Spectrophotometryandits applicationinchemicalanalysis 1
1.1Spectroscopyandapplications(overview)
Spectroscopyisabranchofscience(analyticalchemistry)whichdealswiththestudyoftheinteraction ofelectromagneticradiationwithmatter.Infact,traditionally,theinteractionsofanalytewerebetween matterandelectromagneticradiation,butnowspectroscopyhasbeenbroadenedtoincludeinteractions betweenmatterandotherformsofenergy.Suchexamplesincludebeamsofparticlessuchasionsand electrons.Thesekindsofanalyticalmethodsthatareconsideredtobeoneofthemostpowerfultools availableforthestudyofmaterials’fundamentalproperties(e.g.,atomicandmolecularstructure,optical properties)andalsousedinquantifyingthewiderangeofchemicalspeciesprevailinginagivensample. Inthismethod,ananalystcarriesoutmeasurementsoflight(orlight-inducedchargedparticles)thatis absorbed,emitted,reflectedorscatteredbyananalytechemicaloramaterial.Thenthesemeasureddata arecorrelatedtoidentifyandquantifythechemicalspeciespresentinthatanalyte.Ideally,aspectrometermakesmeasurementseitherbyscanningaspectrum(pointbypoint)orbysimultaneous monitoringseveralpositionsinaspectrum;thequantitythatismeasuredisafunctionofradiantpower. Specifically,overalltheotheranalyticalmethods,thespectroscopictechniquespossessthe followingadvantages:
1. Thesetechniquesarelesstimeconsumingandmuchmorerapid.
2. Theyrequireaverysmallamount(atmgand mglevels)ofthecompoundandeventhisamount canberecoveredattheendofevaluationinmanycases.
3. Thestructuralinformationreceivedfromthespectroscopicanalysisismuchmoreaccurateand reliable.
4. Theyaremuchmoreselectiveandsensitiveandareextremelyvaluableintheanalysisofhighly complexmixturesandinthedetectionofeventraceamountsofimpurities.
5. ControlledAnalysiscanbeperformedonacomputer,andtherefore,continuousoperationis possiblewhichisoftenrequiredinindustrialapplications.
Awidearrayofdifferentspectroscopictechniquescanbeappliedinvirtuallyeverydomainof scientificresearch-fromenvironmentalanalysis,biomedicalsciencesandmaterialsciencetospace explorationendeavors.Inotherwords,anyapplicationthatdealswithchemicalsubstancesormaterials canusethistechnique:Spectro-chemicalmethodshaveprovidedperhapsthemostwidelyusedtoolsfor theelucidationofmolecularstructureaswellasthequantitativeandqualitativedeterminationofboth inorganicandorganiccompounds.Forexample,inbiochemistry;itisusedtodetermineenzymecatalyzedreactions.Inclinicalapplications,itisusedtoexaminebloodortissuesforclinicaldiagnosis.
ChemicalAnalysisandMaterialCharacterizationbySpectrophotometry. https://doi.org/10.1016/B978-0-12-814866-2.00001-4 Copyright © 2020ElsevierInc.Allrightsreserved.
Achemistroutinelyemploysspectroscopictechniquesfordeterminationofmolecularstructure (e.g.,NMRSpectroscopy),molecularweight,molecularformulaanddecompositiontosimpler compoundsorconversionintoaderivative(MSSpectroscopy)andpresenceorabsenceofcertain functionalgroups(IRSpectroscopy).Also,therearetremendouseffortsinimproving(e.g., instruments’resolution,detectionlimits,etc)andexpandingthisbranchoftheanalyticalmethodfor quantitativeanalysisinvariousfieldssuchaschemistry,physics,biochemistry,materialandchemical engineering,clinicalapplicationsandindustrialapplications.
Thisbookaimstocoverchemicalanalysisandmaterialcharacterizationwiththistechnique,this chapteraimstobuildafoundationforthebookbyprovidingpropertiesofEMandtheprocesseswhich ariseafterinteractionwithmatter.
1.2Classificationofspectroscopictechniques
Methodsofspectroscopycanbeclassifiedaccordingtothetypeofanalytestheyarebeinganalyzedor typeoflightthattheyemploy.Forstance,onthebasisoftypeofanalyte(elementalormolecular),itis dividedintothefollowingtwoheads:
1. Atomicspectroscopy:Thiskindofspectroscopyisconcernedwiththeinteractionof electromagneticradiationwithatomswhicharecommonlyintheirlowestenergystate,calledthe groundstate.
2. Molecularspectroscopy:Thisspectroscopydealswiththeinteractionofelectromagnetic radiationwithmolecules.Theinteractionprocessresultsinatransitionbetweenrotationaland vibrationalenergylevelsinadditiontoelectronictransitions.Thespectraofmoleculesaremuch morecomplicatedthanthoseofatoms,asmoleculesundergorotationsandvibrationsbesides electronictransitions.Molecularspectroscopyisofgreatimportancenowadaysduetothefact thatthenumberofmoleculesisextremelylargeascomparedwithfreeatoms.
Alternatively,thespectroscopictechniquesarealsoclassifiedaccordingtothetypeofradiation theyemployandthewayinwhichthisradiationinteractswithmatter.Thesemethodsincludethose thatusefromradiowavetoGamma-raysandcausestochangefromnuclearspintochangeinnuclear configuration(see Table1.1).Onthisbasis,spectroscopicmethodsarelistedbelow.
(i) Gamma-rayemissionspectroscopy: UseslightovertheGamma-rayrange(0.005 1.4A ˚ )of electromagneticradiationspectrum
(ii) X-Rayabsorption/emission/fluorescence/diffractionspectroscopy: UseslightovertheXrayrange(0.1 100A ˚ )
(iii) Vacuumultravioletabsorptionspectroscopy: Useslightoverthevacuumultravioletrange of(10 180nm)
(iv) Ultraviolet visibleabsorption/emission/fluorescencespectroscopy:Useslightoverthe ultravioletrange(180 400nm)andvisiblerange(400 780nm).
(v) Infra-redabsorptionspectrophotometry: Useslightovertheinfraredrange(0.78 300 mm).
(vi) FT-IRspectroscopy: (0.78 300 mm)
(vii) Ramanscatteringspectroscopy: (0.78 300 mm)
(viii) Microwaveabsorptionspectroscopy: Useslightovertheinfraredrangeof(0.75 375mm)
(ix) Electronspinresonancespectroscopy: Usesthelightof(3cm)
(x) Nuclearmagneticresonancespectroscopy: Useslightovertheinfraredrange(0.6 10m)
Table1.1Regionsoftheelectromagneticspectrumandthemostimportantatomicormolecular transitionspertinenttothesuccessiveregions.
