Solid State
SolidS, liquidS and GaSeS
• The cooling of liquid molecules leads to the formation of solids.
• In the solid state, intermolecular attractive forces are extremely strong and as a result the molecular motion is completely stopped.
• In solids, the molecules assume fixed positions and their motion is restricted to just vibration.
• Unlike gases and liquids, the solids possess definite volume and shape.
• The constituent particles in solid are closely packed and this leads to the properties like incompressibility, rigidity, mechanical strength, slow diffusion and non-fluidity.
• Like liquids, solids also evaporate and hence exhibit vapour pressure.
• The molecules at the surface of solid possess more kinetic energy and break away from the surface to enter into vapour state.
• The process whereby a solid directly converts into vapour is called sublimation
• Substances such as ammonium chloride, iodine, camphor, solid carbon dioxide sublime at ordinary temperature and pressure.
• Snow sublimes when the surrounding temperature is less than 0°C.
• The white cloud-like exhaust fumes of high flying jets contain water vapour convert directly into microcrystalline ice slowly converts into water vapour without passing through liquid state.
• The property of sublimation is used in the freeze drying of substances containing water.
• Freeze drying is a process of cooling the substances containing water to below –10°C at 1 atm, where the water molecules freeze to ice. This when subjected to evacuation, water sublimes leaving behind the non-volatile components.
• Instant coffee, tea, powdered milk and many medicines are dried by freeze-drying method.
Types of Solids
• Solids are of two types: Crystalline and amorphous solids
• In Crystalline solids, the constituent particles are arranged in an orderly manner, for example, NaCl, ZnS, etc.
• The solids that do not possess crystalline form are called amorphous solids, for example, glass, rubber, many plastics, red phosphorous and amorphous sulphur.
• Amorphous solids are regarded as super-cooled liquids or pseudo solids because they do not melt sharply at a definite temperature but tend to soften on heating and gradually change into a viscous liquid.
• Isotropy is that, the physical properties such as refractive index, thermal and electrical conductivity and solubility are same in different directions. Amorphous solids are isotropic
• Anisotropy is that, the physical properties as above are different in different directions. Crystalline solids are anisotropic.
• Amorphous solids are characterized by limited in compressibility, limited rigidity, no definite geometric shape, no sharp melting point and isotropy.
• Crystalline solids are characterized by incompressibility, rigidity, mechanical strength, definite geometric shape, sharp melting point and anisotropy.
Classification of Crystalline Solids
• The crystalline solids are four types (i) covalent solids (ii) ionic solids (iii) molecular solids (iv) metallic solids
• Depending on the type of attractive forces between molecules, the molecular solids are again categorized into three types
• Non-polar molecular solids in which atoms such as Ar, Kr, Xe, and so on, or molecules of covalent substances such as H2, N2, O2, Cl2, and so on are held together by weak van der Waals forces. These solids have low melting points and the particles are widely separated than in close packed ionic or metallic lattices.
• Polar molecular solids in which molecules are held together by relatively stronger dipole–dipole interactions. The solids are soft and non-conductors of electricity. Their melting points are higher than those of non-polar molecular solids, for example, solid CO2, SO2, NH3, etc.
• Hydrogen-bonded molecular solids are those in which molecules participate in hydrogen bonding. In crystals of benzoic acid, hydrogen bonds cause the association into dimers which are then held together by van der Waals forces. These are also nonconductors of electricity.
• In ionic solids, the structural units are positive and negative ions, each ion being surrounded by a definite number of oppositely charged ions known as coordination number.
• In ionic solids, ions are held together by strong electrostatic forces and they have high melting points. They are hard and brittle. Since the ions in a solid are not free to move they are non-conductors of electricity in solid state but in molten state and in aqueous solution they ionize and become good conductors of electricity.
• In a covalent or network solid, the atoms are connected to one another by covalent linkages forming giant, network, for example, diamond, graphite, carborundum, quartz, and so on.
• In metallic solids, the units are positive metallic ions surrounded by a sea of mobile electrons, each electron belonging to a number of positive ions and each positive ion belonging to a number of electrons.
