ'IIIlll iOII

llll'<"fSifJII.

Pt)JWiataun in\el :-tann l~ achi\!\'cd hy SUJliHying energy to th~ ~ys1cm, ,o lhm aiUIIl\ wi llab~orb J requisite amount of energy und ~o from the lower lc,·cllo hi~hcr 1c\c1 Tht) 'Jpply C'lf cner~y to the medi um h c tallcd fUtmJdug A 'Y~h.:.ul in w hil'h pupul:,lion ill\'ersion l!i .u:hicvcJ u c--..tlkd :m ot·r/\'f' .\,r.u,•m.

5.3 Operating Princi ple in Laser Om:e popu l;uiunuwcr~u.m i~ achieved, svvm:lnoously COliiiCtl phou.nh C31l inatiare lhc process ol amphf1c-"llon because a Jarge num~r nc1ive centre!' ('lr ntmn<.: an the rcquart:d h1gher ea'\crgy SltJic ore available. In order lo 11H1kc lnr~c numb~r or collision~ between the photons prcsenl and the octi\rc centre\. nC-LJVC medium ;, lO be: pluc-cd hctwccn IWQ high ly rdlr;:cling mirrOr!o M1 ouuJ Ml { f 1ig. 5.3),

Ue:un

. t\~-t•v~·

1----- --

Mcdnun

-----.. ----+ • - ·-

---- ---·---·

:111

1111:

·•

'1 ,;

... Flg. 5.3 E..'(p-trlmctu al set u11 (ur \ htr11ng la'>i n~ aclinn

whtch 1~ known a.s r-:.sonator ·tnu~ in bcl\\'l'Cn lhc twu nurrors. w:l\t;S p1up:tg;.alc :aJong both directions and intcrfc.rc wid1 cnch l)lhcr. Due to thnt ~table standing w:11·e p:mcrn will be formed. condition lor that being the ctii'IIY length (" J) mu~1 ~ intcg_mJ multiple !lf .l./2+Thus tf-= nA-12. i.e... I.C.

A • 2JJ,. where " ;;; 1. 2. 3 .

Thcrdoro. re...onn111 frequency= f = dA. = u!d2d). Thai(: phntoth lhltllrtWI!l p;m,llcl h.llhe ttXh. c;l( the IU'1'iln~cmcnt willtt:lvel h' and fro between the IWll Mirrors 00 tlt:COUill of their related rcncc:tions. Every 1irnc 1hcy p;&:,~ through lhc acth'e medium. -oome of Chi!m t.-ollide wilh cxcilc\1 ltlOUl<; Olld give fiSC I() SlintuhnecJ cmiS!>iOn

or phOIOilt; or $!1111C:. frequency. lhm

way the numb<:r of photons goes on incr"n.<ing enormously and lasing oclion

/...11.\rr. Holop.rapln• mrd Fibt!r Opt1c:r 327 stans. If one or che rmnt'lf!' is made p:trtwUy trJm.p~Lrent then a very powerful p:tmlltJ beam of photons. will (•omc oul of it. Pho10ns which nr'C not p~m•lklao the cc:nrrnl 3xi~ will he ((')sl due 10 tntetncuon with the wnll surfac~. Thus the fo!IU\\'10£ lm.!\k rcqum:nh.:nb. whi ~h mu't he ~:'Hr:-.tie~l for htscr opcrm..ion nrc: (I) 1l1crc mu•a be nn OL'Jivc- medrum \lo•htch emil:-. radJ:JIIon in the rcqutrcd rt:gion of che elec-troma~netrc spe<.·trum (2) Populntwn nwcr.-run mu~t be created wrLhm lhl! mediUm; tlu:-.. 10 turn rcqtiir~;; the ex~>~<on~e ~f ,uuuble tner~y levels (I.e. £ 1• £,1 n~.,o~uuctl wnh l:tsing transition roc pumpin~. (3) For mze l:lser oscdl~nitm them: n\U~I be OJ)tical rccdb:•ck ::u Ihe l~lld\ or the m.ediu11110 ronn rcson:)nl cavuy 111 ord'=r w gel hrghly powerful and colltm::ued. monoc:hromaltC. coherem laser beam.

5.4 Characterisli( rropcrlies of Laser Light TI1c Ol0$1 ampon:mt of thl" propeme~ or 13ser bcarn are iL~ h1gh dtt!!ree uf·

(I) Dirtrfltllwliry: Phcton .. whtch are moving v~•r••llel to the ccntml :1\i~ ~·~m only be suslumed Othe~ will he Jn(,l 11ms the bcnm emerges along the dart«.::tion O( lhC. rtXiS ,lC)' arc olmo.;t perfectly parallel lU C~ICh 01hl·r. (2) Mrmorlu'fJmaticity- 1lu:o. property i~ due 1u two reu,o,.on~; (11) Only an electrotmtgncuc wave of fhcc.J lrL!(Iucncy ~dt:temlincd b)' the energy dlffcrc:ncc ~b) awo marror arrangcmc01 fomls 3 rcsomm\ c;IVH)'• only itS rC!-\l(U\111 (n;qnWCIC' whi'-'h d!!llCild UJ>Oil lht; d is tance hctWCcl1 IWU

£ 2 - £ 1) cnn be omplirta:l

mirror. can be 'ustnmcd (3) CoJwr·cmcy: h io; h1ghl)' coherent ~IIK'C the amphficution i~ due to ~timulntt·d emission.!!. BccUU\C: IJlC luph degree nr t\)hcrcn~y tl\:(otiated wuh la\t'r hl:-oun. his used in 1mmy divcroc ,Lt\:.t:o. IH.c: holo)!r.•rhy. d:u.u pwccssing. t:o1mnuni~.:ati\"ln'

1hnH1gh fihc.r nptk L'tlble. ell (4 ~ lJn.llhtnrH." Uu~w th"• d1n:c 1ll•n:lliry propcrl) . hri~lunc'-"'·thm•' 1hc: llU\\ ct eminod p¢r unll>urfocc "r•• per unn sohd angle from l•~~er source is very largo. If laser l~o1m h focu~d h.) ·• ~tUn'(~ lens m ~omc region then tlu: intenMI) will be

tremc:ndou"i Ul that phu:r. Tha... high antcn~ i ty can be ll!SCd cffcclivdy to 'drill' throughu n~ualic t:trgcl No\\ HI mcdic:al wnr1tl (or surgery, It isnlsuused CXI!!O,ivcly.

5.5 Ruby Laser Ruby luscr io; mudc from u ,jngk cyltndricnl .;ry~tal

\~f ruby.

whuse end'\ are llnl

liJld Otle o( 1flc ends j, Cl11UplcteJy ,jJvered and the other end is partially siJvcrc:J. In the original 5Cl up of Maim:m . .1. flu..s:h lamp filled witlt xenon j?US. w~ connected to u C~tpacitor (Fig .5.4:'1.). whkh w~ charged 10 n rcw tilovnlls. TI1c energy ~torcd in rhc cup~cuor wns dJsclwrged through the Xenon lamp m a few mlllisecond. T lus resulu m a power, which is :~ few mcg!tw:nt.s and coded a'" Opucaii"""Piug since i t is goven by light energy. Some of this energy is nbsoroed by 1h~ acti\'C centres of d1e mhy rod resulung in thc1r excuauon and subS~.;qucn1 lasjng :.eLion. Ruby consi~ or uJuminium oxide (Al:::O,) wub some orthe allumm1um ions (AJ+3} replnced by cbronuum ions (Cr"l). TI1ese chromium ions :are the active centres in the ruby l:tscJ. For tt good J:.hing ac1ion. 1he ruhy crystal cons1sts or about 0.05% or chromium.

328

Englnrrriug I'!Jyth-:t kuhy wd

---~

'----llit--1

Non·mdi>Ul"'t' UWNUf'n

t.,

r=::=l=======fl---

" M

Pump pbtiiOn l..a'lt'.r c:mlulon

,, t'i~. 5.~

"''

tn) t:xpcrimcnbd sci up for ruby lt~scr. {hJ F:ntrgy ltvd dia~rnm sho~<s diff('~DI Jnttrmtdlatt' Slt'p~ ror la.~r at•tlon in rub3 I:.S:\'r

The ~nl!rg}' swtes of t.hc c hromiUm JOil!<o. arc shown in Fig. 5.-llb). The t hicr Chllr:IClcri>liC of lhc Cn<rgy levelS o f 0 thr<lnllUtn ion is Ihe fnct lhfil lhC band~ levelled ns £ 1 and £ 1 arc the ordin:uy tnergy """d' hnvinl' '' lif<tin>e ~ 10 4 sec, whcrt.:.iJ~ the ~•ntc mnrketl us M lms u lOll£ lifclimc which is z; 3 X I o-' \;CC. A ~tate \\'hkll is c har:lCtcriscd hy .s-uch n long Jife i~ h: rnll.!i l ;:1~ 0 IIU!/(lStabJ~ H Olt' rrom mt!ta!'tablc Stt'tte moms cannot automatically lo<tSt:: cnersy by cmir.sion or rnc.li:uion. TNIIISilion from mctaslt blc st:.\tc to ground st:ue i s forbidden by selection rule:::: of quantun1mcchnnics. which govern su~h 1ronsition:-.. Thu~. s).)(')nlaneou:-. e.mis...:;ion

I..Jr.'irr. 1/oluxraplry tmd FiiJ<~r Optics

329

frnm mclastablc! ~tate(~{) i~ no1 pos!<oiblc. Chromium ion in ih !!round sm1e can nbsorb phown. from the xenon Taml), t1f energy (1.! 1 -G) und make :1 trumnuon IU the state it eQUid"'"' ab~orb" photon or ~ner~y ct:, G) :tnd make a mmMtum 10 E, st3tc. lncuhcrca.:.(! uunmcdw.tcly makes n n()n·radmuvc tran~a u on (~1ving cncrsy to L hc cryMal) to the mct:J:,tabh.· state M and ~mcc the \tate M ha~ ra very long lih:timc. 1he number uf :JIOms 1n 1Jw.. .,,,,,~ ~ecp on • ncrc~t'\111~ ~mtl one may achiC\'Cn pnpL~auon •nve1-sion hc1wecn the '1\I:UC M nnd G ()nee popula!JOll uwcrs1on JS uch1evcd. light amplific:mon. lhm JS laser ncuon. cun take pl:tcc by any ~pnnltlnoously ernlltcd phoJon

e,.

Chmmtum 100~ decay rrom nlCill">ltlhlc ~UtiC (j\/) 10 gmuzld 'fliiC ((;) emming ltt~cr light of wave Jcn~th 6C)43 A (red) 1111.s l1gh1c:1n be madl.', to pus..'i aga1n and agam~ lhrough a ruhy rod by u~mg mmor~ ul it.s cncls ~uu.l get~ umpllfi~d. Ruby lu~r io; odt-o culled .r olul ,\tilt~ lu..H·r. l1uc &n S.~1hd n1hy n)ll. In ruby Jasor optical purnplrng is not cnntinuou,, II is In the form of pulses. becau.se the Xenon l:tmp does om operate com,not•SI). Corrcspondmgly the laser nutput i~ also in the form of strong pul!'c~ of VCf) !'hon duration. Due to thm it i~ n.l.so called as pulsed lo.:,.cr. Normally JlUise Jur;:tUon i.;. · 10 tiS Jnd the energy p..:r pul~ j.., • 10-~ J. 1hc uvcrJgc power 111 thi'-. ~olu.l 't:lh.~ 1:~-,:cr in .::tell pnll\c i"' ~

10 KW. Ruby loser" o three level l.1<cr.

5.6

Helium -Neon Laser

lns:cr COO~IUS <tf a llll>. lur~ of He tuhl Nc or :Jh4)UI J(); J. pl.tCCd 111~i dc ol IOIIt! n:UTO\V di~dHtJf.C lUbe (Fig. 5.5a) The prc~!'IUfC ll'l~ldC the tube ·~about I mm of mercury. The g:t..l\ systcJtl is cnclu'>cLI bet\\ ocn a sc1 pkmc znirmr or rt ~~ of conc:1Ve 1ntrror,;, so 11mt a resonutor IS formed. One of t.h\! m1rron: j:,; o( very Tile Hc· Nc

lngh tcOecli\'11)' wh1lc the utlu:r 1s panmlly tHt11"'P11rcnt, w 1h:1t uner.gy may be

com.ng out or the sysrem. here Ne ntoms ore the aw"e centre>. When the ,tj~chflr_ge p:t.))!'~:o. through the tOl!' nuXturc. then act~elc •·ated eleccmns the hchun :~tom.\ Jnd ex-..: ate 1hcm hl d•ffcrcm htl!hcr cncrg) ,talc (Fag:. 5.5b) which i-. known as electrical pumping Some ol lhi! helium iUOml\ nrc ~:Jtcitcd to the le\'d\ F2 :uul F, , whkh h:ipJ'H!II 10 he mtfltl~tnhlt' t. Wit', M• 1he he.hum :Hom!'> eAcitetl to tho:..e level.!-. ~pend a long umc bcfon: gemng de-exdti!d. Thus gradually a large number or helium :non" will ac.:umulate '" the states Fl untf /·, Now ~me oftbe c.xcitctl Mole!'- t1f ncun &11 and E.t (Fig. 5..5b). con~po m.l upproximmcly 10 the \amc c.nettt)' a:- the C:\CIIcd t:nergy ICH!I. F: nnd F'J of hdiurn. So when excited helium atont' from mcta.!'t:Jble: state" P'!. F,eollid!! with unexc.:ilcd neon :ttoms.an energy exchan~~ tnkes phu:~ - The neon illom:. a.re thus nu~cd dm~ctly 10 1hc level-: E~ ;md £ 6 nnd hcliu111 :110111 will h-: dt:·c.xcilcd w the ground stutc. Becuuse or the m<t3Stuble n:uure or Fl and F, level or helrum £tt<un, discharge lhrouflh the go-: mi"'turc continunu~ly p<>J)lllnt~\ the neon nl,)tn, cxcitctf 10 Ihe energy levels ~ and £ ... tlirccdy. Thi'\ hclpc; to create populotion invc:rdon bctwL":cn J~vel ~ l:..'b, If,. and the lower lymg level:.. C's anrt E1 in Ne. l lenc.:e once population in\·ersion h!JS been .tchievcd, uny spontaneousl)' emitted ph01011C3n trigger lasc13Clion. The varioo~ tr.msitions (Fig. 5.5b) l!!ad to e111ission at wave lengths J.391Jm, I. 15 Jllll and 6328 A. the first two W'C in the inrmred rcgiOrl, whcre.~tS 632S A i.s lhc wull kouwn red ligbl fn-tm Ile-Ne l:)scr. This lOIIidt: with

(___ __

. >

_ li ] L'l."<tht-.:.m

,., lk

F, - - -

~~-·' ----.-\~

F,-,_!_ r_ - _ -:. CnetJ;) D1m$IC1

1Jq pm

1!,

I IS J,un

b) ""'lh~~too

L.a..., 6328..\ '- t:m•~<•ot•

SpwtlllDCOU) e:•ni,sion 4\b~·t.-d

1n IM'On·littht

IA.•-t<\~o.i i:UiUJt

F,,- - - . l - - 1 - - II' I

l<"ig. 5.5

(a) Experimental stl up for Ile-Ne la.;et; (bl Eoergy J(•,•e l diuJ:_rum shO\\S dlfTeno_ru .!C.Iep.\ fur Ln.sl'r adlou in t-1.~-Nc la~r

radiation j~ ampfincd by the prt~CSS n( \Cimul:tted 1:-llii~\iou, 111:t.king u~e uf lhc rcOcct iug mirror' (Fig. 5.5al Hl!n: pumping'" called £1;-,.,riruiJiUmJ'mg looincc electrical enc•·gy '" uo,cd for purHJHng 11~-Nc lll><r normttlly rcqu'"'' 5 to IU W nf excm11lon J'<)Wer ~nd produce_, 0 .5 to SO mW of l:\~er uutpul It •~ ;abo cnll~d ~w.~·luscr. since it is originaung rrom u He· NL'

g ;Ho

mixuue

nrc, In genrral. round w c mit light which is more c:hrcclion:al and more monochroonotic.thbis bcc:•u~ ofth< nb5cnc.: of the elfeeL• such o,, cry.t:ollinc impctfec:tion. thcmnal tlttilortwn .md :-.'"dlh.:nng which arc pr.;scnl in solid state G:1s-ht.~cr~

laser" Ga~MiascN arc: capable of opcmung continuously withoul lhe nt!ed for cooling. So thh. al·m c nlh:d n' conunuoa•... llutpul lu\Cr or C\V ltt.'\.Cr He·Nc la~r is u t'our lc\•d la~cr.

5.7

Molecu la r Energy Levels

Energy level d i:.tgr.un :•s we h:I\'C «Jjscusscd (or Ruby or Hc· Nc htscr are due 10 el~ctmnk mnrimu But \\then a molecuh.! :..:1y C01 • is fnnned, then in udditi(lll to lhe electronic mmions. atOm !-. in the moh.:culc.~ may vihr.uc in rlif/runt mrxlr:r nf l'ibratirm ar ''ibmtt· ahmtl wtr;mu axt'.\ . Thu ~ . the molecu lar energy level!- i:. lhuo; c lassified not nnly by e lccuoruc IC\'Cb but dl~o by vibnuionul and rolultonal lcvds. Each t'lr.ctmnlc le"el is 'iplil up in1o varinu' viiJmtitnwl ,mh ll'vd.t due 10 rh~:- une-dimtn$iOnal motion of individual atoms nbuUI n c~ntcr of mn.~. in

l..tMt'r, Jlolo,ttmpln• mul F,.brr Optic,'( mnh:~ult!~

further lncniu

3.1 I

in the c.rysr.nl. J~ sho~o~, n In Fig. 5.6. Euch ~·ibrmu)lltll h•wt is again IIllO mtmimm/ JUb {~t·r/.\ C-<0\linlatc:d from lhc munn~nl or

!<~Ubdi\• idcd

or tht:

muh:c:ul~

ohout \'lJriou.s axes. Suppose the molt:culc h:lS linear the energy£, associated" ith tht! dectronk motion

tlisnc sl~i on' of order 11. 1'hl'n ,_~r n

\'i\lence dectron

of th(• order or

- o- •

0 f tg.

:'.~

Vibroulon of ~Homs in u rno l ccul~t

E~ .. h11mo!

where m '" the electnc m:tss. When n IS of order of lew A unu. then 1h1~ correspond-s w uansnmn frc<1ucncu:s (belwccn v;tnous decnontc lc\'.:I&J Ill du: \'IStblc and ullr-.Jviolcl reg1on. Energy £ 11 a~soc.atcd w1th v tbmL•onnl mot 10n in •• nmh.."C.:ulc IS nf the o1tlcr of f.,, = (m/M) 11'

where M ''the mot~culnr mn:-o~ . .since molecul3f Ol!L'>S M '~ 100 umc:-. b1ggcr than clcctml't":r. rn;''" m, S.' 1::.., '" hundred times ~mnll er then £, :uu.l corrc~pondso ll1 transmons (between vnriou$ ' '•brauonal lc"els) m the near mfmred regaon. Rot.JII('In:tl energy 1~, us,ociuttd with rolahonnlmot•nn •& of the Ctrdcr or Mu:! so

1hn1 m a molecult::

£,

=(m/M) £,

wh1ch ~ ~ dboul I o 1 tunes smaller than 1:.",. and I 00 limes !'nmller than E, .. \\ htch corre~rond.s to U'i1nsjtion (b.::twcen various rotmion~,r lc!\'cls) irt 1hc f:u wfrared

rcg_mn. In CO:-_ lnser and Dye Luser. lnser ucuon takes plnce bcaween various vibr.u10nal and rmaltonal level.)> whicll we will discus.~ now in detail.

5.8 Carbon Dioxide Laser In t:urhcm dto"<idc hucr. lnscr uclion tokes plm:e between rotnLionul o,;ub ic,·cl o( particular vibrutionr.llcveJto the mtation~tl sub level or luw~r Vihr.uinn:tl le\'CI. Then populntion inversion is achieved through a gal> discharge. The ~ffici~ncy of 3.

co, lascJ is ~cncrally increased due to the addition of N2 gas t" C01 gas. when dischnrgc is p~sscd ttu'ough chc gns mixture, nitrogen molecules nn: cxchcd co

the upper ' 'ibrJtionul 1.:-vel ~-""l· Fi8urt 5.7 show~ some cnc!r~y levels of N 1 w1d CO: ~rt~ . The upper vibr.ujonallc\•cl £ 5 of CO: g~L"' is on rhc snmc level o f F1 of N1 bta.~. thus due to :1ti! collision of un~:::xci1ed CO! molecule. with excited N! molecule. which nre m the me,aslable F 2 Jcvel. energy ll'tmsfcr tnkc~ place and

C01 molecules. raised dtreccly to the upper vibrational level

c.,. This creates

900CJOA

1()(..1):-_1,\-= W

(I pm

E, Fl~.

5.7

l'O, Ia.<<'

popu1::tunn mvenaon hemecn tht! lt..•\d ul 1-. \ :u1d lower c.ne.rgy

lcveb.l!..~, ~nd

£1

m co! molecule No\\ hl\t'r ;u.·ti(10 l:tJ..C!o phu;e bt.:lw~.:n rot~Hional "-Ub level£, of upper Vibratlooai level 01 ("Q) lllokCuJc hi <olatiOo:OI >Ub leW I £, and f:3 Of lnwcr vtbr.ltion ltwrl and leotd~ tn t:mb:-.1on .11 wnvc length~ 10.6 and 9.6 Jtrn. wh1ch t~rc in the infrun:•J rc~tltn The co! ga.~o.l:l~Cr j , mur h mot.: e:Oicicm th.m other ga'\-la.~rs bccttusc the IL'\'d" wking pan m the lu~er tmn~uitmc; ure thl" Vlhr:ttio nal ro1u11onul levels of chc lt''"'l.''-t ..:lcclr\mu: lc,•cl. 111~,... h:vcb are v~.•ry clo~c to •he grmmd lc"cl so dcu.citouinn. rrorn Lhc l~'''('"'t I.L,er lc\d 11, th~ ~round levd, mvoh·t, ''cry ~ma ll nmount of e nergy loss whicll h 11111 contrihutmg w the output l:t""cr bc~tm. Hence l:trl_!C portiOn O( t.hc input COl'rgy i .. (011\'l.'f(C\1 intO I.IUIJ>UI hto.;er, f'CSUit ing in ;] \1Cry high efficiency. from SC\ICl"'JI W31b lO SC\'Cnd hundn:d \\.HI~ JWWCr OUlpUl is possihlc rrom C01 la~cr, l ligh power \OJ laser ..:.111 I~ u"~d i11 indu,try for dtilling, welding. coating. ctl. COJ h~l'r c.m ulso ~ u,cfuJ ua npcn air cnnununiculion systems hcdu.M" the wave length from CO~ 111'\Cf ntt..:; in n band whl!re nlmosphcric mtcnu;ujon j,. sm:tll. it can .1 lso ~ uM.:U 111 .10 optical rJdar sysh!m

5.9 Dye Laser 4 Dyes used in the Jascr nrc •lfJ;tillJc :"llh~t.li1CI!s wh1ch ~·hsorh m lhl.! nl!ur ultra' ioh!l. vbibfe Of n~tlr infraocd f C{!IOil,_ of !he ch;clrnnmgnctu:: " P <."!:C if'UII\. 111~SC 1110.~1 comrnonl)• ~olio which .trc dis.~ol<cd in ''arious organic or inoJianic solvenb li"-c wutcr. ethyl ukohol. etc Th\!'c dye ll.t.)Cr.. urc now o f

;uhstanc.:.' arc

gu!:tt intcrc"t bcC-rtU.SC flf Ihe ir two;u.J ::.bSOrplit)JI :tnd norcSCCnt SJ>t!ClfUffi :111d pu-.~abihtics of gewng u chenp and _,imp l ~ lun:lblc la.o;cr. One can also choose uny n.lgi<.m or the visible ~pcc trurn from 1111: lurgt: rang.: t,_\f dy.:s. Various vibrntionnl >ub icv~ls of diffcr<nl e l ~elronic sl3te~ of the dye n~olecule un: rcpon .. iblc fm Lhe Ja,cr ucLir•n in dye la:o.fo.'.l Fig. 5.fl shnw:. che different electronic 'inglet level .. S0 • S1• SJ. cm:h of\\ hich .trt! subdivided imo vibrrttionul levels and each vabrnlionallcvcl ao. again o;;ubda\•idcd into various n•ltttjoualle\·el. Thi ~ h.mds to ~lCh clccuonic level cunt:tining n l:1rgl' number of vibmtional, mtntionnl sui> levels. nnd this dense collc-etlon nf sub levels. leads w o ncar

/.~~.<-., Nnlflil''"f'l"' twd Fiber Optics

:133

t:onlinuum of statC.'\.11\iS dense colletion of sub lev~! I'> is responsible for broud ;abst~rplion nnd ~:.miMion spectnun of dye molceulc

lil 'lt'J

Due 10 tht: ob.. vrptil)n uf li@ht , dye 10t')lc~:ule!~. get excited from grounJ 'tntt: S0, to V!tl'luu.; vihn.tti11nal w t;Uiunal lcvd of the higher dcctronic level Sa. No"'. by the t.hennal rcdb.tribuuon m lt:\'t•l S 1• most of lhe d)·C molecule~ drop 1u 1hc towcsl vibrttlinn:ll

(e'i(~IB

n[ S1. f":"luorcM~cncc (.."'nlC!<. ~L" Laser rndintion when the

dye molecules make atrruJ:;ition from lcvciiJ to any h1ghcr v•b r~UIQnnl subkv\.'1 i1f $0 • ..n \&: lif..:timc t..f UPI'Ioe' L1~c1 lc~~l H is uf the order of 10-9 !i:CC, which is much smaller thun 10__, !<oCt' . Lhc lifetime of upper rnl!la!>tablc laser lc\•cl fur :..olid Mate J u~er. Vibmlioro.l rotional '"b h;\•cls for different c lcc1ronic su'lglel levels :ts S0 • S 1• nnd S2 and 1riple1 level' a~ T1 • T1 ere. for dye molecule nrc shown m

Fag. 5.~ . Dye molecules ols() make non rr.dinlive ltnnsition from B to triplet Stale f 1• Thh. traosllion ts ''cry important to m;.untam laser acllon tn dye loser. Bc.;:~usc 1he absorption S(>CClrum of T1 -4' T~ usu.nlly ovcd:1ps 1he c rms.sion specmun of ~~ ~ So. thus leading to a lo~s a 1 1hc wave lcng1h corrcspondmg to t.hc ltt.!~.cr C!ffil<i!'JOO, dui! to transiuon rrom level /J to uny level of So. Thes~ losses C~tn even Jlfcvem the lorgcro~i l ha tion F(•r gn,)d laser ~clion, one must reacll rhe 1h re~hold level before. signifkonl number or molecules hnvc dropped to IC\'017', rrom 7'1 nets as a upper laser lc\ cl nnd I he l:l.'\.Cr 1mnsa1ion takes palcc from T1 to lnwcr lying :,.ub level of St. Due to tl11~ . an exciting ~ourcc witb very fas1 ri:.c tunc. either nash lamp... 0 1 pul~d 1;~-....:rf I\ 1\~C~S:lty. Dye laser tuning over 500 A 1~ possible by replacing one of the resonance

c:ovily with a difl'r:tction gr-Jting (ofn:nection type), whi<h is adjusacd $0 ah:H ahe

to"t onkr n:llc<lcd beam lor the de>1red wa'c length '"" be along the ax;, u( lite n:'"maocc C.&\ II) 8) rctatint; the graun~. \\ .t\C lc:n@lh t.:.tn be: :altered.. 3.'i to.)' U'tnr Or.l~·, l.a" Emb.~iOD band' of \I)'C' l.a...\Cf .&te U'U.tJI) CO(l<.l~llng Of \~1) 1.1<~<' lr~<JUCfl<) r.tn£c t : 10 1 . 10 " lit or 100 A. 1000 AI. B) u<ong "'"de I<Xl.tn~ h!c:hntquc ~ne can ohtatn mod~: hx.l.c-d. e\lrtmcl) 'hurt h c JO 11 \C'C) uplu.. oal rul~ \t.lth the addiJonal freedom of \\<&\C lcng1h lUniOt!·

5. 10

Semiconductor Las er or Diode lnser and Light Emilling l)iodt ( LED)

\ c.' l n'\' tfH: JUIH.:llflll of tht.! ".COlJCltOdUCIOf d todc CICCifOn'\ :u1d hole~ :tft: injected h1 .1~ cnndiuon:-. :t' nHnor'hy cc.rm:r (Fig. 5.9, 5- H)). The excess nurwnt) c:tmcr (llffU'•Cand rccombtnc with rmlJOnly cam cr. In the Ub!.\cncc of .111 cxtcrnnl applied volt:lgl! no eurrem flows. a~ potenuol barncr {L8 -= t<Vul- pre' l..'nt' 1he nctlltl\\ of earner nnd Fermi lc\cl for I' anc.l" 'Ide w1ll comc"l«! C~il!' 5. 1L.a).

uncll t tnn' .1rJ 1

o· o· o· o· o· o·

0 0 0 0 0 0

0 0 0 0

0 0

0 0 0 0 0 0

o· o· o· o·

0 0

o· o· o· o·

0 0 0

lkpLI:IIUII H'l!hlfl F'i~.

$,9 Fornmlit•n nf dt pldl(tll n.-glnnln I'·N junc'tlon

SponlnnMuS F.mi~sion When e~temal vohaf!C as lpplicLI .t.' forward btu.fii O·a~. 5. 10). e lectron' :rr.1.1rt 11m~•nl! Irom 11 mp and hoi~ fromt' lo n. Thc'C manority carrico. arc! dfCl.--c.ivd> tnJI..'l'll'cJ iJC"ffl'' the JUnction b) the apphC:IliOO Of the C:.liCmttJ \'Oltage 3Dd \."\Jrrtnl .,.,.,. thr<1uph the d<' 1Ce as lbc) conunuou51y d1ffu><' from the 1nterfa<e.

""">

•

- - - - - - - - - FM'rnllt:\d

... . ............ . Fi.:. 5. 10

R~t·mnhin:ltitn1

ur t:urrit.'nf UIHh•r ronumt bfa.., in 1'-N junction

"01is: ,ilunlion. in ~uJUtblr ~rniconductor nlll lcnnl. •all(!\\ ' 1hc nnT;('r n·combhwritm n'ith tltt~ t~miHlrm tif liJ•hl, in thf' th1pll'thm tfi;:ion, which ll":l(h to I.ED (Lill,ht l;,rnined Dlude) and scmH.:onductor la..'>cr. Sincl" hert! forward bla..cd f'. NJum·uon l.c .• ~~-·nu 4'tmducl0r dnxk gtv~ rio;c lh~ L:l~r ; \ cuon. M' ic t"- called w.. t.cnn<."mKhu.:tor tu.'-CI f'•r Diode Laser '1l1c incTcct~cd concenmuu.ln of rninonty ~;;arric~ in lhc op~hi lc 1ypc rcgmn. umJcr f{'IJV.tard bia~l"d P·N j unction lc;tdo; 10 I he r..:~wnhinoi l ivn 11( cotrriCI' with I hi! cnn"stcm o t photons. nero~~ the: band gap m tlw clcph.•ainn rc~a on '" ~' ..huwn In h~ 5. iO. Where lnC':ISVrc or rccombmulion con 0., dell ned 0<

. . No. uf pht1100!~- \.'1111Hcd tJ, = lntc.mJI Li uan~um el fic1~ntv~ = N u. o c 1crtrons .IUJCCtcc. .. .S 1 1

(5 In)

wluch iS unit les..,. En~rgy rclca~d hy tht\ clcctton-holc rccomhinnt10n in dcpli:ction region •~ ~ippnlAilll: ttcly

ctjt.Htl 10 the b;tnd gap energy If.< f!xcc ..., c.lnicr pupul.uion h .• ;hcrernrc. dcc.r~a.<>c.d hyrel'~lmhioat i on, "-'hich nmy he t:.uli:ltt \'c ur nun-nu.liuti\1! In nnn-radmtl\'e recombinuuon. energy l' rclcu~cd 0}. lmuc.: \'tbrJuon and thus hc:ll Whrre.l$ m hand tn bnnJ mdmh\ C tccontbnwlltl11 th~ cnc.rgy '' tdca,cd With lhC Cf'C:ili i"D flf phOitJO Wlueh j, gt\' ing 'f/ltlll/tiJit' tiiU t' nli.HWII llf phOIOil\ Thh il\ the mcchunism hy which light is cmitt~:d fro m an LEO Stl due 10 spt.l nln· neou-. t"trti'-'-icm c>l' photon under forward hi;so: contlilivn J>-N junction :t.:l.s' LED HUI lor the lllJCCtion lo.ser or scmtconductnr laser. 'S1imul:ucd Elni..;.,iun· j, requtn._~ 111 addition 10 au optical cavity and mirror ciTc:cts, ht prm h.Jc feedback of pl mton~. In LED. generally the tnergy rclea~c.l i.:; Ct(IJUI hl the h;uld l_!ap l'n\·r~y t.,:. Su t..he freq uency emitted is

., Jw hv: F., : T For vaAs.