RegionLimits
Wavenumber limits(cm 1)
Frequencylimit (Hz)
Moleculartransitions (process)
1X-rays0.01 100A ˚ 1020 1016 KandLshellelectrons
2FarUV10 200nm1016 1015 Inner(middle)shell electrons
3NearUV200 400nm1015 -7.5 1014
Valenceelectrons
4Visible400 750nm25000 130007.5 1014 4.0 1014 Valenceelectrons
5NearIR0.75 2.25 mm13000 40004 1014 1.2 1014 Molecularvibrations
6MidIR2.5 50 mm4000 2001.2 1014 6.0 1012 Molecularvibrations
7FarIR50 1000 mm200 106.0 1012 -1011 Lowlyingvibrations andmolecularrotations
8Microwaves1 1100cm10 0.011011 108 Molecularrotations
9Radio waves 1 1000m108 105 Nuclearspin 1.3
Eachoftheseinstrumentsconsistsofatleastthreeessentialcomponents:(1)asourceofelectromagneticradiationintheproperenergyregion,(2)acellthatishighlytransparenttotheradiation andthatcanholdthesample,(3)Grating:Aholographicgratingthatdispersestheradiationallowinga verypreciseselectionofwavelengthsand(4)adetectorthatcanaccuratelymeasuretheintensityofthe radiationafterithaspassedthroughtheanalyteinasamplecell(Thebeamisfocusedonthecenterof thesamplecompartmenttoallowmaximumlightthroughputandreducenoise).
Thespectroscopictechniquesoftype(iv)and(v);Ultraviolet visibleabsorption/emission/fluorescencespectroscopyandInfra-redabsorptionspectrophotometryarealsonamed(sub-classified)as spectrophotometry.Aseachcompounduniquelyabsorbs,transmits,orreflectslightoveracertain rangeofwavelength,thespectrophotometricmethodismainlyusedtomeasurehowmuchachemical substanceabsorbs,transmitsoremitsradiationandtocorrelatetheabsorbedoremittedradiationwith thequantityofananalyteofinterest.Therefore,spectrophotometryisaspectro-analyticalmethodfor boththequalitativeandquantitativemeasurementofthetransmission(orabsorption),reflectionand emissionpropertiesofachemicalspecies(ormaterial)asafunctionofwavelength.
1.3Introductiontoelectromagneticradiation
1.3.1FundamentalpropertiesofEM
Electromagneticradiation(EM)iscomposedofastreamofmass-lessparticles(calledphotons)each travelinginawave-likepatternatthespeedoflight.EachphotonofEMpossessesacertainamountof energy.Thetypeofradiationisdefinedbytheamountofenergyfoundinthephotonsandexhibits propertiesofboththeparticleandwave,knownasthewave-particleduality,andcompriseselectric andmagneticfields.EMspectrumcomprisesradiation,rangingfromradiowavestogamma-rays(see Fig.1.1):Radiowaveshavephotonswithlowenergies,microwavephotonshavealittlemoreenergy thanradiowaves,infraredphotonshavestillmore,thenvisible,ultraviolet,X-rays,and,themost energeticofall,gamma-rays.Thewavelengthrangeofeachkindofradiationandtheprocesstheycan initiateafterinteractionwithmaterialisgivenin Table1.1.
FIG.1.1
Electromagneticradiationsofdifferentwavelengths(uppersection)andtheeffectsafterinteractionofa photonofcertainenergywithamolecule(bottomsection).Forexample,whenphotonsof g-raysinteractwith anatomormolecule,theycanexciteK-shellelectrons.
Inthewavemodel,electromagneticradiationischaracterizedbyitsfrequency, v,wavelength, l, andvelocity, c.Thesethreevaluesarerelatedbytherelationship
(1.1)
Thevalueof c isconstantinagivenmedium(e.g.,c ¼ 2.999 108 ms 1 invacuum),whilethe frequencyandwavelengthoflightareinverselyproportionaltooneanother.TheSIunitsforwavelengthandfrequencyarethemeter(m)andthehertz(Hz),respectively.Traditionally,spectroscopists alsodefineelectromagneticradiationbytheunitwavenumbersas:
where l denotesthewavelengthincentimeters.
Theenergyofaphoton(quantumofelectromagneticradiation)dependssolelyonitsfrequency(or wavelength)andisdefinedas
where h isPlanck’sconstant(h ¼ 6.639 10 34 J).Notethatenergyisdirectlyproportionalto frequencyandwavenumber,andinverselyproportionaltowavelength.
Example1.1 Calculatethefrequencyofradiationwhosewavelengthis600nm.Expressthiswavelength inwavenumber.
Solution:Wavelength(
Exercise1.2. Calculatethewavenumberoftheradiationifthefrequencyis2.06 1014 Hz.(Given: c ¼ 3 1010 cmpersec.)
1.3.2Light-matterinteraction
Whathappenswhenlightmeetsmatter?Whenlightmeetsmatter,thereisalwaysaninteraction:For example,lightisrefractedwhenitenterstheglass,reflectedoffthesurfaceofwaterorice,partially absorbedandpartiallyreflectedbyagreenleaf,andgeneratesphoto-currentbyexcitingthesemiconductorofasolarcell.Thedetailsdependonthestructureofthematterandonthewavelengthofthe light.Additionalphenomenaarerefraction,diffractionandfluorescence.Inthefollowingconsecutive chapters,wewilldiscussindetailsomeoftheseprocessesandtheirmanifestations.Forexample,the fluorescencespectroscopymakesuseoflightthatisreleasedbymatter(analyte),withadetector examininghowthisradiationisreleasedbychemicalsintheanalytesample.
1.3.2.1Absorptionoflight
Asmentionedabove,awayinwhichmattercaninteractwithlightisthroughabsorption.Absorptionisthe processinwhichenergytransferfromaphotonofEMradiationtotheanalyte’satomsormoleculestakes place.Thegeneralprocesseswhichoccurduringlightabsorptionandemissionareshownin(Fig.1.2). Chemicalspeciesthatisatlowenergystatemovetoahigherenergystatebyabsorptionoflight.
Thegeneralprocessofabsorptioncanbeunderstoodasfollows.Atomsandmoleculescontain electrons.Itisoftenusefultothinkoftheseelectronsasbeingattachedtotheatomsbysprings.The electronsandtheirattachedspringshaveatendencytovibrateatspecificfrequencies.Similartoatuning
FIG.1.2
Pictorialdemonstrationoffundamentalconceptsrelatedtoabsorptionandemissionoflight. 1.3 Introductiontoelectromagneticradiation
forkorevenamusicalinstrument,theelectronsofatomshaveanaturalfrequencyatwhichtheytendto vibrate.Whenalightwavewiththatsamenaturalfrequencyimpingesuponanatom,thentheelectrons ofthatatomwillbesetintovibrationalmotion.Ifalightwaveofagivenfrequencystrikesamaterial withelectronshavingthesamevibrationalfrequencies,thenthoseelectronswillabsorbtheenergyofthe lightwaveandtransformitintovibrationalmotion.Duringitsvibration,theelectronsinteractwith neighboringatomsinsuchamannerastoconvertitsvibrationalenergyintothermalenergy.Subsequently,thelightwavewiththatgivenfrequencyisabsorbedbytheobject,neveragaintobereleasedin theformoflight.Sotheselectiveabsorptionoflightbyaparticularmaterialoccursbecausetheselected frequencyofthelightwavematchesthefrequencyatwhichelectronsintheatomsofthatmaterial vibrate.Sincedifferentatomsandmoleculeshavedifferentnaturalfrequenciesofvibration,theywill selectivelyabsorbdifferentfrequenciesofvisiblelight.Thisstatementisillustratedwiththehelpofthe absorptionspectrumofhydrogengas.Asshownin Fig.1.3,whenexposedtoaphotonofelectromagneticradiation,hydrogenatomabsorbsitandisinwhatiscalledan“excited”state.Asthisisnotthe naturalstateofanatomormolecule,theelectronwilleventuallydropbackdowntothelowerenergy (groundstate).However,theatomhastoloseenergytodothis,andsoitreleasesaphotonofthesame energyastheoneisabsorbed.Thisprocessiscalledemissionbecauseaphotonofradiationisemittedby theexcitedatoms,moleculesorsolidsagainataveryspecificwavelength.