• The binding force in metallic solids is metallic bond.
• Metallic solids exhibit metallic lustre, high electrical and thermal conductivity due to free-moving electrons.
alloTropy and polymorphiSm
• Allotropy is the phenomenon of existence of a substance (element or compound) in two or more forms having different physical and chemical properties.
• Enantiotropy is that type of allotropy where each allotrope will exist independently, that is, stable over a given temperature range, for example, sulphur, tin, ammonium chloride, red and yellow forms of mercuric iodide.
• If one allotrope is stable under normal conditions but the other allotrope is unstable or metastable, then it is known as monotropic allotropy, for example, white and red phosphorous; diamond and graphite; calcite and aragonite. Under normal conditions, the metastable form changes to the stable form but never in the reverse direction.
• The phenomenon in which one allotrope changes into the other at exactly the same rate as the reverse occurs is known as dynamic allotropy. Both allotropes are stable over a wide range of conditions. In liquid state, Sλ and Sμ exhibit dynamic allotropy.
iSomorphiSm
• When two different chemical substances have the same crystalline form, they are said to be isomorphous (In Greek, ‘isomorphe’ means ‘equal form’.)
• Isomorphism is exhibited by the solids in which the packing in crystal lattice is same which depends on the nature of the forces holding the units of structure together and on the relative sizes and shapes.
• Ionic compounds exhibit isomorphism when the relative sizes of the ions are same and have similar shape, for example, NaCl and KCl are isomorphous, KSO24, KSeO24 , KMnO4, and BaSO 4; all alums are isomorphous.
Vapour preSSure and melTinG poinT
• Solids have some vapour pressure but are negligibly small due to strong forces which have to be overcome to vaporize.
• The temperature and pressure at which the three states solid, liquid and vapour of a substance are in equilibrium is called triple point
objective questions
1. Which one is not the property of crystalline solid? (1) isotropic (2) sharp melting point (3) a definite and regular geometry (4) high intermolecular forces
2. The characteristic features of solids are (1) definite shape (2) definite size (3) definite shape and size (4) definite shape, size and rigidity
3. The constituent particles of a solid have (1) translatory motion only (2) rotatory motion only (3) vibratory motion only (4) all the above type of motions
4. Which of the following is not a characteristic of crystalline solid?
(1) They have a regular geometry (2) They have sharp melting point (3) They have long range order of arrangements (4) They cannot be cleaved
5. If heat is supplied to a pure substance which is just beginning to melt, the (1) critical temperature will rise (2) temperature will remain constant (3) temperature will immediately rise (4) temperature will fall
6. In solids, the constituent particles may be (1) atoms (2) ions (3) molecules (4) any of these
7. Which of the following set contains all molecular crystals?
(1) LiF, solid CO 2, wax, diamond (2) ZnS, silicon, I 2, NaCl (3) Solid CO 2, wax, I 2, Ice (4) SiC, graphite, caesium chloride, rubber
8. A molecular crystalline solid (1) is very hard (2) is volatile (3) has a high melting point (4) is a good conductor
9. Amorphous solids are (1) solid substances in real sense (2) liquids in real sense (3) supercooled liquids
(4) substances with definite melting points
10. Amorphous solids
(1) possess sharp melting points
(2) undergo clean cleavage when cut with a knife (3) do not undergo clean cleavage when cut with a knife
(4) possess orderly arrangement over long distance
11. Which of the following statement is incorrect about amorphous solids?
(1) They are anisotropic.
(2) They are rigid and incompressible.
(4) They melt over a wide range in temperature. (4) There is no orderly arrangement of particles.
answers
(1) 1 (2) 4 (3) 3 (4) 4 (5) 2 (6) 4 (7) 3 (8) 2 (9) 3 (10) 3 (11) 1
CrySTal laTTiCeS and uniT CellS
• A space lattice is a regular arrangement of constituent particles (atoms, ions or molecules) of a crystalline solid in three-dimensional spaces.