(5 "''

t-_ = 1.43 cV. Hence,).= 0.8(>pm = ~(i(KI A

I.ED ''called IREIJ ll11~ ~pclnla! )t.-"'U~ n' CICCtfOfuminC~CellCC fi.c. npt..icaJ cnussion due to clccuic.al field). Thi.! > amount or rachndvc recombination 'lin' H6011 ;\

j., 1n 111fraJ"Cd r~gton. :-.o that

Cllli~.MOO offjgJu from WllhiO the Jiode StCUC111rC I~ knu\\lll

und emission nuunly -.my within rhc s tnu; ture. dt.:~·ndtng upun the ...cmH:<mduc.:tor

m:ttcmol. Sl.imulalcd

t:m•~sion ~nd l.a.~in~:

in Semiconductor l.uscr

ln s.crniconductor la.o,;cr both side!. ~,;.1[ P~N junl'tion arc heavily doped tl"'f'- and n... Due 10 1hn1. popul ation &nversion i s ~I ready achieved. I Ieavy I' dopin~ cnvscs the f'crn11 1(-vel to cotcr mto the V.B in P-suJe. ,..,hcrcu.-. hco''Y 11 dupint; c.uu~cs UJc Fermi level In enter into the C. B. in N·~idc. The-se are callcJ qmJSI•Frnui-lr~·rl Figure 5. 11(0) show~ lhc upcn c ircui1 condition. when Fcnni level for 1t nnd H.. ~;ide will be 011 Lhe s:unc l 1nt!. Thu~ a p •-N"junclil'ln provuJc~ the :t('ll\ c mcdiunl To yet l:1scr acljon. we need population mversJon :tnd opucnl f~ed b:td:. where population &nvers&on has already been nchocved due 10 heavy dopu•8· To ob1ain SLimuluted cmisston. thc:rc musl ben rcg1on of the dcv1cc. where there arc many

excited elcelronl'J ilnd holes rrcsem together. Thn11:.. pos.stblc only m1he J<'ph•wm ft!J!iOil.

l3Cl J:.'ugirJeain}f Phy.n'c.v

Mech:1ni.sm or Slirnulaled Emission in Divdt.:o..L;•ser/Scntil'unduclor Laser Figure 5. 11 tn l ;htlw~ 1h~ P' ·N' JUIICiinn cn~rgy levch under open ctrcuu When a forward hias ""arly equal lo band gap vohnge 1< applied (Fig. 5. 11 b). dlcn there;, dircc1 contluc1ion llt"~ihlc Nnw when photon..; wilh energy 1:1 which i~ less than the ~eparduon l!nergy o l tin.· quu.ri 1-'rmu /el•d f£,1 (£~.: < 1:..,, (where £• = E,.. - E,.· l i~ lnudenl ou the tJ' ~tr junerion, lhenthose pholon~ <::imnol

...

because the ne(:cssary \.B. ~~ n.lrend)' ncc::upled. so those photon-. c~n induce a LhJ\\'11\\<Jrd trnnsition t•f un electron from C.B. to V.B. and thu ... ~bmuluting the c.:nliS~IOil ur :u\othcr plwtOfl and t.hJ~ can be cuntiftlJCd. TIIU~ th~ b:tsk conUition for Mwmlatlug ('lms.urm in sc.miconduc1or laser is depcndcnl ul lhc ..,ua..si-Fc.nm level 'cp:ar:uion energy (/:..-11) :\Swell as band gup f£ 1) energy. :lnd it is expr~sscd as ht

:~h~orhcd ,

r·

r.o

E ••

-·

~~~

\ R

"' CJJ

r·

--1 ..-iu. 5.1l

I 11•1

V.ll.

c.n.

A\'11\'en:g.H)n

lle<t,·ily dopcod I'"·N" junc:lion under OJH!n cirtuit und forwuct hia.... condilloo, " 'here ('"rricr ret'(HIIbimation under ror,H&rd bius ~h·es rl-.e h• .!ltlmuhucd radbtlon tf".tru:hlon 'md acb a.~ dlode·La..o;tr

Lt.lst.•r, 1/nlngraph'-' om/ Flbt•r

£•

=E,••

Opnr.~t

337

- E, • > lrv > E,

•

ll1c rcgjon ncar th~ llt:ltlchon 1:1yc.-. tit.•I <:ontrun~ large number or \!ltctJ'OilS and hulc~·.... unullaneuu.\1) ,, cttllcd "acti V(': n:gion" (Figs. 5.1·4. 5. II b). of thi~~nC~!t , . Thus t~ny rndimion of c:ncrgy (frequency \1) which i.) mon: thnn 1;1 (i.e. H, = hv,:) conl1nc:cl tQ the ;,'ctivc regi<•n will be. :unpllfied. 1l1u~ hc:tvy doping (or called dcgcncnrtive dopping)ol P'·N' junction provide stimulared emission nn<l :tel'" .• St!micondurtur/(1 ~cr"' nH~r¢(~)((: whencxtrem~.:ly high CIJITCill (l hrc~hnld CUrTCJ\1 J,;) h I'~>>C~ through rh~ I"·N' JUnction under high· rurward bia'> whogr. <punmncouo; cm i))~ion becumc~ coherent stimuhucd cmi~sion.111U~ abo\'C tlm•,fu,ltf (lufeltl,

P"" -~JUnctio n

~otnn~

ltLtt:r ac1io11 aud

become~

.rem;crmdm:wr nr tluulr

/nsu(figs. 5.12 :md S. IJcl. Whorea\ ordinnry doped P·N junction (ti••e.< only

Stunul!ued ~OIIIo\«JO U)kHic:·l,:,•.nl

11ueohutd 4."tllu:nr

o,pnnlam:uu-. cnw.....ion :md net~"' LED (Fig~ . 5. 1:\al. Ttw r;hii.~llnn g~uerutcd wuhin the uct1\IC regum etf thickness 1 'q>rcad.s out into tht· ~urrounc.hn,g lo~'Y semiconduc tor (say GJA">· There ,,_ infoc1 !l<tlme Ct)nfinement of 1he mJmtion whhin :1regit'll'l of thidt1 c~~ tl (Fig. 5.14). caJicd mode volume or recombination region. Since the addiuonal carriL·rs nrc present due to Lhe djffusjon r.f c1cclf'OIIS and hole.~ ft..\ minorit)' carrier in tbc a.ct.ivc region. i.e .• depletion region. so tbc Lt~lltotltf'lll ir~IED Sptl$11~ .. (ml-¥>tun

bc:.low thrt"JbOld

~ ,. fat

L•g.ht w1putml)l('dd.•ou.cl

l,.ijtht UUIJKIIlh LP.D

"itb dnmin.:tm ~r m~)dr

mt.lltlpk m(ldc$ tlrlmw th~ld

Wllh

~ lb)

DOO,·c lhrt~hoJd Shmid;~~C"J C'OU!o,\-110

•

(<)

f.lg. .5.13 Vulatlon of ll~bl outpul whh fmaue.ncy ror p •aN' junclion sho-..· surldc.n

lncrcusc: in lh:hl uut&·JUt ttft~r lbrts:hold L"Urrt'.nl, "'ben 1• acts as dlode-la.str. bnd bdort" thrt:shold cu_rn!n·t it nclsilS LED

rcfr.u.:1hc md c~ nf the .ac1h·c rc£ion will he more dun the 'um1unJins. thereby l orrnmg a tUt•h•urit· n•aw guit/1!. i.e. confincml!'nl of mdmtton within n~;uve re~w n

In g~nerullhc diffcr\!I'I Ct.: in R.J. between centre und ncighb..,urmg: rtgton 'IIU;tll ((} I tH 1 1'~ )~J·ig 5. 1..-t ).gCn\lmlly U ()~'k • ..,n the w.t\'Ct,!uidulg ''vel) tnl!'ffiricnl anJ the rodinlifui.:'Ucnd'ii ..,LHI\C way beyond the >lCII \l' rcgiun, thcreh) forming the mode volume (Fig. 5.14). und lhm way somehow thl!'y are Jlmo...11nst Du~ to this :.mall Uiffcrcocc m R.I. ~lwccn center and ,.,._~i~hhQuring rc~ion 'lhll1\n)un~tion la'\.Cr' \liOdc o nly \VOrks just well enough. t«" allow la.o;cr actinn n' •~ \Cr)

n·,ult ur \JgNOU~ pumnhg.

Bt\7tiU.SC (ll

lhb

TC-il'OII

Humtt-junc-tinn L.t.'ICf"' CiUI

unly he npcmh:J m the · ·pul ~cd mode'', nt room tcmpcr.t1un:. hccutl\1! lor very hi~h thh.:\lm iJ pumping. c.•rrcnt density rcc.ruircd i!o. uf lht: onlt•• tJ( J()() A/mm2

Thi(, d1fficuhy e;tn he nvcn:o111c in "Hctcn-..·junt••mn"" nr ..d11ublc hci CR1· iun~·tit:m'· dio>d~ lnscr. Where GoAs " ; nndwiched between cwo !aye" <>I G3t\ IA,, which ha'l w1dcr cncq:,y !l'U P and lower RJ . than GaA~ Threshold pumping currcm dcn'ill )' m J lclcW·fUncti()nlc\'cl i~ con,idcmbly lc~-.. u( th~ nnl~r ttf 10 A/mrn:'.

-L ,.

!"' "'" I h •luniC'• "

...

AhU\'\' tlm.!'lhOill current :l s.mull im:rc:t~e m cuncnt will t!'''c \I.'') lii!!h h)!ht 11'1~. 5.1 ~~ OUIJlUI p<>wer. c. e. very high uuemol ~uoncum dfi<tcncy 1IJ,/. which •~ othu Lh:llncd a~

R:uc of o•ui ... ,ion vf J>lt•Uon

'I'

= R•tc nf ; .rpply nf cl~ctron

R, t·

= R, = "7; I ·: 1,

=eR, I

15.2a)

Rp = r),f,,/,

l .l~ .

whco:. l r {, the fl'lrwnrcl currun1. Nll\\ rnwr radiated by LED or diode laser a:..cn be writt~n .a~

P,:::. Rphv = 'lrlrhv •

t•

= '11 ~1~hc N'

(~. 2bl

\ umlluri,.on UetwL:c.n Scn1konduccor 1..-ta~--cr nnd LED I. l..I;IJ {'tin opcruH.~ at lnwcr c urrent dcnsitic~o, below thn~~holtJ I.."Urrcnt, hut it b c..~..t.!ntiJI for a semiconductor Ja.;;cr. it Man.~ l asing acuon abo\'C threshold current unl) (Fi~. 5 .12). 2. From the LED. cmiutd photon have random phase.·.; bccttU'IC it is caused hy

L.1.1.\'rr. 1/o/ogruphy cmd Fiber OptiCJ'

]39

Sponumeous Emission und tlue to that the lh.:vicc i~ :111 incuhcrcut optical ~ourcc. Out '~cmiconductor Ju-;er i~ a cohc::rent source or li~ht . .::;nee it is due to stimuloted cmisor,ion of light. 3. T he cnc~y nf the .:-nun~tJ phmon ~~roughly cqtu1l1o E~ of the scmiconduc1or material. which give~ wider ,;pcctral line '''tdth in LED (Fig. 5. 13n). 13ut m OtO<Je... Jns:cr thr line ,,,chh 1 ~ very narrow fFig. 5. 13l"). 4. LED suppons n1nny optical mode.< within its structure nnd ts therefore u"cd as multi mode source FiJ;. {5. 1JbJ. St:nuconllutlur lu~·r i . . u~~ tl' Monornode. >ourcc (Fi~s. 5. 1Jc). 5. LED is h~t\ in~ low \'nluc ..~r imernttl qu:mtum cnicic.ncy. The internal quantum cfficinel'Y for .!-Cimconductor kt~er 1:0: \'CI) high 6. In semiconducwr las-cr. powc:r output im;r-.:a.,.cs ~ui11¢''Jh:n hne:trly wuh currem Jcns.ily (Fig. 5 12 ,, :--unilar 10 the spontnncous crmssion or LED. unull a threshold is reached. Arter thn:shold bnghlnC~ increases suddenly 10 a very high order or 1nagn11udt:. wh1c::h b 't(;COIIIJ):uucd hy a dras1it: narrowing or spcc:rcal width (Fig. 5. 13c). 7. Lighc emisston I rom LED due to spomancOU$ etms..suJnl' very wc:ak, It·~ confined only Wllhtn 1he Mn1cture. \\hcrc:L' light outpul from .scnuconduc10r loser is very lntt!ll:i-('. Jn semiconductor d1odc.·lascr since 1hc loM"-r c.nu:--~aon

1~ rcMnCh.:Y w a very 1hin r~;:gio n (a I )lUI) around the JUOc.:l iun cF'i!!. 5. 14 ). io :lCI ivc 1cgion. so the la~cr he:1m u~ually emerge:- oH·r a wlde unglc. Here m scmtconduc.:t~lr lawr. la~r

Cln i~~I()U ()CCU~ hciW1!~1l tYro U b:-mdl. nl Cf1Cit!ICI, Ul1d 1101 l">CI"'Cl'l'l IWO well defined ~nergy lc.veb. Sh lhc.~;:n\i~~Jun ~~ nol as Jtultn'K"hf(mt!Ut(! ~ts ui otha la:--cr. D1men<>inn of ~emi•(!dnductor la."er i" ~mall and 111'> \Cry dlicicnl bcc.-,.w,..: there i:t a d trccl COO\'Crsion or cll.'C'tricul current lnli~ht energy. Due IU lhitl t.h~I'C I~ <.1 din:-cl naudula· lion M:hcmc. By nwdul:uiug L.liudc currcm. u1nput hcam can ;tlso be mudulutcd.

Due I<' the.\.C ~Jkd:tf pmJ1Cnic~ o l ...cmkonductor l.a!->cr. diC)' h.a\ e w1Lit• mnpl"

nl UPJ'Iicullom Tlu.·y un· htt~o•tng :1 grt.'ul JWOI111""·' a'- "-t.lUn.:t.· lt\r h.gh1 in u111h:al fiber commutuc:tuon system~. The ctni:-.!lion """\'Clcn~lh of o;omc ~miconductor JJ..,~I"\ li.._c: GnA:-. or GalnA~P. nmtdt \\ i1h wnvc length re~inn wherl! optical fibers show very liulc aucnuttuon. 1 hey <Jrc expected lo find upplictuiun'i in oplic;al rJdar cqmpmcnt• .,;pace commum<::ltlon!'- 1!1C. Above tnemjwu:d ~cnnL'ullthl..:tos la..,cr opL·rntcd continuolL..,I.Y at ' 'ery lo\\ temperature ( 77°K). At room wmpl.'r:Uur~ ther.: operation may produce laser io puhcd ft'lrm. 11lh ptohl~m wa., rc<!cntly ov~rcome by using hct..:ro-junction lasers. l·lcat produced durin~ laser uctton 1-. ul'>n di"siputcc.l away cOidently by CCIUcnling 1hc diode It' u lm plate whu.:h uct:.. '" n hc•U ~1nL

HOLOG R;\PHY 5.11

Introduction-Holography

An ordinary photogr.1ph repre~cnb :.t two.Jimcmu.m;tl recording of a lhrecdimcnsion:tl scene. h rcc01'ds only imcnsity Uis~ribution :md hence the phase

distribution whoch P••"nilcd '" the plano of the photo£r3ph os lo>1. 11tu> on<

cannot change 1he perspecli'< of1he image in the photogroph by viow&ng il fmn1 different unglc. f/ulograpl&y i> the method developed by Gabor in 19~ 7. in which one nol only rc<:orcJ~ the amplitude but a lso the phase of Lhc light wave.,. due lO "h1ch hvlogr;:tph)' ha~ thrc..:·dimtnsivnal cffc.!cl. ~tnd well known .J.S lhret· lfiiiU'ItSIOIIll/ pftoWj:Nlphy.

lltc b:•sic tc\:hniquc ofholo,;raphy is as follow~. When nn observer i~ looking .tl MUIIC ubJC(.;L before him. ou1 object wave W1 (sc:ancred or r~:l1cch.:d from ohjccc) reaches rhe observer·~ eye. aotl he sees 1h..: objecL tr che ohscrvcr tills hi~ h(!ad. :wurhcr ohjccl w:1\'e W: can reach h1s eye. ~o he now nouce$ some other ob)cct, belund the fir.;t objcct.ln this way the observer obtums a proper perspecll\'C

nl Ihe scene ;.round hun. No'v ~upposc th.: obj~;Cl rncnt1Uned o.1bovc Jl) remo' cd fromlhl' "iccnc. but .somehow WI! manage to rcconstr<IC:t the ObJeCt wowc \V1. \V2 l'll.' .• '\O 1h:11 these w:avc.s re:ach the observer's eye as bc(nre in lhc ;-appropri:n«.! posiuon~

or the eye. Then the observer wil1 now see quite realistic imngcs of objcch. a~ if th..:y w~rc t1u.:.re ~fore hint. Such a (Cconslruc-tiun uf ob,cct waves to g.1vc three dimt:nsional p11:1ures or imng.cs of objects IS called lwlo8rupln·. Thcrcrorc. holo!!mphy iJ the metluul tlt'wdtJped. by Gobm '''hid! gia•c.r thn•t·· tlimt!ll,(l(}ml/ p1nun· of mr ohjt:n. R<•prmlucthm of tfl~t" Jmuw.ncmul inUIJ;t'.\ IS t!tnu• m lh'o Ma,s,:t'\ Tit(" flrsl \tugt• L\ w lr(!(!:,f'' (or rt<'artl ) llw ti~(Jtrrl'ltl ohjt•rt \f(H'(,f by tiStl/1( tfl~ piiCifOUU.'IIOII 0./ lllttrfcrc~nct! of /ig/ll Wil\'("1,f. n1r .rc:•rond Stagt' ''In 'rmjrrt•:.c· ·( r~r rt:'ronstrul'l) 1/w tJbjCt:l wm•co~ b\' rtflll.l: tliffrur tum o/wm•t•.,, 5. 11.1

Re<:ording of llologram

A li1s<:r hcrun is d"'ided by u bca.tu .)phucr 10to

I\\'O beams A ;uuJ IJ (Fig 5. 15). The lr.tn\nllll~c.f ~<.tm B illuminate~ the objccl. whose Jmlugrmu is ltl be rccon.J c.d. rilL' hght St:.;.tllercc.t or r~ncclcd by tJ1e different parts of the UbJL".CI \VIlh l11 ffe:rem ph:t\\!~ fuml\ the oiJjt!<'l wove. This object wavt: fall ~t on the photogrnphic pl:1h.' flS shown. The r~.:nccted beam A which is called ttfc're,._·r wm t .1lso f.tlls o n th!!

~~~·,

Fig. 5.15 Construcliun ora hnlug ram

i I

Lust!r, llolagmplly and

Fih~1 Oplk~

34 I

•

...... ""- ...

-...... _

Fig. 5.16 Recoosc.ruction or the i.m rt~e

(lhUiugnaphic phttc (I') 111c 'upcrpo..,ilion of objer-1 wm c nm.J the rcft!I'Cncc WU\' t'

produc<' on onl<rfcrcnc< p:mern. which is recorded on lhc phologmphk pl:tlo. Thl.' J)litle '" dc\\!h.lJX.'<I nnd fixed. 1t is then cullcll 3 Jtufr,xmm. It h ju.:-.1 .Ill mtcrlef~nce pollh:m and lx:ar., no rcscmbl,mce Ill tht: acllml ubjccl Rut ~inrc i1 i' nn intt.'rfcrc:r1cc pattern, so it ~wres all the infoumuion ohtnHJhc- 'uupliludc-s and ph~~ of the objccl wt\'C.S from the object. The holour.un thuS- records compl..::tc inrurm::u ion otbCU!IIhe \Urf:tcc or lhc object. In 3 hologram, imcrrercntc pa11CI'II i' rec:ur~kd photc•graphicJJiy und made anto t_ran.sparency and fixed J•ke n zone pl:ttc. Keconstruct iDn of the Image i~ nO\\ illun11nated by a laser beam cx~'ctl y the :;.arne w:1y :'" Ihe f(ft.':rcnc~ wav~ CA) used in ils consu'Uction (com pore 1~1}!~ . 5. 15 nnJ .5.1 6.1 Th1s ~;11111:; fUJW ..-::all~,"t.J a;o, rmd (Ill/ \,·av..-. 1111.!. ~i\1 mal Y. a\ c inh:r.u:h Wllh Ill!: huh1grmtt hx inh:rfcrcncc pattcm) und due to diffraction lwo unat!cs. one real. one.\ inu:d 5. 11.1

The hoiQ~r:t m

;.arc pntduccd un two :..ide~ of the: hologram Here I he.: ho1t1tlr:trn m:l-.. JU~I u' u kind ur !tr.lllng. ThL" vinua! i lllli~C uppc.ars :at the uriginnl JW~itinn tM.!t.'.upicd by lhc

obJCCI m tlw conslnlcUon of lhe hologrnm. The <Jiher un:oge (rcol) ts symmetncally ,;tuutcd but on other <ide of the hologram, it oan be photographed hy l''"""'g light ~en.'~illvc medium at the position when: lht: real image b fom1cd. The virtual image :.s seen hy look.ing through the hulutm~m a-.. lr II wen: ol window. The image " rill appear in complctt! three. dimCil\lliOlll form. hi~ l"'"'ibk tn \CC.: the ntha!r~1dc oft he vbjecl a.s if the obJect •~ really hcfurl! the nhscr\'Cr. But l-int.:c it is a vaf'tu:tl unngc, nubody can mw::h it anti i t JJ. um pu\...~ibl~: m phutugruflh it. The hologruph is tlu."refore said to conlnin. in thc·funn of its tnti!rt~r~.•nc~· pattern. all informntion about the geometrical chorueteri.sitc:. of the uhjt.."Ct.

5. 11.3 Uses ur H o lo~tap h y I . l lulography I!) used Ill tilt.: lll ltro~copu.: study ur ~orne lfilllMC.:IlllWCnl~. ln~h:ad Of d0108 prolcm~ed C,t"fiOlin:uion Of S.Oille! smniJ SJ)(.CIIHl'O ~u~pcnded Ill thl" medium, if onC' can take a shon exposure hologram of the specimen. then 1hc rc:con~tructcd holognaphic imug.e GHI be s tudied (o r the same purpo~ n l ~my time.

2. 1-lo lvgmphy i!o ahO U~cful IO pro\ u.k

hi.gh Cot pal"! I)' -,y:,tc.·m (ur image

'>tomgc nnd rc-exammauor

1 r

FIUER OPTICS

5. 12

Introduction- fiber Optics

The 1cnn fiber OptiCS wm• iir:-;t nu rOOuccd hy N S K:tpans ll.;; lh~ ..,rt oj tJr,~ ac.m •r and fUt:~.m·c ~mdtmcr fJj fi s:lll m thr uiTrm•wleJ, '·utblt• and uifran•d rtginm nf the spt•ctrum. ufmtJ1 /rdll.lf'llr<'nt fi/o,•r.l tlmJtt.~lt pr~·determmi•d pntlt.r" In ntO'.I or Lhe :tpplicauon ot •ahcr tlptk~ or opuxlc:clrontc~. t.he opucaJ beam~ tm: Cl\llfinc.·d laterally lo ;J n nite region in sp~~ce. Special opucal clcm.:nlS are US(~cJ to

cunfine and :tllow propag:.uon or 'Utr.'h (lptical modes. An import:lfll :-.lniCI\•re used 111 opucnl ~ystcm is Lhc layered ~tructurc: or the have ~uidt .VIruc·Tun~. As the

nmnc imphcs. Illest! .wruct,lf't'j' nn• un-·tl trt l'rltlfinr-th~ optical wm't"S "'a wt'/1 rll"}mt•._/ "i:""' nnd Jtllidt• tlrnr Jllll{mgmum The: h"t)·c::red s1ruc.:wre~ can he m~tdc from non-l"~rysmJhne mnrenal,. or from cryst:aJhne mo1erinl,. ~or example gin':-. ·~ lHihzcd to produce opncal hbers u..;cd m opucul commumc:ttion whi le '\.Cnucnnduclor \\.'ave gtuJ~..-s nrc lJ'\Cd 111 scnHctmductor Jn.sc.r. The confinement of the optical wave 10 'flUCc 1:, done by a \' i.lrl<lhon m lhc thclccuic.: \:On'\t;ult or1he- guKic m .,pac:c. '11~-e \';_muutm '-=oulcJ lx: 111 smgll.! dune ns1on to produce p bner wave~~~ de (Fig 5 17:t). Whc1c 1hc dielec1ric cnn~t:\ll1 \':lri.:' tn '"o chmcnsio n. 1hen 1hru prod11CCS ( h~ =; 17h) hncnr ur recrnngulnr wave

gtudc. Wave guide produceli from dtcle.:tnc' and scmiconduclor grown cpilcxially. u~ually

p1nner or rcct:•ngular wnve guide lwm. \\'hen the d1elcctric constan1 C)'lindrka1Jy (f!ig 5.J7c), :1~ in optk~ll f1bcr. then C)lUndrkal WtiVC guide " (nnncd. Op1iatl fibcn; (;nne m lhn:c milin ..::atcgorir.!- depending upon 1h..: mgrcd i cnt~ w;ed such u~ uf ~s lh!u. f. l n~l\ .md ptbtlc. Upucnl liber 1~ a cylindr•~·al w~w\! guad..• r-.y~h!m tJ1rou~h which the opuc.·al w:l\'e ~·au JU'nll:,g:ue.1lte pnn~1pk h) wlu~h lig_ht \\ "' c 11 :1vcl 1hmugh Ihe II her 1:-. "1ftlul lm,.nullrefl~ctiou ",without fo!'!io ofincidc.uttmcn~l1)'. 11ll>: ha5ic ~tnrc1Urc ..:ons1.:-b of~~ ~o re :Jl lh.: cc.mrc and t1 cladding layer ttn the uuu.idc. a.' shown in Fig. (5. 1R). 1 he co r~ r ~ 111 a cylinder nf tr:m.!-parent tficlc..:Lric malerial wilh R.I. 111 :md lht" cladding ~s anotherdiclecuic m:ucri:tl wilh lower R.J . u1• The fiber~ have sevcrJI du.'J.... iJicullon' ba~cc.lun the mt.lcx. proFile and th~: core 'iii7.CU!t~lwwn in Fig,, f5. 18u. l1, c), Th~ c:ofc ' i 1.e dctcnninc:. hc,w nmnytnvc.k... nrc he opt•cal wave cnn propag31L! through the fiber. An oplical c:sblc consi,co;o of :-.cvcrnl of such uplkalli1>e.r.lt.. In !-l)tnC ~1('H ical Jibcn.. O\Cr :1111.1 abuvc cl.tddin)!. then: i~ :ulothtr tliclectric mutcriuJ which is culled Uuff'cr. "ho...c rdrucuve i nde"<. n, j, lower thun 11 1 (Lc. arc

\UriCS

"• > , 2 > lr J).

5.13

Total Internal Reflection

II' u r:.~y uf lighl is incidl!nl al ;mangle ,·in c.lt.!IN.!r medium (R l. n1). the refr;tclcd IU)'~ will bcntl invay rmll1 dw llt•rrnul in l:UCI rttcthUIII (R.I. 112) and Snc:Jrs l!m

1.. \\'l'ltlen us (5.3)

l I

•

.r ·.·;, .·l .,

J )

·JJ·· ......,

;~ :-:::-i: : :

r .,... lOlOi-

•

-,.

., .bl r:{ .· . ·.t.<l

-:·.• :-:-!: .. , 1·:-··. ·r :

r • ~

•• 5.18 Stop ind«:(ol <iftd<tt.OO...tb l multlmodund (t) p . d indn muhunnd<

344

Engincrrrng PhyskJ

Ir;~ nay ufligtu is incu.lcnt 01 un uuglc ~ay i, when the angle or rdroc110n r= 90.. then sin

t 1•

(','sin r =san 90°

== n2/, 1

=I J

{5.4)

and angl!.! i, is knt''' 11 u~ airit·ul tmg/,- The vnluc uf 1hc cri1ic.:nl nnglc (kpcnd!<! upon lhc refractive indc.x uf the dcrN!r 1ncc.lium. No\\' if 1hc lighl in dcn.~r med1um is Incident nt an ongk i > f,. then light will be rel1e<ted buck Into the dt:O:\Cr tnct.Jium. l11i:-. Jlhcmtmcntm i~ c~tll\~,1 lola/ inlc·rnnf J'C'}l•·r•rwn, whic.:h il't

u.!-.cd in opt ical fibe r communication.

An RJ~, ,

...

R.l • "t

~;1.:.-..•

' - ..

r > r.

Fig. S.J9 Tohtl hlll•ntul r(•0£."t:tioo

5.14

i>ropogatiou of Lighl in Fiber

opllcal tiber '*' ith clitdding (Fig. ~.lO;t). where n6 is 1hc rcfmctivc nuJeX O( :..tir. "1 1he tOdCX Of CCirc and II:_ lhC.:: fndcA of cladding (Ill > 11z > llu). Con~uJcr an

Supp<>$e a beam of light is incodcnt m1o the

optic~l

fiber ot ltn angle

a witll

Cv«

(>I

Jh)

Fig. $.20

l..i~hl

propuJ:a1ion through stroiatu nnd curve s tep

with cluddlng

ind c.-~

opticnl Ober

n(lrmnl at 0. and uftcr rcfrucbon n willtr.avcl Lhc palh along OA. lluough ~urc rcg1on by mnk1ng 010 ungle fJ w nh nnrnUtl m 0, n1:ut..CCJfC boundary and in cadent on cor~4cladding boundary a1 .4. a1 an angle with nom1al to corc·cladding

inlcrfacc:... N(.lW

tf1his ruy OJ\ nmtcs un JJnglc y ~ ;, whh nvnnul ;H A. lhe gla.Jos..clndding

inttlrfa~c th~n

it will ~11ff.:r IOH1I intcm;.tl reOc<:tinn ;mrl willtrave;;l :1long i\R. In \ inulnr WU)' the beam will tUIIIiUUOU.Siy "oUffcr toi:.IJ tllh!Nlill rcncniQil Until II emerges out of1hc gla~'\ core at the nthcr end. E\'cn lflhc fiber curvc..'i gradually. il

light wtlltmvel il\ emu-e length 1Fig. 5.20hl ami amrc m ~l< ulher end. T11u' a fiberc:m tr.m>mlllight energy 1111itt dlic•cntl) Tlttre rnay he o\IQut 1.000 rcllccung p<IHIIS like A. 8 per meter. Tit~ los' )l<r rellccung potnt b "' low ns 0.().1% due lo ubsorption C-Lc. F<•r ltllal inh:rnal rcnccliun lO mke~ place y~ /,... ~in r= "~'"' (rmm ccrualion S..S) sin I = SIO r= llyll, =clu (from Fig. 5.~0a)

Hence

•

i.e. critical nngle

= y = \HI

(

From the .1.101\C in (F,g, 5.20a)

15.5)

I lh

....:...

(5.6)

~~~

OA = a, OC =,., tiC = b

Then~ fore

Thus

(5.7)

Now by applying Snell's law •H poinl 0 . we gel n11 ~m

i.e

a ::: u 1 ~in fJ

(5.8)

r.-nzln ,...-;j = ~ltj (, -._-. ,i

nusma=n,,t l

Which is C'.tllcd nwnnktllllJn'rlmr t N.A. I a( slu· {ihr1.

(5.9) Fortfficicnt Lrnnsferoi light. Ihere shoultJ he Jl\ ) rcfr.tclaon a1 t\. B.ctc the glas~ duddmg intc:rfacc, Ot hcrwi~c ligllt e nergy will be lut~t through wnJls. From Fig. 5.20(a). it it.: clear lhallhe nngle of incidence ya11he gla~\-clr1dding in1crf:.ce will depend o n Q nnd /1, and if y ~ ;r• then nnly totol intem:tl rel'lecuon is poc;;c;ible. which hclfl$ the pmpagmion of hgiH through upticul

fi~r.

So c.vndition

fur totul internal reO«tion requires thnt. the angle of lnCJd~nec for all the roys :11 the entrance should be h:s.." than the unt•puuu',- tmglr of the III'H!r. Ar·ct•pltmn· wrsll' is tit~ maximum angle uf incide~uct' {a1 fvr wltidt Iota/ im~mul refl~t·tiou i.\ po.t.dblr mul fihrr nm nmt/u('t Ughtwt/;(' nthl'r ~ml If the an gil! of inc:it.lcncc is more than a then that my will go m cladding a fit:'r refract inn fmm rhc l'Ore. [Fig. 5.20). Whoch me>ns. that infonnauon will be h>SL Th< acceptance un~le C<

~ive n

by the N.A. e<pression reqn. 5.9) a.

a ='in

~i )

1 (

(5.10)

f'lws. the qumlllt,\' 'nu sm a · ('flll<•<l ,,,. 'numcrklli (1/lff/llrr. ( NA J (Jj thr jiher. IS a m r•u,,urr of tltt" llbilt't\' af 1/tr fibt-r tn art"~pl I1RIH for trnn.wu.Hum. Usually n J c

and for air nt1 = I

Thus.

N.A. = t~u:>ln(.f=!iiii((:Juf

'' h.;re

...\ -

~~~1

1~Jf

n?=u JI - ,itnf :. n J"fE 1

"& -

"•

fS.II)

''2

is cnllcd rcbu'c- r~lnu..'ll\e 1ndcx difference when u 1 :; u1. '111c diclcclric cl::u.ldin~ un gla$.~ con: n.•duccs .scaucring loss. prmccts core rrom nbsorhing external optical di~lurhanccs and prov1des mechunic:ll strength h) moun ~m·c ~~"'' fil~r Sutnctulle' thcr~ i:<~ huffcrcb:lling nvc1 cla<ldul!:t \\hich ndd.s fun he-r .strength 10 the rr..tun tiber und protects fiber from mcchumcnl 'Jbrm1on!!o nod llllj)l'ICI

5..15

Different Types of Optical Fihcr

S.JS.l

C ludtcS> Fiher

Solllc uplic;tl fihcr-. u ..ctl in pr~u.:licc.: '"''hich 4.1o no1 huvc c lm.tdint;. h 'hOW!-~~ of hght U"'Jvcl> thmu~h rnnJcrn I)'JX' nf cl~dte.,s libcr.

r.•y

S.tS.2 Graded Index Flbor (Grln Fihorl Grin imJc:\ fiber h u :'\fJ'\!Cl~tl tcdmiquc 111 which lit(. core u l the l1hc:r '' tu.uJc "tlh \':trying_ rcfntCi tvc trull.!:.. ''hid• 1l\ a fu u~fi1111 {)f core rudius. TI1c I'Cfr:tcuvc index t~ grca tc~ L :11 1hc centre of th: con: nnd ckcrcascs conlinuously IO\Vard~ [X'tiphcry. bul con• R.L n.•m:tin, ~~~\\..iY' !!rc:ttc.'l tholn daJding R.I. Thera~ .. tr~l\i'l :tlvn~ a ~l nuMl i dcaJ p;1tl1 (Fit!'· ~ . 1 &.~ untl 5.2 1n) thr\'~ugh thil:' 1ypc nf ,gl'tldC-d 1nd~~ libcr.

"·

"' _:::;"'"?i~

n:-f.ii:"'o

..,

"t>n~>"

Cll&dl.bnf.

ButlC'r

(b)

fig. ,5.2 1

Light propOJ!Utino in molli·mOd C f!nulc:d index :md .\ h:p indt•~ fifwr

Thc~e ~ncJ

libl·rs c;tllcd :•~ wave guides arc

\'f.!ty

much uscc.l for telccommunicntions

other Hl>plications employing la~e.rs.

5. 15.3 Step Index Fih<r In thts type of tiber Wig; 5.2 1b and 5. 18a. b) ccntr.tl core ;, up (If ttJa...;. rcfmcu vc indc• lilt) between 1.5 :tnd 1.6. Th" core "•urrounded by claddtng material Jil,c (u;cd 4•urtt R.I. (II, : 1.425) or pla,lte 111, = I 25) ur glru.' IU.

"""lc

"l < n 1• An1untlthe t.ladding there ,._., boiTcr COilhng 5.1 5.4 Pass'h'e and Active fiher fhe liber• ~e:.cnbcd ntxwc arc calico l""sivc fif'<'p; A /tl>u merely guid~~ light and dent lln it from an external M')urcc. An fld'' c! jih«1r cmih l&ght o.s well a.'i guide:, part of it along iHt length. Scintilldllng filx:ri .unJ ln>.;ing Jihcr:-. l1r~;

!'"""''

c':unplc.' of active fiber

5. 16

Types of Rays (Meridional and Skew Rays)

I . Mmdwnal R<>.l': The plane contatntng the centrul ""' or the fiber t; call« l me:ndian plane:. Mcrid•onnl rays remain ul the mcndlnn plnnc which .,:~m lll: divided., roiiO\\"S: (o) bound my• ihat PfOJ"'£UtC olnn~ """(Figs. 5 lla, b) and (hl unhnund ruy$ that are nol bound along i.IXI\ tmd an: rdl'itCtcd mu of th!! ~.:o re anti ab...urhcd in cladJing or hufrer

(•I

(b)

Fig. 5.22 (11), (b) Merldionul :111d (c) skewtd ruys lJMJ)llgiUion lhnmgh nbre oplic.s c:uble.Jighl

2. SJ.Pw Rn,•o;· The r.ty-o which enter the fibe.r obliquely. which nrc 001 CCU\fined lu a pl:uu; anc.J follow :1 hcl ic~tl pnlh :m.mnd the nxis i.tr~ known :ts skew ray~. They are ~ n sc:mcred nul of I he Cttflo! at bends and irr.:gularitic .. nntlthu\ do no1 contnbutc ~igruficantl) lll11pllcotl cummunicallon (Fig. 5.22d

5.17

Modes of Propaj!ation in Fiber

In Fig. (5.20) we have dra" n only one r:ty. lhat 1~ called a n•y d.Jngmm. bUI 111 rcalny an u1rin11e nmll~• of ... uch n'Y' (fig.,, 5.lla. h) a ll sligtuly (li~pltlced from each other. also can be propagated nt a um~ whtch nre called dif!ut mmml-. o/ f"''fHlgutum , 1lley w1ll follow diiTcr~nl p<tths mlht> fiber ut the llmc o l pn1paga11on ns shown in Fig (5.23) ll Now when lig.hl if\ tlt ..cribcd ;a ... ;)JI elcctrornagn:tlive wave. ic COO.SI!'I!' pcnodicatly vnrytng clcctnc licld F. nnd magnatic field H which are P"rp<:nd•cular lO each other. The nlode> whtch arc shown in Fig. (5.23) ore called rraruwr$r uux ir., wh1c h •lluSIJule lht: C.:U'C when tlu; dcclric ti!.!IU (if) IS pcrpcndlcul:tr 10

u~ ~·~··---------------------------------~--

,...~ L1>ddUII pcnttrnum~

. t::L~---m: l

FiR. 5.23

Dlffcrcul modes

or li~ht

propagation thnJUgh St('p lmlt'.x Obrl!, "here tell > Yl > )': > ~ ... > }'t

a.,. = a~pt::ma: anJ,tll:', Yc = crilic:al angle tlnd whtrcas ao < a 1 < a1 < a., .•. <a.,.