Foratomsexcitedbyahigh-temperatureenergysourcethislightemissioniscommonlycalled atomic or opticalemission andforatomsexcitedwithlightitiscalled atomicfluorescence (see fluorescencespectroscopy).Formolecules,itiscalled fluorescence ifthetransitionisbetweenstatesof
Absorptionandemissionspectraofneongas.Also,foraparticularanalyte,theemissionintensityofan emittingsubstanceislinearlyproportionaltoanalyteconcentrationatlowconcentrations.Atomicemission andmolecularfluorescencearethereforeusefulforquantifyingemittingspecies.
FIG.1.3
thesamespinand phosphorescence ifthetransitionoccursbetweenstatesofadifferentspin(seeinthe chapter9fordetails).
Wehavebeendiscussingonespecifictransitionor“energyjump”inoneatom,butofcourse,inany physicalsystem,therearemanyatoms.Inahydrogengas,forexample,alloftheseparateatomscould beabsorbingandemittingphotonscorrespondingtothewholegroupof“allowed”transitionsbetween thevariousenergylevels,eachofwhichwouldabsorb(oremit)atthespecificwavelengthscorrespondingtotheenergydifferencebetweentheenergylevels.Thispatternofabsorptions(oremissions) isuniquetohydrogen(see Fig.1.3):Nootherelementcanhavethesamepatternandcausesa recognizablepatternofabsorption(oremission) lines inaspectrum.
Extendingthisabit,itshouldbecomeclearthatsinceeverychemicalelementhasitsownunique setofallowedenergylevels,eachelementalsohasitsowndistinctivepatternofspectralabsorption (andemission)lines!(Seediagrambelow(See Fig.1.3)forhydrogen).Itisthisspectral“fingerprint” thatastronomersusetoidentifythepresenceofthevariouschemicalelementsinastronomicalobjects. Spectrallinesarewhatallowus,froma“spectrum,”toderivesomuchinformationabouttheobject beingobserved!
Exercise:1.3 (a) IntheabsorptionspectrumofKMnO4 (shownin Fig.1.4),whatwavelengthoflight ismoststronglyabsorbedbyKMnO4?Whatwavelengthsarethemosteasily transmitted?Whichwavelengthswouldyouselectifyouwishedtouselight absorptiontomeasuretheKMnO4?Whattypeoflightatthiswavelength(UV, visibleorIR)?
2. Theinteractionsoflightwithchlorophyllareusedinremotesensingtoexamine theplantandalgaecontentofthelandandsea.
(a) Intheabsorptionspectrumforchlorophyll,whatwavelengthoflightismoststronglyabsorbed bychlorophyll a and b?Whatwavelengthsarethemosteasilytransmitted?
(b) Whichwavelengthswouldyouselectifyouwishedtouselightabsorptiontomeasurethe chlorophyll?
FIG.1.4 TheabsorptionspectrumforKMnO4.
FIG.1.5
Absorbanceasafunctionofradiationwavelengthforchlorophyll‘a’andchlorophyll‘b’.
Solution:
Thestrongestabsorptionoflightforchlorophyll‘a’occursatabout450nmand660nm.The strongestabsorptionoflightforchlorophyll‘b’takesplaceatroughly460nmand635nm.Wavelengthsbetween500and600nmhavethegreatestdegreeoftransmittancebybothchlorophylls‘a’and ‘b’.Smalldifferencesinthesewavelengthrangesarepresentforthesetwotypesofchlorophyll becauseoftheirdifferentchemicalstructures,whichcreateslightdifferencesintheirenergylevelsand inthetypesoflighttheycanabsorb.
(a) Themeasurementofchlorophyll a and b wouldbebestperformedbyusingthewavelengthsat whichthesepigmentshavetheirstrongestabsorptionoflight435nmor660nmforchlorophyll a,and460nmor635nmforchlorophyll b,whichrepresentvisiblelight.
Ifyoulookcloselyatthespectraofchlorophyll a and b (Fig.1.5),wewillnoticethatitisthelight thatisnotabsorbedbychlorophyll a and b between500and600nmthatgivesthesepigmentsand leavestheirgreenandyellowcolor:thecoloroftheabsorbingspeciesisdeterminedbytheremaining typesoflightthataretransmitted(orreflected)bytheobject.Forinstance,thepassageofwhitelight throughabluesolutionofcoppersulfateindicatesthatbluelightisbeingtransmittedwhilethe complementary(orangeinthiscase)isabsorbed.
1.3.2.2Transmissionandreflection(visiblelight)
Transmission: Asaresultoftheabsorption,theintensityofthislight,afterpassingthroughthesample willbelowerthanitsoriginalvalueattheenergythatwasabsorbedbythesample.Theremaininglight thatleavesthroughthesampleissaidtohaveundergonetransmission.Inotherwords,thetransmission isdefinedasthepassageofradiationthroughmatterwithnochangeinenergytakingplace.The amountoflightthatistransmittedbyasampleplustheamountoflightthatisreflected(orscattered)
andabsorbedbythesamplewillbeequaltothetotalamountoflightthatisoriginallyenteredthe sample.Aplotoftheintensityofthelightthatistransmittedbyasampleatvariouswavelengths, frequencies,orenergiesiscalledatransmittancespectrum.
Themechanismfortransmissionoftheincidentlighttotheothersideofatransparentmaterialis understoodasfollows:Transmission(orreflection)oflightwavesoccursbecausethefrequenciesof thelightwavesdonotmatchthenaturalfrequenciesofvibrationoftheobjects.Whenlightwavesof thesefrequenciesstrikeanobject,theelectronsintheatomsoftheobjectbeginvibrating.Butinstead ofvibratinginresonanceatlargeamplitude,theelectronsvibrateforbriefperiodsoftimewithsmall amplitudeofvibration;thentheenergyisreemittedasalightwave.Iftheobjectistransparent,thenthe vibrationsoftheelectronsarepassedontoneighboringatomsthroughthebulkofthematerialand reemittedontheoppositesideoftheobject.Suchfrequenciesoflightwavesaresaidtobe transmitted (thisprocesswillbediscussedintheconsecutivechapterindetail).Purewaterisaclassicexampleof analmostcompletelytransparentmediumforvisiblelight.Aneyeexhibitsseveralportionsoftissue thataremoreorlesstransparent,suchasthecornea,crystallinelens,aqueoushumor,andthevitreous body,aswellastheinnerlayersoftheretina.Amediumisalwaystransparentonlytoacertainrather thanthewholepartoftheelectromagneticspectrum.Forexample,waterisopaquetoradiationinthe infraredrange,whilethecorneablocksradiationintheultravioletrange.
Reflection: Reflection ofelectromagneticradiationisthechangeindirectionofawavefrontatan interfacebetweentwodifferentmediasothatthewavefrontreturnsintothemediumfromwhichit originated(see Fig.1.6).Inparticular,whenthewavesofradiationencounterasurfaceorother boundarybetweentworegionsthathavedifferentrefractiveindicesandbouncestheradiationwaves backtothemediuminwhichitwasoriginallytraveling.Alternatively,itcanbedefinedasfollows.If theobjectisopaque,lightwaveofunmatchedfrequencieswiththenaturalfrequenciesofanelectron, thenthevibrationsoftheelectronsarenotpassedfromatomtoatomthroughthebulkofthematerial. Rathertheelectronsofatomsonthematerial’ssurfacevibrateforshortperiodsoftimeandthenreemit theenergyasareflectedlightwave.Suchfrequenciesoflightaresaidtobe reflected.Common examplesincludethereflectionoflightbyamirror.