• The positions which are occupied by the atoms, ions or molecules in the crystal are called lattice points or lattice sites
• The smallest repetitive unit of a crystal lattice which is used to describe the lattice is called the unit cell
• Crystals possess the same symmetry as their constituent unit cells.
• Primitive unit cells are drawn with lattice points at all corners, and each primitive cell contains the equivalent of one atom.
• When a primitive cell contains one or more constituent particles present at positions other than corners in addition to those at corners, it is called centred unit cell.
• In the simple unit cell, the particles are present only at the corners of the unit cell.
• In the body-centred unit cell, there is one particle present at the centre of the unit cell in addition to the particles at the corners of the unit cell.
• In a face-centred unit cell, there is one particle present on the centre of each face in addition to the particles at the corners of the unit cell.
• In the end-centred cell, there is one particle in the centre of two opposite faces in addition to the particles at the corners of the unit cell.
CrySTal SySTemS
• There are seven crystal systems, arising due to different symmetry of the crystal lattices.
The Seven Crystal Systems
Crystal system Axial distance or edge lengths
• A crystal system is characterized by the dimensions of a unit cell along the three axes (a, b, c) and the size of angles (αβγ ,, ) between the three axes.
• The various types of unit cells possible are given in the following Table and their shapes shown in the figure
• The total number of three-dimensional lattices are 14, which are known as Bravais lattices
Axial angles Possible types of unit cells Examples
Cubic a = b = c a=b=g= 90
Primitive body centred, face centred
Copper, KCl, NaCl, zinc blend, diamond
Tetragonal a = b ≠ c a=b=g= 90° Primitive body centred SnO2, White tin, TiO2, CaSO4
Orthorhombic a ≠ b ≠ c a=b=g= 90 Primitive, body centred, face centred, end centred Rhombic sulphur KNO3, CaCO3, BaSO4
Hexagonal a = b ≠ c a=b= 90 g= 120 Primitive
Trigonal or Rhombohedral a ≠ b ≠ c a=b=g≠ 90 Primitive
Monoclinic a ≠ b ≠ c a=g= 90 b≠ 90
Primitive, end centred
Graphite Mg, ZnO CdS
CaCO3 (Calcite, HgS, Cinnabar)
Monoclinic sulphur, Na2SO4.10H2O
Triclinic a ≠ b ≠ c a≠b≠g≠ 90 Primitive K2Cr2O7, CuSO4·5H2O, H3BO3
Primitive (or simple)
Body centred Face centred
The three cubic lattices: all sides same length; angles between faces all 90°
The two tetragonal lattices: one side different in length to the other two angles between faces all 90°
The four orthorhombic lattices: unequal sides; angles between faces all 90°
less than 90° more than 90°
Side view
The two monclinic lattices: unequal sides; two faces have angles differnent to 90°
number of aTomS per uniT Cell
• In a simple or primitive cubic lattice, the lattice points are located only at the corners.
• In different cubic unit cells, there are mainly four kinds of lattice points. The four types of lattice points and the contribution of each particle at the lattice point to the unit cell are
(i) A particle in the body of the unit cell belongs to that unit cell only and counts 1;
(ii) A particle on a face is shared by two unit cells and contributes 1 2 to the unit cell;
(iii) A particle at the edge is shared by four unit cells and contributes 1 4 to the unit cell; and
(iv) A particle at a corner is shared by eight cells that share the corner and so contributes 1 8 to the unit cell.
• In a simple or primitive cubic lattice, the lattice points are located at the corners of each unit cell and can contribute only 1 8 of each particle at the corner to the unit cell shared by 8 unit cells in space lattice. So a simple cubic unit cell has 81 1 8 ×= particle per unit cell
• In a body-centred cubic unit cell, particles are located at the centre of the cell as well as at the corners. Therefore the number of atoms per unit cell in body centred cubic unit cell is 8(at corners) × 1 8 11 2 +×= () at body centre particles
• In a face-centred cubic (fcc) unit cell, atoms are bound at the centre of the six faces of the cell as well as at each of the eight corners. The number of particles per unit cell in a fcc is 68 4 1 2 1 8 at centre of each face at corners ()×+()×= particles.