, Lnscr. Jlofogr(lp/ry (lllc/ 1-'iht:r OptkJ the dirccainn hf rrupng.:uion (Z) !Uld hent.'C

of II

349

Ez =-0. but u .:orresponding component

an lhe dtreclion of propagauon. Sn the..tW! modes are called transverse

electric (TF.,) mode'. Sunilnrly. w hen 3 component of electric field

is in the

direction of propaguaion bul 1/ 1 ;; 0. the mode:, fom1cd urc callcll LrJnsver:,c; ma~ncuc (T/Ifm> mudc:-,. The mode number m arc incorpot:ued uno tlu s nomcncl:tture hy refcning 10 TE,. or TM"' modes. cte. Each v:tlue of m is a.;.!~ocmted

wilh a distinct wave pnuent or mode as shown in Fig. (5.231. within the wove guide lhcy follow diiTercnt I'Ktlh~ For t:nch v:tlue of m there b :1 \'aluc 01 yc ~..,. r~ contokt volih!S mih~ rnngc r, to Jr/2. whtch imjtlie• thot thc .mailer the value ory,.. i.e. Ym closcr1o )'t. higher 1hc mode number nnd vice.. vcrs:a. From Fig. 5.2..'\

ll is clear Lhat the hi!!h~r order modes. carry :1long with tJu: rn u higher por11on of mode energy whhu11he claddinl!. 11w;: pan of fhe wave which i$ cnrricd in 1he cladding IS referred .t.'i the "cvuncsccm wave", (I) For free -;pnc:..; commun1catul n, l h~ lola I clcclromagn~t•c field lies in ahe Lrnnwcrsc plane. where bmh fz = 0 and Hz = 0. which is called tr:UU\'Crsc clt~ctrom:•gnctic w~l\'l~

(TEM) TEM wuvc occur in nl<:l:tllic <.:onductor hkc co~

;JJti(ll cahle bur 1101 111 upuc:1l wu,•c guide.

(2) For plannr Jl.u•~e. ~tenerolly TE(l! , 0) and TM(H1 0) modes nrc obtamed. (3)ThecyllnUm:•11 wa,·c guide w.1n opt1t;al fi~r. tS bouOOed 1n twv lhii)CIC)JOn~. rathc.l' ahan one a~ 10 plnoe w:r\c ttuiclc. Thus. two antegers I :-.od more occe,sary in order 10 spccif) abc: mudcs. in cont.ra!'ltlo the sing.lc imcgcr (m) required for planar guide. ~n. fo n :ylindrit;ll wn,·e guide we rder TE~,m and TM1, 1 mode!' The TJ:.1"' and TM1"' modi!' corresponds 10 meridional r.~y~ (Hgs. 5.22a. h) winch arc Lro.velhng w11h1n the ribcr. However. hybnd mode!'- where 117 :md il7 <~fc non t.cro abn \Xcur "1thm the cylindrical wn\'C guide TI1csc mude~ which rc~ulh from :..kt!W l'il )'\ rrn?il!taliion ~Fig.. S.:!2c), within the fiber l l rC dcsignlllc.d il., HEhft and £H1,.,. dc.fK'Jlding upon whc1her Lhc components of H ur f mal e l:trge:r Clintribution w th~ lr.mwcr..c field Thc~c ~l.ew r.ay~ an: c;tl l~.!d lcaly ray!> untl corrc.... poru.ling ll1tK.fl!, rtrc .,;.•lied lcal.y mode..'-. 1101 bound moc.lc'- hcc:tu ...c

they can propugnt~ only nppredublc lliswnce bcfure being lost from the llb<:r. In most prac1ical wn\'c guide~. the refractive indices of cor.: nnd dndding

differ fro rn each Other by only (I few percent und in that case the Cull St:l or mock;, (i.e .• F.H. JJE and 7'F.)c:tn be approxim:ned by a single set cnllc:d Hm•urly polurilt>d (LP1"') modes. An LYrrw mode in gcne.ra.J has m Cield maxima along a rndiu.s vector and 2/ fie ld maxima round a circumference as shown in Fig. 5.2...S.

LPI\1

Fig. 5.24

I .P:.I

l..inearly po h•risl"d nmdct'

_\50

E ll )?iiiC:t' I'IIIR Ph\',fif.','{

5. 18 Multimode and Monomode Fibers ~tel'' inde.\ fibe~ allow the pr'Opag~nion of 11 IInne number of gmdl~d modes along 1he channel The number or gu idcd modes i., tlc::· rendent u1)0n the phy~iC'nl p::.n:une1ers. a.e., ahe refrttctive llldCX. dlfferetlCe hc.1wcen CON ;md c:laddutJ;

Multamodc

(l.c .. N.A.-:!::': \' '' ~ - 11 ~ ~.core rodiu.s or the fiber a and the wave length (I~} o f the tr:m~miuct.J ii ght, arc .111 in::1udecJ in lhc ' n o nn;l liZ.cd fTl'tjUCO\.:)' V' for lhc fiber wht•r< V

= 2{

" IN.A.)

=Nonnnlizcd fr«)ucncy. Tho tutal number of guidod

m•xlc< for ' rep indc~ libt:r is rdarcd "' V.by rhc ~pproxirmuc Clprc;sion M, ~ \ 12rl

(5. 121

whc:rc "' lm g.rudt·d indt·x tiber M , .. V:!l-1 Monumodc or S ln~:lc Mode Fiher II c:n1 ~ >ltown thot when V < 2.40~. only the Lf'01 mode con prop~goac, l.o. fibl!r lh:c<une..-. smgJc mode fiber. Ther('trl!tic:tll). J.l •fn mutJI! wall rn'l(la{!Utt' nu mauer hm' smotll lht' V vo1 uc. i .e .. no mnth:r how '\m:1ll tht: t.:urc nu.liu-. u.

(5.111

Since l lcm.:c When V < :!.J05 thc!n 0

2A05J.

< 2 1!' (N.A.)'

(5. 1~ )

lur single mode fihcr In gcncr.sl in ~lnglc mode noc~ cc•rc' tend ((I he onl) ·' (C\\ micron~ in di;unctt:r. hut it h;•' an adv~ull;l£1.! from -.c:vcml pninto( \'IC\\' if ..:ore ..:an be mndt' u-,. l :u~c :t'I~Jc;sihlc Fruntl"'c ubo\'C c:x p,·c:~~ ion . we ~cc thou tf11 ~ may be dc:u1c b) reducing lhe N.A. vuluc. o.e .. by making core • nd cloddi n~,: IU. very clo•c to .:m:h t')lh~r One of lhc m•1jor advunlag~!> of u~ing :.inglc mode Jtbl'f IS that mtcr U1Uclel di~r~~iun IHI longetCXiStS, and ~n they ilfe CilpJhfc t,J( C<trryiJl~ very li1TSC: bnndwidth ''gn:al for Jong-rhsumce communic-:uinn.

5. 19

Oispers ion- lnter Modal Dispersio n

{I) ,..m multima(/t• .\ICfl itNir.x fllwr. whc:n tJn: ruy of different m,KJc:.:-. fullu\\ different p:nhs. lil e 'umc f:t)'S (AA'. Fig. 5.25a) whkh prc'J.,ng.tiC ••lung tile filll'r JXi~ and ~;,ome of whicb propl1£:tle along

the t.rajcc-torie!<. of LJu~ t'bhquc tn)'S ('-a)

CC' t'~r 118' ) :'~ "hnwn in Fig. 5.25(a). Then lht.:n: is n difFcrcnc'-' in lime l:tk\.'11 J'm diO'cront niOOC$ ta truvel a distance /. Now lh< R.I. a n!Cdiulil i< <Imply a

rnet,,urc: c)f vclu""Y nf (lfCI~agauon u t1f the hgl11 in the mct.lium

Now

II =-

R.l =- ~ Um

u..

U, : -;;-:: II

where u" (= t•) is the velocity o fli ~ht in nir and tJ111 the vel()city oflight in medium

Lnw!r, 1/alogmph~ mul Fibrr Optk:r

•:

~6PX";:;,_

~~~ ~

P..

351

S:L; ==---· I

R' •

fig. 5.25{n) MuUipnlh lime di.spel"!'linn ror mullimucJe :<il fiJ index osllical Obtr

Now lhc a.xiol my 1\1\' uavcl an nxml dasta.ncc I ulong the fiber m tlml.! (5.15)

Is= 111 1/c:

whereas the t.'lbhqw.:. roy 88' tmvcls 1he .::a me nxlaJ dislancc /along the pnth 8 18) 10

'he ume

r.. = !!.!. __t _ = »a . c cos IJ.. c

( ·;sin

r. - ~) "•

(5. 16)

Thu; of owo my• (IIA' and fJR'! aoo launched logcohcr ohc) \\Ill be <eparatcd on arrival or lhc other end hy dtsperst~m time.:.\ T. where JJT ~

h - t 1 .e -n o -l ( " - 'I)

JT= -"'- .It .\n

{\\hcre .lu .:u 1 -n1 )

"J r

(5. 17)

Thus :1 pul~· con tainingr;~y~ ;II :111 pos~~oiblc :mglc~ ..,r,rc:uh out during pmp:lg:uum by nn :unouno given by

"•

..111

[5. 18)

- ,- : "1 -,-

nus is known as mulllj)utlt timt• duptw<wrt of lhc:

~lep

huJex fiber. whkb

caU.)C~

pu l ~c bro~a dcning

xruJ~d imli•,, multmuHII' flbr•r. diff.!rcm modes: will follow diffcrc.m paahs, sonusoidnlly. Tho r.>ys making larger nnglc> (Fig. 5.25b) tmvcr<e lon~cr pMh booothey do so in lower IU . oren and hence ohcy orovcl wiah hoghcr speed of pmpngnlion Since R.l c hanges grodually in grndcd index Iiller. so Ihere is o >df

(2) Fur

focusins machnnism tlmle;uls au" >mailer vnlue nf pulse dtspersionthan ah:n nf

f'lg. S.ZS(bl

L<lS multlpAih tin>< dl<)X'r,;lon for

~r•drd

indu fibre

Vi'l

J:.'ngine~rin~ Physir.t

!\lcp mdc>. fiber. Thu~. for lnng distance communicaiJon graded mdc.~ fiber will he more useful than MCJJ mdcx fiber. which causes lcs~ ume dispcr\JOn.

5.20

Losses in Fiber Cable

11tc losses m f'ihcr. l.c .• rm.:nu:.~tion. are mainly tnused by absorption u11LI sc;aucring. ! I) AbsorptiOn is bosi~o lly n m3ttrinl property. nt nil wove lengths it oecu"· \\hen decrm111c lmn:-.•hOO!<o take place " 'ithin the mnh:rinJ and arc f~tllowcd by non-radiative rclnxl\IIOn proccs))c~. A~ a rc~uh there j, an im:reu:-.c of ~hr:nnul cn..:tg}' in lhc material. C2) St;1ttcring 1s also p:mly tl material propcny hur i~ nlso <:nu~ed by the imperfection on the fiber geometry. It occurs when the mode of propo~ntion of li!!hl is changed, sodt lh:tt ~omt:: of the oplical cnerc.y lenvc~ the Dbcr. (3} Lu!<!scs duc.1o bcnd•og: Tight bcml.s: of the fi ber .:,i111Hnrly c;msc :-.orne of the littht not to b~ internally ~eneclccl hm co prop~1gatc imn rhc cl!tddi ng .nu.J Ill; lo:o.~. 4. Lo~s 1.luc co impcrk('tion: The presence of hnpt•rfcetton '" fiber material alc;.o cause pow~r lossc~ from ~he fiber OJ)Ii.; c-ahlc~. 5. Conrli..:CIO~ and ~l>li<:C!. which required h) conncc1two fiber.\ temporarily or permanently also cauSe! row.:r lo.s.s for long distance conununicntion cable~.

5.2 J P hoto Detector Aft~r onf<>nntttion carrku by fiber optic< cable. it should b.! detected by photo· dele( tor. The lll0:\.1 conunon ).1,:miconductor photo dclc:ch'Jr b the phuto diode or pht'!l<.H..ronsistor. The pho1'' dcteclor dctcCIS the opticOtiJlOwcr !'oiling ut·hm 11 ~utd con\ en' the van~uron ol lbis opucaiJ>oWcr into n concspondingly \Jtrymg ell!crriccurrent. In OJ>IIC:ll fiber communicatton most commonly used ::.ystcm is IMIDO. wln.•n.• lnt.:nsny or 1hc ooucnJ earner. Modulated b) bto5ting cum:m m LEO/ Drode l ..n.....:r {IM) nnd 1tu:r vari:U JOn of optical power Dirt-cdy .. O"·tcctl'U HJ photodoh·ctor c DDl

5.21.1 Mechnnl<m of Photo.Oiode Figure 5.:u.ca) ~howt- the b:tsic structure and open:uion o l ;1 extrinSIC' 1'-N JUnction Set Ikon pholo diode. ln nnrmnl opcmtion a sofficrelltly Jorge reverse bHt:-. voltage i~ applicJ aero.\.~ the de\'icc. so th:u depletion region :ts well a..'ii barrier potential will he large. No'A "' hcn th..: light mcrdenl on the rc\'Crst! bi;tM!d I'·N junction. th~n i( Ihe cncrg)' or the hghr qu:1r113 (IIV) whiCh asc::'llkd fi\ phmmr, t:-. nlOfc tiHln the hand gap enorgy (!~,. i.e lov > E,). then the absorbed photon excite on I'IWII.H.'\111'('111

flt

Low light

~~==:;:::::;ac:::;.. No ht!-bt <h)

f o)

R. IJ. \OII~e

f<l

Fig. 5.241

Working prindplc of Photo-Diode-

l.lz!ctr. flnlograpln• ami Fibtr Oplh'J

153

electron from V.U. to C.U. :.tnd lcavmg ;1 hole in V.O 11u; clectron·hulc 1mi~ ci'Clltcd

due to mcidcnt hght, whtch arc obsorbcd m the depletion reg1on coiled ns plww carner.J

As clcc.:tnJn uncl hole now 111 lht depleuoo region (l).k.) in oppv$1te d ltCCIIOil umlcr re\•cr,;:e bi:•~ voh2ge. some of the clecLron~hole pairs will recombine nnd hence lost. The distonce they willlf3\'erse bcrore they recombine is called diffusicm lc11g1h (Lo and l.p. for electron and hole respectively) and tl1c lunc 11 lake~ for no elec•mn and hole to recombine is known 3!\ earner lifetime Cfn nnd Tpj. The carrier lifetime nnd diffusion length can be related a,, Ln = (On Tn)l/2. Lp

=(Op Tpi 112

whcr< On nnd Op arc the el<c. and hole diffus«•n coeffkienl. rcwecti\'ely. unit etf whn:h ~~ cm2J'>t..--c Pho1on~ cun he :.tbs.orbcd in depletion region (O.R.) tl" well.~ an tliffu:,mn reg10n (D~F.R .) ahll, which i!- in gener.ll indic:.ttet.l USllbsorplintl l't'J)ian (A .R.) in Fig 5.26b So this reg• on bcCCJnlCS a void or rn:c photnl.!:lrricrs Nlil.\' wilhin the

dfpletion region these

~Jcctron-hole p~ir

cannot

r~combtne.

because of the

main elcc tru\tatk licld cxisl.:t due to the depletion rtgiun Htlto~ge . Ar'y phOh111 mduc."Cd clcclrun·hulc r,:ur therean Wtll be separ.uecJ otnd drn\\11 ,,ut ~ In opJh1\ite dircc1ions) h~ 1hL' combined effect or cquh•alcnt depletion rcg:ton voltage :1~ well .t.~ revcnoc bia'i \1ohngc (notice thai lhc~e twn \'Llhagc pol:trilic-.: rtrt.~ in 1hc '~uHc ducctinn) Tht\ dfcct leading IO tJ phOlO·CUrrt.'lll now in lhl! C\tcrnnl cm:uit I Fig. 5.26:t, S.26cJ, '" pbolll c:uTicr.; drift nway acrOS>Ihc dcplelilln 1cgm. Typi<'UI out put chi111lfltri~tics ror R.B. P~N phohl diode l'lrt' shown 1n Fig. 5 .26(\!) Diffc-rcnt npt.•rating conJitinn.s nrc giving from no light to high Iii! hi level. Wh~n thc:f4! i~ no inLident light. then also a small reverse current will be there. \\'hich i~ known ~ darl current here If 1h.; clcCiffUI-holc p:tir nrc produced out,.ide the r~bsorplion reg.iun ( A .R.} Olen they ha\'C Jugber probability 10 recombme. in wh1ch (':Jii-C no photo currl.'nl wtll he '1\'aihthle. II i~, therefore. necessary ln make the top player a~ thin us possible and cffccl•vc dcplclion region as wide ttS pos.:tible in order to maximw: the efficiency of the photo-diode u.s photo detector. whtch is 1cferrcd as quomum efCiciency. Quantum efficiency or the photo--diode can be mcre•l"ed 1i one goes rrom orainary llhOtO·dliXIC to PIN photo di<XIC or avalanche photO·dic><lc (APD)

or reach through

nvnl~nche

phmo-diodc (RAPO). Idea bchtnd I'IN. APD or

RAPD 1~ 10 mcrcasc d'fcctrvc depletion region which w1ll mcrcase <it•ontum eflic-tency. D:uails of 11-!osc are not d1.scussmg here. Mc:ml cnm.11.:1

I•) t-1~.

5.21

(b)

Fl'(llll Illuminated and side fllumlnnll'd Photo-Diode

Tht:re arc genl!r.tlly two different structure JlOSsibl-.: for photo d iode. one ~~ rrom llh1rnut:Jted (Fig 5.27;,a) OJlCrdtin.g at 0.~ to 0.9 tnn nmJ;c. otll('r is side i11ununmcd Fig (5.27b) Opcl'uung u1 hi~hl!r wuvelcn1!1h 1 .OtJ ,uan ran~c. 4

5.21.2 Ounnlllm £0itienry nnd Responsivity For u phoiO dctcc-ror c-Juilntun'l dliciency ('1) :md n::~ponsc speed or rcsponsi"iLY (R). arc 1wo impor1an1 charucrcnsr,c-s Thcse pan•mctcr~ dep<:nd on the matcnal band gnp. opcr:.uing wJvc length. 'l o( dopin£ and 1hiclmcs~ of P :md N region. To :'chi eve high qunmum dlicicncy. tht~ i.lcpl~!uon layer mu.st be Lh1ck enough 10 pcrmn " large fracuon or liiCidCill lighiiO be ahsorbcd. l)uc 10 lh:ll PIN or AI' I) phmo-doode os beucr 1hnn ordonory pMI<'I ·doode. Qunn1um efficiency nnd respflrl!lil\'ily cun b.: defined :1~ follows:

. Qunn1um el.1•ococncy 11 = -Rc Rp

I_. ":.:' : •.:.·c:;':.;'":.:"7ih.:.:":.:' · ·::::cl = -.:.R.:.".::'":,":;: . •'-'P·c;":::'r:,g,_c:.:'";::":;.rn::•.:,cd::,:';(c::l,:.cc:;J:.:sc:: R:otc of onctdcnl photon (phoum/,oc)

Thu' Jnu.•malttuttntum cfficicnc.· } ns gi vl'n in cqun. t5.2u) 11,

= n/plr 1

n - // l\'

=~ (5.19)

= 1/IJ,

Rcsponsivil)' = H = lf)l/'o = Outp:omg photo currc;!nl/lncldcnt optic;JI power (~ .20)

und incident op1ic:1l power

(5.21)

wh(;rC /p = phow cumn1. (' dwrg~ tJI dc-~:twn. Po /Hr.- energy of pho10n nod (' ;- vclucit) of h!!hl

=mcillC:nt optu.:al power.

5.21..l l.ong WoH Lc11glh Cut-OfT ll i!i csscmial when con~idering imrin".: nb,orpunn pruci!'\S. 1ha1 the cm.:rt!Y uf Ihe incidcnl photon (lu•) '""uld be gr<aocr than ohc h:uul gap energy (1:, ) or oho mdlcrial used n~ photo.Jjode, other wi~e elcctmn--hulc- pair will not s~ncr.lll!, I.e. (5.22) 11tu..; th~re w111 be th~es:h\)ld wave l~ngtb for d~le<.'tioo. which IS conununly

known os long wnve length cu1-off !A, 1. H ohe in~idcni wav< lont<lh or phot<'ln (}..) " more llwn A_.• then phutu dctcctur will not wurl.

5.22 Components or an Optocleclronic Communication System ( Block-Diagram) The hlm.:k ~lla~:ram for fiber oplh.:s l'Ornmunicalitm i' "'hown 111 Fig. (5.28). Tlu! to~ ttansmitt~d (dat.l. vokc. music c1c.) is firs1 coded by a coder anto a .:arracr wave of1nc OfJliCo.tl signul. Tlus requ~rc~ a pr'OJ)Cr llh'tdul :uor !uld :ll\ opticul source. The must prummem smu·cr 10 be used in opticaJ commumcatJon anformution

Laser, /JQ/ograph] <md Fiber Optl<"s i~

L£1)

or .H:m wcmJucta'

lt.~.~e,.,

355

while the detector is PlN or tJWtlcmclltt photn-

dwdt or pltnro-trmuisiOr 1l1c ophcal beam lhat carries the .nfonu:uion is chmiiCt~n k:J hy n:.; :unptHud~. frequency. mtcnsity. Alll.hcse parameters can be lll(ldulaccd w coJe the lnrormatiun properly. ·n,c. l)ignal b nc~ l coupled co un opucal fiber. A~ the ~i~JI p;.1~~~ through the fiber .u some St.nh: h may need tv

be switched U> another channels. This roqult"-' proper switchmg element>. One< lhc: d..-::,imd P')HH. it~ ~ \Jclcctct.l by lhc optical dl.\tcctor, ·n1e gerl¢r:•l

dat~ reachc~

opucal .sigrml is amplified. decoded h)' clcccxler (demcx.lulmor) .s~ eii-'Citu:al 'liign::tl

and tecci\'Cd hy the r~ccl\'cr. Repeater unil may be ncces>ilf) over relatively long-das.lance cummLnkalion w eountl'.r the cffecLo; o f fiber Lnmsmh.sinn lo:..sts and dispeNiun. In ;.1 repc;ncr 1hc. sign3 ll ~ dctcC1cd. tunplificd :mU chen n:crniucc.J. A ~cpnro te

power supply lin¢ must be provided ror all these units (Fig. 5.28l. Ncpc:a.ler unll I----------~ ~VWC'r fC'td hnc I

SIJlfl!lh h. :

: 51):11111 WI

--------''

'-------f.mlliCf

Enun.l!f

OR n

~lpllbes

llyTI R I I(IUC.:I) IJb{or

COinie)

n.OOuJated input inform.111nn~ S'W1chin~

dn:u.il

RR 0

~-{f.i:=l R•B"'==='~wr

} -

f'holo·dJodc- ' 11

De<:"' J)eml,11(,1lllllti'W

()ul pUI

mc...;sagc

Phum·tr.ln ~ lfol<lC

Fig. 5.28

Ulo~k diug.rn_m rnr opticnl communitalion system lhrough optlcol Obor cable

t·l~.

5.29

llundlc of up! leal foher

t\n op1icul commuoicauon c:yMcm is quite "lmilar m cunr~..·pt w elcctronu.· cnucmwnveJ communica1ion )y~ccnl ( I04 lb.) nnl)' the: frCt~ul'.ncy r.mgl! b differcn1 (10 11 Hz} uml oplical fiber inMcnd of metallic tiber.

5.23

Uses of Optical Fiber

A s ing lt opricnl fiber cnn LronJ:imtl lig_hl energy vcty eflil!tcntly (F'igs. 5.20 :md 5 . .:! I). But in ordc:r to transmit an inmgc of an object "'c nc.cd assembly or

bundles of fine g lass fibers or plnsuc ribets bccm•:.-.c cnch riber lransmits rnys irom a very l)mull region of the object (Fig_ .5~29) TI1e quality of the image tlcpcnd' UJX'IU rhc dittmtte-r t:~f lhc fiber. ll cun be as small :1s I o-,. m 1\ bundle tn:•y conco:i'' of thous!lnds ofindi\•idual fibers.

Applicnuon of fiber opucs 10 medieme ore wide ranging. Wi1h 1he help of llhcr opltc-s. 1t1~ possible to srudy d1c uncno•· of parts ofll1e humnn body wh1ch cunnol be Vlewcd d1rccdy. ll a.s also useful in Lhc S:ludy of li:o.sucs :and blood \C~,.c•~ r;"lr helow lhc :o.kiu For 1111, purpo\C. u bundle or fibers IS enclosed in a hypodem11c needle. These nexJhle fiber bundles used 10 med•cinc are called "F.ndo~cope>''. endoscopes are employed 10 make obser\'nlions inside lhe hum3n hody, at • place which can he npproachcd only along a cur\•cd pnth.

Advan tage.~ of Optica l Fibc.r (AI I. Abilily 10 unnspon hghl nlong nexiblc palh<. Thh cnahlc.' viewing of ureul\ whu:h could not be nbse:rv~d OLlltr.vi.se. 2. Ability tu acr-cpt .mtltmmport hghl without h.t:-.1'1 Ulh!n~Hy. 3. Abilll) emit liglu us well a' well1'" guide il a long ;1 p;llh. 4 . ,\bilit) 10 propagme. nnd or couple dd't'erent discrete w"vt:- guide modes.

5.24

,,f

•o

(Ill I. Fii'>Crop1ic oommunicuuon ~y~tcm huvc a lurgc b:tmJ "'idth 16 Hz. The bnod width is lhe ma.xJmum rule at which in(Oml;.ttion c;H'I he tr:tnsmiucd. 2. r.'or under wutcr conununicauon it is very \}c.e(ul. 3. High •ecurily ogoins1 10ppi n~ . .S Thq nrc kss expensive than copper wire 5. Gin~ libcrs hiiYC: no fire ri~k o.nd there arc no .short drcuit problem~ 6. liigh capaci1y-onc laser beam can curry "lHO l.IHl.OOO 1elcphonc

convcn;auon!" or 100 different colorT V prog.r.unmc:s. This extraordin-ru-y cap!lcity lo hnndJe communication Lr3fli<: is rmunly due 10 lhc fu~t thai laser lighl CliO be s witched on ond off much faster lhnn mdio wnvcs or microwaves u~cd in comsnunitttlion

PROBLEMS I. Con ..ldl.!r a mul1rmode ) ttp md~·< fibe-r wnh ''' • I .S:\ nnd n:""' 1.~0. :and A.= I 11m If the C(lrc r.uhu~ 1.. 30 IJtU then ca.h.:ul:llt: the ll' mnali~d lrcttuem.'") lht! ntJcr (V) and dtc numbc:1 uf gu.tdell muc.lt'.

••f 0

I' = _2,.. _,_t_ N.A:! u _2_x_J.:.:.I":..::".::.~::.l.:.>_:I::;U_'·--:::x~.[l~I.:.I.::.Sl:::l~'_:-:clc:l::.5::_01c._ ). IXIO' \' • 9J 72 :; Nmm;dt!ooed Crt:lfUcm.')

St,lurum

I" Tmnl nnmbcr o( guided mode = M, - T

~ J.J~

l.. In "'rdcr tu nuskc the abo\'e fiher ~tngl~ n1<"1c wh:ll wi11 kc I he cute 1tu.11u .. d ' .' For ~ul,g l c tuudc lihcr

2.405). _

llr(N.A.)

a< L27

1.-IOSxl x 111• 2 x J. l4 x SJ)' (I'll) '

X lO-t~ ut

"< 1.27 pm• .3. The numeric11lopcnure uf au uplkrd fihcr ,_.. U.S :md cuJc. Jcl l"a.CIJVC Index 1.5'1 ( l) Fmd R. l

,,r chKldmg. (2} Calculate the c hnngc: in cm'C chu.Mm,g rdr-.1C'I.J\'C

1nde.:< pc.r umt R.I. of the core:.

Numcricnl 11penurc of upcical fiber is

'"'= n1

N A. R.l

u( corr:

= R.l or cladding N.A.; 0.5, ••; 1.54

:=;

'*' a= J''i-,-...-n~,

Therefore lien~<.

- "i· •: : 1.456

R.I. or cluddin~ = 1..!56

till Chunge or cure R I of I he core ~.. Nu l'l~ m::::tl :apcnur~

<lnddiO~

111

R.l p<r unil R.I. M <he core.

; . ":

1.54 -~·456 .;;; 0.054~

11b(r ~~ 0.5 ond core I"C!'fr.tc:ln'e index IS 1 -1~ Fltld claddinl1 rcfrnc1hr indc' ;m..J :•e«p1ance angle ua

Numcncnl .tpc:nure R.I. uf oore

= rr 1 =- I .-18

l-Ienee. R.I. of chu.klint: AcccplatlCc :mglt=

S<t " l =- 1.393

'': • 1.393.

=- () =- "''" 1 (N.r\.) = l()0 ,

QUESTIONS I. E..1pl:uu1hc t1J:Ientluti11.Ji llc·l"l! laser wrth dmgr:un shov.'1ng e~~nlral componl!ll1' 2. I!Aplum I hi! run,lmdivn ,.( upt1calliher and Iheir use 1 l~l)l:t he1unc:e~Hf uh1i\iningthrcedimens1omd image by lhe hoJogrnph) rucd1od ·1 \Vhut 1:'!1 N.t\, t.lf un t)PI • ~I tiber .t What is ib sagniftc~m.:c? S l)e ..cnbc th.~ e11:rre!-"t('ln fN N A 10 tCrmi tlf R I of 1ht 'ore n_nd 1he claddmg loll an tlptk;tl fibc• b. L•f: hl lm\'dlmg m :ur ~~ n~t'"' .~}!.!:toe:, pl;:ue at 11 gl:mring ;~ngk 33° Whil~ ~o1nlun~ the J!.l:•s-" pltnc. p~Ul u( 1hc hc.un 1S reOcclcd and pan is rdrac1cd. ff the rdnh.:ted and reflc....: 1~d bunh mat~ :111 an£1C ~V', ~'llh uch other, lhen: (I) wh:11 io; the rcfmctin~ indC). or Ihe ttL")<t, ;md C2) \\hAl i~ Ihe .;rhlcal !.LO@Ic for lh!U gl~,...,

Solution

Fnun hg. ~-=IJiaJ

' ;:;:: 57f J • 11W'-. 1hc rdr.acli\L' 11t1n ul g l:a~ Jl

::.MOl: 'l11 f

15J9~

r = '• re~)""

1-h:.nce

i.e..

'i ll$ ' · • . S.29b) - : Jl _.. Urom ftg Slllr Jl 1

~tu l, : _1_ ~ __ I_

11 1 tj •

1.5398

I \ I I

40.5°

7. ()i~UM~ col laM:r and sive ~nmc uf II.( pr:tclic-alt~pplicalion. .. S. Giv~ hloc l. di:.gmm for upl u;al comnmnicmion through tiber optic cah1e. Wh:n •uc I he "dvunlltU-:~ o( O(liiCul cnmmunlcmion? t) Whou ~~ monomodc .mll rnuhimodc opllcrtl lihc(• How i.s N .J\ in\•olvctJ wnh

thcru'! (~'or Jong dJstancc comrnuna:-atiou wltich as prtfernbl.:? 10. Whut il' hoiCigrnphy? I To-.· doe.( it differ fronl ordimary photographic tcchn1<1ue?

I•

Lmr't, Holo~:mp/1\ mul Fiba Upucs

359

.., I,

(~I

Fi~ .

II t~

I' 1-'

16 t1

5.2!1

I hm 1' mtcrr~rence ;~nd d10'r.1CL1un rd:u.:d "- 11h constrtai:tum .mJ C\.'\:\•lt'ilru..:lhm ''' the h ~ln~r.1n1 Explain In dcuul with s.uit:ahle \h:.g.r:uu In '~but "")' l~r hght .:U\d ~tnrli~ht .vt- suniiM'! In v.lut w;,y "to they "li ff~r"! \\'tmt ar.: nppmxuu:tte wnve length r:mgc for X· rny, l:t'>cr :mt.l unhn:tf) li!!hl fVNbh:n Wh11:h way arc they ~l mtlar and \\htch \\,t) ..!11 they ~lifter ' Wh> rue X··r!lf :ami baser 1u pov.dul1ha.n IHtHnlll) ''"lblc lj~hU With 'ull1.1blr c.Jia~mm show li~bt p10pagllltOU lu 'l<.'JJ mlh:X .ttull!IUOCd uu1n fibe r E.~plajn ttuw the 1!-r.tdell irJ~~ fiber p•x•Jm:e~ leli.S th~p!:n;ion th.m :.tcp mdc' lib..:r'! For long·du.umce curnmumc:JtiOn whteh \\ 111 be prclerable'! Hnw 1\- mh.'rle-:mcc connected m hul ~•graph}' ..tn frre.1c"' the uhJL-cl.and ditltuctmn 1~ umner.lt·~ •·m unfre..elc·· lhc ohjecl'' Wllal .u·(' 1he ~·nll~•rilk~aniJ Jis:o.imilmit~ bctW«"U X·ra). b~r .md urdin.u)' 1i!!.ht! When l x l t) 11 1>hOtllUs ....:.ch wall• "a\e knstb M OS!'i Jim .tn: lntuJcnt on :1J>hot,) (lrr)t:lr., on m enj.!c 1.2 X 10 11 electron.-; .ue t:cnerrdeJ Detemllnc quanuun dllnc-n..:y .md rt'!\pilO"'i h ·!S)

~ululi•m

\.lU:ttUuln EffictC!fh.'.)'

= ~:

= 1.2 ><

l~u

x 1011

= 0.4

Re~puu... i\'l t ) ' ; ~·AIIw:;;

1.602 .X 10 ... )( O.ti.5 "

10 •

6.626x 10 · x3x 10 8

R;;. 112:7-t A/W

lh::nce 18

0.4

A ~thC~ln phl.ltO thode hrl\ q uantum dfu:umcy •ll 6~tJi wnh p hoton c ncrg) 1.5 x I() •• I. ll> ~>nd N' Cll<fl!Y " 0.67 ev. C1lcul:ue (._) J.ong \\ri\C fcnl!lh (b) Rc,)pun~•vnv CH)

CUI

uff (J.. )

(c) Incident pu\\er rt."tiUUi!tl to ub1.1111 :.1 1dm1u current ~.5 J.l;\ (P,,l'! (a1 Bond gJp cncrg) = £t = U.t•7 ..:'\ ~ 0.67 x 1.6 x W Ill J • JrrJ).,

Soll,non

lienee

Cut nfl \\;1\e lc:n~lh

=-A., =

6.626 X 10 0.67

H X

J X 10'

1.6 X 10

., 1

.l= I .~S4x IO"m

,,t. R ; .!..!!._ :;; Pn

(hl

J]f.Jif\';: I( :

0.65

1.602 X 10 ~ l.~ 'X 10

(l,(l9·1 A/W

(~:) Nm~ R.;;, .!r_ ;- U 64..1.::; 2.~ x 10" P1)

11)

Fmtl hO\Io' rn:tn) Phntm .. Ul! retJUircd pi.'l )\C,•nni.l lu Produl!c J.a)or beam uf lm\lo'

pow~r. wh..-n ''·"" 1cn)!llt nfhN:r hg.h11'- 69-0

St)IUiinn :-

POWl'r =- J> = .l 11 " =- J x IU ' W ur H~cc

r:. ~,,. .::. ( nhf· )f••meJ/~1. luue

, : nund'k.•J uf llhown

Jn·-=

fl::A

n :;: ; -

1..-

II ;

=~net~)

IJ.)~8 X

uu~ photon

l l< III 1 l< 6'143 x I 0 IO 6.625 X Ill '">< 3 X 10•

(~ • n ee

ltmco ~~one

sewnd•

IU 1,.

10. lmemal en lie~;~ I nn)!.lc ftl core...cl:•dding inlc.rbclt" or 11 ''ep mdex libc.r

caleulftle mn1mum acce~1an ec angle when clndding R I i< n,: l 48 SulUllun:· lntc:mal .;nli:al augl~: '· ;. sin 1 ~n~/r1 1 )-;; l:i0.610 So m:axunurn .t<.'ccpl..encc :an~lc a.,.-= sin 1 ,J ,; - u{ : 14.1311

80.6

6 Radioactivity and Nuclear Reactions 6.1 Introd uction Radiuucti vity wu~ originully db4:t.>V~red hy Bt:Cttuerd In

I S96.1lu~

r;hcnom..:non

is confined almosl cDtircly to Ihe hca' test .:l..:mcnl All Ihe nuturaJ iy occurrint; rildHt<.tCII \'t c:lemt:nts lie. Ill lh~ fiill!!,l.! or :tiUillll.: munbcr z =lSI IU 92. BcctJUC:rcl discovered chat umnJUm gave ou1 ~lmc type of ntdi:nion' whkh were highly penetrating, could aflect phmogr:tpluc plate v.rmppcd m thtck black p:tpt!r. mnoe g:l~\ :md C~IU~C ~cintill:nit111 tm nuurc~ccnl \C,:TCI:I1 Aflcr IWO years. :1. Frent•h couple Pierre Cunc nnd Maroc Cun~ found thai a <ub.oruocc polonoum frC>m

also emitted rt.HJu.tou.:hvc n1Ji;&tiun:, "n'hich wns muny million~ or times moreacti\•e in cmi.s.'iion lhan urnnmm They n:un~d lhi.) c.lc.-meru n~ 'r:tdium• . The SUh$UmCQ which emil lhc'c IYJlC" nu.lhiiiC.tn!O. arc known tl'\: ' n:u.Jioacllvc substances' and lhe phenomenon of 10ponwneou~ e.tnissiun llf rudiation from mdiO.lCiivc sub~t:.mcc.s i~ called 'nuJioactivity', Ur.uuum, polunium. rodon. ion1um. thorium. Dctinum etc. arc rndi\m~t1ve subst:tnces. II Wil'i ul~t) r('lund thut the rndioachve hchn\'iOur wa~ umdlccled by phy~icnl and chcmic:1l chan~tcs. Radio.t.:tivity j, cs.!oentially a nude~r phcnomcufu\. h b n tlmtk proccM bccuUl,c tht.! cl~:mcnt t:hnngt:~ in kind due to this emission of r.td ialion. h is a ,;pomaneOt.J' ancl :u1 il'n:VCt.sibTI: ~el f d is1ingruling ;.ctivity. Radioactive subsmncc..~ nre usually ruunll en ~mH euher a-myl\ or ~myf>, sometime..( t.:mis!.u:m of y..r:tys accompany the.sc a and jJ decay. I. a-ray is doubly-ionised po>ilivtly chnr&ed hel ium nooms <,He4), wilh bolh of their electrons removed. 2.. fJ· ray consists of electron~ ( ,c0 ) wilh e-ve) ch:trge and a1mosturo mass. fJ*-mys consist-. orposi'tron r. 1e11) with (+vc) charge. snme in magnitude as :.ln clcctruoi bill wi~l OppOSilc >ign :lnJ ulnlosl icro liiass snme as eleclron. 3. y-ray or phoooni is on electromagnetic wove hu,•ing frequency higher thun urhnium ore.

thai of X-mys. They have no charge.

6.2 Electrical Counter

Instrument~

ns Detectors/Geiger-Muller

loniZ31U')Il ~hambcr, l)f\1J)(trtion:tl counter, nnd G.::ig\lt-Mucller counter. cuch uf these three dctl.-ctors, used 10 detect radit1.1c1i\•e radia1inn. is based on the productjon of ionizndon in a ga..'li nnd the separation and collection o r the ion.~ by means of

362

Engmi•t•nn~

Physit•s

nn elcctmslatic field. 11lc: diffi!rcnce~ in th~ thre~ systems cnu be expJ~aincd with th\! aiel o r Fig. 6. 1 which ~how,;. n cylindrical t;Oilducting ch~unlx:r contttining a ccmral conducring clccuodl'! located on the a.x i~ of the chtun b~r aud in... ulutcd from it The ch:ambt!r i!: filled \\ ith :1 g:.~ Ill :l rrc~~ur(: nr one :lln'ln-tplu.:rc l U lc.::~o,. A \'Qitugc \' 1s r1pphlt:d lx't"'·een the waJJ and the central electrode lhrou.gh rc5istanc\!: R .shulllcd by the CO:tpaci!OI' r: lhc ceru m l eiCCir'Oclc i:-. til n posiuw pvlcntinl relative l u that of lhc chmnbcr wall.

FiJ:,. 6. 1

Nudcar ddcdur rur deh.'<'lin..:

a nnd fJ rn)S·

lcl U:O. suppose lhtn SOillC ionization OCCUrS in IJ1c sas because or the p:hS;ig" of~ c.:h;ug.cd p.a niclc. E:..:.;h ion pair consists of a poSJIIvc ton ~and nn elc('tron. Now tor a g1vcn initln.J iOOJ1.."UtOn. how many mn pairs arc c()llc~ tctl or how mnny electmnlj re;u.:h llu: c~;;ntral e;:lectrod.; as the upplicd voltage is vunud. is

::.hov.:n 1n Plg. (6.2). where curves of total !On collecti(ln nre plonct.l n:-. fuoc uon!>oJ ~pplicd voltage. For convenience. the logarithm 10 Lhe. ba~c 10 of' lht.~ numbc1 (log") or ion p~un. has been used a;o;: the orJinate If there ao;; no voh;tge ncr(H•:o. the i:h.·~.·u·od.:s, Ihe ions will r\!<.;(.)fn&inc and no charge willappe~tr on the cap~tcltor. A:- the voltage 1s incrca~cd. say to a few volts, then &here h competition he.twc.:n the l o::.~ of ion pair:, by recombination and the removal of ions by collect ion on the dt:t.:Jmt.le~ . Snme !!h:.nrons will reach chc central dcct.rodc. ;\t n vohugc v, of th~ ord(!r of s(lme I0 volts. the los..c;. of ions hy recombination hccomcs rh.:~Jigibl.; ;111d :111 electrons rc:.ch the centr.d electrode: lug 11 r<:tt'he> the value unhy. A~ voltage is increa~cd from \11, " stays constant unlil :.1 \'OJL1gc V1 it-. rc3chcd whit'h may he ""n~ lens ur hundrc<.b of ,·ulls depending on 1hc condilion> or U1r experiment. Titc region' between \11 and V2• in which th~o.: uurnher of ion p:.i1' collcctcll i:t. indL:pcntknl of the applied voh:•!!c and the curvt" i' hori1.om:al. t.... c;tllcd lhc imd:.lllio" dunnbi!r reglon, When voltage is lncrensed above V 2 , " incrc:tses Jd,ovc 10 bcc::msc

•'f a

phenomenon (.'ailed gas mulliplkution or gas amplilicntion. 111eclcctron~; released in the primar)' ionization acquire e nough energy to produc.-c ndditiona) ioni7oUion, wht:u they collide wi1h !F~ molecules. and n incn~nse roughly cxponcnti111ly wilh V. F.ach ini1i:tJ electrOn prodm::es 3 :o.tn:11l ':rvaliltlChe' or clec.~ tron~ \Vith mu~l or these secondury e lectrom liberated close to 1he central e leclrode.

tr number of

[ 1 G<itn

• ~ "'

•

:I T R=-

1: IIHII /-UII\IIl

: ch~.tllbt(

""'

[)

t I

1'1

' fo'ig. 6.2

I'.!VIJ(orttort:tl ~(t\&tl\Cf

4[)(1

~hwlkr cnuntr-t

,.,

1',

XCI() Voh.t~e

1!00 lVI

Varialiol of l nlnl inn p::tir prndun•d (lug n ) " ilh applied vultaJ:;t (\')

p:urs arc fOI'mcd rnumlly '" mnrc. curYC b results; 11 as par.t.llcl to curve a'" the iom7n.tion chamber region nnd '' ..cpoaruh:d Irom u hy ~me una I on 1hc 108- " !"\:a.lc. TI1e- bduwiour of 1hc ,,.. u ~.:u1 n!' :lhovc V2 i:o~: imere..,Jing. For some range 1011

O( VOltage~, Uptn \ f \• C:lCh e lectron :J.Cb tndl'pendently ;and give~ itS OWD avalanche.

not being ~ffccled by •he presence of the ,,thcr clt!ctrun,. Curve ~ 11 :tnd b com•nuc

to he parallel with ra dlffcrcncc bet\\ ccn them of nne tll111 un th..: log " !;C:tle. the numlx-r uf mn r>•nno collected i~ 1hcn proportional 10 tltc Between V: and inhiltl ioniJ.31iOI1 Tbj~ i!t~ Llu~ region Of pmpont'tJilaf CUUIUtT nperatt'Oil. Abo\'e V3 , the ga1 muluplicauon eft eeL continuc..s. to rncruaM: very r.tpidly. nnd ;L~ more electron'{ J)roducc ~w;alanclu.:-... the l:mc.r hc1:1in co i ruc.r\'!UCI wnh nne ;~nolhcr: lhe posllivc 10n spncc chnrg< of~"~ :tvnlnnehc mh1bhs 1Jw dcvcloprncnl ut tht: next ;wal:uu:ht:. 11ae l.lisch::trgc of lnalinl clecWm!-. 1n curve b is affected with a less numbc.r or tnilial electrons which increase) lcs' r.&pidly than c.;un'c a: curv~ (I und b ••ppn:xK:h c..'lch other tmd C\ cniU~ally n\I!C-t m V,.. 11le region between V, and V,. is the rf'ghm of UmilrJ tJtnfJm1;mwHty. Ahovc v.~ the charge colh~cted becQmes independent of the ioni~;Ui(.m inithHing it, '111d curves uand b hecornc!o. identical. Gas muhiplicouon increases lh< lOlaI number ions 10. value lhal is limited by the charnclcristics of the chambe-r and lht: extc:n"al circuit. The region tabo\fC V..a is the rrgluu of Gdgcr-Mm·llrr t'mmtcr uprrmlrm. It e-nds a t a voltage

v,.

v, where the dtschnrgc tend, to propagate itself indcfinttcly: V, nl:~rk• the end of the useful volta!!.c scale. the re~ion abo\'C bciO£ th.nl of t·omifluou., dirdwr,C?t'. I( the 101Ual IOnil.atlon I'\ ver}' huge. curve cis ob1amed It IS similar to CUr\'1!' a nnd b. :tnd p3rllllc11o them between V1 and v,, the pr01)(1rluula1 c.ountcr i'Cgion end~ sooner. m~1ead of nl v,. Thus. the extent nf thai region depends on the uuunl ionrzauon As a rc'i.ult tlf 1hc bch3\ our or 1hc ion~ of 1he !!i•' in 1he clectrcht:JitC field.. three detecuon instruments have hc.c n devdopcd. A. Til~ iom':.atio" chamhu whtch operntes nt vohages tn Lhe r:angc V1 to V1, · ~ chnractcnzed by complete collectiOn, without gus amplificoliiOn, of i ttl the

electrons mtually libcmted by the pas<ngc of the pllrncle. SubJeCt to cenam conditi on~. il wi ll give a puhe pa·oponional ao ahe numhel' of1hcse dccu'(ms. Fig 6. I schemaucally shows a chamber which could be used as an wmzauon chamber between 10 and 200 voles. approxmHalcly. The numbe~ m Fi£. Q.l wmtld be ttppropn;ah.' foro counter with an oulc:r cylinder I em m mdius. a w1rc ccmr~al c leclrodc u Ul \.:nl 10 radau,,and tilled wHh gas lOu prc~l\UO: uCtt rcw ..:cnurnctcr\ of l~g (e.g orgon n1 al>oul f. em of Hg plu• a liule alcohol). 111e counter length '' ould he about I0 em. ·n1e eJecu odes of nn ionlz.·uion chamber rna~ a l~o he parnllcl pltttC> 8. The Proportioual counter which opcmle:s in the V!.)ha~c rcgaun V.! tt1 \f:, a:; charactl"nzcd hy n ~a!'l mulu):4ication independent of the numbcrorinitio.l clcctrnn!'. lie nee. ahhtm~h ~:-t' muhiplic:.Uk\n b tnilized, lhC pub&;: is always pmponional to the initml wnrz:uion. TI1e u:-;c of thb, cnun1er perrnil"' hmh the cuunling :and energy detcnmn:nion of p:ullcles which do not produce enouGh ion> to yt<ld n dctcctoble pulse tn ~lc ~osion Vt to Ill. The pmponionnl eounta, therefor.. p(fcrs. ad vunldl;C" fur pul-.c-cypc mcu~urcmcnb of bela ntdiation. an .tpplit:;tlion ff1r \Vhich mnitntion chnrnhc:r:_( .arc ntll ::.c:nsiti vc cnou~.h C. Geill'r-.llu•tlrr Cnuntu (G·M Counttr or G-M Tube). n1o C<'igcr-Mullcr {G·MI cuullleJ , n:uncd nFtcr Its lnvenwrt- ls !l very ctncien1und uccurmc dcvi..:e for counting tndh•tdunl 11. bur 11 panicles emiued from rndioactive >Ubstan,·c>. illlr>Crflh'!.:.. In the vollogc rcgann V4 10 V, nnt.J iS Chnmct.~ri?.Cd by lh~ .'Jopr~ml ofthu tliscbargc throughout the tntirc length of the counter. rc.!ioultiug in a pulse