Whenlightisreflected,itscharacteristicsandpropertiesmaynotbethesame.Howlightisaffected bymatterdependsonthestrengthofthefieldofthelight,itswavelength,andthematteritself.In addition,externalinfluencesonthematter,suchastemperature,pressure,andotherexternalfields (electrical,magnetic)influencetheinteractionoflightwithmatter.
FIG.1.6
Schematicdiagramforreflectionfromasmoothmirrorsurface(left)andirregularsurface(right). 1.3
Similartoabsorbedoremittedlightreflectedlightfromasamplegivesinformationaboutitandhas beenusedinsometypesofspectroscopyinwhichreflectedlightfromananalyteisdetectedbythe instrument’sdetectorandanalyzed.Agoodexampleinmaterialscienceisanevaluationofoptical propertiessuchasrefractiveindices,absorptioncoefficientandthicknessofthepartiallytransparent thinfilmofmaterials(e.g.,metalsandsemiconductingmaterial)byanalyzingthereflectedlightfrom thesurfaceofsuchmaterials.Dependingonthenatureofthesurfaceoftheanalyte,thereareseveral typesofreflections.
SpecularReflection: Iftheboundarybetweenthetworegionsthatcausesthereflectionisaflat plane(smoothsurface),thereflectedlightwillbeinwell-definedmannerandwillretainitsoriginal imagesuchtypeofreflectioniscalled Specularreflectionorregularreflection (See Fig.1.6).The fractionofthelightthatisreflecteddependsontheangleofincidence,theratiooftherefractiveindices ofthetwomedia,aswellasfromthestateofpolarizationoftheincidentlight,butitdoesnotdepend onthecolorinmostsituations.
Anexampleofsuchaprocessisreflectionbyplane,whichmirrorssmoothsurfaceofwater:In specularreflection,amirrorsurfacereflectsabeamoflightsothattheangleofreflectionisequaltothe angleofincidence(e.g.,theangleoftheincominglightisthesameastheangleoftheoutgoing/reflectedlight).Thediagramshowshowtheincoming(incident)lightisreflectedoffthemirroratthe sameangletotheperpendicularline(whichingeometryiscalledthe‘normal’).Foraperpendicular incidencefromairtoglass(orforaperpendicularexitoutofglassintoair),approximately4%ofthe lightisreflected.Forthetransitionfromairtowater,thisisapproximately2%.
Asshownin Fig.1.6 (left),inaperfectreflection,allthelightwillbereflectedfromthemirror surface.Inreal-life,non-perfectsituations,thebasematerialofthemirrorandthesurfaceofthemirror may:
n Absorblight:thelightisabsorbed(theenergyofthelightistakenupbythematerial).
n Imperfectlyreflectlight:Thesurfaceisanimperfectmirrorandsomeofthelightisscattered.
Diffusereflection: Roughsurfaces,suchasapieceofpaper,reflectlightbackinalldirections. Thisalsooccurswhensunlightstrikesthewallofahouseorthegreenleafofaplant.Thankstothe diffusecharacterofthereflection,weseetheilluminatedobjectfromeveryangle.Diffusereflection occurswhenanincidentrayoflightstrikesasurfaceandthelightisscattered.Asshownin Fig.1.6 (right),inperfectoridealdiffusereflection,allthelightwillbeperfectlydistributedinahemisphereof evenilluminationaroundthepointthelightstrikesthediffusionsurface.Thediagramshowstheway lightisscatteredbyadiffusionsurface.Althoughthediagramisonlytwodimensionallightscatter formsahemispherearoundalightstrike-point.
Thisgeneralpicturewillnowbemademoreprecise.Themostobviousisthephenomenonofthe colorofthereflectingsurface.Thewallofahouse,beingilluminatedbythesun,appearswhitewhen itspaintreflectsallwavelengthsoftheincidentlightcompletely.Theyellowcolorofasunflowerarises throughtheabsorptionofblue:together,theremaininggreenandredproducetheperceptionofyellow. Ifasurfacepartiallyabsorbsallthespectralportionsofthelightuniformly(50%ofit,forexample),it appearstobegray,thatis,withoutanycolor.
AsindicatedintheIst paragraphofthissection,thedegreetowhichlightwillbereflectedata boundarywilldependontherelativedifferenceintherefractiveindicesforthetwosidesofthe boundary.Thelargerthisdifference,thegreaterthefractionofthelightthatwillbereflected.Thisidea
isillustratedby Eq.(1.4) (theFresnelequation),whichgivesthefractionoflightthatwillbereflected asitinterstheboundaryatarightangle.
Thesymbol P0 inthis Eq.(1.4) representstheincidentradiantpower(original)ofthelight(inthe unitsofWatts),whichisdefinedastheenergyinabeamoflightthatstrikesagivenareaperunittime, Pr denotestheradiantpowerofthereflectedlightwheretheratio Pr P0 givesthefractionoftheoriginal lightversusthereflectedlight.Forboundariesthathaveonlyasmalldifferenceinrefractiveindexes, suchasbetweenthevacuuminspaceandair,thefractionofreflectedlightwillbesmallandmostof thelightwillpassthroughtheboundaryandintothenewmedium.Ifalargedifferenceinrefractive indexispresent,asoccursbetweenairandthesilver-coatedsurfaceofamirror,alargefractionoflight willbereflected.Anexampleofacompletelywhitesurfaceisprovidedbysnow.Itswhitecolorhasa simpleexplanation:thetinyicecrystalsreflectthelightwithoutanyabsorption.
Exercise1.4. SomesensorsontheTerraSatellitemakeuseofreflectionpatternstomapthesurfaceof theEarth.
(a) Ifabeamoflightpassesthroughtheair(n ¼ 1.0003)andstrikesthesmoothsurfaceofthewater (n ¼ 1.333)atarightangle,whatfractionofthislightwillbereflectedbythewaterbackintothe air?
(b) Ifthisbeamoflightstrikesthewateratanangleof65.0,whatwillbetheangleofreflection?
Solution:
(a) n1
ðor2 03%reflectionÞ
(b) Ifthelightisundergoingperfectregularreflection,itwillbereflectedatanangleof65.0onthe othersideofthenormalfromtheincominglight.Ifthesurfaceofthewaterisroughanddiffuse reflectanceinsteadoccurs,thelightwillbereflectedatmanydifferentangles.
1.3.2.3Refractionoflight
Whenabeamoflightmeetsasmoothinterfacebetweentwotransparentmediathathavedifferent refractiveindices,bothreflectionandrefractionoccur(Fig.1.7).Therefractionoflightisthebasisfor theopticalimagingthroughthecrystallinelens,eyeglasses,andopticalinstruments(e.g.,magnifying glasses,microscopes,andrefractivetelescopes).
Theincidentrayoflightontoasurface,refractedandreflectedrays,andthesurfacenormalall lieinthesameplane(Fig.1.7).Theamountoflightrefracteddependsontheratiooftherefractive indicesofthetwomedia.Therelationshipbetweenthetwoangles a and b isspecifiedbythelawof refraction:
FIG.1.7
Refractionattheinterfaceoftwomedia.Theprimaryrayispartiallyreflectedandpartiallyrefracted. a and b aretheanglesofincidenceandrefractionwithrespecttothesurfacenormal,respectively.