objective questions
12. Bravais lattices are (1) 10 types (2) 8 types (3) 7 types (4) 14 types
13. The three-dimensional graph of lattice points which sets the pattern for the whole lattice is called (1) space lattice (2) simple lattice (3) unit cell (4) crystal lattice
14. Which of the following type of cubic lattice has maximum number of atoms per unit cell? (1) simple cubic (2) body-centred cubic (3) face-centred cubic (4) all have same
15. Which one of the following is a primitive unit cell? (1) simple cubic (2) body-centred cubic (3) face-centred cubic (4) both body- and face-centred cubic
16. How many basic crystal systems are known? (1) 7 (2) 8 (3) 6 (4) 4
17. Which of the following systems has/have not been correctly characterized?
(1) cubic ab c =====° , αβγ 90
(2) cubic ab c =≠===° , αβγ 90
(3) monoclinic ab c ≠≠==°≠° ,, αγβ 90 90 (4) tetragonal ab c =≠===° , αβγ 90
18. The number of atoms per unit cell in a simple cubic, face-centred cubic and body-centred cubic are, respectively, (1) 1, 4, 2 (2) 1, 2, 4 (3) 8, 14, 9 (4) 8, 4, 2
19. Tetragonal crystal system has the following unit cell dimensions
(1) ab c == and αβγ===° 90
(2) ab c =≠ and αβγ===° 90 (3) ab c ≠≠ and αβγ===° 90 (4) ab c ≠= and αβ== °90 and γ=° 90
20. In a crystal a ≠ b ≠ c and a=g= 90° , b≠ 90° It is (1) monoclinic (2) rhombic (3) trigonal (4) tetragonal
21. Example of a unit cell with crystallographic dimensions ab c ≠≠ , αγ== °90 , β≠° 90 is (1) calcite (2) graphite (3) rhombic sulphur (4) monoclinic sulphur
22. For a certain crystal, unit cell axial lengths are found to be a = 562.Å, b = 741.Å and c = 10 13 .Å. The three coordinate axes are mutually perpendicular. The crystal system to which this crystal belongs is the (1) tetragonal (2) orthorhombic (3) monoclinic (4) cubic
23. If the three inter axial angles defining the unit cell are all equal in magnitude, the crystal cannot belong to the (1) orthorhombic system (2) hexagonal system (3) tetragonal system (4) cubic system
24. A match box exhibits
(1) cubic geometry
(2) orthorhombic geometry
(3) triclinic geometry
(4) monoclinic geometry
answers
(12) 4 (13) 1 (14) 3 (15) 1 (16) 1 (17) 2 (18) 1 (19) 2 (20) 1 (21) 4 (22) 2 (23) 2 (24) 2
paCkinG of equal SphereS (STruCTure
of meTalS)
• In metals, the atoms in a close-packed layer are arranged in a regular hexagon.
• In metals, the close-packed layers of atoms can be staked in two ways.
• In hexagonal close packing (hcp), after arranging the atoms of second layer in the depressions of the first layer, the atoms of third layer are arranged so that they will be immediately above the atoms in the first layer. This results in AB AB AB ….. pattern.
• Metals that crystallize in hcp structure are Be, Mg, Ti, Zn and Cd.
• In cubic close packing (ccp), the atoms in third layer are not immediately above the atoms in the first layer. This type of stacking of layers results in ABC ABC pattern
• Metals that crystallize in the ccp structure are Al, Cu, Ag, Au, Pt and Ni.
• In hcp and ccp structures, the coordination number, that is, the number of surrounding atoms in contact with an atom is 12.
• It is impossible to pack identical spheres (atoms) together with coordination number greater than 12.
inTerSTiTial SiTeS or inTerSTiTial VoidS
• In a close-packed arrangement of spherical particles (atoms/ions/molecules), two types of voids or holes are created.
• The void created when six spherical particles are in contact with each other is called octahedral void or octahedral hole.
• The void created when four spherical particles are in contact with each other is called tetrahedral void or tetrahedral hole.