independent uf the initial ionization II i~ specially Ubcful ror CO\Jilling lightly aoni1ing, Jl~•nicle:. s uch as b panicles or g-mys. The. G-M counu:.r uo;ually co n c;i,l ~

of u fine wtrl' (e.g. tungsten) mounted nlong the axis pf the rube which n>ntuin> go.~ at o pro~surc of about 2 to I 0 ctn or Hg,. The tube muy be u nlCt.ll •ueh ns

•

~Opper.

or tt metal cyl inder m;ty b.: s uppo rled insiUc a g ins' tub..-: tt mix-aurc of 9(1% Argon nnd 10% e thyl nlcoho l is ~uit ahlt:. A rut. which may be between 800 to 2000 \'Oits. is applied bct\\Ccn cylinder and wire which act!. a.). fi.JH)dc. The value of lhis vollagc is adjusted to be somewhat below

(f ig. 6.3a),

the breakdown potential of the gaseous mixture. Wheo tlle ionistng pt111iclc passe' thJ·ough ahc tube. it iooiu:s the gus~ous mixture. thcrchy rtlc:l!iing n number of ion ~pairs. The (+vc) and (-vc) ions so produced arc drawn tow~trdS the appropriate electrode~ nnd the resulti ng pulse or n current through che aubc produces a vohage pulse t lO mV) across R. An electronic pul.~e amplifier

Glu~s

(PI

Ti) :rmplifi~

lbl

fo'ig. 6.3 Ct;"iJ!cr-Mucller couuae.r and Geif,ter-Mueller tube

acccpls the--e pul"e \'Ohugc~ and antplific~ thLâ&#x20AC;˘ntlO :lbout 5 tu 10 V. Thi!<o :wlplificd omput I\ th..:n npplicc.J w 3 rci:J} type recorder or to a counung-mte meter. '1;.0 the rm~ of commg of b- or g-r~l)'$ cnn be measured. For very high pui\C r.nc:-.. :& suitable sc3ler t:-. used ir. conjuncuon with the G-M tube. G.M counter lUbe dncusscd abo,,e as suiUtble for fj.. ood y-r.tys, measuremen1 , il is not s.unable for cc-panicle'*', because the walls of Lhc glass tube arc 100 thick for a-pamcles to penetrate. Fordell.-ction or a.-particles., lhe Oeagcr Poin1 Coun1cr shown m Fig 6.3(b) I!; used. 11 consj!'IS of an ~iully mounted fine wue nl~tde a tube which is maintained ot a (+ve) potential w.r.t. the tube. The tube contains

dry air ul ;t1nlQ!!.phenc pressurl.!' aud

an e~tre.mely thin foil wandmv

;"tt

one

end. The a -panicle.< to be dc!ceted enter the tube through tbe v.indov. (W).

6.3

Radioacti ve Disintegration or Decay

A lorn.'\ of heavy clements like ur.tniUm, 1horium. polonium and radium e1c. arc con.stnntJy breaking up tmo rrr~h. rndJoactJvc atoms w1lh the emassion of a-. P. M y.mys. from their nuclet. In the pn>ecs.<, the origm:ol (parent) mom dâ&#x20AC;˘snppears and gives rise 10 new (daughter) atom. These new atoms are also. tn general. mdmachve and hence spontaneously brenk up. m the1r lum, thereby leadmg to 3 long ch:Jin of diffcrcnl radior~ctivc elements ln the fonn of 1:1 rndioacuvc series

umil 11n mactive elcmenr (usun11y l c:•~l) ~~ ~tchcd. For n:tturully occurring

ntdioacth'4.' elements the three wcll·known :.e:rics are ''rwtium·rtiJium ,trrir:r, tlwrium M•ries und actmmm uri~s. Thb :-.ponL:mcou~ hn:ukin~ up oflhc nucku~ j, known n~ rmlimzcliw• tlisimegrntlrm. F'm t!}:UIIIplc ~11 clcmcnl X nr m:t~~ number A :uu.J ;tlornic number while cnulung an cx-p:U1lcle (zllc•) is convened in1o another clement )' havins mns> numher le..~~ l h:m 4 fuhl .11omic 11unlhcr Jc,~ I hun 2

~~::u:'~«>

«,Th:'• + : l·lc'

Simibrly when an c1cmem d isi.ucg..·::uir•g b)' 1he emiso:ion of fj--rays. il is turned inro nno1her new element whose :uomic number (numberQ(prmon) \\1111 HICI'C.:lSC

by I whereas mass will be the same. .r X

6.4

p•

~ .r. 1 Y

yruy~

Natura l Radio-Isotopes

Rtn~rnll) Ihal I he pnwlur l ••I" rnclm.u;un• ch~Ci1) 1-.: il5«."1( rndioncli ...c, .Uld thnt t!ach of the dc.cJy prrKfuct~ he have chemically in u di ffl!renl manner

I1 "'"'' fl'•umJ

frum iiS hnrncdialc p:arcnt nnd ils daughtt.~r pmducl. ltmnpe,·· Let us coa.sidcr lht:. followin~ rJJioacuvc ~1 1ou.iurn !Y1 ~ IUIR:a!M

dj ~1n1cgn.uion\.

zHt:~

where ~~Rn110 is the product t"Jf disi•Hc~rminu " f lunium. ~n,~ ehcn1kal prupenics uf•k;l)oni um 1Jll turned UUt tUbe similar h.!lhthC of ll!UUf31J'j fiCCUtring J-:ldio:active dement Thorium (')(lrtt~ 12 ). in fntt the two dcmem~ when m1xed couJd not be '>CI'ar:ued chemically even with cxtr~mely S\msili ..·e mclhods:. Mor~ovcr. ionium ttnd thorium were found to be spcctroscopicall) identicaL llws the pair of e l emen t~ "illlonium1\l) ar1d 90Th1 ~ which were chcmkuJJy idcnlicnJ but dlfTcn:d in atomic \"'eight arc called iJ'tJitJ /It',\ . lso1opc:s rue~Ul!\ 1bc s~uuc position in periotJjc la.ble. fh11s

'j two momic spru:;ex zX'i nml

1 )"".

whit'lt lun:e diflt1.t,-•m tJflmtic nm$.ft!..r

(A. A;) im·tnte of beinR diff~r~m tltmt>m omlllow• snm~ momic number (Z.J aud itlrntirol l'hemical propcriics. then tlwst difftrtlll sptcif!., <Jte called isotopes. y;eUI:H-' ~wd ~ilu llz..M arc n:.t.turnl hotopcs. \imllarly ooJoniuml.'~J. tJOTh! 12• 90 UX ~lJ. are all tu.ltural

i~o topc,;.

lwbars: The followingc1cmcnt'\ 90 UX ;u. 91 UX ~l.t. 9:_UifU..a all ha\•csame mass number !A) but Btomk number (Z) is different ~o they arc che.mically different c;~lcmc.nl. Tlrf:~e cltum:ntr ~··lrich nr~ hm•ing Mm'e masJ· 1mmht:r (A I but cliflercnt utmu;c 11umber (Z) a~ ctlllt:d i.,obars.

Rmlimu~lil'ily

6.5

om/ Nurle<lr Reat.-'ltOIIS

367

Law of Radioactive Disintegration

From t.hc experimental ol>servntion Rutherford and !;oddy fonmalotcd ahe theory of rndioacli\'.; ch,lfll;C The rnte ut whach :1 rnrhcular radioaclivc mtllerial dbintcgrnttt~ or decay~~~ o con~r.1m. th.d is 3lmosr completcl)' independent of all phys1ctll and chemical co ndit i on~. Tial' in tcn~uy of Lht: rndioucLinty which b called 1\ctt\•it\', j.,. propmtiurmT 10 1hc no. o f atoms whic)1 disirHcgrotC..'i per untl lime. If dN i• the avcra~c no.• lhot will decoy in a smnll lime intervnl d1. il i> found Lobe pn)JlV11iQnaiiO lhC 110. or atoms N pre..~nl Hl time/. llmt I~ the rule of distnle~rorion. - dN/d1

= - AN = AIC (6.1) where A is the con st. ot rropon1onalny. known as d1simegranon ro11st. ()r dc'M)' cmut. It as I he chnroclela:c.lafS of a pm'licular radioactive isotope ~nd indcpendcnl dNid1

of all external condiuortS like tcmper:uurc. pressure (-vc) sign indicates thar lhere 1~ a decrease m the ongmaJ no. of atoms m present clement. In E.qn. (6 I ) A is 1hc a<.:llvity :md C i~ lhC dctcctron cocfficicnL N nnd A are always mtcrchnnguhh: by the tclataon AIC = - J.N. Now rroan E<1n. (6.1I wo ~cl c/NIN = -A.t/1. If m 1 = 0. N N0 ond at r 1. N N then h) an1egm1ion \\llhan I he hmitlllo

we gel

J.'

dN= -A d1 "'> N o

II0!! Nj'Nn'

= [hj' , logN = - A.1 ·•

.1!.... = ('

l ienee

"'"I

log N 0

N=N· ·- A·

(b.2)

Equmion (6.2} shows tl:at the no. of atoms of o given radio:lctivc subsmncc dccn:ases exponentially "ilh time (Fig. 6.4). This graph shows thai N i< theoretically

never zero blll N -->0 as 1 -) o.:t. 11us lheorettcal decay cqu:uion b. cx.perimcnlnlly proved for chc dec-ay of many r:.-dioac-Live clementS.

6.6

l:lalf Life

A radioac1ivc nuclide may he ch.tr:tctcrilcd hy the rare at which il disintcg.r.:ucs. From Eqn. (6.2) and Fag. 6.4 h is clear that mfinue time will 00 token hy n rodionctive subc:r:tncf.! 10 dis.appcar completely. So the quan1ity whu:h JSgenerally used 10 ch:aracleri7.e mdio nuclides is the lwlf /if~ (T111 ). the time in which lhe number of rndio:tc1ive aroms :lrc reduced lO one half of its origanal v'Liuc a.c. NINo= 112

In general

NINo= r'1 '

when t = T 1n I hen NINo=

t' ATtn ;:;-

112

J.T1n. = log.2 = log 2 x 2 30'2(> : 0.3010 X 2.3026: 0.693

17v1 "' ¥] 6.7

(6.3)

Nuclear Force

11lc nuclcw. ~ortslittues or positively chnrgcd prutcm:-. aucl neuu'lll neutrons. Because of the p<lSitiveJy charged protons. there ffiU.SI he repulsive e lectrostatic force~ hcl\\CC:n the prottlns, lending to push lhe nucleon!' np~111 B\U it i!i. apparenl from che smnll 511.<' ond l~c density of chc nuolcu~ chac. nudcor forces muse be very ~l rong m compouison witb lhc (orw;cs between the nucku:-. nnd the cxlrn nuclear elt!CII'fll\!'o, I knct! 1f Sl.ilh!t: t:Hmpkx nude• nn: In 1."\1'1. lhcre 111ll'l be ourott:th•c (nrcc:o., ~pccificall)' nuclear (or~:e' hel\\t!Cn ;, pml<ln :uu.l ..t 1lCUlt'\1U, hCIWCC.Il l WO ncuLron .. or bl!twc:cn l\\10 proton.'>. They stocm to ~ more comJlle.x 1han the gr.wu:ui~tn:t l or cl~trum:Lgnclk· r(_m.·c~ of cht.~t~l(::.tl phystcs. The nucl..!ar :ltlracti\'C

forcc5 must be \'Cr)' strong at disumccs of the: nrdcr nf nudcur radius r.c., mtc:l~a,· }flrct!.'i arf! short range forcrs. OuL<oidc Lhc nuclcu.!) they decrca.~ very r.spidly.

·nu.: motgniiUdc of 1he nvclcM forces bone rnillion tim~ greater than the: fore-~ needed Lo ~cparnte an e>.1ra nuclenr e.lecLron fmm the mom

fn 19:l5 Yuk.aw:1 predicted the cxistcm:c t.•f :1 partu:le. now c~tlled a •·meson ...

having a rcs1 mass belwccn chc clecuon ond nucleon masses. He pro)10scd a lhcor) h,l ch'""ify the nuclenr force..:; wilh lhe hciJl of 1h..: •nc._<ton nnd i:-. referred to a~ ..meson theory of uuclr.ar force..~''.

NUCLEAR BlNDING ENERG Y

6.8 Packing Fraclioo The .:xislcntc or II !\li~hl hut S)'Sh'lnlllic departure of the atntnic m;JS!\CS from the \\!hole number in every cn.se wus Jirs-1 smdic:-d by Aston. l-Ie gave the following formula for chc'Cking the stnbilily of lhe utom.

Hmliom•tit•ih•uml Nudt'(lr RctiCtimu· 369

Puckin , rmction !::/~ Actual .:nomic ma.~s- M.L~s number & Pttc ~in~

Ma."s number fmclion

=/= M •·.•11 - A

(6.4)

The packing fraction is the mean gain or loss per panicle in utomic mas~. In order ILl pack the elemcnt(lry particle to fomaa ~table nuclcu~. The variation off with mu ..s 110 . shown in Fig. 6.5. From tbc grJph it i-. clcur thm cA..:cpl for <.mflllcr and hither value.~ of n>Ms no., 1he graph is havin£ almo>l Oa1 minimum wuh (-ve) value" oif. When fi\ (-vc). that mecms ffi(~' no. A 1.) lor~cr than ocwul nt(nuic rnfl.\:\, "hu;lr rmpl1c~ lht! ~l nbility of the ntl ciCII:\. Whcrt fi' I +vc) 1h111 tlh!<llb tht: nudeus is un.,rablc.

r. ,.,.,

- 10

6.'J

Binding Ener gy of the Nucleus

It ndght al [in;l he SUppctSCd that the mn~s of nn lUOnt should be.· the ~lim of the n\USSCS it\. consliuu:nt panicles. But u -.urvcy tlu: :uumic ma~Sl"\ ~how~ Ihut

t.lr

the a1omic m:1.~s ts less 1hnn ~1e sum of iLHonsu1ucn1 pnrucles tn the free s1n1c. Tu nccounl ior thi.b difference in m&~. Einsldn"s mo~~ ljncq;y n:lulion b used The grouping togethe-r of the c leme.mory particles (pi'Oion\ and nc.utrons) imo ::r \lnblc nucleus. involves n certain inlcrchungc of energy. Thi!O 'energy' is the 11

Rlndi11g energy" (BJ!.) of ahc nucleu, i.e. the cnt:rgy whkh i' chh!.!r libcr.\ted

or ubsorbed when the constituent particles are bound togelher lmo a nucle u~. If tlM is lho decrease in mass \'-'hen a number of prolonl'-. neutrons a nd

electrons combine 10 form 411 31om. omnunl of cntr8-)' C<(Ual I()

~len ~~e

above principle SIQicS thnl nn

I tl£ = tlMc' I

(li.Sl

h, rclca.~d in the process. The toame nrnount of e nergy would be nel.-dec.l to break

the a1om m1o its conslitucnt panicles. Conversely if Jl.Af ic; the

i ncren~ m m11~.S

dut: to th~ combination of pnltons. neutron' and electrons m fonn lhc ntom then the amount of cncr~;,y E = tJ.Jt;l will be :tbsorbed in this process :tnd \Vhcn the atom will break. this much umou111 energy will bi! n:lea.~cd. The t!itTc.rcnee iu mass. IJM Is o:•llcd tho mms dtfrn it is that amount of mass which would be cotwcnetl lnto energy. Thu~ the energy eq,,iv:,Jcnce of th~ mass d~fecl i ~ tht~ref(m' a mcMun: of the binding cncrg) or the nucleus. Lcr I he constituCnb of rh-: .:uom be : protun.;. ;:..elccltoru. antl(l\ - Z) neutrons. Mas!\.CS of Z·pl'(liOitfo Hlld Z-clcc rron ~ 3tccqujvalcnttfl nHtSS orZ-hydmgcn alOms, So the mass dcfcc1 can be written n~

where Mu 1113..<!!- of h)drogen atom in a . nLu M" = nHL'\S of ncuHOI! in :. 111.1,.1 . Mu, = atomic mass. the actual moss or the

atom in a.m.u.

Since the ma<s of an elccoron is very ne~lig,blc so the main contribution 10 the mas~ <lf 1he al<lnt is due to the nuclc.as. i.e. tlu~ tc~ the. miass of ruolmb l1nd mnss of neutron:.. So we can write the mass clefeel as

whc1~

MP i~o 1hc m:lt-' of pro~t.m m tt rn.u

Since I a.m.u. 15 cquo\'alcnt 10 9JU~ MeV. so B.E. of the nucleus i> B.E. = LIMe-- ; 93148 [ZAI1• +(II - Z)M. - M:tAJ Binding energy per nucleon

!1>.1>)

1 "'

A J,;ntph of I hi<!' ll.E. per nudeun as a funcl1on of the mass no. is 'ihown ln Fi~~

(6.6). Wi1h ohe exception He". C 12 • 0 10 1hc vulucs 1he B.E./nuclcun lie on or cJo,e 10 a ~ingk cur.•c. The .graph @:i vc~ us 1he follmvin.g rc:suh~. 1. B. E./nucleon for "orne \•cry light nuclides arc very ~ m:t11, say for H. He

etc. 2 . B.EJnucleon rise~ sh:trply nnd reaches a rnux:imum value or8.8 MeV in the neighbourhOOil of A ; 50. , ~me maximurn is tJIIIh,: n ~ll. nnd thc B.EJnucleon j~ ~t ill 8.4 MeV at

140. .J. For hi~hcr m.1s~ no.. lhc vrtluc B.E./A tlecreuses to abou1 7.6 MeV 1:H Urnniurn ;u A 2J8. Two t!nd$ of 1hc packing (rnction curve ~hows 1h:11 packing (Fig. (1.5) rraction f•s (+ve) for hght and heavy nuclides due 10 WhiCh B.E.IA is also l::ss ror light :tnd lu:avy nuclides. h IS llliS ti~Cf('(t,t(' in B.E.IA wluc/1 r.t 1/w fiuulamemal amS<! of rrl~ttSt' (lj cnt'rg)' 111 the jitSl(m or Jigh1 CICill¢:111$ 3 1ld Ill spfillmg (jis.~ion) Of a heavy clement. 5. Over :a con.~idcrablc range mass numbc~ I where packing frucLion[is (- ve)j the B. E./A has au :~vcragc value abou1 8 MeV.

RadiOlJclil•il\• mul Nucl~:ar Rraclitm.t

371

• g

(

• ~

•I

,; 3 ~

F"lg. 6.6

lf>O

2011

2411

\'ariallun t1r bl.udlng t"Ucrgy pt'r nucleon (8.£JA) wilh m:•s~ numbt·r A

The (+vc) value of 1hc B.EJA for all values of A <how< the <lability oft he nucl~l. 1ltis shows that there will be att.ructivc nuclcur force~ bctwc ..·o the rn•cll-ons AmJ since-the nudci docs not t.."'ik\J)'\C, the.~ rnrcc.c; u\ll!;t1)Cerunc

of O.E.!A vnry in :t very Jlt!Culi •• r m:wncr from nucle:u~ to for very light nuclides. There is a rnpid incn:,l~C m B.E../J\ f01 light nucle1 w th u notable pcuk utA =-4tt (say for carbon ~ 1 ~. oxygen .. I()). Ttus reflects lhe peculiar Sll.lbilily or the a~pnniclc \OlrucLUre. Above A> 20the B.EJA •s rcmarkahly const:llll lurto IO',<,J 11•is renc<tS

repulsive for very close dislance belween nucleons. The

' ' 111111!

nuclcu~

no •mponnm property of chc nuclear forces. cu lled Sacurauon Ch~U'l:tClcnstics. This

CJ.

indicate thnt R.E. IS nearly prOfKH1ion~lto A 1,c the

nudcar constituents Jntcrnct w1tJ1 only a lim1tcd number of thc1r ntt!!hhour Ol' ch~: nuclca1 forces nre snturmed. Dlsconrmuitics in 1hc B.E. curve were obs:crvcd h) 'cvcrnl workers when I. or N cc:rualt(lthe magi<: number 2, 8. 20. 50. 82. 12ft where B.E. i< very hi~;h.

6. I 0 Q- Value A nuclear n:;u; tion C""dn be :tnalyscd CJmlntitivcly in h!mb. o( tht! ma,.sts, :.nd ~ner~ks of 1he nuclei amlche panicles invol\'ed.1ltc unaly~is of nuclear reac1lons i~ one of the main sources of infonm1lion abou1 nuclear propcrtic,., ·n1c analysis

is same as chemicuJ reaccion cxcepc cbac lbe rclutivistic relacion between mass (&.nd cncJl!Y u1ust be IJ.kcu irllo nccount. Coosidcr;:. nuclear rcuchon n!l)resented by the c.quation ((>.8)

where X is chc cnrgec nucleus••t the bomburding panicle. Y the produce nucleus .r b H1c product particle. II will be i~sumcd thai lhe targ.:l nuc.:lc:u:; X is

ond

initially at rest ~o that it ha.'j no kinelic energy. Since 1.he tot.ill energy of a particle

f ot :uom 1s the Sum o f lhc rest encr#y :md the KnlCIIC energy, the Sltltcmt:nl thor the toral energy is con~rvcd in the nuclear rcac-rion means th'u

(£, + m,c·2 )

M,c" =(I:,

Myr)

(1:,

m,c2 )

(6.~)

herem,, MA. "'"· M,. re:prc~cnt the

mas~eR ollhc lllCidCnl panicle. tnrgct nucle us . produc t pun1Ck and product nuclcu.l\. rc.."\pcchvdy. The 1:.... .., rcprcscm thc kinetic CllCrg.ic."'. flt'rt< ,•,.ntNI \'tall' oj prmhtf'f nuc/(•!ts. om/ rhe em1s.tlmr of mnf'f' than mw paail'lt• 1\ nol takn1 111111 tU'('Otlllf

Now (l represents the Mferencc bet"een the KJOetic energy of the product' of the (CilCtion aud thai of the HICtdL~Ilt particle

I Q = £,. + E, - F., = (M ,v + m , - M r - m,')c

(6. (())

The quantity Q is called lhc "cnergy halnncc" or the rcnctlon or. morc ct.lmnlonly, thC Q· Wl/ur. ff the v:tlue Of Q I~ p<•~iliVC, kHiehC ( 11t:r'gy of Ihe. prOduc l~ I~ gn::;ah;r than that ol the rcac tanL-.: the rcncuon is Lhcn said to be 'exmhermit··. The 1o1al lnttss of Lhc rc:;ac:tonb h ~rcJtcr thun thru ol Lhe products in t.hh c&e. If Lhc v:tluc uf Q i..; nc-g_mivc.., the rc:.cti.1U i~ c::allcd •£n(/01hermir' ft i~ appartnl (rom &Jn (b. I 0) that the 'mulysi~ or nudc:1r reac1ion" can. therefore be used l(' obuun infunnativn nhout chc ma\se~ of nuclei, ubout potnicle energies, or ttbouc Q· values, depending on what infornullk.n 1~ t~Yntlnble. ~nd which quantttic~ cnn he mc:~ured

6.11

Artilicial lhmsmitalion or Artificial Disintegration 7

r:.cl that radioact i \'C :tiQIIh undergo !~opOnHtncous disimegr:uion lecJ In speculation about Lhe po,..-.ib1lity uf cnw~in g the di~imegrauon of 1hc o rdtnllf)' imlclivc nuclides . \Vhen by S<'m'-' anificinl means it is possible to conven one t ype of "'tom Into nnothcr t y(IC then thnt pmcc.s.~ i~ known as ~ut itici altrn.nsmtlluhon or .srtifkiaJ ch!illlh:gmtlon~ 1111:-. prlll.Cl!'' is cntlrcl) different from spontaneous

The

.JisnHcgn•tton

6.12

Ruth erford's Experiment

In 1919 eorlicst experim"nts on :•niticia1 nucl~nr c.lisimegroaion were J>Crfos·med by Ru1hcrford. The disintegrJiion was caused by a-p:miclcs from 1he ..RuC" and resulted in the cmis..c;ion or 3 hs,ghJy cncrgcttc proton from ordinary ni1.t0gcn nuc leus. The disimcgrurion of theN urom due to the bombardmcm of a · panic le may be rcprc.scmcd by an equation analogous to those used for c he mical rcac1ions. 1N 1.c

+ 1 Hc"--) (qF 131 __,.t~0 11 + 1H 1

The a -panicle b ile'' ) •sc~pwrcd by N11rogcn a10m us i1 hils. and o new unSiable compound nuc leus J9P 18] is ronned which emits proton. This unnsmutaHon can

lx rc;prcs~sucd by 1111.! abbrcviilh:d nol•ttino N101 (o.. p)0 11 ,

6. 13

Artificial Radioactivity and Artificial Radio-Isotopes

In 1934 Curie and Jolio1 while studing lhe errcct of o p;ltlicle b<lmbardmenl on

the light clcmcms Jll..c: Al. B. Mg ubst!rvcd that the product of U1c induced nuclear tr.msmutation arc also radioactive. ·fbe elements bombarded by <X-~uiidcs <:Outioued lt1 t:mil r.u.liation (Proton. Neutrorl), ~·~ expected from the known (I}. p ), ( Cl, 11) fC,tCtionscvcn when I hi! soure~ or t;Y-pantcles hnd been removed.

In oddotion to lhcsc panicles. positiv~ electrons I.e. positrons were nlso observed. (+vc) clecl ron or poshroo ~~ 1J1c fund(mlemal pan ide \\ ho~c rest ml}s)_ is the ~arne ~t~ that of an cl..::ctron anti whose charge ha& the same mngniwde but opJK>$1te stgn from lhat of the el<:c"l!on. ll was o~.J so observed that the nue of emission of positrons. $1'nd u ~tHy dccrc:..t.I\Cd with tiruc, tt!- in the C!l.Sc! of nruuml rudionctive elements C.V =Not.~'). They thererore concluded that the product

nudeus formed ht the ra.. ,,. reae110n tn each case wus on unstah1e nucftde. i.e.

the product of nuclear tmBSffiULation IS rndio3Clt VC wluch then d1sintcgrntcS Wllh 'he emission or a positron Thjs proct:~S 10 which a sw.blc nuclcu~ changt:d I IllO ••radwocrn•e r.tmop~" by some anificial mc~ms i ~ called "anificial or lnducetl nultoarttvit)'~. This process ts cnt1rely differem frorn 1he ssx.nuoncvu~ or nalural rad,oactiVIty. The whole pro.:es.• for AI can be cxpla111cd ._, follows: n Af~'7 + ~ He"~ [ t\ P ' 1 J ~ 1\" p "'r

--+ t.tSi "" +

t\ piO"'

+ on 1

Heu

nucleu.;;; nller l."rtptur ing the a-pardcle is convened ioto an isotope of Phosphorous t 1 .y'~~·) '"'th lhc ~jecltVJI of :1 n~utron ·n,e Phc)sphorou~ ( 1sP30") so

11lc AI

produced is not stable ~nd is n radto-isotope which disontcgrotes sponl(~neously 31ld fOnllS a S1~tbfe I~OlOpe of StliCOtl (uSil(J} With the emisSIOn Of 0. poSitrOn (.,e•). Some olhcr reaction~ for an_ificml r.sdion i!Clivilies

~trc:

I. s B10 + 2Hc" ~bN 1 .. )~ 1N 11;· +on 1

1N 1 to ~ t~C 11 + l. 11 Na, :.l + 2He 4 t ;\

1 N 1"

11 e

-t nAI!t~•

+ un 1

A ly.· ~ 12 M~ 26 l- . 1c 0

1 HC

9 pa~ ~

11F1,..

+ on 1 "on + .. ,co

All the e1ements with • mark :.re the anifida1

r~dio-i~otopcs

or that respective

clement, , 1c0 is the po:;ilron where~ _1c0 is n:fcn:d to as electron.

The s tudy of the n.u.lioncsivily of the :tnllicially m3dc n10mic nuclcis, used w cltuify lhe concepts of constitution and stability of nuclei. The artificial rudio nuclides will dcc3y either by cl eccl'()n emission, or p<:•sirron emis.liion or orbil:ll

electron capture Ucpet1d.s on Lhc energy available for the disintegration. The nuclear reacrions mduced by protons. deutrons~ neutrons and photons can also result 1n radioacuve produciS. 'Tltere is some corel:ujon between the mdioactivity or un ortiticialnuclide llnd tho tr.~nsfonnation by means or which il is produced.

»·

Electron emission is common for activitie.• produced by (11. (11. p). (11, a) und (d, p) reactions Since these reactions decrease th~ +ve charge to nt(t.-.s raho o l the nucleus.

.aQtn'' !o(n. y) "yln116': .lollltt• -; SQSnll6 + ,e~~.

,N"Cu. Pl6C 14 ·; .cw -> 1 N" + 1c0• Posilmn cmi:;,ion

IS co mm~n

for ac1i vi1y produced by

(fl.

(J. 11) and ( y. ul rcac1ions. \\hlc.h increase lhe (+vc) t;htllg\!

r,. (p. 11 ). (a. 11).

tt)

nli.t'~

n.ttio of the

nuclc.u\.

.c"(p. y' , Nu·: 7N13.......c'' + • 1c" 111 Ni$~'(p.n) l~Cu'ti·: :!oJcu.ss·

~ 28N iss + , 1\!0

rc:>ction< u'ually lc:•d 10 '"'l>lc pnlducos. fhb <llscovery of un1ficml or induced mdioocuvioy by l<llil>l and Curie. in ttJ1.4 .;tanct..l new linl' of research and hundrcd.s or rndiom:llvc nuc1idc~ ha\'c.: nm\ been tntlliC by vuriou~ ntcthod~. Say (or example Iodine h:t.\ only one '1ablc 'fM:cie.,.. ~,1 1 17 conl:tinin~ 53 promns .md 7d neutron~. Tht!rc arc ho wc\•cr 17 tlnilki:olly nodio:oclivc isotor.cs possible. contuinong from 6K to 86 ncutroM. The ln\'C..\tigation of lhc. r.ult:thOilS frun1 I he naturnl nnd nr11ficiul rm.lin nuclides hat. shtlWll Ihat. the nucleu\ h3!. energy levels analogous lo the atomic e nergy len· h . Nudc;u 'pcctru:-.op<:opy. which tica l~ with the identification nntl cla\.sificmjon of 1hc~c level... j, an impunant source or infonnmion about lht !Mm:lurc uf the nuclt.!us. At prc ..cnt nearly 1200 rndio nucl ide..~ lt:Jvc h<.-en idcmilicd.

The (IX. I')· (f'· u) und (d.

6.14 Radio-Isotopes of Transuranium Elements All dcmclll!\ \\hich hn\'c Yi!lues uf Z gn:aler than 92 arc c~dlcd tntn~ur.mium clement'> hcc.u.to;;c 1hcy lie hcy(uld 92U238 in 1hc periodic Ulblc. 11\C fil"\t vf these.:. Neptumum \'-''Is dclectcd when a beam of slow ncutrlln is mcident on 'l':!U!.\11 then the C()MIUOil radio-i~OtOpc U:J? i< fOm\ttJ whiCh gi Vt$ {J i!mi ...Mt)l\ IH J)tUdUCC neptunium (q 1Npm) fZ = 93). Neptunium cmils p· panicle.' 'JlOnluncously and t.:haugc_, illW l'lUh.lntUIU c.uPu 2-w). the 94th c::lcrncrn. In thi_,.. wuy new member' ur thl" pl•rlodit: tahlc ~rc incre:bing. ,au~~ + ot'' ~ tu U ll')· + Y .,2u~w· -+•\Np'2w•

~1Np'-' • ~ cuPu1311 9

6.15

+ ~teo + ..1c0

T= 23 min T = 2.3 dny

Uses of Radio-Isotopes

Rudie~~ isotopes

ure used in diiTcrl!m fields. The impotunt :.1pplicntions of mdio-

l$otopcs depend• 0 11 the fnCIIhalthc chemical properties of Ihe radio-osolopc of a £1V(n elcmenl ore essentially identical. But a radio-isotope can be detected cm.ily by lb r-.tdiOaCLivlly nnd st;.iblc isotope by a mass spectrometer. Radiot'IIOlOpcs ure used in diffcrem (jefl.ls. ns rollows:

6. 15.1 In Biologi<'al Field I When u plnnl grow•. It >bsorbs Phosphorus ooth Crom the <oil and from rcnilil.Cr. In urdcr co ~now, wh:H is lhe efft.:CI or ft:nili7.cr on the planl . h ·~ lmponnnt to k now wh:u propon·ion of Phosphoruc: comes from cuch 5ource~ If

rodio-isowpe is us1.-d in fenilizcr the exact proportion will come out easily.

Rmlirmrth•lt~· mul Nttdrc~r

2. Similarly. for bl<>>d

lran~fu<i<>n

Rrnctions 375

il is holpful to dc1ec1 whether the given

blood is s uitable for the palicnl or noL

6.15.2 In Medical World J. RJdio i~Otopcs have been used to locale and detect 1hc presence of turnouli>, particulnrly hrain tumours which an: difficult to ddccL 2 . Radio .sodium ha~ been used 10 swdy Ctt.\C.' o f restricted circulation of

blood.

Pumping action <1f the heart has been ..tudled hy u'ing. mclio-sodiurn ur

n.dio-ionlldinc.

6. 15.3 In lndustriol l'ield Radio isotopes arc use<i in inclustrinl field. I. Alloys arc frequently s ubjected to diiTcrcm trc:ttmc ms such :as :mne~ ling. quenchi11g etc. Rndio-iso1ope:s have bct:'n uS<.·.d to liiH.t the effect of such treauncnt. 2. The self diffusion in ntctnl. i.e. movement of nron1s in merru withjo the

CI)'St•'l I:Ulice has be~n sludicd by radio-isotopes. 3. Uniformi1y of mixing during blending of differe nt m:atcrials. has been achieved by labelling one of the conslitucnts with r::u.fioactivc !racer. Carbon Oalin~ In G~olo~ic:ol Field has three 1mpon:un ISOtopes 12. IJ. 1·1 ha\•ing relauve abundonccs of ~~.89%, 1. 11 (_ij :lOd ZCn). rcSpCCIIVCiy. ()r lhC:\C (" 1" 1:0, un:,lable, It disintegrateS h)' jJ cmis~io n a~ 6.15.4

C'~rhon

•'" -+ 1N" + fJ 1111! b:Jsi~ a~stunplion of1hc carb\111 datin£ method is th;tl the relative a.bundnncc

of c:trbon isolopes has remained unchanged for last f..::w thollS<lnd yca1;,. Wlt<.!n n 1i\'ing organism dies. iL~ intake of co:u·bun cea~c:. and the amount of rndioactt vc C1" in it ~ec~~a:,~;~ contmuoLLo;l y. A dctcm1in~uior1 uf iL' pr.;~.;nt C1" content per gram of substance, IOgethC-t with II knowledge or iL!to half life, yields the ~lf;C: Of Lhc sample. The concentration o f C'd in nil li ving pl;uH~ i!> the !tame due to the faclthnllhc COl l:lkcn rrum lh~ :umosphcre comain; a COll<13n1 quanlily But when :1 living plant dies ilno longer lakos in C01 nnd >Utrb to decay by {Jt mi<.•ion with hull' life :r,n} ol' lhc value 5730 ± 30 yl's. l'~y lh<ll way one can calculate 1hc time of it.~ deo:uh. lt.l!o follow:.

ore".

We know

;/!

A = decay cons1. = 0 93 , IJJ

T 111 = 5730 ± 30 yrs.

wlu:rc N =-present activity COUntS Of CH of the Old ~pecimen

Nu = nctivity a1 the time of de;,Hh 1 =- time pltsscd ufLCr dea th No. the originill count number u1 the time of death, i~ the sumc as present count mte of the {J- emission from nny (jving maucr. Hence. 1 c::m he determined.

376

Engmet!riiiR PhV.\' it',\

Whenever other rclioblc nh.:lhods for dcLcnnining t.hc age of such :,.ample~ wen: nvailahle. Ihe: l\\.'0 mcthod-- .(pvc t,;4)11Sislcnt resuh. Ages of such sample.\ cx•end upto 5000 year~.

6. 16

Nuclear Rellctions

Ocpcndmg UJ~)IJ Lhc nature or projectile panicle and outgoing panicle. the v~rinu~ nuclear re;tctinm. :1re cla~o.,.ificcl :'H. follow.s: fa ) 'l'rtlO!tmutation b)

I C(.( -

a ..PJ:irtldc

p) rc~tclion

•rt~e gencrnl (a- fl} rc:lct•on '"'

,X"+ :l~c"

,.Aiz' + 2.

(a - rt)

_, I t. 2C n" 44 l ~ ,q Y"~.-3 +

11-1

,uc• ... I,P"I ... ,.s;w + ,H'

reaction

·n,c gcn.:ral (a - n) reaction i.s tX"

,l ie" - • 1,, 1.Cn"t41 _, u 1 y"-+l + 0 n1 , Be"+ : Ho' -> I•C"J -. 6C12 + un' Tlu~ (tx - n) rcnclion i~ w..:ll kn\•wn forth~ d~tc.ction o l n new p:miclc neutron (0n1) w11h large mas-. and no charge. dnne by Chadwick m 1932. t

(b) Trnnsmutation hy l'mton I ~~· - a) rcuction 'fhc gcllcr.tl c p. a) rcacliou b. 1XA + 1H' -ti1.. 1CnA•J 1 ~:t ·•Y"' J + Jle.t ,Li1 + 1li 1 -,j,BoAI->2He' + 2He''

l11il't (/J - a) reaction prm·idcd nne of the earliest <luanutati\'C proot \ o( the \'Oiidit) of Em!.tcm's rnass e nergy relationship.

2. (p - n} rcacth.m The ~cneml type is

tX" + 111 1 ~ In (p - n) reaction~. endothermic.

Cn"'•'l ~HI Y"+un 1

[ ,.1

,,n'

+ 1H -+ (6C 121-+ 6C 11 + the mass change i.s usually (-\'c).

3. (/1 .... Yl reuc1ion The gcncml type •s 7X"

+ 1H1 -t ll+,Cn..,..11-+ ,.1VA, I+ y

,LI' + 1H1 -> ),Bc8)-> ,Bo8 + y (c) ··l 'runsmul.n tion by Oeurr ou.s

l. (<I - a) reaction The g~nl!ntl type is

1he reactions :tre

RtufitHlrtivlry tmtl Nudear R~nrtlrm..f

,.X"+ 1111 -Jo f1

•

1CnA•l1 -+

377

.,_1yA-! + l H e 4

,Oib + ,H~ _, f"tPu' f -4 1NI" + l Hc"

The