Keepinginmindthatlightisscatteredwhenitencountersanobstacle,theexistenceoftransparent mediasuchasglass,water,corneas,crystallinelenses,andairseemsquitemiraculous.Insidethese media,interactionsbetweenthelightandthematerialsstilloccur,butitonlyleadstothelight’s travelingmoreslowlythanitwouldinavacuum(Refractionisaconsequenceofthedifferingspeedsof lightintwomedia).Tounderstandthis,wefirstnotethatthefrequencyofthelightvibrationsremains thesameinbothmedia.Therefore,insidethemediumwiththeslowerlightspeed,thewavelengthis smallersincethelightmovesonewavelengthfurtherduringoneperiod.Thisslowingdownis quantifiedastherefractiveindex n:thevelocityoflightinthemediumamountsto c/n,where c isthe velocityoflightinvacuum(c » 300,000km/s).Forexample,inwater,lighttravelswithavelocityof c isabout 225,000km/s(n ¼ 1.33).
1.3.2.4Dispersionoflight
Therefractiveindexofatransparentmediumisslightlydependentonthewavelengthandincreases withshorterwavelengths.Thisgivesrisetodispersionduringrefraction,i.e.,toabreakingupofwhite lightintovariouscolors,aswemainlyknowfromprismsorcrystals.Thecolorsoftherainbowarealso basedonthedispersioninwaterdroplets.Newtonwasinterestedinthechromaticaberrationofthe humaneye.Itsfocalplaneforbluelightliesapproximately1mminfrontofthatforaredlight.Itis amazingthatweperceivethechromaticerrorofoureyesonlyunderrareconditions,eventhoughthe differencebetweentherefractivepowerforredandbluelightamountstoca.1.5D.
1.3.2.5Lightscatteringinmedia
Thetermscatteringreferstothechangeintravelofoneparticle(suchasphoton)duetoitscollision withanotherparticle(e.g.,anatomormolecule).Onecommontypeofscatteringis‘Rayleigh scattering’.Themechanismforscatteringisunderstoodas:Anisolatedatomscatterslightbecausethe electricfieldoftheincidentlightwaveforcestheelectronsintheatomtooscillatebackandforthabout theirequilibriumposition.Bythelawsofelectromagnetism,whenachargechangesitsvelocity,it
emitsradiation.Lightisemitteduniformlyinalldirectionsintheplaneperpendiculartooscillationbut decreasesinamplitudeastheviewingangleshiftsawayfromthatplane.
Anoutersurfacedoesnotalwaysscatterbackallthelightthatpenetratesit.Instead,thescattering canalsotakeplacedeeperinsidetheinteriorofthemedium.Amongnumerousexamples,theblueof theskyisthemostwellknown:theairmoleculesscattersunlightandmainlytheshorterwavelengths. Withoutthescattering,theskywouldappearblacktooureyesandlightwouldcomeintooureyes whenlookingdirectlyatthesun(Theblueportionofthesunlightisapproximatelysixtimesmore stronglyscatteredthantheredportion).Aglassofbeerabsorbslightofshortwavelengthsandscatters lightwithlongerwavelengthsinalldirections.Thescatteringoflightbyparticlesdependsonthe particlesize.Thescatteringduetoparticlesthatareconsiderablysmallerthanthelightwavelengthis knownasRayleighscattering.Rayleighscatteringoccursinalldirections.Thebest-knownexampleis thescatteringofsunlightbythemoleculesoftheatmosphere.
Forlargerparticles,e.g.,fromatmosphericpollution,withdiametersontheorderoflightwavelengthsorlarger,thescatteringtakesplacemainlyintheforwarddirection,anditislesscolordependent(calledMiescattering).ThescatteredlightlosesthebluedominanceoftheRayleigh scatteringandbecomesincreasinglywhiterwiththeincreasingdiameterofthescatteringparticles.A nicemanifestationoftheforwarddirectionofthescatteringofsunlightonatmosphericparticlesisthe whitishappearanceoftheskynearthesun:Thescatteringduetowaterdropletsandatmospheric pollutants(aerosols,saltappearanceofheavyclouds)derivesfromthefactthatthelightcomingfrom aboveismainlyscatteredandreflectedbackupward,whileonlyasmallpartpassesthrough.
1.3.2.6Diffractionoflight
Diffractionistheslightbendingoflightasitpassesaroundtheedgeofanobject.Theamountofbending dependsontherelativesizeofthewavelengthoflighttothesizeoftheopening.Iftheopeningismuch largerthanthelight’swavelength,thebendingwillbealmostunnoticeable.However,ifthetwoare closerinsizeorequal,theamountofbendingisconsiderable,andeasilyseenwiththenakedeye.
Intheatmosphere,asshownin Fig.1.8 diffractedlightisactuallybentaroundatmospheric particles:mostcommonly,theatmosphericparticlesaretinywaterdropletsfoundinclouds.Diffracted lightcanproducefringesoflight,darkorcoloredbands.Anopticaleffectthatresultsfromthe diffractionoflightisthesilverliningsometimesfoundaroundtheedgesofcloudsorcoronas surroundingthesunormoon.Theillustrationin Fig.1.8 showshowlight(fromeitherthesunorthe moon)isbentaroundsmalldropletsinthecloud.
FIG.1.8
Exampleofdiffractionoflightbyatmosphericparticles.
Allformsofwaves,includinglightwaves,arediffractedwhentheyencounteranedgeorpass throughanarrowopening likewaterwaveswhenpassingthroughtheentrancetotheharbor. Adiffractionimagecanalsobeunderstoodasaneffectofinterferenceamongtheentityofthewaves thatextendfromallthepointsoftheopening.Strictlyspeaking,diffractionislesstheconsequenceof certaininteractionsbetweenlightandmatterandmoretheexpressionofaninnerpropertyoflight:its wavenature.Thisconceptalsoappliestolightwaves.Whensunlightencountersaclouddroplet,light wavesarealteredandinteractwithoneanother.Ifthereisconstructiveinterference,(thecrestsoftwo lightwavescombining),thelightwillappearbrighter.Ifthereisdestructiveinterference,(thetrough ofonelightwavemeetingthecrestofanother),thelightwilleitherappeardarkerordisappearentirely.
Acuriousphenomenonofdiffractionwastheobjectofcontroversywhenthewavetheoryoflight wasbeingestablished.In1818,Poissonpointedoutthat,asaconsequenceofthewavetheory,abright spotmustappearinthecenterofasphere’sshadowbecausethewavesoriginatingfromalltheedges wouldarrivethereinphase,irrespectiveofthepositionofthescreen.Tohim,thisseemedsoabsurd thathebelievedhehadthereforedisprovedthewavetheory.However,ashorttimeafterward,the “Poisson’sspot”wasactuallyobservedandbecameoneofthepillarssupportingthewavetheoryof light.Diffractionalsohasaninfluenceonimageformationintheeye.
DiffractionofX-RaysbyaCrystal: Itispossibletopredicttheanglesatwhichconstructive interferencewillbeobservedforX-Raydiffractionbytheatomsinacrystal.Thiscanbeachievedby usingtheBraggequation,
(Note: Eq.(1.6) canalsobewrittenasnl ¼ 2d(nhkl)sin(q),whereh,k,andlarelattice parameters).