• If tetrahedral voids of second layer are covered, hexagonal close-packed (hcp) structure results.
• If octahedral voids of second layer are covered, cubic close-packed (ccp) structure results.
• In a close-packed structure of N atoms, there are 2N tetrahedral voids and N octahedral voids. The octahedral voids are larger than tetrahedral voids.
• The radius ratio of different voids is 0.225 for tetrahedral void, 0.414 for octahedral void, 0.155 for triangular void and 0.732 for cubic void.
Tetrahedral hole (a) (b) Octahedral hole (a) Tetrahedral and (b) octahedral voids.
loCaTinG TeTrahedral and oCTahedral VoidS in CubiC CloSe paCkinG
• In cubic close packing, there are eight tetrahedral voids two on each body diagonal at one-fourth distance from each end.
• In cubic close packing or face-centred cubic close packing, there is one octahedral hole at the cube centre and 12 octahedral voids on the centres of 12 edges of the cube.
• The octahedral hole at the centre of the cube is surrounded by the atoms belonging to the same cube. The octahedral hole at the edge centre is surrounded by three atoms belonging to the same unit cell (2 on the corners and 1 on the face centre) and 3 belonging to the adjacent unit cells.
• Each octahedral hole on the edge centre is being shared by 4 unit cells. The number of octahedral voids in cubic close packing per unit cell is 4.
objective questions
25. Which of the following statement is wrong?
(1) The coordination number of each sphere in hcp arrangement is 12.
(2) In a close-packed array of N spheres, the number of octahedral holes is N
(3) In a close-packed array of N spheres, the number of tetrahedral holes is 2N.
(4) Hexagonal close-packed arrangement of ions is described as ABCABCABC….
26. Identify the false statement
(1) In ccp arrangement, the total number of octahedral voids formed will be 13.
(2) AB AB AB ….. arrangement represents cubic close-packed structure.
(3) If the coordination number of an element in its crystal lattice is 8, then the packing is bcc.
(4) In an fcc lattice, the number of nearest neighbours for a given lattice point is 12.
27. When identical spheres in the adjacent rows have a vertical as well as horizontal alignment in such a way that each sphere has four nearest neighbours, the type of pattern is called
(1) square close packing
(2) hexagonal close packing
(3) cubic close packing
(4) body-centred close packing
28. If three spheres of first layer and three of second layer enclose a site at the centre on a closest packing arrangement, then this site is called (1) interstitial site (2) tetrahedral site (3) octahedral site (4) none of these
29. In a closest packed lattice, the number of tetrahedral sites formed will be (1) equal to the number of spheres in the lattice (2) half than that of the number of spheres (3) double than that of the number of spheres (4) triple than that of the number of spheres
30. The intermetallic compound LiAg crystallizes in cubic lattice in which both lithium and silver have coordination number of eight. The crystal class is (1) simple cube (2) body-centred cube (3) face-centred cube (4) end-centred cube
31. A compound contains two types of atoms X and Y. Its crystal structure is cubic lattice with X atoms at
the corners of the unit cell and Y atoms at the body centre. The simplest formula of the compound is (1) XY 3 (2) XY 2 (4) XY (4) XY2
32. A Compound contains two types of atoms X and Y. Its crystal structure is a cubic lattice with X atoms at the corners of the cube and Y atoms are at the face centre. The simplest formula of the compound is
(1) XY 2 (2) XY3
(3) XY2 (4) XY 3
33. A solid has a structure in which X atoms are located at the cube corners of the unit cell, Y atoms are located at the cube edges and Z atoms at the cube centre. What is the formula of the compound?