m~~

change

usuully in

(d -

a) retiCiion (+vc) so the reaction!-. are

111

general ..:xothcnuic.

2. (c/ p) o:::.ctiOrl 111e gencml type h. ,X' + ,Hl -l(,. ,CnA•ZI - 1 ,XA·I + ,H'

.c'

+ , ~1 ~ (,N"I-+ 1

.c" + oll 1

Here in (tl- pl reacticn ISOtopes will ronn. The Q value for thc.."iC reactions IS uso<llly f+ve) so 1h~ rc:•cuons ure an general exolhenntc.

(1/ - II) I'CIICIIOn

The gcm:.ral type b

z.X" + ,112 - > 1H, Cn"·~r -+ yA•a + .,n' t.C11 + 1 H~ _,!,Nul_,. , N11 + un' (d) Tl"llnsmutation h) Neutron I, (11

a) ll.!m;IICIIl

The gcncrnl

I) pc

is 1

X' + un 1 ~ t.._Cn" .. 11 ~ t~~ yA -.' + 2 Hc~

,Lo' + un 1 -+ j,U1) - > 111 3 + 1He' 2. (11 - p) nmclton 1l1e ~encmJ l)(lC '' ,XA +on' 111 7N

-t

t,.C n"' 1-+ z.-t Y" + ,H

+ i>'l 1 -+ IJNu ) - ) ,.C1.e + , H 1

3. (u- 2u) reaction

The genor.ol 1ype i•

.,XA + gn' -; ll.CnAII)

txA- 1

+ on'+ onI

,AI17 • .,, • --> I ,AI281-+ 0 AI26 + 2.,n 1

The OltlSS chnrge tn (u cndothcnnic. 4. (fl - y) rc~JcLiOn

The gcncroJ typo is

2n) reac1ion ts :tlways (- ve) 5:o lhc I'Cachon is 111 geth.:rnl

11 1::, ihe c.:onHnoncsl proccM wh1ch results from neutron cap!Ured 1n r.u.lion<:tive c;.aphtrc. Compound nucleus thu:-; fonncd cmito;; o ne o r more ·f·ri.l)'S :•nd final nucleu' 1~ ;~n isowpc vftht ~~•rgcl nucleus. T he Qvalue is a lway~ (+\'e). T hus thcy) reacllon is e~o1hernuc " 'llh <·xccs~ cnt.•rgy bemg carru:d away be "(-rnys.

(tl -

lli\1!7- un I _,. f u i\111\J - ) I \All~ + 11i

+ 0 n --< ( 1 11 1 --+ 11-1

+ 1'

Th< mdtuocti\'c cap1u11: of ~1011 IMllron uf1cn n:~ulb in pmdu•L nurlei. whirh .m:. nl~o r.Jditlaclivc. '\0 1hi,' redCiil"n is one of Lhe mUM importunl ~ource or ~an afichLI

rndiO!ICiive nuclid~::;:.

, XA + )'--+ (,CnAj _,,X A I +on'

.. u~ ~ + Y4l,l3c<il _. JBc3 + l)n 1 4

Q \:due i" (- vc) 2. (

~o lh~ rcll~tion i~

cndCtlhemlic.

f') reaction

The gcnernl l )'JH..:. is 7X A +

y-> 11CnAf

1YA

+ 1 1i 1

1\Mgl."i + y-+ ( 1,,MgL'-) ~ uNaH + 1111

It ha!> been seen thai same nuclide!\ c an he lmn-.muu;d m a number of diOCn:nt wuys. depending upon the }):tniclc U.!\Cd 10 JU'oducc lm."ttml:tliOrl ;md upoo lbC p~trtich.~ ~iven

6.17

off during tre rcacuon.

Theory of Nuclear Fission7

lllc iaucgnuion prucC!-s in ~·hich hcav)' nm: h.•u'- :1flcr e-:.tpumng :1 neutron. splits up in1o 1wo ligJtter neuclei of nearly equal masse$ i,; c:lllcd fission of the nucleus Of nuc/rnr jiS.\iQn for CXUIUJ>h:

Whe:n 1h1s fis..~1on occurs, a large amount of energy~~ relemK:d wrlh lite c nliS.SIOn

of nculron.). which produce funhcr fission. 1l1is energy tS l..nown ns nudenr ..:.nc1·gy or tis!tion ~ncrgy. Some or Lhe prorK:.nic.s of nudc:;tr forces (~uur.nion. shon range) are annlogous 10 the propcrtic...\ of the force.s w hich hold u liquid drop togclhcr. foll!nl.!c a uucleus m:1y be considered 10 be !ln::tlogou!l. 10 !i dtol) of uncuntpn:ssihle lluid C1f very high d~n>ily C~ 1014 gkc). This idcll ha> been u•cd in 1939 by Bohr and Whee ler.

Logcthc.r with other clas~ica l ide•' \UCh

11~

eloctroM4111C' repulsion nnd ,urfac:c

lension. lo explain fission proct.u wlth thtt ht tp of Uquid tlmp mrulr>l. In the 'Pheric:.l l i~uid drop nuclcu>, the shape uf the drop depend> on

Rl,diQlt<'IIWty and Nucltar Rrorrwn.,.

379

balance mvol,'ing the surf"cc tension fore~ und the coulomb repulsive: lorccs. [(energy j~ added 10 tl1c drop. US Ill the fonn Qf lhe CXCitHl iOn energy fC$iulliJl8-

(rom the C!lplure o( ;1 dow ncutrOil, O!t~clllations nrc SCI up within 1he drop. 11l<:SC tend lO di"H.H1 Ute sph c ru~:ll shape. so thai 1he drop nmy become e l hps01dal m

.shape. The surfaee ccnsaon forces trnd to make the drop rcwm Hl ih origin:1l shupe. While the C}lCiHtlion energy tends to distort the ~hupe l-lill further lr lhc excit;uion cne'8.Y is suflicic:mly large, the drOJ) may auaiu the shupe of;~ <.lumb bell 11H~ coulomb repuJsJvc ft1rcc;,. m01y rhcn pu.;h the two "hell\;'' :tp:m urnill they split into two sntll l druJ" Hc.wter nuclei (large A) hove lurger volume ,md they arc lc>S stable. •light<<! provocation from the ouL<idc (Fig. 6.7) cau•c ullimalc(hsmplion olthc nucleus inh) l\\OOr more frng.mcnts which 0)' (jpan :lt high spe.c:tf~. 111i:o- is lnown lJ,\fll'l'irJtt and a large ammmt of energy i.~ rrlea·wd ;" fi:nhm pmf't<.S.\. T11c product nucUUc~ rnu:-.1 be in highly exei1ed Male' .u the inMant of tiss10n. Some uf thi!<- cn~rg) i< rcli!al<ICd o.lmo.\t immcdilllc.-1)1 and carril:d oway by the prompt neutro n~. The remaintng e~cess energy wi II l>c r<lc.,,cd by neutron~. or a-purlick;l- or /S-tlccily-.: ur )Lruy ~mi:,~ion .

000 8 fig. (,,7

UquJd droll

m~drl

(or nud~Ar rlS.'iiOn

However 1f the cxeHnuon \!1\ergy is not large enough the clllpsou.l w1ll n:~curn 10 1he spherical !iht•pt. lo th:u ca~ e"citntion energy is given out in the fonn of

y.rnys and the procc}s becomes one of the.

rndio~•ctive

capture process rocher

thnn liSSIOil procC))S. The value of critical dcrorm!ltion energy £critical was rirs1 cakul:ned by Bohr and Wheeler oo ahc liquid drop modd :lnd from chat they derived the COndition tQr ~J)OOHH'ICVVS process :l\; Z2/A ~ 4). Tius ShOWS U131 require..~ more

energy thW1 Ul)!l 10 tniliGtC fiSSIQO , It is now known that ns~ilon con be produc-ed ror various heo:.vy noel~• under different conditiOns. Uranaum nuclei, wl-k·n burnbard<.-d with neuu-on~ undergoes lission and ic split,. into two nuclei of imcnncdime :uornic weight. h w:ts round thnt ~lOW OCUltOO CJlU~C rt,SIOil Of U:US but OOL of U231 , fns1 neutrOn5 wilh energies greater than one MrV. cause fission oflx.11h U:J-S and Ul.'8•ThQrilml und Po 111 undergo fis.~ion hut only wnh fast neutron•. Some heavy nuclei hnve been found to undergo "Spnntan..-ous lis..~ion" In this process. th.; nucleu~ divide!) :tutomatic:llly in the g."t>und !'I talc wi1hou1 bomhardmcnt by pan ides from ouLSidc. CXCil3h011

Fission J>rO<Juets Due to (i~))ion the heavy nuclei can be loplit up in many difl'crcnt

way~.

1llc

Uranium nucleus is c:1p:thle of spliuing in over 40 di rrerent way~. Abou197il of the uiD nuclei undergoing n~~ion y ield products which ralls into two groups, 3

"hght" group (A o 8$ 10 104) and :o ' heavy· group (A o 130 to t49), which is cle:tr from following rencti<>ns.

U2l> + un 1 _.[U 23•j _. Mo•s + La 139 + ~n 1 + Q

uns + on I

....

lu'-"'1 .... ,.,Ba 1" + ,.Kr"2 + 3nn I + Q

Arter fissinn. the lis~tCln producb nrc m u h1ghly excited Mmc and have too m;lny ncu1ron.s ror stability. Such an uns1able nucleus nugh1 be expected w approach

smbllity hy: either (I) electron etmss1on or \2) 1r the cxcuation energy is h1gh enough, by ejection of nne or more nculmn : 11 ho.s been found exr>erimcntaJiy thai both Of lhcsc proCC..'i~CS OCCUr. I f•,~ion frag.mcnl~ wh1ch dccny by clccuon cmis.s1on. They ~tan a ~bort radioacti\'C series i.nvohing the .successtve ema'l.sion o f electron~ unull they 1C-:lCh hl u ~tatic f:tablc prvduct These serres ore called fiss1on dcc:.1y series. ln above CC!UOlJOn Mc)JS and l..'1 139 nrc the st:iblc producls. An example or fission ~t.:ncs u l one rission produc t is a." follows

2 N~utron cmJSS"JOn 1n fis~ion: It h t1wo1;.ht I hut in r.~~ion. compfJund nucleus HJ1.'-f•). first split into t wll frngmcnts. each of which hn~ I()(~ m;my neutron~ for !l l ~1bili ty. und also execs~ energy (6 MeV or rnnrc) needed 10 expel :1 neutron. 11lC cxcih.:tl. UllStab1c nuclcm. cons{'quently ejects unc or more ncutmns with }'r~yr. within n very short lime aflc1 it~ fonnation. T11i~ nJc:t IScons1xHutt with cxperimemal

result. £nerg_' Release in Fission One urI he most ~trikmg prupcr1 i~s of Lhc n.. ~iun prOCCS!I IS Ihe maJ;-nitudc of the cncrg)' released per fis.."ion. which is ahout 200 MeV as compared with ~cvcral MeV for other nuclear rcKiion. An estimate: of Lhc amount or energy rdcasc.d per n~,inn c:.n be m:,dc hy con~idcring the blmlin~ l'OCrg)' CUr\'C (Pig_6.6). Til e value ol IJte:a\•emgc bindingt:nrrgy per panicle hac. !I h1••ad ma~imumt1f:1h-<1ut8A MeV

In th~ range of mass number• from 80 tn 150 .1nd 11 has hccn shown thai nearly :til tlf th"~ fission protlu\!b hos ml'~ nunlbcr~ m tim~ mng~ . The: uvcmgc B.E. per pan icle i~ about 7...$ MeV in the ncig_hbourthood ul ul':mium. l lencc.: nverttgc B.E. per p11niclc is aboUI 0.9 MeV grcmc r in Lhc fi'i$ion l'mdu~L\. thnn in the compound nuclcu' I U 216 ) ;ond the exec>;, 0.9 MeV, i~ lib<:mtcd 111 th~ fission pro<:css. The total amount of cner~y released per lission shnultl be roughly equ.ollo the product oft he number of p;uticb ('236) multiplied b) the execS\ B E.lparticlc (0.9 M eV) i.e

236 x 0.9

1'hc aotal

20<1 MeV

en~rgy

lll:C<!IC-' Of

released per fi.ssion can also be colcul:ned from thl! nuclear (U"6 ) and :1 typical pair or lission products in the followmg way.

Considering the fission equation

ulJ> +- on 1 -. IU1·\6J , Mo'}~ + Ln 1 ~~ + 2r.n 1 Atomoc mass of um = 235. 124 a.m.u. Atomic ma.""' Clf 0n1 =1.009 a.m.u. Total mass or reactants = 236.133 o.m.u.

R.mlhm<:th•lfy mul Nm.:lt:ot RcuttinnJ 381

Atomac mn..~.:; of La L''~ Atomu: m~ nl foihlQ<i

Atomtc mass of ~n 1 Tol!al

nms~

=138.955 n.m.u. -=

9-1.946 u.m.u.

2.0 18 a.m.u.

--of prcducts =235.9 19 a.m4u.

From abo\'e twn cotkulauon~ we get ··Q-,•alue.. and amount tt( cncrg) n.·lc;t\Cd pl'r fi"~l<m. c:m tl~: c:a1cul:ucd frtun cqu:.auon (6.10t a'

Q " (MiL'~ <lf the reactan~ - Ma" uf the pmduCI\) x r'

=(236. (33 Sene~

Q ''

n; l e~~cd

po~lh\'e ~tl

235.9 1'1)

lhc reacthm

•~

931

~leV

exothcnnh.: nnd the anmunt nf energy

per fis..,ion is

£:().214><93 1

1'18MoV

2U()McV

1 a.rn.u. = 931 MoV

whcrt:

Although there .srL" :11 lcm:a 30 Uirtc.rcnt way' m which the Ul11'1JX1Und nuclt.!th lUJ-'6 l \::m d i\•ide. b•JI the mass: excess i"' appwximutely the \tune for all the~..: pr~t·"...c' and 200 MeV i~ the avernge nmount of ~llt:l'g)' rdc.J ...cd ~r lis:--1\ln. ns cukulnh:d in thi.!\ wuy which i:\ in good ·•grccmcnt with C~pt'nmrntnl votluc

6.18

Nudear l' ission as » Source of F.ncr)!y

,sJnmlnl or Crtcr~) rc!Ca.....Cd 10 fi~'lol(nl, togethe-r Willi the cmi,,u)U of more thnn one neutron. has made il possible hl uic the fi~s ion procc.'s a.~; a M•urce nf cn.:rgy. The .:rnb)iun. on thC! 3\'C-r.lgc. of 2.5 ncutwm. in lht• (j,,.ion of u~'~

11h.!

lutgc

nu.:Jcu~o. JlCnuit~ :1ch:•in reaction 111 \.\1)\lch t hc~c ncutrcuh produce more fi,,ion' .tnd more neutron< and so on. Under some condition•. the ntunbcl'l> of r.ss10n and neuiH'Ib im:rea,c-. 1.!\pnne.nliaJiy with lilllC htc3USt 1.!.1\!h fi't-...,IUI\ f'll'odUCC:o- n\M~ ncullnn't ttmn the lUlC nb:-,.orbcd. and the .tmount nf t.!ncrgy rclc.J'Ctl can ~tune cnornwu ... The- time inten•al between ..ucce"~:sivc gcrlt:mtion uf fi~,ion~ can be ' 'Cf) ~m:tll. fmction of a second and Lhc energy released in the chain reaction can take the form of ::u· explosi ve: the. result js au •·mnm bomb.. This is ca.Jietl unco~~trolltd}ission . Under other conditions lhe chain reaction can be controlled. und u .stendy sl~tlt: ceo be ouamcd in which just tiS muny neutmn.' ure produced per unu timc as nrc uscl.l up. This is called "controlled fi~.stoal" The mtc m which fis!'lion occur and cr.crgy is released is kcpl consum1. and Lh..: result is a ..:hntn n:ac1io a~ pile. or Nurlt•nr Rl!ltelor. which c::tn be used :ls ~~ source of n eu t ron~ or o( nuclear power.

Nur/ror rncrg~': llu: amount of e-nergy released by the complclc li~ion or I nf Ur:anium can be ~;o,ulcultue:d in 1hc following wny·

l:ncrgy rcleas.:d/Fission = ~00 Mev So IOH~ energy released per lls.ion = £ a

200 X 1.6 X 10

Now "''o~a, J'~ N•wober =N

= 200 Mev

l<f' a 3.2 >< 10-ll Joules or Won sec,

=6.02 >< 10'6 per kt: i\tQm

ihu' energy l't:lc-n:c.cd hy the n~~h'ln or I ~ g A 10m ol U1

E,. 6 .02

11111'

~.2

10 ",. 1 .9~

t., or 2..15 kg of U1\' i'

10 1" Joule;

lienee amou1u of cncrg) "t:ll'.a:-.cd hum I kg(= m) or ll 11' Ill

N F./A= I

I •n

)( w••,n; =8.2 "

So Totnl P<>wer output per dtt)

IO" Joule• <If wnu ,ec

mN E P = -..- T 1

= I X (>.Ul X Ill""

)( J~)(- HI

whcr1.•

t\ -=- A•omic ma.s.... of

u!'., -= 2J5

• c.

I' = 11 f = 9.48 x 10' W.ttt

2>5

X 2~

>< ItO X ()()

lien,· b) complete .t:ty.

1000 M wall (appHl,\ 1

(lt. ll 1

fl'""" con '"PPIY appro•. I000 M watt or 1'"" a/

1:./crtdcil)' Bt(ll;,.ulwtt c.~· If thl" [lCl\\ c:r out pu1 hy tis_,ion i'> L'h.anget.l Hl dcc1rid1y.

:11 ~~ "0''4- ccmvcs-..i•"'IH cflincnc:y t = 'I L Th~n cli!l' trn pll\\l'f ~CUI;:.Illl\..~1

rn·ml I I.;; t lf

.. ,c;

mN £

= p = '1 A

I.C Elc-.:u·u,; (".1\\er p:m:r.llcd tnml I kg ol u~,, With 30~ cflic:lcncy x 'I= 1(100 x !IJ ~IX! M 11 :m/Drty

46 L!i

= p =10()0

Thi:- i~o. rquivalent to 1J1c thermal fk"'wcr plont "h1ch consumes nboor lOU tonncs of coal per dn~. that '' the :.d\ antngc of nucle:ar po\\-c1 (JVcr thc•maii"X)\\C.I. Nuclear a•o"er ...,~ di)ocu,,cJ ;ahfl\t' Ih.; fj,,iuu nr \llh.· l l~-~ nw.::11i!U' rdC<l'IC energy 3.2 X I() I I J nr \Vatt.!'oeC Hcnc.:~. fil'>MOil ntt~ tll ll.:!l\ rnr fll'tlducintt f)UC WUil or ..:lc-ctrk [X)\\t,.'f = 1/3.2 >< 10 ·II = 3. 1 >< Ill" fl<>tllltlscrond I h:nC:l' time n.~~,uirct.l rur .UH! lh .. illn = 1/3. 1 X 1010 - 3.1 X 10 ·~ 1>-CI.'

Sine~;" t hi~ fi!'-, iun l';.tlt.' , ... \'Cry l:!rge ~md l;tr!!c amount fj...,,ion encrg) '" relea..o;ed in Urt CX1tcmeJy t;hOfl IIHt:rVal Of time (• 10-9 \CC), c;;t) il.!'. J)ft'ldUtllml

lead ... to a very JXlwcr(ul explusion unless its rtttt t')f production is <.'ontrollcd .

(>.I'J

T he Contrul kd Chain Rcactiun System

Con( rolled 11:0.."'10 11 dmin fC!ICIIOll arc c,;.scntmJ ror nuclcor rc:acmr. The achiC\'CI11Cnt of ;t chain r'C~ICiion with unuuum tkpcnd!- un ;1 favourable b~tl;mcc nmong (our competang rn-.cc..'....C.:O.l Fit.M<m or umnaum nucl~•. '"'llh 'he cmiS.i'JOn of more neutron.s than ;u\~ captured. 2. Non· I ,,,jon capiUrc or neutron~ by uramum 1. Nou-fh~ion '"'~'JHUr~ tlr nc.u1.rrm, hy other m;ucriotl~. 4 _ l::scupc o f nemrnns wilhom hcing cnplllrtd. J~ I he loi-.~ e>f ncutnm1'-

h) the lttst 1hrct: IJruce!-:-.cs i'o

tc~s

th:tn or cqu:1l Hlthc

Radioacti\'il)' nntl Nctclcor Rr{l(:llnns

383

_:..urplus neutron produced by 1he first. 3 ch:1in reaction occurs: othcrw1sc it docs 001.

One of the mos:1 unpon.am factor m ma1dng favourable condidon for nc·u1ron bahlllCi.' I~ the SIZC ur the sump!<.• If flu• ,ftl,t' tJ/ lht' $11mplt• is ft\'i,\ , IJwu m~ulflm will xn 0 111 1~{ 1/le sump/~! wuhout producmg fi$$1011, on lilt Olhtr hand if ,flU IS wo big llrcu produrtion mtc or nrutnm n·UI bt: mfJre: rhau r·.rt·a,u•, so f'XplosiotJ takc.f J'lon• Thus, there is a cen ain size called the "crliictll .du.. of the snmplc uf:l.nnun, \\h1ch io:. neces~ for the production of n~utron in controlled (.hain

reacuon It should be ju\1 equal 10 their loss by non·lission cnplUrc und c<c:opc nod that help:\ to m:unt:un 3 chain reaction. The calculation for the critical :;i7.e of the so.mplc 1s one of the main problems in rC;,.ttWr' design lh-:.ory

6.20

Basic Idea for Nuclear Reactor 7

A nuclcur reacaor as a de\' ICC in which nuclear fiss10n can take plnc.:c at a controlled r:llc. A nu c l~;1r ~.lctOr CQnl~ins. :.n 3mCH.IOI or fis.sio,wble n~uuml urnruum culled fuel. large enough. so ohao ohe loss of neuoron by loakagc may be noglccocd. Noturol uranoum conwms 98.28~ abundan<'C of and ll.72'.'1 abundance ot U1 \ S Jr IOOnlC :O.JlOil1\tne()tJ~ fi,SIOO OCCUNl, ll wiJI release :tbOut 2_1j fU!< l OCUUOilS wilh average energy 2 Mev. Thcfi.\'!lion cmu·sectiou (probabilily) or1wo •solope~t of llr.ID.IUm u'"' and ul'Ci (or lhe:~e fma OCUI.f(Hil' are ulmOSI ~;uue. Rul 'lllCC aburlllance uf U"1JK 1$ very lnrge. ~o 1he fis..,ion ncmrorl~ cnu~c (unher fiss,on$ WhiC'h Will nminlyoccur ifT U;t.\8;, Tilc...'i;.C OCU1n>OS CUO ~urrcr (l. fi~IOil, (ii) mdi;UiVf.' capture o.nd {iii) cJuslic or mcla:.lic scollcring. Since lhc lasl IWtl pmcc:,:-:c:o; an.: nwr.: p1 obotblc :w .;!hain fi:).,,ion reaclitm h no1 pos..,ible m nuturul Ur.uuum. 9-1Pu 1~9 will he produced 1n a nan .. fission caplure of neutron' by u l.'- :L' 'hown in F1g . 68

- - - - - - - - - - M i l ) CXUJ)C" Ofln:t)'

~\•JI1\k

Wllh

Fig. 6.8 OifTtnol steps O<<urr!n~ lo ll.islon pro<es•

A chain reac1ion in nawrnl urrnnium cnn be made po~si b l c by u~ing modcra1or (i ..;. ne utron s lowing mascrial) along wi1.h naturnl unmium. The runclion of the modern tori~ to ~lnw down the fa~t fission ncutron.'i by collis ions (i.e. to thc mlalisc ohcm).

The fission cro~NCCI.OJ\ or u'-'" ror slow or lh~rmni 1\CUII"OIIS is ptuclicnlly ?.em whereas that t)f U1 i:. very J:nl!t.:. l·ft:nce .. self pmpagating chain reaction

b.:-comcs pos..'iiblc. Hcnv)' wat~r (0:0) and gruphitc have been u:.:cd succcs~rully as moderators with natural uranium because they are light. huve low atomic numher, 1hey con.s idL:rd bly rcducl' the ,;J>l'CIJ l,)f neutrons ut c-tu.:h colli~ion and they have low eross ~ scction for neutron nbsorptifln. When D10 I~; the moderatnr. t1rnnium c:m

be d issolved in it

Th i~

type of reactor is. knO\\ n

...Jwmos~·neous u•t,cwr''.

When ~fi1phitc is U.\cd a!' u moderator. uranium is in the fonn of rods which are disuibiJtCd in t1 r.;gular w:ty thmoghout the ~r.1phitc thereby fonnin~t a lattice.

This kind ofreac1or in Whtch fuel is uranium nnd modernlorgmphilc arc separa1ed is called "ltrtt·mx,.n(·ou.r rr•arwr''.

6.21 Critical Size ror Nuclear Reactor The nLo.ed for a favoumb l~t neutron bnlancc sets cl!nain condi1iom: on the $:ystcm whl'rc c hain re~1cuon 1s occurring. The most 1mpor1ant factor tS the size. If Uranium i~ distributed in a rtgulf'lt' wny throughout the f'ISScmbly. Ihe ncuuon production depends on lhc \'Olumc o f the system (i.e. proportional tor'). whereas the prob~1bi lit y or csCc1pc of neutron. depends on surface area (i.e. proportio nal to ,l). Now i f Ihe

~y~tcm is very sm:lll. 1hcn the surface 10 volume ratio ( =~)

is large. th;H mc.;m;. the rntc of non ~ J'lssion c:tpturc and escape of nculron i.s more than producliOti rntc of IH:utfl•n, mth~tt ca-.l: c hniu tc:tc til)n ~~tllnc)t ~n:\tain.

H ..;n ct~

it depends on the siz~ pf thl! sy:-tcrn. I-'or l:~r,g~r size. grcntcr will be Its radius. sn then ~:-;CaJ~ rate will ht. ,m;alh.:r ll' cump:tred tn production rate. ;md c ht1in reaction will !'u~tnin . Rut if the si1.e i~ vcr) big then production roue of ncutmn \ViJJ be much bigger th~m escapc nr absorption rJtc. which will result in an explosion. ·nms for effective nuclear reactor we need a critical size o f the sys'tem for which production of neutron by fi~sion will be just equa l to their loss by rH''Ht· fission capture nnd escape.

6.22

Essential Pa rts of the Nuclear Reactor

Nucle:1r reactor i~ a device. whe re 1hc nuclear fis~ion is occuring under :1 "ell suswining controlled t hmn l'l' tll~tton :m<.l is used ns t1 high e nergy power supply.

The essential parts of the nuclear reactor arlo!: ( I) l?eactor Core: It b IJtc muin part of the rl·aclor where fi s..~io nablc mute rial.

called reaclo•· fuel like U!'\S. l12.u. Pt•2'Qnrc u~ed. Oue to tlucleur reacUO!l, huge a mount o f hem 1s gencrall!d. Reacror core ~enera lly has a .shape or right circular cylinder with :·• diameter ,r f\!w meters Gcncntlly rucl eJcmcn1s arc m~dc up or rods of uranium. In gencr:ll. reactor core bas fuel eleonems, moder-Jior. conlrol rods ~knd cooling matcn:'tl, housed in a 1,rcssuriscd vessel (Fig. 6.9). (2) Reflcior Moderato,.: The function or moderator is to slow down the ras:t

RatHoactil•if.V tmd Nudt•nr l<rartiom· 385

neutron. 1t should huve high holling point, large scauenng

cro~s.. secuon.

small

ahsorption cross-section and low at<Jrntc number. CommonJy uo:::cd tnodcmh>rs arc heavy wntcr rD20l. gmphile ole. t'1.dnutun

toncrol Nod'

Ileac

Sh1tld1ng

(3) Rtmctor Crmtmi: The comml of lhe thciTilal reactor can be explained by nqu:mt.aty K,.. known nseffective multipltcation factor. whkh t;,;nntrol.s th4! condition of ret~ction at stc::tdy t t;uc. l11c muhiplicntivc rncwr K, rell1- how the n~mmn

concc-nmuion would mcrca.se rrom genCttiUOn w g(n~r:.ttwn. fr no neutron 1t.•"kcJ uut fn:nn Ihe ~y:-,tcru, In orde.r In gel ;t ~.:unlmllcd ch;lin r.:acuon in a reactor. muhjplicalion fuctor K,. should be combined 111 '>VI11C ""') "ith the quantity whtc:h tclb M'll1lCihln! nhout neutron h:•akagc, anJ that i~ ~ ailed Effective Multiplka1ion Factor •K,), which is tJcnncd a' p K, = 1• A+-

where {' = production r:uc of neutron..:

A = obsorption rnte of neutrOib

L c. leak;_tg~ rule neutrons K.. J sready stare. crilical cont.li1 ion K~" > I super critic") K, < I sub critical

Now. us di,;clLssccl c;trticr in Sec. 6.2 1~ produc1ion r:uc is proportion:tllo (?) the volume or the reaclingsystem, whereas lhc. lt!;llagc or CSC~1pe 111lC IS pmponionnl to r 2 , 1hc s-urface area or lhe reac1ing ~yslcm_ lltercfore K

«-ocr

' r'

386

Ettgim•t!ring

/~l,ys Jcs

where r is rntliu~ uf the n:ac:ting system. Thu!\ effective neutron multiplication factor (Kt) depends on r. i.e. the size of the nuclear rcac1ing system. Now 10 make cffecli\'C rnultiplil'Uiion racwr K,.-= l' ror maintaining controlled ~:hain reaction in a nuclear r.:act<.1r. we nectl a critil·aJ size of the system for which production of ncuaron by fission will beju:.t balanced by thl' non~fis::ion cn1>turl" uncJ c::~-cnpc.

Now Pro<hiCIHllt

rau: of ne1.n mns I'= Rate of thsion process F xA\•cmgc number of neutron ~mission per ft.Ssion N P=NF

I,C,

Hence.

K =_l!f_= N(FIA) ' A + L I +( U tl)

"lb~: r:llio /·1A depend' upnn the amount of fhs:ionnblc and oon·fissionnblc

nmtcnul :md On thtil Clll.!-:--,CCiit)ll~ fi~sinn ;md neutron ~;:~lpturt:. In :1 nuell'UI rL"UL"Hir. fi.;,ion nne L' OII be Controlled t'ly C\1ntrol nll.b, !;:Cncnally mndr up nf Cadnuum '" Bvron stc(•l. By ndjusttng the positton ol tit< control rod' 111 tht.!' Cm'l.: l Fig. 6.9). mlc l'lf absorption of excess ncutrun.; c.:m be atiJU~tcd t.t:. Fli\ .:an he t:nntn 1IIN and thu_:;. we can maintained the value of K~;; 1. 10 get contro llt:d fi.;~ion If Kr (. 1. rrc.,h fhsionablc lllUlcriDI should be adtJcd. tJ • R<-m 101 Rt11PfltJr The 1c.1~agc of neutron~~:. from th~: ~ctorc;m h: rcthu:ciJ hy c.urmundwg lJ1c ren.L101' w1th !I reOc:ctor, made of we~tl.. 1lCU11un ab,mher: gruphltc b nftcn u<:ed f01 lhl< purpose. 111c rencctor knock~ the neutron' whtch lca\'C the n:;11.h>r baL:k to it. und the dccrea,cd leakage. reduce.... the cntical ~ir..c of the rcactt,r, with n n--~ult i ng saving of fud. The reactor sy,tcm including rcflecaor, mu't he: cncln)t..OO in :.s shidd, usunlly of L'-Clncn:tc. tc) reduce tiH• inu:n~ity

of the reductit,n of neutron~ and r-mys lca"ing 1he rcac101.

c5• Rrncltlr Ctwlmu: Th.., material used to remove bent produced "Y thsion 01:"1 f;,~t Mit 1' lihcr.ttcd. j, J..nO\\n :a~ rtfl(fur r·t>olunt, The C(}ul.lllt j:o; ~~ncrully

pumpcc.l throu~h the reactor in the fom1 of liquiJ or ga~. h is cin:ulntcd thmu!!hout t.he reactor S<l a.' to main:ab1 a uniform tcmpcr.nurc. The mutcriuls propo~ed for coolant cnn be (I) ordinary or heavy water. (2) liquid metals. (3) org.mic liquids

(hydro-carbons). (4) g!Ue$. Both ordin:lf)' water and ~vy woter nrc good <'OOinnts. us t.hcy '"m '\CI've both us mvc.lcrator and coolant. but doc to lh..:ir l1.1W boihng po1nt. rhey s lullrld he pre...,suriscd.1llc cool:mt should hnvt: the fol lowing properties: I. High U.P.. (2) Higl1>p<!ciflc hem. (3) Easy to pump. (4) Chcop. !5) CltcmJCfill)' ~table .

\\'h en the- e-nergy gener.ucd inn renctor is to be convened imo electric power. it is lrJnsterrcd rrom the coolant to a working liquid. to produce steam or a hot

ga,. l11\! rcgul~111ng vapeur or the gus cfln be used h' gcncrnH~ of turb i n~:~o.

J><>W~r

by means

6.23 Thermal Power Reactor Power rencto" nrc those which arc primarily intended for the production of is prodw;ecJ from the rncrgy rel t~H\cd

u~ublc pj)W~;r. ·n,ey t mns(l"lfll\ the hcnt which

l<ndwacri\•itJ' and Nuc•/rt~r Ht!nction,f

387

m fis..~ion into clccuicily. The hent i~ transferred to a fluid pa:;sing through the core of the reactor. The hot lluid h then passctl through 11 heat cxc.hangcr when! energy is- trnnsfe.rred nod utilized by more or less COD\'tntlon~tl rneans. Tbc busis principle or one IYJ>C of pmver renctor i!-1 "'hm~o•n in Fig. 6 .9. A

quantity or enrichedurnnium in !he fonn or n pure metal. fonns !he centre of the heal energy !.OUfCC. The r.~sion rotc tUJd hence the role or productiou of heat I. which is done hy 1hc energy is contro1Jed by keeping rhc: value of Kf' rnu\•emcn1 of cadmium rods. 1::or decrea.;ing the tempcnuure. th~! cadmium rod.~ ar~ pushed little funhcr co ab~m·b more neutrons 1hf.!reby rcducmg the fission rote !FIA). Por raising the temperuture. they ""' pulled out control rods n liule further. \Vhcn the reoi!CII.lr becomes ~ubcriiiCOI fresh rissiunablt: JJI:ltcriul i~ added. LnJuid sodium is u~d us •• primary cool:111t because n01 only is il a dense m::ucrial with good thcnnal conduc1ivi1y but at n.lso hns very low nb~orption cross-~eclion ror thennal neuLrons.. Soc.Uum is usua11y :llloycd with pmassium w

lower the melting tcn>pcrnture. Tile energy obsorbed by this primary coolant 1S mmsiCrrcd to water in o heat cxcbonl!.cr. The stcnm that 1S gcne.rot\!d dnves u turbmc which is coupled 10 an clccuic gencnuor 11lc electnc power so produced can be used for lighting citie..~ or running rrn:tonc' Ol' for driving ships and subm:tnnc~ or lnrgc plan~.

6.24 Bret."der Reactor 7 The pos~ibilily of the dtwetopmcm or a power indu~t..ry. based on nuclenr fission,

r.ai-.cs the qucsuon of the nv~1i l abi ll ty and Cc.lS1 o f fiss ionnblc matcn:tl. Generally. the fissionable mntaials consitlcrccl have been U2-"t. Pu!l". o.nd none of whtch u.re available muurolly in large amoum~. II would be: u~t.:Hicient to get power on a large scale from the ris~ion ol' uv~ because only 0 .7ll- or IC..Ii.S of the available uranium could be used clirenly. Plutomurn cPu 1 ' 0 ) ha...; been made by the fiSSiOI\ Of U 235 in a reaCIOr CQill::tinmg l l!..\ll• hUl thl~ ('fO<.'CS.S IS CXJ>CUSivc, Similarly, which does not occur m n:uurc, can be nmdc m tt rctK:tur contauung Th'!.l2. Although the problem or availobtltly and cost of nuclear rucls is a sc.riou~ OfiC. {I UOIQUC und ru1narkabJc. solutiOn I.S po~stblt: bet'UU~ of OOC. ol" the nuclear propcnics of the fissio1l process. Ttus pmpcn). is the cmi~si,,n on a1\ average. of more than two ncuuons per fission_ Suppose. for the so~ke of example. th:u 3 ncutr~ms nrc emil ted per fission. One <'~'f these is needed 10 keep 1hc chain rcncuon going on to induce fission in another fuc:l atom. sly an atom of U lU. 0( th..: two n~;utrOn5 that nrc lcll. one

uu'.

um.

may be used to con·,cn an atom of U~18

one of plutonium. leaving one last

neutron. Lf this la.st nt:utrOn could be U!!ocd to produce unocbcr atom of plutonium (Pu2l9) from another :u.om of U 238• then one :1tmn of uu s would lutVe been u~d :and two atoms of Pull9 would be made, le.avmg a profit of one atom of fissionable m:ut:ritd. In mhcr word~. mor~ fluionuhlt> mtJtrrhJ/ W(m/d 1~ prmlll('fil than cot1s11mtd. It is inevitable thut some neutron> should be lost by lenkage or by absorption. bul SO long US more ihan tWO llt!Uiron"i arc produced Ill li,.~iOO lhCtc is a possibility thnL DlOrc nuclear fuel may be produced than is consumed. Thi~ process is called 118retdit~g''. if it could be made to work, n reactor could make new fuel for itself and, in addition, a st<K:kpilc or fiss ionnblc m:ncrial could be

built up for use in Dl:\"' reactors.

In the pmces" of breeding, tis-sinnabll' 1\'l:ltcrinl depends un (\\ o ruatcriuls. on~: of which i< "fissiomlblc" a~d the 01hcr which is ]crlll<". Urnnium·2.18 and l'nZJ? form SUI!h p:lir. !lnd Th!lZ and u!-H Conn mmlhtir pair. Con~itfer Lhc rirst pair

a nJ suppo~c that enough Pul.l? i~ rwajJ,,hle to uchili!\'C fl cham rcucllvn in u system \\hich can be U'-t:d 10 produce po\\o:r. 11le lhtl'rll,ll fj~~iun Pu 1"' yiclt.ls J neutron!., !<.O that if o;omc of th(~sc neutrons could bC' absorbed 10 U1-',. to fonn llltlre Pul-111. o brc~ding C)rle might be ~achi..:vt!d. In thi., \::J~e. ifM i,\ 1/w ferlih· uwtt•rial bccaust' uflhaugfr il i3 ttol t't.,t!lf u.w:full-.• fi.\,\ttmablr, Ina 11 t'tm lw um1't•rt~d imu «good jil.si·unublt- 11uturial, and it is co nceiv~1hlc 1hat a reactor