Where l isthewavelengthofthe X-rayspassedthroughthecrystal, d istheinterplanardistance(or latticespacing)betweenatomsinthecrystal,and n istheorderofdiffractionfortheobserved constructiveinterferenceband(e.g., n ¼ 1 forfirst-orderinterference).Theterm q representsthe specificangleatwhichthe X-Rayswillstrikethecrystalsurfaceandproduce,ontheothersideofthe normalandatthesameangle,adiffractionbandforthegivenorderofconstructiveinterference.
Exercise1.5 If X-Rayswithawavelengthof0.711A ˚ arediffractedbyacrystalofsodiumchloride (d ¼ 2.82A ˚ ),atwhatanglewillfirst-orderconstructiveinterferencebeobservedforthiscrystal?
Solution:
Rearranging Eq.(1.5), andsubstitutingthegivenvaluesof n,d, and l,wecanfindtheterm q.
ðqÞ¼
ðqÞ¼ 0 1260r ¼ 7 24o
Thesametypeofcalculationpredictsthatadditionalbandsofconstructiveinterferenceswillbe seenatanglesof14.6o (n ¼ 2),(n ¼ 3),andsoonforhigherordersofinterference.
1.3.2.7Emission(fluorescence/phosphorescence)
Fluorescentmaterialsareutilized,forexample,inlaundrydetergents.Thevisualeffectproducedfrom fluorescentmaterialoftenoriginatesfromblueorUVlight,whichilluminatesamaterialand,inturn, excitestheemissionofyellowororangelighttowhichoureyesareespeciallysensitive.The
FIG.1.9
Fluorescein.Left:transitionscheme.Middle:absorptionspectrum(a)andemission(e)spectrum.An absorptionmaximumat485nm,emissionmaximumat514nm.Right:formulaoffluorescein. 1.4 Questions
conversionalwayshappenstowardthelongerwavelengthand,thus,inthedirectionofdecreasing photonenergybecausesomeenergyisconvertedintomolecularvibrations(heat).Thisbehavior (absorptionofshort-wavelight,emissionoflonger-wavelight)istermedfluorescence(Fig.1.9).The namestemsfromthemineralfluorite.Thisphenomenoncanoccurinorganicmaterialsandalsoin minerals.Ifweirradiatemineralswithultravioletlight,wecanascertainthatindividualmineral samplesshinemoreorlessbrightlyinvariouscolors.Fluorescentmaterialsoftenproducelightweakly.
Theamountoflightthatisemittedbyasamplewillbedirectlyrelatedtotheconcentrationofthe atomsormoleculesinthesamplethatarecreatingthisemission.Wecanrepresentthisrelationship throughthefollowingequation,
where PE representstheradiantpoweroftheemittedlight, C istheconcentrationofspeciesemitting thislight,and k istheproportionalityconstant. Eq.(1.7) canbeusedtoestimatetheconcentrationof theatomsormoleculesthatareinexcitedstates,afterinteractionwithradiationorotherexcitation sources(e.g.,thermal).Detailsofmethodsforsuchanalysiswillbediscussedinchapter9.
1.4Questions
1.4.1Subjectiveproblems
1. Describethreewaysthatlightcaninteractwithmatter.
2. Transmittedlightmayberefractedorscattered.Whendoeseachprocessoccur?
3. Whydoesmatterincreaseintemperaturewhenitabsorbslight?
4. Compareandcontrasttransparent,translucent,andopaquematter.
5. Whatwavelengthsoflighthavethemostintenseemissionwhengivenoffbythesun?Which wavelengthsoflightaretakenupby(orabsorbed)tothegreatestextentbyearth’satmosphere?
1.4.2Numericalproblems
1. Calculatethewavenumberofradiationwhosewavelengthis4000nm. Ans : w ¼ 2500 cm 1
2. Calculatethewavenumberofthelinesoffrequency4 1014
Ans : w ¼ 1:33 104 cm 1
3. Radiationwithawavelengthof700nmisvisibleredlight
(a) Calculatethewavelengthin A ˚
(b) Whatisthewavenumberandfrequencyofthisradiation?
4.
(a) Whatistheenergyofaphotonthathasawavelengthof500nm,ifn ¼ 1.00?
(b) Whatistheenergycontainedinonemoleofphotonswiththiswavelength?
5. Oneapplicationofemissioninremotesensingisinthedetectionofforestfires.Oneofthekinds ofsatelliteLandsathasasensorthatdetectsactivefiresbyexaminingtheiremissioninthe wavelengthregionof1.55 mm 1.75 mm.
(a) Whattypeoflight(visible,ultraviolet,etc)isit?
(b) Whataretheenergiesofsinglephotonsoflightatthesewavelengths?
[Hint:IRregion.Ans:(b)energiesofsinglephotons ¼ 1.2 10 19J]
Furtherreading
[1]D.A.Skoog,F.J.Holler,S.R.Crouch,InstrumentalAnalysis,CengageLearningIndiaPvt.Ltd.,NewDelhi, 2012,p.158.
[2]Guideforuseoftermsinreportingdata:spectroscopynomenclature,Anal.Chem.62(1990)91 92.
[3] https://www.nist.gov/programs-projects/spectrophotometry,visitedon:7/23/2017.
[4]M.G.Gore,SpectrophotometryandSpectrofluorimetry:APracticalApproach,OxfordUniversityPress,2000.
[5]G.S.Jeffery,J.Basset,J.Mendham,R.C.Denney,Vogel’sTextbookofQuantitativeChemicalAnalysis,fifth ed.,1991.
[6]B.K.Sharma,InstrumentalMethodsofChemicalAnalysis,Krishna’sEducationPublishers,2012.
[7]Ref.FortheAbsorptionSpectrumofHydrogenSpectrum(OrSimpleAbsorptionandEmission).
[8]Ref.FortheAbsorptionSpectrumofKMnO4
[9]J.Inczedy,T.Lengyel,A.M.Ure,CompendiumofAnalyticalNomenclature,thirded.,BlackwellScience, Malden,MA,1997,p.433.FromHage’sBook.
[10]D.S.Hage,J.D.Carr(Eds.),AnalyticalChemistryandQuantitativeAnalysis,International,PearsonEducation,Inc.,NewJersey,USA,2011.
[11] http://blair.pha.jhu.edu/spectroscopy/basics.html,Visited:07/14/2017.
[12]A.T.Young,Rayleighscattering,Appl.Opt.20(1981)522 535.
Theoryandinstrumentationof absorptionspectroscopy:UV VIS spectrophotometryand
colorimetry
2.1Absorption(UVeVIS)spectrophotometricmeasurements:general concept
Traditionally,thelightfrom185nmto760nmisgenerallycalledultraviolet visible(UV VIS) region.However,withtheadvancementoftechnology,themodernspectrophotometerscomewiththe extendedwavelengthrangefrom185nm 2100nm.Inordertoknowwhatwavelengthoflightis absorbedbyananalytecontainedinagivensample,wemustknow(ordetermine)theUV VIS absorptionspectrumofthestandardsampleofwhichwewishtostudy.