(1) ZXY3 (2) XYZ (3) XYZ3 (4) ZYX3
34. CCP is same as (1) bcc (2) fcc (3) hcp (4) None of these
35. A packing consists of a base of spheres, followed by a second layer where each sphere rests in the hollow at the junction of four spheres below it and the third layer then rest on these in an arrangement which corresponds exactly to that in the first layer. This packing is knows as
(1) hexagonal close packing
(2) cubic close packing
(3) square close packing
(4) body-centred cubic packing
36. The two principal types of staking of closestpacked layers in metallic structures are called (1) body-centred cubic close packing and hexagonal close packing
(2) square based cubic-close packing and cubic close packing
(3) hexagonal close packing and cubic close packing
(4) cubic close packing and body-centred cubic packing
37. If the spheres in the first and third layers lie in different interstices of the second layer rather than in the same interstices, then the staking pattern is called
(1) cubic close packing
(2) hexagonal close packing
(3) body-centred close packing
(4) simple cubic lattice pattern
38. When a sphere fits into the depression formed by three other spheres close packed in two dimensions, then the void formed is called (1) an octahedral void (2) a tetrahedral void (3) tetragonal void (4) a rhombohedral void
39. The arrangement of the first two layers, one above the other in hcp and ccp arrangement, is (1) exactly same in both cases (2) partially same and partially different (3) different from each other (4) nothing definite
40. A tetrahedral void in a crystal implies that (1) shape of the void is tetrahedral (2) molecules forming the void are tetrahedral in shape (3) the void is surrounded tetrahedrally by four spheres (4) the void is surrounded by six spheres
41. The octahedral voids in a face-centred cubic (fcc) or (ccp) structure are located at (1) 6 at edge centres and 8 along body diagonals (2) 12 at edge centres and one at body centre (3) 8 along body diagonal and 6 at edge centres (4) all at edge centres only
42. The size of an octahedral void formed in a closestpacked lattice as compared to tetrahedral void is (1) equal (2) smaller (3) larger (4) not definite
43. Which of the following statement is wrong?
(1) Ag crystallizes in ccp structure (2) Cobalt crystallizes in bcc structure (3) In hcp in two layers one above the other, the coordination number of each sphere will be 9 (4) In a fcc lattice, the number of nearest neighbours for a given lattice point is 8
44. An alloy of copper, silver and gold is found to have copper constituting the ccp lattice. If silver atoms occupy the edge centres and gold is present at body centre, then the alloy has the formula
(1) Cu Ag Au 42
(2) Cu Ag Au 44
(3) Cu Ag Au 43
(4) Cu Ag Au
45. On increasing the temperature of a crystalline compound, (1) it decomposes
(2) coordination number increase (3) coordination number decreases (4) None of these happens
answers
(25) 4 (26) 2 (27) 1 (28) 3 (29) 3 (30) 2 (31) 3 (32) 2 (33) 1 (34) 3 (35) 4 (36) 3 (37) 1 (38) 3 (39) 1 (40) 3 (41) 2 (42) 3 (43) 4 (44) 3 (45) 3
effiCienCy of paCkinG
• The atomic radius r is expressed in terms of edge length ‘ a ’
• r a = 2 in the case of simple cubic lattice.
• r a = 22 in the case of face centred cubic lattice
• ra = 3 4 in the case of body centred cubic lattice
• Ionic radii of an ion ‘ r ’ in terms of edge length in different types of ionic crystals can be expressed as rr a ca+= in the case of simple cubic lattice
rr a ca+= 2 for cubic lattice of NaCl type
rr a ca+= 3 2 for a body-centred lattice of CsCl type
• Volume occupied in an fcc arrangement is 74.06%
• Volume occupied in body-centred cubic (bcc) arrangement is 68%
• Packing efficiency of simple cubic lattice is 52.4%
• Packing efficiency of hexagonal close packing is 74%
CalCulaTion inVolVinG uniT Cell dimenSionS
• If the edge length of the unit cell is ‘ a ’ pm, that is, a × 10 10 cm
Volume of the unit cellcm
Density of the unit cel =× a 3303 10 l Mass of the unit cell Volume of the unit cell =
• Mass of the unit cell = (No atoms or formula units per unit cell) × (Mass of one atom or one formula unit) =×Zm
Here Z is the number of atoms present in one unit cell and m is the mass of a single atom.
m M N = A , where M is gram molecular weight and NA is Avogadro’s number (60210 23 . × ).
Density d ZM Na = × A gcm 330 3 10
radiuS raTio: STruCTure of an ioniC Compound
• In ionic solids every ion is surrounded by a number of oppositely charged ions.