~y~ie111 c<1uld be buih in whjch more pluwnium Is produced than it.: consumed. ~n,l.! nuc h!~lr propcny ahru d~o:1crmiue.& whether the possibHity of br~cding exists, IS uo1 tl1e value of the number of neu1tons cmiued per fission ( v) hulthc numl>cr o f lh,':Uinm produt..:C-U per ru.sion Obsor'bcd in tl1c fuel ('1). because Lhe nun· lission

capture c)f neutrons by the fuel can be large e nough to interfere seriously with breeding. Ttu: value or '1 fl,r plutonium and dlcrmal llCUII'On.~ i.s 2.08 ± 0.02 nnc.J tum., out to be only shgha1y greater than two. 1lus result seems to ma.k~ impracticaJ the breeding (If Pu:w in n thcrlT'I:ll re:lctor. It is CXJlC:Ctt:d. on Uu!:on.:Ucul ~;round~.

thnt Lh\! rntiu of the li!'o!!oion cross·scction to the total nbsorpiion cms~·~ec1ion :\hUtlltl be do:,er tO unhy at tu~h neutron ('ncrgic~ tlum for ~low neutrons. and that 1J s hc;uld he clo..:e to v in a fa.:u re;u:wr. Consequently. breeding uf Pu 1\0 should be pos.siblc. in~~ l"ns1 neUiron. Pu1.w -U2.1x o;ysaem. A rcacror.thc EApcricnt;ll

Ureedcr Rcac1or. or EUR. has been bUill 10 study the fcasibilily ofpo"<r production and breeding in such u ~yst em.

l11c \'tLiuc uf 11 for U1" ond thcm1ol ncmrons is 2.28 ± 0.02. which rnnlc;\ thchreectintf: ()f U1 " from Thn2 in tJ1emwt reactor sys1cm feasible. kcsearch :md developmcnl work urc 111 p-ogres._~ on such syslc.ms. One de~•sn uwolves 1he u!'c Clf :1 "'OIUUVII Hf U~" 0 .!$04 111 0 20: U,OVthCI IOV()fVCS the USC Ot U SOIUliOn Of u:," Bl in hquJd bbmulh, wiLh graphih! as moderator. The u:J'l Th!1! ~YSICill t,:uuld a lso be u~..:d Ill a fu.':tl reactor. but u greater value of v for Pu-\'' favnurs.thC' U\C of 1h~ latrt:r Hl<.ll~rml rn IU.':tl br.xdt.:r rcuctor:s Ifhrccd10g CuultJ be <~'!hien.:tl, UllS und Thln COuld be COUVt!rted IUIO fiss:JOnuble mmcrinls. The resulliog ancrcus.c 10 ;WII:lblc nuclcM f\IC-b. would be :1 Slcp 111 the

dtrccuon ol economic nuclear power. Much infom\auon 1S no:cded conccm'"g 1hc ems.:\ :\CCtloos for reau•vn~ or fast r~ud uuermedlilh: t=nt:rgy neutron' wuh tission:1blc nnd fcrti lc matcrial:'ii. and much work is needed to be done in this field~

6.25 Ther mo-Nuclear Reactions or Nuclear Fusion Nuclcnr fusion is the process of combining or fusing two lighter nudci imo :t sUiblc and lu:avier nuclide. Wben this process occurs among the ltg.ht clement~.

energy ~~ tl(\1131ly rcle:'l!"C(I because the m~s.:: or the producl nucleus a.s lc~s thun 1he sum of Ihe masses of d1e nuclei which nrc fused. This propcny of 1hc lighl clcmclll'i •s shown 10 the bmdang~energy curv~ (Fig. 6.6) 10 wh1ch B.b./A rises mpidly whlt mtL\S numhcr i11 the region or sm;lll mas.' numbers. Under :1ppropriatc conditions, fusion rc:tclions can lit:M.:r.:uc v~ht :unounl o f energy, amounls rnuclr gre-ater than lhal relea."~;ed in an mom humb l~.lplo.won 1Im• m Ji.t.'i;IJ, pmt'es:.f. Fu~ion ronclion wkes place at very high 1cmpern1ure ( I09•C). soh is nlso called

Rtu/i{J(tt•tiwry am/ Nudt-nr Rt•<J('tium

3~9

tlr~r·mouuclt-w tenNi•m~ Thi~ tlu:mtmmrlf'tlr rcactio11 foJ'uu· til~ lNu·;s oj tlu: 3'fl t:ulletl tltcrmonudeurtxplusitm ur hwlrogtm bomb explosion due 10 fu,. u.)n proce~s. For example when two dcuttons nre broughttugctbcr 10 fonn an ll·particlc the following reacuon tuke~ plnce wilh the liberation of 24 MeV energy.

H 1 .., 1H 1

---t , lt e~

For fusion to ta.ke pluce. thl! componcn1 nuclei mu'l he brough1 w within l0 · 11 em. Jn on:h.:r to :~ppronch l>O clc-.scly. I hey ~hould be impartc...-d high cn~rgil!..' so that two positive!) chnrgccJ tlcutrons may overcome the repulsive force Mid fus.:d together. Tho <lnly prneticol wny of fusing the nuclei together is 10 mise !heir 1Cillpc-ra1Urc LOa cxccs~h·cly high \'ltlue of th~ order of 1 0~°C. l·usirm rt!.llC:tion can tal..f! plttct" at stdlllr tt'fiiJiemturt 1.r. Ott .\U/4 um tm nutlt

6.26 Stellar Thermonuclear l{eaction

The arn<mm vt cllc.rgy mdltlll'.d by sun j,. ea 1026 J/sec. hs age i~ • 5 x 101.1 y~. Hydrogen ond h<lilllll tog<ther form 90~ by weight of sun·· muucr ami the tcmpcrntur~ a1 1hc centre of the sun i:\ J x l07uc. Fusion reaction is thercfur-: con1inuously taking place in fo!un which h the ~ouroc of 1hi., ~tellnr ,•nergy. Two SCI!\ of lhcnmonucl!.!itr rt.!fiC:litm" huve been proposed u~ ~ourccs of ~nl--rgy in the MUI. (I) I"Jroton ..prmon chain (Zl Caroon·uitrogeo rbuin Hc1'c we discu"s proton-proton chain in detail. 6.26. 1 Prolon-Proton Ch ain

Bcthc m ItJ3C)

~u~a~t!sled

1h;.tl m prntun-pmton c.h:un, proton is conLtnuously

1ransfonncd amo helium In 1hc fi~1 'tcp two rro1ons fu.sc logcth~.:r to fom1 01

dcutn:m. rclcu'mf:!- n po'ilmn umJ cm;rgy. t111t + 111 1 -> 1H' +{J' + V+Q) X2

(I)

The dcutron then combine!> with :Jilothcr proton and fonn~ helium ( Hch isotope:,. ( 1 H'

+ 1 H1 -> , He·'+ rl x 2

(2)

Two zHc) then fuse together to produce 2Hc nuclei ,He'+ 211e1 = 1 1le• t 2 1H1 + Q

(.1)

v b, the .. neutrino" proc:lm:.io::d in /J-dt.:cay. :m clectrh:ally m:Uir~tl panicle h:.tving a very o:m:tll ma,:-.. and compared to electron. t.he neutnno m11~!'1 rnny even f.>c tcru. F'4X the third re:tclion 10 CX:\!Ur, c.:lch or the fir.atwc.t r~nctinn' must occur twice. ·!1\c ovtraJI effect of the 'above sh.:ps is In Eqn. {I)

I ~, Ht ..., 2He• + 1{3' + 2y+ 2v+ Q

(4)

Th«: abo,·c.: reaction (4) is cxothcnnic iind nmount of e nergy released hy 1 111~ proces~ can he l.'aJcukued a!'l

Alomic mass or 4 proton or 4 hydrogen Awmk m~t~S

or I helium atom

:nom~

4.0325~ "·"'·" ·

= 4.00387 a.m.u.

DiHCrencc in mass belwc~n r..-:actants ancl producb

= 0.02871 n m.u.

Q b pc.hitivc, so energy rd~:tt-:c..!dlfusic.m ~ 26.7 MeV = -12.7 x 10 B J Smcc UllC grnm or the sun·~ mancr contains about 2 X u¥' proum.~. 1l•us the avndablc energy s upply would be 21.31 x I 0 10 J/~. Such a vast umoun1of energy will be rclca~d from only utc gmm or s un's mutll!t. The ::tbovc reactions of the proton· proton chnin occur" extremely s lowly which is fonunate bccaus.c Ihe sun c;UI then huvc a reasonably lt>ng life.

6.U•. 2

Cl~rbon · Nitrogt• n

Chain

In carbon and nicrogcn chain, we found lhem lo have the rcmarkahlc JltOJl<:ny l lml 11h.:y cnuh.J be lbrmcd in1o o cyde in which c11rbon unLI mr1ogcn nuclei arc-

used up. but 3Ie regcncnucd. Titcsc nul'leJ net a~ :1 c :ll:tlyst in a series of reacuo ns tn which d pi'Oton:. arc converted into n helium nuclt!uS nnd about 26 MeV o f energy (ltC liberGied per reaccion. 0(11

'TI1c scqut.!oCc of r~;•lcljon is

C" + 111 -> N''" + r N n· -. C" + P' -t

C 11 + H 1 - l N 1" + y

N" + 1-1 1 -> ow+ y,

o•s·-> N 1" + 1r +

N1' + H1 - ; C12- +He" ~n1e

overall process will g ive

4,1-1 1 ;

6.27

2He4 + 2P' + 3y+ 2v+ 26 MeV

Comparisons Between Fission nnd Fusion Fission

hiS IOn

Huge om1oun1 of energy released~ A hcaV) nud~u· is sptil up into 1wn nucld (e.g. Mo"'. L;.. 139)

un•

.l The

procc~~-o

il<> pos~ibJe

room

ICillf'CI':IIUI"C

4. The links or lhis process is ncucron.

5. TI1o orh:r~y/nucleon i~ -

0 85 MoV, 6. Availabi lily uf atom.' u.ed (U2" . U~l8) i:- limit\!d and CO~Ily. 7. Mnny isotope... arc rormcd w: J)roducl panic le>.

l. Huge :-.nu)ull1 of energy rdea!)etl.

2. 1\vo lighter nuclei arc ru.~ed wgecher (e.g. ,11 2• 11-1-'J. 3. This proC-cs!- i~ o nly PQSSiblc at vcr)' high 1<mp. mill ions °K.

4. The linlo. iu th1~ J11'C)C~ss is proton. 5. The energy/nucleon - 6.75 MeV. 6 . Avoilobilily .,r ;uom• used ( 1 H' . 1H 3J is unhmited and cheap. 7. In gcm:nal isotope~ :ue not funned.

RadioCICfn•it y and Nudct1r RC'urtimrJ'

391

PROIJLEMS t. 111(' OOmbarJmcm of lithium t$t'l0P(' ,1 •7 ;u 1-e.o;L. lly protem" product;.." 1wo U• part1d.:.. per rc:atlu.m, nu nlhct pani.. k.'. arc fomtc:d ff the enc!J)' uf eac-h rc I)Jnidc produce io, 4) I~ MeV. culcul.•tc tht! c:nc1gy l•f the bornbardmg proton. Oh en 1luu Ma.~ or ,l.J'= 7.01!:1:::32 u.rn.u. MM) of «·j1Qr1aclc • J ,OQ1X7•1 :1m u M:'"-'~ ul JUUiuu :: l .(i08 1-i5 u m.o I ,omu :~11 M eV

Sufl,tw"

111C I'ClK:IIOil 1-.

7_0U~232 ::t m u Atom•c mil\.~ of r.t·pilrhclc = 4 .003874 a.m.u. Atumt~: ma~' til rrnmn = ,H 1 =- I.OOlH·t5 a.m.u.

AIOU IIC Ulit).\ Cll , L1 1 ;

So lhc nub.. dcfc..:l •~ J,,l • 7 01 82~2 + 1,(1(18145

= K.026'177 ~\f:.

(4,()0~~74)

~.0077•1X

0 018(,!9 ;1m u

Q\;tluc= UOIM629x93 1 = l 7_.l..t36McV

ami

where l:r a Rcl'lll1 c u<'-rg) ot tht puKluCI nudcu.'). F., s- 1\. l'-. nf the JUtlduct part.Jdc. 1~·. -:::- K.E nf lite mcidcnt partiCle, K H. or lht' LIJ)!CI

nuclcu~ · ~

ccm'iitdcrcd :a., lCro. :mf.l m cqu:t11on j I) the pn'Kfucl

nucleus ~llld Jlroduct p:miclc Is o;;unc i e. '"'0 a·p.;miclc..ii So K E. of mridcm pro1nn fruml:.~n' f2J and (3l

~.->

£4-= "JI!.,

Energy o l c.tch

t.r·p~HUciC

= IJ. I .S MeV -= J::t

"1F,-:; K e nf tWO (.(_•ptmtcles = JS J.()

M ~.:V

So 1., = K.E. of tm..itJcnt proton= 18.30 - 17.343(, I<. E. of incldCOI rt()fOO -:; 0.9564 MeV 2. In :m llnC:OI!trolled n~sion re:'tclton I m111igr:un ..,r u 2'' fiO:\I(ln~ out in ' '11C mo~oos.con< Clllculoll< ~tr po.!W<I of r•piQSion Gi...,lllhllt the tll¢rgy pnxlltc<'ll per

fis~ion l lo

SoltltiOII ;

200 Me\

A:-conhnt: 10 the: Eqn 6 II, i'<'~A'er out pu1

mN E

,_,-=Ar when.; m ;; Ma.,, C)l U11 ' U'C:d a 10 1 ~111. ,... a A'<ugatd's Number a (1,U! X ut l pc.r gr.uu ;\t•mt. 11 £ • Eneq:y •~l~ased per fissron In Jouk<~ • 200 x 100 ~ 1.6 x lo- 1~ • 3.2 x Joule.!.

ao-

\ c 1\Comu: OliW\ o( U!l):; 235. r=-TilnC 1ft ~C ;- l(l-to \et'

Sop«wt'rofcxplosmn= f':: 10 ·' x6.02x.I0 11 x3.2x 10 235 X 10 -4' • 8.197

X l(lfl

wnn

3. Complcl<" che foliO\\ inE nucl~.nr r"caccion. tJM~~·-+- ._,

.,. ., -"

1 111 -1

~- ~1.• "'" 111 + on 1 1

,oNe: 1 .._ ! 11 .....

? -tt '! +: lie,.

--, . , _ 'J

+ ,,.

Snlutum

I !M~:.' • 'f- l a:t"IS 1~-+ roNc:l' + : •1c 4 !-. ,11 1 -+l.ac•l _,.:He"+ _,11c..a

,,,--+

.~.

'*·

,u•+or'' -, I,H-:1 __, ,B: + hv

A nu<.;fcJ.r cc~c.1nr proc:h.1cc;s 100 M'' o( u~dul dl'~o"lril po"-Cl lltc thermal cffidenc) c•l lhc re.tCIOt I!> 4(Y.; . As~u1 m n• em:r~y rdc:t'l-t.'41 per fi_,,iun m hl- 2:00 Me\ , rind the rn:t.":o; uf l1 7 , .. 111 kt;.tl.ln,..umr-d m tlr!t lla~

A\ l)g:trd\. Nn :::. (,,01

1n 2() per LJ.!. iUrtlll

Sn!utmn t\ccnnllng to 1hc Eqn (, 12. pnwcr om pm \\ 11h -'Ul' efflcicnc) mN -£ p;: ,, __ ,\ T

where') • cffincncy = 0.4. m = Mtt~~of U1Y' uwd = ''''. N =- A\'ogard's Number l>m X Ill"' pel kg Al<lm. ,.. = Fner,j:y rel<>~~-:d per n..~it'h In Jc,ulc< • 2.00 )( I (11 ) 1.6 y In 1'' -=- .1.2 X Iu -II Jttlllc..... /).: IOU M W:.tl.l

"" ;; Atomic mass of u t.n ;; 235. SU III:l.'<.!>Ot ul"w:ctl:

•u-=- ~~~

r:;; ·run.: Ill ...t!'C

: ( JUU x

;::;

w )( 60 ~('".

IO,.X2,~X1J ~t MIX60VfOA X

tiOJ X 10~ X 3.2 X 10 11 1 t.<

5. When a h}'drogen bomb nplode:-.. a the-nnonucle<IT reJclinn fnr lh~ funnaliun or ~Ill.!.. l'cc ul"\ from deutc:-riam f 1H:l.md trnmm t 1HJ), I Wnl~ the equ.1ho n of lhc nuc1et0' rc.tclJ•>n

1. Ftnd the energy per rclclion Hber:Jtctl ("h~~ nl!l~-!'C'

"re: 2 11·1

= 1HJ474

a.m.u.

1Ji l-;;

3.0170U a.m.u.

()111 ;

I.OOS9R6 .Ltn u

Rm/i(J(Jctl\•il)• t.md Ntu·lc!ar Retli'/Un'-'i J93 !l·le'' =: 4.003880 a m u I

m u. = ~)J 1 MeV

Solutum:

( I J The thcnnwmdcar tcaetlon

1 H~ (2) Atomjc rn:K<tJI 1 1 1 ~

hydJng,co

t 1H3 - ;

t~Jmb cxplu~inn

, lle -+ un

: :!.0l.t74 3.m.u

Atomic mass o( 1111 :3.01700 :uu.u

Tot"' I m~~ ol react:ml

= :S.03174 ::un.u

Atomic m.IS:; of .;>lie~ =. 4.003880 tt m.u Atomic m:~ (JI nn 1 = 1.008986 Oll. m.u.

1otal moss of product

.5.01286<1 • m.u

Q value= 5.03174-5.012860

111crdurc

=0.018874 =17.572 MeV 111u~.

omourn of cni!~) rt!ICil~d per- rcRcticm h 17.572 MeV

6. (""lcul:uc Htndmg energy per nudoon fur 1L1 l atuuL :-.las.s. of Llatl"l!U a 7 .01~Hl( :a,rn 1.1 M:n.ot o f l lyd~cn {11-1 1) Mom= 1.0081 ::un.u Mn:-.s ol Ncutuii'J ({)11 11 = 1.009 :a.m.u.

o~.utlt...-;;

\)31 Me-V

Sulullull (j

~ Jnudcon uf JLi 1 i~

= In (l ~·tu + .o.! M• - Mr..s.' of ,Li7 ) =

1n (1 xI

lXlXI+ 4 ><I O!N

7 UIKI~I

=an vO J212 =0 017 1 X ao··· lli. U B b.Jnu~h:on of

(.'oku l~tc po~·er \lUI pu!

1 1La ~

:6.0171 xY31

HI ' MtV

5.60 196 MeV

n nuclear rector which consum~' I Q kg ol ll:!.lS per day. Energy rcle~d per fission is 200 Mev.

Solution : Accorchng 10 the Eqn. 6. 11. power nul pu1

I' = mN g_ A T

where 111 =Mw u( um used= 10 kg. N =Avogord's Number

= 6.02 >< IOU per kg. Atom, E = Encr~y relea;ctlj>er li>Sion in Joule; =200 x I0'' x 1.6 x I0

= 3.2 ><

10" 11 Joules

A : A!OOliC mass o( um =235, T =Time in SC". = 24 X 6(l X (,() SC<.

so power ou 1 pul ~ p ~ 10 x 6.02 x 10

235 X 24

~ 9.48

x 3.2 x 10

60 X 60

Io• wan

QUES"fiONS I. Whttt uro r:tdio~asotopco;'' H•'w 11n: they produced'' C1ve:. s.hon :tccm•m ofindU$1rl:tl

npplirauon' ur mllu·I>Ololl<>. l . Disti 11~uh.h bctwtcn tl~ fu-.mn ;md t1~~1un re-act ton,;. Whtch o ne of them i .. ml)n: cc;onomicnl'!

Why'.'

3. A nucleolr reo.ctor prOOUI.:t::o. 100 MW of dectric p~Jwer. 1l1e rhcrnml effictcocy b. 40~ A.ssunung 200 MeV or energy per uu~ fi-SSIOn. C'llculolc the amoonl o( l'l:Uut31 ut:mium fue l (in l.g) con.Sumcd pet llay. Nalut'JI UF.snium cOntain~ 0.7"' nf

u'"·

Solution: l~•llnw the !'ame ,tcp' a~ dfine in problem 4. 111e :mumnl o( Ul'~

required (or lhl.! proJ•ction o( 100 MW f'O"l:r i!' 0.2-61 kg. Now NntW\ll Uronium conHlJll' 0.7''V> of u~·) Hcn~c. the amount or n3turul uroojum consumed/day _ IUOxCI1bl _ 37 ,. ' " Q.7 •• o 6 ~· J.

A nuclcru reactor colltWnlnt_! u l.n is OIX"r.tllll!! at power Jevel of 2 MW. Cakulttt-: the rf U<;S ofUl-1' UJIL\lllnL-d/d;t)' by lhl$ reactor. Enagy/Fi.SMOII =200 Mev. AvtJt:,;url'!O numher -= 6.03 X Iol"lk~ ntom Suf,hcm : Accordaug lu lh..!' btu. 6. 11 . pOW\!r uut put

\~.'herem e Mas:; of U:)!l u~-d = ,' '!, N = t\\'08ord'$ Number= 6.02 X 10~6 per ~g. At e-m, £: Ent'tg) rele:J..\ct.lp~:J

fi,M(.IJJ Ul Jl'IUJC~ :

200 X lfY1 X 1.6 X 10 19 : 3.2 X JO II Joulc=.s. r = 2 Nl Wollt, T= Time m $C'C: 2·1 X 60 X 60. A tomiC m un of u2"} = 2)5

mo;<;' nf uz.n

u~d a

m;;

~f~

~ 12 X ICJ" X ~JS X 14 X 60 X 60)/(6.03 X 10'• X J.2 X Hr 11 ) lit:

I .C.

2.1 X J0

kg: !.I gm

5. Flnd lh< binding cno:rgy p<r nucleon of: ( i) ~.~c'1 and ( ii)

9'1u 7'•

Mas'> of fiC 12 :::: 12.00380 n.ru.u. Moss trf 1)11 1 =- J.00898 I.Lm.u I a.m o ; 931 MeV

6. Whol ts the Q v;.Ju~ oro~ nucl~.ar reacuon'.' C:tlcul:ue it ((lr lhe re.tclion 1at ing plucc ln Rutht-rford '~ experiment on ortlficial disjmc:gration of nitro~eo by bornbatdment with C·partide. Relevant mas.'ie:S uJ a..m.tJ. arc:

1 1N • •

,u.•. HM11837 1

l-LU0751 S

,o". 17.<NlJ~.n

= 1.008 142

7 Comp)c(e the JolfuwmJt nuclear reocti~n'~

,L{ + 1H1 - l : He'..._ ? uCI '~ + ., - t u~S'; + 11ll'~ ,Be• ~ ! Ht" _. ,,n1 +., 1

~ The .uomit.:. m;"' ur !lie: ... 1.CH6U1. c I) Wh;ll i .. il-. hindm~ COCil!Y'' j .H WhJI I\ 1b butdin,; cn<!rJ:!y per nut'leon'! Y Thf Rmcllng cnfr') or u.f-:c;o Ill. 160.6 ~·leV. f-'uuJ 11" n1omic mlh,. lU When 14 , l i!J( undC~(J('.. n"~lon, :tbom () If¥, •"~r du: ong1ru.l mu.,, '" u:lt:atoed a" • m . tncrg~ . lhw mulh energy 1.. r(ltJ..••&:d when I kg o( l)lU· umlcrgfll"' ra._..mm 1 J t . 1tow n1ut.h q~UJl" rnu~t uru.lc.rgu li<\!iiun per day ina nucll:.u-rc.trlor that pro\ ille ..

cner~;) to 100 mcgawan ( 10~ \V) electric: fH>\\'trphmt7 Assume pcrfecl efficiency. 12. Wht:n co:tiiS burned. aboul 3.20 X 101 J/kg. uf h~J' i$ hbcr3h:d ... ,,..... I»Uil)' ~~ or coal would he ~:on..,um~d per da) by a ~nnvenliUnal cu;~l !i..:ld \\ lm:h l'rotlucc .. 100 MW elc\'"tnt power pla111'1 Compatt' lhe resuh whh nud(;,r reoH.tUr Solt111011: C)tll fl UI powrr 100 Mw : ! ()() >t tOh"

Energy

f'uwer: - - fllllC

So tut.al t.•ncr~.)' hb.:mlcd : power X: cjme

: 10' X 24

60 X 60 : 8().1

1.c. amomu ul cnal u~ed Per day ~ I.e.

205 )(

S6-l X 1010

, x 1 26 101

1(110 J

-= 265 X I (I 1

ut £1U coal will f'roduce 100 Mw powc r/d:l}

( 'mnmento;,. Jh we h.ne :<.een rn problem 4. th.:tt in .a nudear re.actor w uh I t)U~ ;afti..:iem·~·. IH'i ~m if'~ will produce 100 .Mw powcr/d.,l)' Su m themMI power plam :! x ICf" tlmc!lmnrc coal w1ll be rc:q1nrcd 10 produce s~mc powr out pul/d"y Thu"' IIU\.'kou r~a.:tut 1\ li1U I\! u~du llut haghc1 rule ol t~nh:a o;,upJJI)'.

'-'r

13. Of:set 1be the co!Uitrul'tion and working of G .M. Hlbc. I.J Wh:lt ~~ Q·\'alue of :t Nudear Rt."aclion't

1 7 Superconductivity 7.1 I ntroduction A., temperature decrca.;.c~ cont.luctivuy incrl"ase5. but u was found ror

~Ornl'

m:ucri:tls that suddenly :l t ·' p.tnic-ular tCmJ>eralure ( T:-° K) c:.llcd tnmsithJn fl'lltpcraww.conducuvily become:.. lnfinile, Lc .• n:si~l:UH,'t; \Udt.fcnl)' ralls to zero (Fig. 7 I ). Such motcrinh arc ••lied .rupcrrn!lductor·s. Bul n superconductor ;, noc 11\¢rcl) u good conduct()r gett1ng hc11 er. th\! mc::c.:h:misnt lh:H cuuscs 'upcrcundu, lt \'ity 1!'1 d1ffc.l\'nt tmm thl' mcchani:o-m thm cau.~c~ conducth·uy. Man) good conduc10rs like Aa;. Au, Cu utl' not \ upcrconducaors. There i~ rtn intl't't'\ti"R i1pptm1nt purm:n '· tlw Juxhrr thr t-rJ·unvif\· m mom tempertwu"(! tht· mort' likf11y il is, thm tm•wl tn// hr " wprrc·mulm·wr wltrn roo/rd. The cx:m1plc nf snrnc ..:upcrc<Jnducaive elcmcna.; :aru gaven below. i1 can be a metal or alloy u r scmiconduclor. SuJ>crconducri,·lty j, :tl!'.n nh\Cn c.d in st·u nc org:111k ' llthllHICt!'

'rnhh• 1

Mrtal

AlltJI'

3. 75• K Nb1Sn

Tin 1Sn1

YBa~C'u ~ 0 7

Tantalum ( ra)

Ni<>bium (Nbl 9.46"K Molcbdcnum (Mo)

Cd !Cadmnun) AI (Aluminium) l-Ip (Mercury) Pll (Lcud)

·n Ua,C:o1Cu,0 10

18. 1° K Si. Ge (Tilin lilm or 90•K under hi~h prcssur.:l J;!5° K

0.56•K 1.19° K 4. 16° K 7 .22• K

Supercooclucthit)' C'I!Sult:s trum ~ lmng couphng betwee-n conducLing cJcctmn:'l' and the lauicc. For nonnnlt:ooducril10 there '" a WCit"- couplwg bctwcell wtlcncc electrons and the lntticc:. Because rc..~isli vity ari"c~ due 10 clcctron·phonon (lrHii~) 1mcrnc1inn. S\t h:~s.

good condtu.:10r

m~:m:-.

1lm1 lht.: dcctruu-plw non intcrnccion 1.!-

i.e., coupling ~~ weak. But on the commry for supc.m:unductors elec:tron· phonon intc.ractinn is high, coupling i~ w.ry strong. This !<~Uperc()nducting cffecc wn:, first observed by Kancr-Lighoncn in 1911 at Lcickn_ A::. the list ~i\'cn

Supc•rronductil•ity 397

- -- r K f.1st. 7.1

Variation or n..'"\islnnet: "ith rempe:ndure

vI-'

1'\

v fol (bo

Fitr;. 7.2

( a) Ptn<'lntion of magn~ti<" nux thrnuf!h normal conductor: I b ) Exc:lu$ion fl( magnet it> nu:,; lhroU.j.t.b super(onduclor

nhove m Tabl e L. the tempcralttre (T.,O K) wluch IS' culled trmrsinrm lt'lllfU!rtlturr

is different for different mctnls or nlloy<. Many of them become superconductors under ~pcdrd conditjor:_s like high prc ~u rc, thm film. nrnorphous stale cte:. n~ mentioned in the above t<.tble. The electrical re.~isaam:e in supen.."'nduc tjng .state become~ zero. strong e•idence for lhnt is. found rn the Ma..-.sacbuseus tn~titute of Technology (Mrn. wh"e an induced current of scvcr(tllilindrcd (ullj)cfCS tn 3 superconducting lead ring showed oo change in lhe magnitude of tho currem. for n penod of more than one yeur. which tS only bec~1ose of its zero res,stnncc. But 10 some metals s upercoraduc tivity has nol been ob'iervcd e\'e n below I °K say for Lt. N<~ . K. etc. Below I°K soy nt 0.08-0.0<J"K they nrc found to be <ttll n01mnl conductoN.

7.2

Meissner Ell'ect

It has been obsc.rvcd thu superconduc tivity not o nly consisl'i of z.cm c loctrical resistance. the magnctk property or the ~upcrconductors are also dntnnuic"lly

change: til critical tcmpcr.nure. h " 'a,_. fi rst cxpcrimcmally ob~crvcd by W f\1cl~;.sncr 111 R. Ochscnfeld tJ1:U whe n u bulk ~umple is cooled inn magnetic field through

the lr:msition tcmpcr:nure for <upcrconduclivity. the magnetic nux llri~lnnlly pr~.,l!nt an the :.~~.< imcn '' flll~hcd nul of lhc ~pccuncn. It ill<,IS() ub,~tV\!d Iha l it doc$ no1 matter how the nus~nctic fidd j, C.'\tablishcd-by nn cxrcrnaJ magnc1 m hy n current nowmg in thL" superconductor Itself. This effect ~~ callcc.J ··nux cxclu ... iun·· ur cvnununJy the Mt:IN~'nt.'r rfft't'l , 1lw ~ in(; ide the bun. supt:;rl;nmh•cting

<Jl<'dmen the ma~n~tie lndiiCiion 1ii) is zero (Fig. 7.2b). As it wo.- discu,~cd in Pit•1-l Clwpt~o-7 (:;'1"· [7J) lhltl

iJ =14> cif + M>

B=O Then

tt(//+Ml=O Xm = MIIJ =-I

where iJ ·~ th~ opplicll mngncllc licld nnd

M Ll1e nH&gnclit<.Hion.

Thus. when

Then m:tgnetu.· '-u•.ccplihility

(7 II

l.lfl = Mill =

11m:-. mliJ:Ilt'IU" S/1..\Cepuln/u)' 111 a superronductor i.sfowul to be m:gum·e. which IS referred to us prrfect tHnmr1.1ttU'ti.Hn , which meuns thot ll hulk Sllf1C"I\Ondur tnr ; , tJ U't•ok m flgn t'll•· j},•lt/ tl('h II.'C fl pnfrcl t/wmagnl'l. TI1is cffCCI is known :1'\

"Mct>sncr effect". whoch os tt unique magneuc propeny of a superconductOr and

or ccnLml aml)()r1ance for the chnntcteri?...'ll.ion o f the superconduccjn!_!. ~Uth!: in contrust to a t>crfct conductor. only w1Lh 1.cro rc~islh• aty.

The lour wc-ll·known Muxwell '~ (."C)uations under Sl~llc C<.mdllmn. \\luc h arc ha~lc l:"tw' p( dec.:rncity :mtl lll<.ttllltlis:m given :ltO:

1he

V (•: En

F. =Q.,I£0

V i>: Q.,

( I)

E= ij = Elc<tric in.Juction) V -ii=O or V- fi =O VxB= ~ 11 J

(21

Vx H=J

(31

(•: fJ,~H = 8 = M 3gnetic lnduc1ion) (-I)

where £ a nd fl arc clcctnc field and magnetic field vectors. Q11 i!r> the volume c harge dens ity. J Lh~ current (lensiLy, Eo the pcmtitivity and J1(1 is the. pcnncabilily

of free

~pac,.:.

Now rrom Maxwell's 4th equation. we get

V x E =C:.rl E= - iJB/i)t and frnm Ohm'> law. we get V = IR or 1i!: 1= Y = j x Ax R tl

Sup,•rcmulucti,,ity 399

£-

=pJ-( ·: p =-R xA 1 1

Rcsi511\'lty )

(7.2)

From equuLion (7 .2). we 'cc that if rbb.tivity p goes to Jeff_! for ~llt>ercunduclmg 'tall! while.- current density J is finite. then ..:1cctric field £ must be 1.cro. Now from Muxwtll '' cqu•tion (4) we get \Vhen p = 0, E become< tt•ro which gives i c.

(D)

e COnM:Jill

which i< the «L'c uf a p<rfe<:t conducwr (Fig. 7.2n). Thu~ the ahovc rest.1lt predicl.~, from r,ero TeSL suvily =- 0) for perfect conductor. that 1he magneLic nux 8 is constonl not tcro. ll c:mnot chungc on cooling th1ough tbe. tran:,it1on tcrnpcrnhJrc. The Mcis~ncr effect contradicts thb result und ~uggests thnl prr/ec·r

diamagntJii.wn ( jj.:: 0) and uro re:ri\·1;,.;1)' (p 0) llft' lh'O mdt'f'"ntlt~m l'.Ysrmwl pmprrlles of I he wlprrrnntlucling ,'ltfllr which i." tllffPrl'lrl _(null 11 IHpmlu!llrnl P<iftct <<>ndu<'tor (h'l~ert p = 0). Meissn<r etTeet m supercondueung state can be verif1~d

hy Londun e'IWtlion, dis<:.U!ot.st!d luttel' m lhas chapter,

11'1

\Cellon 7.6.

7.3 Thcorclicnl Explanolion of' Supercondu ctivity: B.C.S. Tbeory8 The <upereonductlng s~<tc is known to be un ordered stat,• of the conduction electrons of the mctol. Tbe order i> In the formation of loo>cly associated pair of c)c(trOru.. At tcmpemtwt below the lr'UnSitiou tc.rnpcl"..t1UI'I;! tlu: clcelJ'ons ure :1rrang.cd in an n1·dcr, but d1ey bt..~ome disnrdcl'cd :.buve the lran,ition t~mpcrasure. rhc nature and ongm of the ordenng was explnml!d successfully by quantum mcchamcaltrentmcnl off.Upcrconductivity.1lli~ w:~ firM );IYen by B:1rdcn COOIX'r. •nd Schrieffcr. who wcr~ awarded the Nobel prize in physics in 197~. nccnrding h) Lllt:tr 1UIIl1C II IS C:alled :aS IJ.C.S. lhtOI'y, When an electron is noving through o latLicc at mtracb the {+vc) aon core wward"' n. and changes the chnrge den'\il) in 1~ YICtnil). J.e. 10 lhnl posi1ion. the crysl:tl has more (+vc) charge density than usual and hence 1 111~ region :um1CI.S more vlhcrdtC\runs. lu lhi.s wny, indiret:l interJclion prnc;ccds bctw~cnclectrons. when one elecu·on stron,ty intcrocts wnh the lmt1CC and d~forms it. Thus there 1:, un ullHtCII\'C force behveen two electron~ over JepuiMve fon:e thmugh (+ve} JOn core. This fomlS a bowrd sy.fltm chm11J(Ii .flmnk c·ouplin.s: bth\'C')" IWtl apposilr•J.v

spinned e/crurms :tnd n" trnrurer or energy tukc~ place from this bound system l;mice ion Now whe.n an extcm;.JI electrical field b. =tpplied m the ~ubstaru;c: in superconducting st:ue tbe pajrs of elccuons g:un ltddhional K.r.., accquire c;omc Jncrea~c iu rnotncrllum nnd give ri).c 10 u current whu:h con1inuc."' wilhout changmg Its volue liS there is no tronsfer of cnorgy from the elc<tron p:ur bound sy5tcm 10 Lhe l:mke. TJu's ran U!llam th,.JHtmdt).Kialfilcl, tltuJ m d goiJJ rnndurlt>r thr rlc·rtrtm-plumfm (+,·r ion lmt ict'l'lll't') cuupli"H i;r poor. u-lricll tJjit•rr makes them poor suptttrrmdt,Ctt.of'.f. Whereas 1ho~e met:t)$ which have higher rcgbaivity. i.e.• the more int~rnction between electron and phonnn at room tc.mpcnuur~ chey will be more likely 10 !)<: a go!Xl sup<:rconductur when e<>oletl. These el<clron pairs are coiled Ct>OJIU {1(11Y und the above theory is called

B.C.S. 1hcory. Electron.< in 1hc Cooper pair have opposi1c spin. so wtal ;pin or 1he Cooper pa1r 1s 7.Cro ond it nlso hll$ many an ributcs or Boxom· (Spin Lero panicle). Single electrons are not bosons IIley have± 112 spin. they ore called Fc:nuimt.~. Fort\ superconducring cleme:m when lC:mpcr..tl urc inc-rea5es from very low value, then a1 u·otu·itit.Jtr tempermure (T_.) tltr Cooper pair(8fi.'(On) brrak up lmo two £•1ecurm.f (/~t•rmionr) and Jl behaves like nonno.l mnterial.

7.4

Pairing En ergy Ga p in Superconductor

h:~vc lh(: hinding energy A called the pairing energy which i> typically in the range ol 10-' ln 10 3 cV. The crilicaltemperoture 7~ for 111Mt of the ~upcrconducln,... i~ between I -- I0°K as g.ivcn in Table 1 corrc"ponding to KT.. in 1hc s::~mc nu1~..: ~~r J(l " lo 10 ' cV (where K is the Bohanan's con,tantt Tim.\' tin• rritit-ul t~mpl•roture l.f directly rdtllt!ll w lht• pain'ng tn~rgv fnr 11 .ulpt•rc:multwmr. It hfJJ' ''alue t:,. = 4KT.... lllis energy gap scpanuc.s supcrconducling clcetrons, whi\!h nne av;ulahle Wh\w tho gap£~. from Ll1c nonnol electrons. of which very few M< availnble above the gap (Fi~. 7.5b). Gap energy is detec<ed in cxpcri-rnenh on beat capacity. infrared nbsorption und tunnelling.. Abo,•c T,.. 1he CtM)pcr pair~ ~trc bmk.s.:n (md rmllcriaJ bt.-<:omc.s nonnal c..'Oni.luctors. T he nltr3cl ivc tnlt!rnclion hcl wccu clcclrons is r~J>Ons iblt for tht.: fortuacjoll of clcctmn p:ur. The b1nding energy of the Cooper pair introduces 3 pairin~ energy g~tp 2 .1 in ennducliou bouu. l belwtcn hOund stnte :uu.l excited .)tate. Fig~. (7.33. h) !'~how conduction bantl for nonnal anrl s upcrconduc1or. The cncr~:-y gup in superconductor h of an entirely diffcrcm nature than the cncrru gap in insulmor. In in~ul~uor the gap i~ lied to the lmticc. in superconductor the gnp i!i tied to the Fenn1 gus.

The Cooper pai.-.

to)

(I))

fig. 7.3 Conduction band ror nom ml ('(Inductor and tha i for supt>rconductor " ·i tll a pairing t 1~t tgy ~up M. .-u·owid K; I~ It is Clh:rgcticnlly favoutt~hl~ (nr dl..'"(tfOni, ne.·u th'-' Ferm1~er1e.rgy h.wd (/;1) in superconductor to bind togt'Lhcr in Cooper pairs. A~ a rc.."'i"ult the dcnsi1y of :-.tales n(f:.' ) dccrca~c' to zero within tJlC: intcr vnJ ± .d of 1:.',-. with corresponding increase Inn(£) ju>l aho\'1! >nd ""low (E.p) (Fig. 7.4b). Figure> 7.4(>, b) '"'"' lh< resulting density of the stnte> 11(/;1 for nonn>l nnd ;uperconducton: with lhe p:uring energy gap 2A forsupertonduc tor. AbOve T, the dcn.<ily or SllttC' of the superconductor(Fig. 7.4b), wiUhe like nonnal conduclor (Fig. 7.4a). The pairing ene-rgy ~np begin~ to Opal .l~ lh<: :.npcrconduc10r b, cooled below 1~.. the gap ene-rgy iocreaU!S a\ the tcmpcr.uuredL'C~ase..fi:, reaches ib maximum a..~Tnpproachcs tt

~ -~

..----

i>l

L- s

£,-

£(t.V) -

(b)

Hg. 7A Varhulon of dtuslly ofstau:s n(E) "·ltb tnergy (£) ror nnnnal conductor. atu1 that ror supt'rtondurlor with u pairing energy g.np '2.6. nround F.-= Er

10 0° K. Wherens. .u. lcmpcmture increa.~.. energy gap tlecrea.st:~. t~nd m T.., It

bccQmc zero. The O<'CUpnUOO prob:.bility Of electron ..UitC!: in SUpen:onductor c:an be [oun(J out in the following '"uy,

Occup•oion probabluy;" (£ ) · F (£) ; N0 (£). where F( £ ) =

1, vn

l+l" li:.• J

is ohc Penni foetor, which is the probability that

n sunc of energy E. b filled up by electron :tt -r>k as we h:tve di..cu;.:scd cnrlicr. in pan- I chnptcr-6, section 6.5. The l'cnni Dime dlstnbution (f'(li}( runc1ion wnh energy E in fig. 7.5(rol shows, that all the levels belo w £, are filled up by electrons at T t 0°K. Figure