Asmentionedinthepreviouschapter,mostofteninspectrophotometricmethods,theelectromagneticradiationthatisprovidedbytheinstrumentisabsorbedbytheanalyte,andtheamountof absorption(ortransmittance)ismeasured.Theradiationpower(i.e.,theenergy,intheformofelectromagneticradiation,transferredacrossaunitareaperunittime)oftheincidentradiationdecreasesas itpassesthroughthesample.Theamountofdecreaseinradiationpowerisproportionaltotheanalyte concentration.Inotherwords,essentially,theamountofabsorbedradiationincreaseswiththe concentrationoftheanalyteandwiththedistancethroughtheanalytethattheradiationmusttravel (thecellpathlength).
Applicationinquantitativeanalysis: Asradiationisabsorbedinthesample,thepowerofthe radiativebeamarrivingatthephotondetectordecreases.Bymeasuringthedecreasedpowerthrougha fixed-path-lengthcellcontainingthesample,itispossibletodeterminetheconcentrationofthe sample.Becausedifferentsubstancesabsorbatdifferentwavelengths,theinstrumentsmustbecapable ofcontrollingthewavelengthoftheincidentelectromagneticradiation.Inmostinstruments,thisis accomplishedwithamonochromator.Inotherinstruments,itisdonebyuseofradiativefiltersorby useofsourcesthatemitradiationwithinanarrowwavelengthband.
Applicationinqualitativeanalysis: Also,becausethewavelengthatwhichsubstancesabsorb radiationdependsontheirchemicalcomposition,spectrophotometrycanalsobeusedforqualitative analysis.Theanalyteisplacedinthecell,andthewavelengthoftheincidentradiationisscanned throughoutaspectralregionwhilethetransmission(orabsorption)ismeasured.Theresultingplotof transmittedradiationorabsorbanceasanoinstructionfunctionofwavelengthorenergyoftheincident radiationiscalledtransmittanceorabsorptionspectrum.Thewavelength(s)atwhichpeak(s) (maximumabsorbance)areobservedareusedtoidentifycomponentsoftheanalyte.
FIG.2.1
UV VISSpectrophotometerwithadoublebeaminspace(Shimadzu:UV-1800).
Withinrangesoflight,calibrationsareneededonthemachineusingstandardsamples(samplesof analytewithknownconcentration).
Asanexample, Fig.2.1 showsaUV/Visiblespectrophotometer(productofShimadzucompany, Japan)whichiswidelyusedinacademia,researchandindustrialqualityassurance.Inparticular,itcan measureopticalabsorbance,transmittanceorextinctioncoefficientfromultraviolettonearIRregion (190 1100nm)ofelectromagneticradiationwitharesolutionof1nmwithuseruser-friendly features.
TheUV VISSpectrophotometersavailableinthemarketcanbeusedeitherasastand-alone instrumentorasaPC-controlledinstrument,comprisingofthefollowingknobstoeasethe measurementprocess.
1. On/Offswitch
2. Wavelengthselector/Readout
3. Samplechamber
4. Zerotransmissionadjustment/blankadjustment(orautoZero)knob
5. Measurementmode:Absorbance,Transmittance,Extinctioncoefficient
6. Measurementtype:(i)atabroadwavelengthrange(Spectrum),(ii)atasinglewavelength
7. Absorbance/Transmittance/Extinctioncoefficientscale
2.2Principleofabsorptionspectroscopicmeasurements
2.2.1Absorptionandemissionprocesses(conceptfromquantumphysics)
Inatomicormolecularabsorptionspectroscopy,followingtermsandmathematicalrelationsareused toquantifytheanalyteconcentration,tostudyaboutthestructuralfeatures,opticalproperties,andthe functionalgroupspresentinamoleculeofinterest,andsoon.
Anyatomicormolecularsystempossessesenergyonlyincertainspecificamountsorquanta. Thesearereferredtoasenergylevelsofsystem.Asetofquantizedenergylevelsisshownin Fig.2.2A.
From Fig.2.2,itcanbenoticedthatinorderthatsystemmaygofromenergylevel E1 to E2,itwill requiretheabsorptionofanamountofenergyequalto
Thisenergycanbeprovidedbyelectromagneticradiationoftheproperfrequencyiftheradiation caninteractwiththesystem.Thustheenergyoftheradiationabsorbedbythesystemisrelatedtothe energydifferencebetweenquantizedenergylevelsor,
DE ¼ hw; Bohrcondition
However,ifthesystemweretoundergoachangefromstate E4 toE3 thentherewouldbean emissionofenergyequalto
Andthefrequencyoftheradiationemittedwouldbegivenby
Theemissionofradiationoccurswhenamoleculeoranatominhigherenergystate(calledexcited state)returnstoalowerenergystate(orgroundstate).
However,inordertoobserveandinterpretaspectrumwemustkeepthreefundamentalconditions inmind:
1. TheBohrQuantumCondition: Whenasystemmakesatransitionbetweenquantizedenergy levels,thefrequencyoftheradiationabsorbedoremittedisgivenbytheconditions(see Eqs.2.1 and2.4).
2. Electricdipolarinteraction: Inanatomormolecule,ifabsorptionoremissionofonephotonof radiation,thedipolemomentiseithercreatedordestroyedduetoelectronchargeredistribution. Insuchasituation,theelectronictransitionstakeplace.Ontheotherhand,ifthereisnonet changeinthedipolemomentonredistributionofelectroniccharge(i.e.,chargedistribution remainssymmetric),thetransitiondoesnottakeplaceanditissaidtobeforbiddentransition. Thus,ontheabsorptionoflight,adipoleiseithercreatedordestroyedinitsexcitedstate.Incase ofmoleculesag-state(g:gerade)changestou-state(u:ungerade)orviceversa.Thismeans,in thecaseofamolecule,transitionfromthegroundstatetoanexcitedstateisallowedonlywhen thetransitionisfrombondingmolecularorbitaltoantibondingmolecularorbitalandviceversa. Thatis, u 4 g; bondingMO 4 antibondingMO
3. Selectionrules: Thecreationordestructionofdipolesrestrictthetransitionsthatoccurbetween energylevels.Theseselectionrulesareaconsequenceofthesymmetricpropertiesofthewave functionintwoenergystates.Forexample,theatomicwavefunctionsororbitals s,p,d,f are alternativelysymmetricanti-symmetricwithrespecttotheinversionabouttheoriginofthe system.Theselectionrulesforallowedelectronictransitionsforlightdiatomicmolecules:
^¼ 0; 1; D X ¼ 0:
[Note: DS ¼ 0meanspinstate.Alltransitionsaresinglet,doubletsandsoon.Intercombination singlet-Tripletandsimilartransitionsareforbidden]. 2.2
Absorption Emission
FIG.2.2
(A):Quantizedenergylevels.(B):Thedistortionofchargecloudduetoradiation.
2.2 Principleofabsorptionspectroscopicmeasurements 21
2.2.2Molecularorbitalpictureofexcitationduetoabsorptionoflight
Afterabsorptionorlightbyanatomormolecule,theelectronchargecloudaroundanatomor moleculeisdisturbed.Thedistortionofchargecloudproducesadipoleinthedirectionoftheincident radiation.Thisphenomenaispictoriallydemonstratedin Fig.2.2B
2.2.3Termsemployedinabsorptionspectroscopy
Inabsorptionspectroscopy,amongtheprocessesafterimpinginglightonanobject,thefollowingare measured:Transmission,absorption,reflection,scattering,andrefraction.Belowwediscussterms associatedwithabsorptionspectroscopy.