• The number of oppositely charged ions surrounding an ion is called as the coordination number of that particular ion
• The arrangement of ions in a crystal and the coordination number of an ion depends on the radius ratio of the ions or atoms surrounded it.
• In the case of ionic solids, the ratio of the radius of cation to the radius of an anion is called limiting radius ratio
• In the simple ionic crystals, anions are normally larger than cations and arranged in a closest-packed array.
• Being smaller in size, cations occupy the voids. If all the octahedral voids are occupied by cations, the number of cations is equal to the number of anions. If all the tetrahedral voids are occupied by cations, the number of cations is twice the number of anions.
• Relatively small cations occupy the tetrahedral holes while larger cations occupy the octahedral holes.
• If cation is too large to fit into the octahedral hole, the anions make larger cubic holes for cations.
• Coordination numbers of 5, 7, 9, 10 and 11 do not occur because of the impossibility of balancing the electrical charges.
• When the radius ratio becomes equal to 1, ions of the same size are making up the crystal. This is found in the crystals of metals.
• When all the octahedral voids are occupied by the cations, the crystal will get the rock-salt structure.
• When half the tetrahedral voids are occupied by cations the crystal will get the zinc blende or sphalerite structure.
• If all the tetrahedral voids are occupied by anions while cation adopt cubic close-packed structure, the crystal will get the fluorite structure and the formula of the compound will be AB2 as the tetrahedral voids are double to the ions making cubic closepacked structure.
• If anions adopt cubic close packing and cations occupy all the tetrahedral voids, the crystal will get the antifluorite structure and the formula of the compound will be A2B.
• Packing efficiency of rock-salt structure is 79% and that of zinc blend structure is 75%
• The type of hole occupied can be determined from the radius ratio.
<0.155 2 Linear
0.155–0.225 3 Triangular 0.225–0.414 4 Tetrahedral 0.414–0.732 6 Octahedral 0.732–1 8 Cubic
objective questions
46. If R is the radius of spheres forming closest-packing lattice and r is the radius of the tetrahedral void, then these two parameters are related as (1) rR = 0 155 (2) rR = 0 225 (3) rR = 0.414 (4) rR = 0.732
47. Close packing is maximum in (1) simple cubic (2) bcc (3) fcc (4) None
48. The edge length of face-centred unit cubic cell is 508 pm. If the radius of the cation is 110 pm, the radius of anion is (1) 110 pm (2) 144 pm (3) 618 pm (4) 398 pm
49. Suppose ‘ a ’ is the axial length of the body-centred cubic unit cell, then the distance between nearest neighbours is (1) a 2 (2) a 2 (3) 2 4 a (4)
50. Platinum crystallizes in face-centred cubic crystal with a unit cell length ‘ a’. The distance between nearest neighbour is
(1) a (2) a 3 2
(3) a 2 2 (4) a 2 4
51. Calcium crystallizes in fcc lattice. The axial length of one unit cell is 556 pm. Calculate the radius of a calcium atom.
(1) 278 pm (2) 241 pm
(3) 481 pm (4) 197 pm
52. Lithium crystallizes in body-centred cubic lattice of unit cell length 352 pm. The distance between nearest neighbours is
(1) 150 pm (2) 75 pm (3) 304 pm (4) 122 pm
53. The distance between adjacent oppositely charged ion in rubidium chloride is 3 285 .Å, in potassium chloride is 3 139 .Å, in sodium bromide is 2.981 and in potassium bromide is 3.293. The distance between adjacent oppositely charged ions in rubidium bromide is