7.5{1>) shows a high occupation probahlity (N0 (£) n(£) F(£)1 or Ute supcrconducting ~uucs just below 1hc. cner,t;y gap. 1\ bovc the gap n small density or oonnal (unpaired St3tes) occurs. Figure 7 .5(b) is obtained by >upcrinlpO>ing Pig. 7.4(b) over Fig. 7.5(3).

TI1e energy gap for superconductor can be obt:uned by electrons ounnclling method. The tmnsition in l.ero magnetic field from the superconducting state to nom1al conducting Sl:'l!e is revcrsnblc. and il is a 2nd order phase. transition. The transition between \'llpour to liquid is aiSt) reversuble but it 1S I st order phase

1:.()1{

t1<"----

l>l

1 f

-=CI~ K

(hl f"i~.

7 ...:; (al Varin don of fermJ taccor F( 11) wilh rne~ (,.; ) :tt OeK; (h ) \':triution of OC'l':up-ottlmmJ IJrnhahilily N,.(J;') with t n trcy F. for ~UJX'~onduc1or

tr.uhition. l:..t urth:.r plta.,<;e tnmsitltln is char.tclcri~I.J by latent hcou ;md dbcontinujty of th-: energy gnp. Whcrca.'i at 2nd order phn'c tfitO\it km there Is no latent heat hut there i~o. discontinuity of hcnt c-apaci1y and the enct[!y gar dl!Cfc:a~c., to 1.cm :11 h.:rHpCt:lturc

iru.:rct~c

7~.

The penctrntion depth. coherence length. cntel"gf!.'\ a:o; nntur.ll (()llSCCtllt:nees or B.C.S. lhCOI')'• London I!QU:Jlion i.s obtained ror magnetic field lhal VUI)' :\lowly in space. The Mcis~ncr effect i~ also l')btumcd in u nnturnJ way

7.5

Effect of External Ma gnetic Field on Superconducting State

poNJlhJc to de:,troy ~Jt:>er<:-.,mc.luctivt ly by lbc application o f ~ufficicnlly magnetic field The critica1 or thrc~hoJd vnlue of the.: t.1pp1ietl fie ld ror the dcsLruclion <lf superconductivity He'. is a function of temperature (T) The critical ttt:1gUl.:lic field H, Wi11 be t..cro :ll T~ ·r,_. TI1e critical field varies whh temperature :tccordmg to the p~rnbo l k l3w as h

I')

~trong

H,. = llu I I - (TfT, ) 21 where H11 1s the cnticaJ fie ld at absolute zero nnd

T. IS the mmstiJon tcmpcnuurc.

n1e vanation of 11,. for different clements Ql'e ;hown In Fig. (7.6). A SP.,"<Unen t> supcrconducting below th~ curve <llld nonnoll ••OOVc the c urv..:.

II,

T"K

Fig.7.6

Vur'iatlon of (Ht• ctitlcal magnrlic ricld. which dc:.tro)S SUJJt:.rfOUducthily

ror di.O't~fll tJtliitlllS

Titc critic:t1 magnetic field which cau.s.cs o supcrconduc1or to become normal. is not necessary to be extemnl applied field. h nlay :1ris~: as a resull of c lec1ric cun-ent 11owmg m the conductor. tn a long s upcrconducting wue or radtus H. supcrconductt VIIY may be dcs1royed when current/ exceeds Lhe value/" wluch at the surfnee of the wttc will produce criucnl field H,... given by /,. = 21T RJI,: which js known as Sil:rbt>r :,· ru/r.

Type I and Type II Superconductors There nrc two types of superc<>nduc:tors. I nnd II In a bulk •J>eCin>cn of 1ypc I superconductor, the .upcr«mductlvity c~n be completely demoyed ~y lhc upplicutiun ol cxlcmal m;•gn~tlc licld 11. Typ\! I :-.uJH!r CmlduCI()~ :u•c called 1dcal ~upereonductors In Fig. 7.7 m~•gnclhuuon vc~u'

._pplied anagnetic field for a bulk spt:&:amen

c.xhibib ;, complete ~1eis:\nl!r ~ITeCl (perfect dium:•gncLisaLion). Nonmal !)late will be rC>torcd whe~ opplkd magnclic Ocld H > Hr. thi< is called IYJX: I

;upcrconductor nr idoal supcroonduc1or or 50fl sull<'rconduc1or (Fig. 7.71. The value of u. arc alway:,: trH1 tow lor type I MIJ)\:rconductor~. 10 have any technical application in coi l.s for ">UJ'k!t(ondm:ling magnets. In Fig. 7.7.- JJ.oM is ploucd on lhe verlical >eale. (-\'C) value ..r M corrc:..,ponds IO Jiamagnctism (·: M xll. X the magnetic susceptib~lty Js - ve thr diamag:nctisation). Above fir the magnctismion is: 100 small to be ~ce1t tHI this scalt!, and specimen becom~ normal conducror A type II supercor:ductor l~nds 10 be alloys: or lrnnSilioo metal_,; with very high \•alucs of clectricnl rcsi,livity in the nomtol stole. A type 11 supcrconduclor ho.• 1wo critical lidds H, 1 < II, < 11,, Type IT <up<rconductivily SP<'cimcM hnvc ~upcn:onductingclcclrical propcn.ics uplo field 11, 1 (Fig. 7.8). but bc1wecn H.1 and H..., the magnt:tit flux density 8 ~ 0, the flux .stan.s to pcncaratc- the spt--cimen al 11( 1 lower thnn Hr nnd ahe Meissner efl'ec1 is sajd robe incompleL~ In •he region bel ween fl,. and /1, 2 • the sull<'reonduc10r is lhreadcd l>y Oux

404

Errgin~t!rillX Ph~sicJ

~·

II,

lVI ..-i~t.

7.7 Varintlon or magrwt:lsaclon (-J..C.I\1} with Qpptitd magntlk field (p f)/1), for type:· I supcrc-ondutlor. Ntgalivt \'aluc of M correspOnds to dh•naoi~ udi.~m. whcu II > II~ S'pt•Ci.nlcn hecunu• nnmlul c.~undu('IQr

lines and '" :'aid to he in tl1e vonrJ. :ame. H.-! as I(KJ Lnnc:i or more than H,., . :.bovc IJ, J the specimen i~ a normal conduc1or. Type II o,;upcr\:onducror as called ;1.\ ncm·1dral or hard superconduc1or. Between llq nnd H f"l . type II nunerinl dnc.~ nul exhihir u pcrfccr .Mci~sncrcffccl, nor docs it obey the London equal ions quantitatively. For technlcaJ use when one needs n material wh1ch reol•l•n~ MIJ)c!n.'unducling in large m<~gnclic fields one must usc type II superconductor, Nb_,Sn is un example of type II .soperconducwr.

'lyP<-11

I'! /I

.I I I I

I I i

I H,

~---------L-------L----------~~-- JJ,/1 ,~,

ti~ . ?.H

7.6

If.:

Variutiou of (~1) wilh (JJ411) ror 1)'1)4:'-0 supuconductor. wb~rt betw~n H , 1 (tud ~'~ r: suJX-r<'Onclucling dement issalrl to tx- in a vonexsl3l~.A bo,·c 11.., spcclmr.n b«:ome: oormaJ conduClor

London Equation

A thc<.>rcticul understundtng of the phenomenon associated wilh superconductivity can be undcr<tood in several ways. Certain result• follow directly from Lla~rmtx.lynamic~. Many imporllml results can be described by phenomenological

Supen·umlm·tiw't~·

405

condition.).. Londun ~uat ion is one o f the mo~l important phcnomcnoJogicnl t:.quulion which explain~ the Meissner effect ror the ~uperconducting :tlntc. As Mut.li.:d c:lflicr in!'>cc.:tion 7.2. we c;umol dc..~ribe~.llhc: uni(1ue chHr:tcterilluion of the superconducting ~till~. i.e, 8 = 0, in the opplicd m:•gneuc lic.ld only by cunl'.tdcring lh~ .. upcrconduccor ;1s :;t mcd1um of tcm rc.snai,•ily. I lem;c H h n<ctssnry 10 mo<liry (h< Ohm'' law drn.,licnlly. in Ol'dcr 10 dc_,cnb<: 1Jlo 1cro rc..~i'ltivny 1111tl Me.i,~nadTcct simul t.ancou~ly in the supcrc.onduccing Mutr. without modifying lhc MtucwcJr, equations. Ohm-~ law Eq {7..2) cnn nlso be wriuen u.... l = Contlucti\'ily, J- = Curre111 d<"'ily) J- = a £- (·: a= p

(7 ~)

Since in asupcrconducclngsr:ut electrons behave difr~~ntly. suit was aM:am1ed thai tn.:tupcreonducting state. the current density j is directly proportional cu the Yt..-crorpotcnunl ,\ ofloca.l 1na~nctic field, where tbemagr~c:ttc indoction li V x A i.o. jj =Curl ii. and <lecuic field inlcnsily i = - aii1o1.

j«ii

where

B=CuriA=VXA

'l11oconsl:tnl of propomonnli1y in eqn. (7.S), ha.s wken inS, l. unu "' - l/Jiol.l_ . where AL tS ;a t.:4J11Milnl wilh dnncnsion~ of lenglh. and of value A] = mJp 0 ne 1 Hence Eqo. (1.S) becomes

,,., -

J= -Poif - - "'A

(7.7)

in~acad nr J = a£ :h in Ohm'~ law (eqn. 7 4J. when:, i~ 1hc rruc c lctcrnn dens:hy, t' the elecuomc- charge. m the electronic nut.;s ~tnd A '"" the magnctu: vector polcnlinl. Equation (7. 7) is called 1he Ltmti<JII £q110111J/I from lhe norno ll. London wh<l proposed thl ~. London l!qu:ttion C.lll be derived in ~• Supi:rCOnducung :~l:ll..: mlhc- fullowin~ \\ay also. In a ~upcrcontlucting state rc..~isti vily p = 0 $0 11tc l'let,;tfl'm)l, tun be freely nccclcmuxl. the nccdarution is given by

tlii =

.£

(7.8)

d1 m where. U h 1hc vclochy or the rree electrons. Now by multiplying bolh l!oide..<i b) tW. WC' get

t1 ue 1 m• 2 c- aA> (ntV) E: - - - - dt m m Ot = currc:nt density. Hence by ilucgroting the above equation w.r.t.

=--

Now m:V 1

get -

ntt 1

J = - - A= - -111

JluA7

which is same as cqn. (7.7). the London cquution. where constant o r intcpntjon

is mken co be zero.

MeiS.fllt"l' ttf/n:l m :ruprtrr·nJm•lmJ: 'ilot1· r•rm bt• t•fpluinrrl hy 1-Amtlmr rqmltimr

;,,

{allowinx ,,.m·: By 1a~ing curl un bolh side' of Eq. (7.7). i1 bt:come'

til~

•

llf* l

X ): - -

•

(/ X

jj PoA.]

(7.9)

X II: - - - : - - -

tJoA~

Now hy considering Curl or1hc Maxwell's c.quutlon (J) under ~l31 ic condiaion n~

¢ x (V x i.i)

=l'o (V x J 1

Vx<Vxlil = V<V-8t-V'B= Jlu(';.xh

by using vcc1or Identity, Bu1 V · ij = 0 fruut MaxwciJ'> e<Juution (Z).

Tbus.

Vx(Vxlh=-'V 1 B=Jtu(VxJ)

(7. 1())

By substituting equation (7.9) in (7 10), we get

,jj \1·8 = A' =Con'l:un

(7. 11)

Thb CCJUUtion caccounts for lhc Mt>1s.w er t!J/ec 1. as ;, Joe.'i mn u/Jow a snlutimr mlifiJrm ;, ,)JHICC'. whu.:h rnc·Ju.s lhal a uniform magllt!lic /ir!ld cauum exu1 ur a .tupl'rY;mulucmr. TI\ough umfom1 nmg.;nuc lield iJ exr:-IS> outSide 1hc super· conducto r. if gradually decrease$ cxponemblly 10 uro according to the ~ol ulion of the cqu:uion (7 . II) ns

8<,, = i.hO> ,. .n.,. where A, i~ the: dcplh or pcnCII':II iun tlf lhc UI:IJ;;!!IICiic field knnwo

as ..U.mdon

pNtt!tmtiotJ lfepth.. h::t\•mg dnncn~ion of lcngl h (F1g. 7 .tJ) ttnd of m:Ignitudl!

:l!i;

1----· fig.. 7.9

Pem·h··d tlon d t pth

An 3JlJllierl extemal mr.gnetic li\:ltJ Jj wi II pcnclr'Jtc n th..in li Ito. if the l.hjckue~~ is much lc:» than AI . i.e., in tl thin film Me issner c n·cCl is incomplete. But for

bulk specimen of S\IJ)\!rtonductor. Meiss-ner effect is complete. Thus. the shape

Suf'C'It' mulur uvif\•

407

of th~ ~ ~~c-imcn ha'i. ~ocry irnponant cffc~t. which :1~ 11implc: nnl}' when the: specimen hm. the shape of li10ng cylintlcr whose .L\i'- i:o. p;trulld tO lh~ :tppJica:J mugnctic field.

7.7

Properties of Superconductor

1, AI room tempcrmurc. ~uperconducling matenal huvc gre~ucr rc~buvhy thnn other.

2. The presence of trace nmount of pure m3gnc11c substance rn the ~upercdnduclor severel y low~r.. the trJnsnion l~rn~rJtur~.

3. Oy wcrco~ing th¢ pressure the mmsiuon temper:.ttun: can be mereascd for uhr:.t low transition tcmpcramrc specimen. -L In superconducung state there is no change m 1hc crystal sulJcture. as found by X·ruy difl'ra"ion mctho<.l. 5. Entropy oncrcoses on going from superconducting state to normol stat< bccuusc: entropy a~ u lfiCi.l'•urc. of dlCd iwrder !lnd ~ul)l'r<:Orlduct ing :\1:tte "mcxc mdered 1han 1he normal ~tate (l. For an ideal or rype-1 superconductor, there i!. a markf...~ dwp an Ll1ermnl conductivity when the :-,upcrconducti"ity :-cl~ 111. Fvr non-idc:1l or typ..: It

SUJ>erconductnr, an some CD.!'Cs there is an ancrca.sc of thermal eonducuvaty an supcrconduc.ting 'late 7. 11 ha~ hecn c.Jh,trv-ed rh::u critical tc:.rnpcraturc;; of SUJlC-rconductor \'~tric!'> \~<ith i.sowpic ma~~. Tile rch1tion is M m 'J~; Con~1rtnt or

\\hereM is i.smopic runss. The dependt!nce o f 1: on the isowpic maM~ venues that lntucc VJbrmion and hence ekcnon latuc~ intc"'c.clion~ nrl! Uc.c.ply lll\'ttlvccJ 1n supcrconducti\ uy. Thert b no other rc:t.son lor the J-tupcrconducung tran;mon tt.:mpcr.durc 10 dcpend on the number neutrons Ill the nucleus.

QUESTIONS I. Whut ricli.l

I) 11 :;;uper.:onductor'? Uphun criticAl temperature T, and cntu:al Hr in ;, <rupe~onductor

1111ll!U~IIC

2 Whm i~ MtJ.s-~nu ~rre..::t'1 ~pJIDn wnb tliQgnun 3. fup1ain the ~l:ttouem "Supcrcooduc1or in t1

wca~

mag.nc•ic field :acts as o pcrf't."CI

ili•uuugnt:l•• 4. Wh1.11 j., Lnmlun cqu011u.m ;and pcnc:Lnahun tlcsttb'•

5. Give some ~un•plt ~ of 1h.e ~letmnu o.nd aHoy< which can be .-.uP"rtlmducwr ut u partu.:ul:&r te.mpcntture. 6

StJJlc whclher supercunductorx llft: 111 gencnal gootl ur bat.l conductor!> ;tl MIU.tiiQO'f AI wh;u condm<m they become sopen:ontluclor'J

ntH

7 ~~pl:1in B.C.S. 1hcory for .\Upcrconductiviry? 8. f!xpJnio the effect of CIICC~y gap in the forru:.nion of .)UJ)Cf\."'Ollducting ~tme

mal

References lmtrHiarrion

tfl

Solitl Stmf' Ph>•Jirs- C Kittcl-~11• lidhiQn-WIJcy Eastern l.td ..

New Delhi. 2. Trf•Mi<:tors Dcnms Le Croissette - Prem,cc-HaiJ of lndln, Private Ltd .. New 0c1ru. 1975. 1 tl Tr.u /look •if Of>tks- Submhm:my:un Brij l..ai·S. ChlUld & CornpltnY Lid.• New lklhi. 1993 .l Optirs- 1\jay Ghtnn~ - Tttln-McGro" Ifill Publhhing Comp::my Lid., 1992. S. Optoo l c~tronj cs - J W1!son - J F.B 113\\kC~ 1•rcnucc-linU ortndm l'rwatc Lid. New Dclho. 1996. (l Qmmuw1 Muhot~fr.r-l...«~n:•rd I Schiff- M c-Gn•""' Hill-lnltmatlonal Studcn1 EdiliOJl. 1 Nuc:ll'llr f'l•ysir.f"-Jrving K:1plan-Adth.son -We~Jey Puhlistung Cornp:my Inc:. Indian Student Edition, Nnros~ Publishme House 8 . Pl1vslcs. 4 121 &.lh.Jon. V\11.· 2. Exlendal-llalhday/Re....-mck/Krnne-John· Wlley and

Snm•• New York:.

Subject Index

1\bsorption of rndintioQ, 323

C.B mOO< 141- 1•4 C.C. mode. 141 C.H. mode. 141 , 145- 147 C.R.O. 257- 263

J\cccpmnct: angle. 3415 AcowlJC-Idly g,ood hall, 87

Carbon doling. 17S Carbondloxidc la.cr. 331

A~.:oustic.:ti.

C nt-.<:S o r imperfection. 2.->

•\bsenl '"""'"'· 205

Abrorption coeff., 88,01-93 Absmber, 92

87-96 Adv3n<Age or opli<al fb<r. 357 Alph:a (C>I d<cay. )20 AIUJllific:r, 70

Chaan n:acuon. 382-334 Clmr.u:tcn,tlc X-r.1y \pcclrum, !lS-111.

22')

Anuly:r.cr, 2 16. 2 17

Chame rcrh.t ic~

Applictuioo of Ultr:.asc.nic, g0-32 ArdlJicctuta.l aco\Jstics, 87

Cluargcd p:u1iclc:. 244- 270 in c-ro.'\SCd dcclric & magoctic field.

;\tlJii~:HaJ rt~diOa~liVIIY :u1d i.sotope~. 372 1\s1on mass $peetrogrnph, 266

Atom bomb. 38 I

Acomic model and UlB{tnCtlzallon, ISI Atomic p:u.:klug (octOt'. 13 J\ttlm il: mdiu,., 12

IJ.C.C. Crystal. 7- 14, 13. 2~, 35 fi \ .S. thenry for supe~onductor . JW Rra.in Unllgc rnii$S Spel1togn•ph, 269 Bnnd. b;u1d I•P· 100-103 Hunum ut.anatc. 31 - 33 B ;trkh.au.-~en

jumps, I.Sl

l)nrrier Pcnecrncion. 320--)22 B()tricr poceoclal, 125-126 8:UTie:r cunnelhng, 3 17- 321

Basis. 04, 05

Biaxial crystal. 214 Butdm&etsagy of m1cjcus. 369-371

Rircfrin¥tnce.. '2. 13

Bohr's cheory. 231

uf l...akr. 327

2·18-251 tn Jl:lmltel drctric neld. 244 in tmnsvcn•e cll.-ctric field, 245

in tmnsvcr.-.e mng.netlc licld, 2ol7 Oild-U.ngmu1r l.tw, 64 Cin:ulttr-1)• PCI1uri:l.c d h1;h1. 2 17- 2 1C)

Cl.odding. 3-H Coordinate~ ol Iaiiier pomt. OY C't~n·t .. e h\rcc. I IIi~ Coh•ut~

m thw film. J(.j(

Compadson bet\vccn fission & fu~ion. 390 Compan.son l>t:-1\I.CCU tunc-. 1llatc ruld cumcx l en~. 193 ComponentS of optl\!"111 romnu,&nic:t~tlon. 354 Compcon cffC<I. 28>-288 Conduct wit)'. In Il l< meml. 113

cxtrin!ie \CR\iconi.Jut:tor. 118 tnlnnliic )Cmicumloctor. 116 Constmclivc i nt crfc.n::m;~. 162-167. 170. 17 1

Brusg'!.law, 23 1-23) llmmf5 spcctromctl!r, 234

Conltnuuuo.: X·r.ay spc1.:uum, 227-229

Brnkin~.

Coo!i~ge's cub<. 224 Co..01dlna1um numt'lt:"r, I I. 34

227

8m\<i.<:i SJlltCC h utitC, Oi

Unx:ckr reactor, 387 On:nustrnhlung. 227 Brews.ter's :..ngle, 21S l:h'ews ter·~

law. 215

Controlled chJ..in rcnc1ion, 382- 388

Core, l4J Cntical ungfc:, 34-t

Critiffi magnetic field on Supcrconduclor, 402-4().S

410

Subjl'cl lndt•x

Cntac:.•l Su,t' h>r nuclear rcndur. 3SJ ]8(, Cro~S·SCCiion l'iS$1QP.

383

Dispcr'!li\C Jlllw..:r of ltr.:tling, 206

Dom:un - f~rronuq;,nl!tll: . 1S7

Cro"'H;.cctlon nutr-un ah~<.1rp11an, "lK.I \rJ• ..t:ll dcn.. lly. 14. 15

T)onuun wall, 157 Douhle Rdm(!liun. ! l l

C.-y~usl t'lcmcntaJ, 0.1 Cry.!ltnl lmpcrfc~:tion. 2.J-2.'J Cry'lt3J .on•<.-. 0-1

l)ye laM"r, ;\32- :l3~ c/rn II'IC:'I:SUrCIItCIU by TitOUl$011 UlCifh>tl. 250 lUfcchve nc-uuon muluphc:.hnn fac1ur

(,;,;, 38S. 186

Cl)'"tal plane, lf. f'rr•tnl ''"'clun:. \- X lxKJ) CCOh"cd, 07 f:.c~ centr~d. 07 .!.UIIph: cubtc, 07

E1gt:n funl'Liun. 31 ~ f;-•t:en value, ll:l

Eins-tein':. ptloto~lettnc Cf.tu3tnm. 2M2

Cub1c:tl Cooli~ur.mon. Jl Cut ie tempc&o~t u rc. l2. 156 Curie's Juu.. 1 ~5

Electro· Opu~ crtc~CI, 22 1 Elt!Ctrun microscope. 296

l!let:trQ!<.t:tiiC

(ucu~ mg.

153 25$

EJem(..nml ccy~tal. 04

Cut ic~\Vu!·~~ '''"· I Sb Cutin \'Ullage. J10 C)'Ch,ltrun, 2b l

Elliptically pt11ariLcd lisht. ! 17 ! 19 Em il-~ tun uf mdi:uion. 323 En<''I'Y h:md 100-101 En<I'J'Y b•1l<l ~ap, IUO ~ I 03. 117

l)aviwn•Vt•nncr c -.:pcrnncru. lCJO

Eu;hlon

De-Broghc '~

External

hypmhc.-s.ts. 2lN-:!93

Otcay· r>.ldloolciiVC". 'b5 lk.Oct:llnn 'l!ll'ilivhy. 2.~2

Dcnsny of a cry,taJ.

14. I 5

enoct. 96

mtt~ n et 1 C

field un

~UfK'-rt'Ond uctor,

J02- 1().J

R<lrn ordin11ry my. 21 ~. 214 f!xtrimie semJconduuur. 109 II 3

Depletion rCJ!.iOn. 12\ l)t:;:I,NC(IV( 111l-.!tf~t'(JI\.'\:,J62- J67.17(), 171

I·.C.C

l>eiC..:hOI1 \JI UIII;J~~oUUC.

F'trmi (actor. IU.S Fenni level. W5 e.\U insic scrnkontJucto(. 112 1ntnnMc Kl'lli<:Onducto(, 107 vnri.ation \\;lh cempcnuurc. ll 1 Femxlc~tnc cry:a1011. .\2 Ferromasr)clic dom::.in. 157

J'>c•ccllon uf ).,.r:,y, 22 ~ ONc:nnlrtmJlHI l1f "-a\c length by ~~~IIlii!!-. 20~ OextrorotllhlT> ay-.tnl, 220 J)i;tntt1~11CII~ lll.IICrtolh.

131

o.a.mund :-.lru~tutc. 2~ 1 J Dichroi~n1, 2 1S l:>tffntctll'R• 1~7 -209 ctnrral monimum. 19'J !Juublc: ~hi. JO(.,_J4)8 gmling. 19~-!fM') primllf)' ma~im:t. 199 rc,ollttlli iRitrNI), 2UI - 2(t\

Cry>tol7~1·1,

22. 3(>

Pe:nom~netic ~nt 1

matt-rials. I 55 rerro rn:agnt.:tiC m;nc.nals, I 56

rem

Ul~lgncuc

lllilll'fial!>, 156

Fibt:r grnded index. 34ft Fiber opt tc~ communu:allnn, 354-"lS6 Fiber step index. 344. 346. 347 hs~aon .

J7H-388

>IOgio 'hi. 194 1%

f i>SiOII tro>;•>CCIIOII.

x .. n,ys:. 21 1- 237

383

Discovery or X·r..&y, 223

floc-using, 252-257 clectrosuni.:. 253--257 •nag nerosr:at u.:~. 255 -2S7 Frnunhofcr difrmc:1io.n, 19-' Prr.nkcl ~erect. 26. 27

l),)lolocatiun. 28 edge:. 2~

F1C.:1.nel's diffruchon. INS. 194 Frc$ners l"laJr poeriod Zone, I88

$(r'e:W, 29 Dispersion time, 3S I

Fringe widlh, 171

Oaodc ns rectifier. 65. 1J2 D todL' c har-.tt'lcn'lilto . 6()...()3, l lO Direction of :tlinc:. IR. 19

i nlc mu>tl::tl, 350

Fri 11g~

an wedge 11hn.• 169-112

Fusion.

3k~-3()()

SllbJeCI /nt/e;o; Uanuna r.ay CJ~pcnm~:nl, 2'J..J G:&ug~;

lntmtlu<.:ltOn tu l~r. 323

melee. 8S

Gei~e.r-Mu ller

4 11

fiber-oplics.

34~

hulop.r:lphy. 3.39

cnunter, 361- 36S

Gl'all1.·d i nd~);. llber. 34() (ir:nmg. 19~-200 ahsenl "J>t!Clr.l., 205

l\upcrcondut1iVIlY, 396

Inve-rsion 1cmp.~ ra1urc• .a().....~ I{ lnml' cr~·.st:sl, 04

Jispcnivc power. 206 l.a>cr. JB-339

fruunhufer theory. 19g

m:udrnum number '-'f urdcr pm.sihk.

2()(• Mtf3$Urem<:m

lcnglh.

Of unkaown W:I\'C

em lxtndiuxtdc, 331 ChlraCIC<I<UC$. 3l7 d)C• \12 lic-Nt::. ;\liJ

20~

opcra1ing prindJJII!. 325 popu1nuon lll\'\WSson. 325

overlapping CJf spcecmm. 207 rcsulmm imcn,o~i ty, 201-205

spcctntm formation. 207 GruuJJ ,cJocjl)'. 30b-30K

U:11J cooffic,cm, 120 If all \ o11agc:. 120

mby. 127 scmiconduc1nr M dtn<le I.Mcr. "'3+-339 La.;.ing achun. 32.... )2$ Lmttcc ~lrametcr. 06 pluuc. u.a. s . 15 ponu, C).S space lnuice. OJ \'ector and dn-ccuon. 18. 19 L:aw of mtt:rmct.h:•lc meaoi,·4K ~lh:.:c ~ive temperniUn', 49

Height o l the potential barrier, 125 1-lca"!nbcrg U ncertainty principle, 29:\ vcrilicmion. 29.4- 29l

Laue IUt.·tlh>d. ~5 I.ED. 334, 335. JJS Lc:ll Cm:uktrly l'olanted hgh1 (LCt>),

Hcls\.lfl.\·neon laser. 329 llolc. 1114

Li'll'\'ttmloUdr)'

Half life. 367 II aIt rcnod i'..Onc. I ~g

linlf w:av"' ploce. 220 llall c: ll r.cl~ l 19-12 1 ll.oll nnglc. 120

219. 2!0 (.'ry.,MI, 220

Ligancy (8, 6. -t. J). 34- .W L1,gh1 pr<,p:'l~t~tion in fiber. ~.W Lim: ~('l'CII U IU ur X-my. 1!..i-227 Lmearly Yulamcl.lllght. 21!- 21S J.i.;.~ajnu~ Pnucm, 262

11nlu cuncnt, 105

Holography. 339-34 1 l fuygcnc·~ Wa\'c TI1cmy. IX7 llyt.lf\lgcn hnmh, 389 luop, l!iR

Hy,tcrc~is

London OI'IUlnion. ·10.~--407

hnpo(tant tcatutes of Mtll~1 Uldsccs. ln:~ ul011ur, IUJ lnt«:l1$it)' distnOuti\ln, 1b7. 20.. l ntcl'(cr~ncc-th i n fil m, 164--180 cQn..-tructive, 164- 167. 170. 171

Lon~ "'""CI\!n~th

Cut-ofl. 3~

L'):-....,0 m titx.:r• .152

Intrinsic ('tUTier conctntrmion. IOS

Mugnctostmie focusing, 255- 257 M:.gnr uc 1muen:•J:.:. l:H - t:Jg Mngne1i1.:uion cun·e. I '8 M:agoeto-·suiclil)n effect. 7<1 m.cillato(. 74 M:•lu:> 1....1w, 216, 2 17 Ma.~ ~pecuugropb, 266-270 A\ll)U. 266 R:tin bridge:, 269 Mctm rn.~ p1ath ().). 115 Mc3Sul'(:rncnl c.lf :lh.S'IfJllmn co-t:ff. Yl, 93 Meissner cffcc1. 397-399

Jnuinsic S(:rruc<mductor, 104-109

Merhhnn:sl my, 347

demucti"c· 16-l-167. 170. 171 ~UCIO<Cficct<dloglu.l64.169.170. 1 7 1

Oue h) tr.uasmiucd li!hl, 166 hHcrmedi3le mtUII, 48 hn("mrd quontum efficlooc)' ( TJ, ), 338 lmtrpl:ulcr di$1llnt:t. 20 ~pacms.

defoc1. 26 lmcn:;htsal vmd, 32-J.:J

1ntcr~·1iti;,)

412

S ubjefl lnde.< Oscillator. 7 1. 7•1. 78 (h·crl;~ppi ng Qf "ipectrum. 207

M1.1t:ll, 102

Meta.smhlc ~uue. 32.4 Mtller tndiccs. 15-24 daf(crent btttu:c p hmc. 16

direcuon. IS. 19 Mobility, 114, I I(i Mmlenuor. l8d, lK5 Modes o( rrop.:tgmnlO Ill libc.r. )4g Mokcular tidd lll!oide a M.t.gnctic nwt<ri~l. M QSCicy·~

I ~1 JSO

Nccc):Sity of bro;~d source. 168 Nc8ative Cr)'lit:lL:! 14 Ncutr.tl temperuturc, -'6 ·•·U·

Ncwtnn'1l ""!:· 174--17&

or bri~ hl ftnl!, 177 J mmctcr or durk nn~. 177 dinme t~r

Nicol pnsm. ll(, analy~r.

!l~

pnlariscr. 216

216

Nonrcflcctiul! llhn. J7CJ Normalishtu>n com.l1110n, 305, :l l 0 n·p-n tm nsistm. 117- 147

CB. CE. Charoctemtt.,.,, 141-H? II•I)'JlC .scmicnndi.ICII)t, IUri, 112, 11 l N uclear force.. 168 (j~$.101).

Ph"'< difTcn:ncc. 263 Photn c:ll:ctric: e ffect. '279--281

3-t~.

Nawr:ll rJdio ,..mopes•.l()(1 Nature of intcrfcrcm:e p:Htrm, f72

..._,

PornUel film_ 164-167 l'rtt:'lmagnetlt MutcrbiJ . 154

!'base I'Ciociay. 3()(>->01!

Jnw. 229 2:'\ l

Multirnode, monomod~.

P:tck1ng. fr.1cciun, 368. J69 Pa iring t!IICf'SY ~ap In ~ upc.:tct)l ulu c:tor. 4(1(\-402 .

.178- 381'1

(uscun, JHR-390

r<:Kction. 176-378 383 388 S(reentng lottOr'. 230 N:3<:tot.

N umbc:J o l Atum.JM olecuJ.:~ per unu

Photo cfilSIICtly, 22 1 1'1\oto Detector, 352. 353 l'hoton, 279. 282, 283-286, 323-326 J'hysic;IJ signific;ance

P1oo dt.-ct.nc crystal. 7li effect, 76

o.o;.cillouor. 78 p-o JUnction. 125- 136 r · njunc:1ion Forward bias. 127. 01.

134-136 p-njuncti(ln Rever,;ebla'i., 127.111, 134

116 ;1~

LED. Diode lfi.,er. 334-33')

ns rectifi er, 132

n:vcrsc bios. 127, 131.

Pulam:ulon. 211- 221 circuhlrly polnri$Cd lig hl. 217.218

clloptt<AIIy polmse<llight, l17. 2 18 hnearly poln.ri!>cd hghl, 212. 215, 2 l b ,

Poltu'U.cr, 2 13-2 16

Octnhedral conligunui,m. 16

Polllriscopc, 2 16

21 8 Po l :tn~in)J

O~n

winduw unit, '12

Opuc.:d Activity. 2.20 Opucal dtfTrnction, lt-!7-200 Oj)tkal fi lxr cu.nmun i c::1 til'n~ 354. 35~

Optimum rc\'erbt.:mtioo tin'k!. 87-9 1 Ordmory my, 2 13, 214 Ongu1 o l color 1fl thul l'ilfu, 16K Orig1n or &oeebeck effect, 44 Origin of X-roy. 225-229

13~-J3(,

V-1 chUllctc:fi.stic-$., 130 Ill '-'.;l.h opphed \'Olla~e. 127 u.•ilhout npplied \IOirogc. I'lS r~· n·p lr:!.Jl.~ l S I ()(, 137-ld7 chanw:lcrislk,\"·CB. CE. I.J l- 1..£7

cell, I0 Numencn1 opcnurc. 345. 3.t6

Optic axi•. 2 13, 214

Of W;:IVC ( Ut1C(j011 1

304

A ngle, l iS

Pohtroid. 217 P\)pulation inversion. JlS Posilive cry1ua1. 214 Powdel' method, 236 fJo \WI reactor, 386-387

Prhnnry m:1ximu, 199 Principal plane. 2 L4

x..

ProdUt'lion of rny. 223 Prop;•gllhOn o l h ghl m fiber, M4 Propoenies or m:uter w:ave. 292 ProperliL·S or SUJ)('rt"Ondul'tOr. 407

Subjrcr /nd.:c 4 13 IWpc:rue.-. or X~ruy. !31 p·l)'~ semiconductur, 11 1- 11 3

Pumping electn.e:tl. JJO

S.C. Crystal. 7- 1.\ 21

Optic:.~ I,

20.1

Sceh<ck cffccL 4-1• .15 co effit-lenl, 46-18

Q-valuc. 371.371 Quanwm c-mciencyt!l). 354 Qutmtum physics. 278-322 Quantum theory of tadtaiiOO. 27K Quaner wotve pJ:u~. 219 Qu:tsi Fc1nli level, 336, 3.l(• Quenching, 25 RadiO ftCll"ll)', 361-J7·1 wt•ric::utl. 372 Rudio i..,ntopcs W111iciol. 372

Radto tsoto~ ntuural. Mt6 Radio isotope._< uses. 374 Rcae10r Nutlt'tu, 383-388 brttd<r. 387 heterogeneous. 3~4 homogeneous. 384 pow~l'

Ma.x1m~.

Sccandary Mimm:, tmd

327 PZT ceramu:s. 83

theou.al

h me d.cpc.ndc:.nt, )08

"""independent (STIE). 31 1

Jg6

Rec1ilier, f\S, l:\2- 1:V, l<ecuner equ.:umn, I)4 136 Refroctive inde~. 341 Rc-Jrounion time 4r). 115 R<>idulll n .. demuy (8,). 158 Resolvin~ puwcr of clt"Ctron mic.-wscope:. 296 Rcwn:mcc \\ 11lun a iSuddmg, iJb R e~pon&ivity. 1"iJ ReJuhnnt intcn\hy, 20 1-205 double slit. 202 grating. 20~

origin, 44 Scnucontfuctor. I00--150 conductivity, 11 6-1 i9

ele(IIOn. bole. 10-1 ~trinsie,

109-113 f"crm1 level, IO:i-109. 112- 11 )

Fermi factor. 105 rormatl011 of energy band. 100 m1rin&ic, 104--109 I·V cltamcltri<ric,. 61. 128. 131 n-typc. 109- 113 n·p-n lfoMistor. 137-147 p·type. 111-113

p-njunc1ion,

1 2..~ 134

p•h·P u;tnshtot, 137-147 rl"ctlfier. 132 I :l6 tr.tn~bt or ch:ar.aclcnstu:s. 141- 147 Senlll:onduetor lasc.r. 3J.4-339

Sctl\iti\'11)'. 252 Sevcu c-ty.sta1 S)'SLCIU. 06 :)1b;bt~'!o.

Skew

rule., 40)

'">"'· 147

Sonr~r,

Space charge. 61

Sp:•ce charge lmited cmnnt. ~2 SJJ;~cc t:hllt'ge reg1on. b I Sp:tec luttice, 04

Spe<trognrph. 2116. 269 Spectrometer. 208. 234 Spc!!-trum lonnnuon

s iug.l~:

l'li1, 20 I Rcverb<rntion. 87-91

grating. 207

\JVcrloaJJpulg t~r ~pet:tnun.. 207

Revcrber:nion time, !7-9 1 Sabnme'.s IOmm1a, ~

Spontaneous C!mis~ion, 32.1 Spontanebus magnetizadon, 155 Statu;mary ~uue..<:, ::\ 13

Rkhllrdson-Dushm(lll equntion. 58

Stellar thennonude.1r re~Wtion. 389. WO

Right C"';ulorly l'ol•m.<d tight (RCI').

SumulnlOO e:miss:ion. 324 sw~ control rilm. 179

219.220 Kot:lli ng CJ)'SUII MlCihod, 216

Ruby '"""'· 327 Rutherford'\ cxpcrin:em.

~72

Sabine's fomuda. 90

Schollky

dcfcc~

Sthr()din,;er wave ~ation. 304-322 application~

uf S1'11!~ 313-322

Supcrc,onductivity, 396-407 B.C.S theory, 399 cclelpet pair. 39Q critka.J n'Lagndic fidd, 402~0..1 London ~llliiiOn . 4~7 MCISS(!Cr effect. 397-399 pilltmg energy gap, 400

penetnllion dep1h. 406

ptop.:nlc:s.. 401 te.tnpemturc, 3% ~upC'rposiliun uf t\\-u 11lane t)Oianscd lr:tn~it i on

W!l\i.:,

ll~let::lJun. us~illutor.

79 74. 78

jHudut:liou. !•9. 74. 78 propcnl¢~.

217

Llllr.asomc trnn-.chu:cr, lH Tcmpc:r.nurc I111111W current. 62 T~.~mpcr::nurc U('Utral46-l8 111\'C.rSIUII.

Tt,lin~

the

171

Ttlfillttdml \:Hnfigunuton. ~7 rtu:l'tn.li pu\\ cr 1..:.Jl10r. 386 Thermt.;h.:r. ~I, 117 Thenni' nucle:tr rconction, 3~¥-~'X ) rhc.rruoelcnnt crrect• .S4-56 puwcr. 47 ~eric~. 4~

thc:nnotUclcr, 49 Themmdo:~richy.

4.$- :'i6

'fl1m0011tn1~ Cnll\'i"lltO,

rcocl!fi\!r, &.5

lb?

nature u l illh:r'fcrcnec po~u.:m. 172 Hnp:in ut color Ill thm film, 16& rcflcc tt.-..1 li~lu . If~ traU.\.IIUIIl'i.J hJ";Jil. 166 Three tlunt'n,innul plmtoltrnrh. '\.U}

"lime

vulta{!c, 130

llt~pcn.IOn.

;~~295

Venical dcOecuon, 251. ~52 cle<.UI~ ficltl, 25 1. 1.)2 mlll!J"~Ik liclrl, 252 scnsili,•ity. 252 V·l chamctcn~Uc!o>, 61 , I!M. Ull Vo11n ~I!Jt e, Jf)4 WA\'C funl.'liOn, J0-.1

de\'elormcnt of wrwt.• equauon. 106

'alve, ('!() ·nud.nc..., ul lite wcUge. 172 Thin film lmcrfc."rcncc, J64-: K6 (01\\tJULh\'C. 164 I(J7 t.JC\111J.Ch\C', lfl-l--167

lh~:.lmld

nl ClJ)hcll fiber, 3Sb

U"C" ..r r.•dio hntopcl\, 17J '74ii lhc:. ' vi \·ha) tlaUrucuon ptiiU:rn. 2J7 Vcrifit.:;liiUn uf llc1.;cnh<rr pnncaplc.

57-67

dMriJCtCriSt iC~. ~3

lnh,'OSII)'•

Unp(llafiJ..td lip.hl, 213 11~-.

4fl-1X

Outne:.~

Uma'< t;tllf)Stnl, ll•l

35 I

pltyMcnJ ~tgn 1 fi~:"U!CC, J().l

Sc:hrt'lding.cr wave cqu.umn. 11111Urt!

~lc:

w.., ~ r~\ kc&. J07

\V1lVt" ll:1rt1Ck .JU~lhty, 2~K Wcdl_!.C" film, 169- 17J

X· ruy. 121-117

dmm... tcnstato.' spcnm. 225-2.27, 2.2C) t>:tlllltnu<Ju:o. .:.pectr.t.

:!58--260 Tolftl mtcmnl rcOt.•ctiQn, 2 16 1.42-3.~4

d.:tccuon. :!25

Tc)t:JII} n:nccun~t film, 179 Tronsj.,.tor. 136-147 (' li.C.E.. C.C mode. l·ll- 147

C'rigm. ll."i 229

chlaructcn~lics.

IJJ-147

·rnm~ihon

tcmpcr.uurc, 3%

Tnm.sur.meum c1ernc:nt~. ;4741 Tra~tngul :lr configurouon 1 38 "l'nggcr CIU;'Uil. 2Sft-2(l() Tritgcr pul'>t'., 260

'fu.nec.l cirruit. 71 lunncl I.IJodc. 32 1

227- 22'1

d!s,covcry, 22:\ J1HJdut·lion. 223 X ray diffr-aclinn. 2J 1-237 Burgs'" law. 231 - 2:n Bmgg'\ :-ipcclronttlcr, ZJ4 differ~•" m~thods

for ;\-my

dtffr.lcliun. 234-237

C':tiplun:ltl\lll to.r x· ray d!O"mcltun. 233 usc'\ 1if X -my diO'r-otcdon, 217 Zone p1;t1C. JIJI - 19-l

Zcmc plate compM!son wuh .:onvex. Ulw~onoc.

69-83

opphea.tion. 80-82

l!2

••f p11H1dc. 2M~ Hmttl•'' hyput hes 1 ~. 2l.W [)cvl,\10 <1cnncr e x;pc:ritn~nt , 2'Xl

W.a\C'

Tnneb.t.~. ~<ncrator.

r·o·p. o·1•·o. 137-147

~W..I

Wn\C n.uun· u( light 1<".1

ICO!I., 19.\ Zone hoJf. pcriod. I R8