Transmittance: Transmittance, T,isthefractionofincidentlight(electromagneticradiation)ata specifiedwavelengththatpassesthroughasample.Thetransmittanceofabeamoflightasitpasses throughacuvettefilledwithanalytesolutionwithconcentration c isshownin Fig.2.3.
Thetransmittanceofasampleissometimesgivenasapercentage,asgivenin Eq.(2.5).Inthis equation,scatteringandreflectionareconsideredtobeclosetozeroorotherwiseaccountedfor.
where Po isthepoweroftheincidentradiationand P isthepoweroftheradiationcomingoutofthe sample.
Absorbance: Absorbance,orabsorptionfactor,isthefractionofradiationabsorbedbyasampleat aspecifiedwavelength.Forliquids,thetransmittanceisrelatedtoabsorbance (A) as
Inthecaseofgases,itiscustomarytousenaturallogarithmsinstead.
Intensity of incident light I0
Intensity of transmitted light I Sample cuvette with c moles/L of absorbing species
FIG.2.3
Schemeforabsorptionmeasurementofagivensample(DiagramofBeer-LambertLaw).Lightsources provideradiationwithvariouswavelengths.Monochromatorfiltersawavelengthoftheinterest,withintensity P0.AfterpassingthroughthesamplecelltheradiationintensitydecreasestoP.
Thetransmittanceisdirectlyproportionaltotheconcentration (C) oftheanalyteandwidth l ofthe sample(whichisdeterminedbythewidthofthecuvette)(Notes:detailsofderivationisgiveninthe consecutivesection).Thatis, A isdirectlyproportionaltoconcentrationandpathlength:
where a istheproportionalityconstant.Whenconcentrationisexpressedinanumberofmolesper centimetreand l isexpressedincentimeters,theaboveequationbecomes
where ε isthemolarabsorptioncoefficient.Aboveequationisknownas Beer’sLaw (detailedderivationfor Eq.2.8 isdiscussedintheconsecutivesection).Beer’sLawstatesthatmolarabsorptivityis constantandtheabsorbanceisproportionaltoconcentrationforagivensubstancedissolvedinagiven soluteandmeasuredatagivenwavelength.Accordingly,molarabsorptivitiesarecommonlycalled molarextinctioncoefficients.Sincetransmittanceandabsorbanceareunitless,theunitsformolar absorptivitymustcancelwithunitsofmeasureinconcentrationandlightpath.Accordingly,molar absorptivitieshaveunitsofM 1 cm 1.Standardlaboratoryspectrophotometersarefittedforusewith 1cmwidthsamplecuvette;hence,thepathlengthisgenerallyassumedtobeequaltooneandtheterm (in Eq.2.7)isdroppedaltogetherinmostcalculationsA ¼ ε C.
MolarExtinctionCoefficients: Inchemistry,biochemistry,molecularbiology,ormicrobiology, themassextinctioncoefficientandthemolarextinctioncoefficient(alsocalledmolarabsorptivity)are parametersdefininghowstronglyasubstanceabsorbslightatagivenwavelength,permassdensityor permolarconcentration,respectively.TheSIunitofmolarattenuationcoefficientisthesquaremeter permole(m2/mol),butinpractice,itisusuallytakenastheM 1 ,cm 1 ortheL,mol 1 ,cm 1.The molarattenuationcoefficientisalsoknownasthemolarextinctioncoefficientandmolarabsorptivity, buttheuseofthesealternativetermshasbeendiscouragedbytheIUPAC.
Molarabsorptivities(¼ molarextinctioncoefficients)formanyproteinsareprovidedinthe PracticalHandbookofBiochemistryandMolecularBiology(GeraldD.Fasman,1992).Expressedin thisform,theextinctioncoefficientallowsforestimationofthemolarconcentration(c ¼ A/ε) ofa solutionfromitsmeasuredabsorbance.
Extinctioncoefficientsforproteinsaregenerallyreportedwithrespecttoanabsorbancemeasured atornearawavelengthof280nm.Althoughtheabsorptionmaximaforcertainproteinsmaybeat otherwavelengths,280nmisfavoredbecauseproteinsabsorbstronglytherewhileothersubstances commonlyinproteinsolutionsdonot.
Example2.1. Theabsorbanceof5.4 10 4 MsolutionofFe3þ at530nmwas0.54whenmeasuredina cellwitha1cmpathlength.Calculatethemolarabsorptioncoefficient.
Solution:
2.2.4Beer-Lambert’slaw:quantitativeaspectsofabsorptionmeasurements
Creditforinvestigatingthechangeofabsorptionoflightwiththethicknessofthemediumisfrequently giventoGermanphysicistJohanLambert,althoughhereallyextendedconceptsoriginallydeveloped
byFrenchscientistPierreBouguer.GermanscientistAugustBeerlaterappliedsimilarexperimentsto solutionsofdifferentconcentrationsandpublishedhisresultsjustbeforethoseofFrenchscientistF. Bernard.ThetwoseparatelawsgoverningabsorptionareusuallyknownasLambert'slandandBeer’s Law.InthecombinedformtheyareknownastheBeer-Lambertlaw.
Lambert'sLaw: Considerabeamofmonochromaticlightpassingthroughasamplethatabsorbs someofthelight.If P istheradiationpoweroflightincidentuponathinlayerofasampleofthickness dl thefractionalchangeinintensity(dP/P)aslightpassesthroughthesampleisproportionaltoits thickness,
where a istheproportionalityconstantandiscalledtheabsorptioncoefficient.ThisiscalledLambert's Law.Lambert'slawstatesthatwhenmonochromaticlightpassesthroughatransparentmedium,the rateofdecreaseinintensitywiththethicknessofthemediumisproportionaltotheintensityofthe light.Thisisequivalenttostatingthatthefractionoftheincidentradiationabsorbedbyatransparent mediumisindependentoftheintensityofincidentradiationandthateachsuccessivelayerofthe mediumabsorbsanequalfractionofincidentradiation.Theintensityoftheemittedlightdecreases exponentiallyasthethicknessoftheabsorbingmediumincreasesarithmetically,thatanylayerofa giventhicknessofthemediumabsorbsthesamefractionofthelightincidentuponit.Thelight intensitytransmittedthroughasampleoffinitethickness l willbeobtainedbyintegrating Eq.(2.9) as
Integratingaboveequation,forradiationpower P 0 to P andpathlength0 1cm,yields:
Asstatedin Eq.(2.6),theterm‘ log
¼ A
istheabsorbance(formerlycalledopticaldensity, O.D.).
Thusamediumwithabsorbance1foragivenwavelengthtransmits10%oftheincidentlightatthat wavelength.
Beer’sLaw: Lambert’slawconsidersthelightabsorptionandlighttransmissionformonochromaticlightasafunctionofthethicknessoftheabsorbinglayeronly.Forquantitativechemical analysis,however,largelysolutionsareused.Beerstudiedtheeffectofconcentrationofthecolored constituentinsolutionuponthelighttransmissionorabsorption.Hefoundthesamerelation(Eq.2.10) betweentransmissionandconcentrationasLamberthaddiscoveredbetweentransmissionand thicknessofthelayer.Thatis,Beernoticedthatwhenlightpassesthroughthesolution,thefractional changeinlightintensityofabeamofmonochromaticlightisproportionaltotheconcentrationofthe absorbingspecies,c,inadditiontothethicknessoftheopticalpath(samplecontainerwidththrough whichlightpasses).Thatis