(1) 3 147 .Å (2) 3 385 .Å (3) 3 393 .Å (4) 3 439 .Å
54. How many unit cells are there in 1.00 g cubeshaped ideal crystal of AB (MW = 60), which has NaCl type lattice?
(1) 60210 23 × (2) 25 10 21 . × (3) 10010 22 × (4) 60210 24 . ×
55. Packing fraction (fraction of volume occupied)
(1) depends on the radius of the spheres (2) depends only on the nature of packing (3) depends both on the radius of the sphere and the nature of the packing (4) is independent of the nature of the packing
56. The low density of the alkali metals is due to (1) their body-centred cubic structure in which about 32% of the available space is unfilled (2) their hexagonal close-packed structure in which about 74% of the available space is unfilled (3) their cubic close-packed structure in which 74% of the available space is filled
(4) their body-centred cubic structure in which about 47% the available space is unfilled
(46) 2 (47) 3 (48) 2 (49) 4 (50) 3 (51) 4 (52) 3 (53) 4 (54) 2 (55) 2 (56) 1
STruCTure of ioniC CompoundS
Sodium Chloride Structure
• In NaCl, each Na + or Cl ion is surrounded by six (coordination number) other oppositely charged ions octahedrally.
• NaCl structure is regarded as cubic close-packed array of Cl ions with Na + ions occupying all the octahedral holes.
• The unit cell of NaCl has 4 Na + ions and 4 Cl ions and thus 4 formula units per unit cell.
• The ionic solids having NaCl-type crystal structure are HgO, CaO, SrO, NaBr, KCl, and so on.
ZinC blende or SphaleriTe (ZnS) STruCTure
• The radius ratio 0.4 of Zn 2 + and S2 in zinc blende suggests a tetrahedral arrangement of ZnS.
ay2 Type ioniC SolidS
fluorite (Calcium fluoride) Structure
• In fluorite each Ca 2 + ion is surrounded by eight F ions giving bcc arrangement.
• Each F ion in CaF2 is surrounded by four Ca 2 + ions tetrahedrally.
• Since the number of F ions is double the number of Ca 2 + ions, the coordination number of Ca 2 + and F are 8 and 4, respectively.
• Ionic solids having fluorite structure are UO2, ThO2, SrF2.
a2X Type ioniC Solid antifluorite Structure
• In antifluorite structure, anions form cubic close packed arrangement and cations occupy tetrahedral holes
• In antifluorite structure, coordination number of cation is 4 and that of anion is 8.
• Ionic solids having antifluorite structure are Li2O, Na2O, K2O and Rb2O.
Structure of Some Solid Crystals
• Rutile is one form of titanium dioxide. Its unit cell has a tetragonal structure in which titanium ions are at the corners and at the centre of the cube. The titanium ion at the centre is surrounded by six oxide ions.
• Every titanium ion is surrounded by six oxide ions and every oxide ion has three titanium ions as their nearest neighbours.
• The ratio of titanium and oxide ions is 1:2 and the formula of rutile is TiO2
• In ZnS (zinc blende) each Zn 2 + ion is surrounded by four S2 ions and each S2 ion is tetrahedrally surrounded by four Zn 2 + ions.
• In ZnS the coordination number of Zn 2 + and S2 is 4:4 arrangement.
• ZnS is related to cubic close-packed structure and Zn 2 + ions occupy tetrahedral holes.
• Since there are twice as many tetrahedral holes as there are S2 ions. It follows that to obtain a formula ZnS, only half of the tetrahedral holes are occupied by Zn 2 + (that is every alternate tetrahedral site is occupied)
• ZnS has face-centred cubic structure in which S2 ions occupy the lattice points and Zn 2 + ions are at one-fourth of the distance along each body diagonal.
• Each unit cell of ZnS consists of four Zn 2 + and four S2 ions making 4 ZnS formula units.
• Ionic solids having ZnS crystal structure are BeO, CuCl, Cu, and so on.
Wurtzite Structure
• Wurtzite has hexagonal structure. Sulphide ions occupy the triangular faces. Four zinc ions make up the corners of tetrahedron centred on another sulphide ion at a central point in the cell.
• The coordination number of each is 4.
Caesium Chloride Structure
• The radius ratio of CsCl is 0.93 which indicates that CsCl has bcc-type arrangement in which each Cs + ion surrounded by Cl ions and vice versa and the coordination number of CsCl is 8:8.
• In CsCl, if the ions at the corners are Cl- ions there will be Cs + ion at the body-centred position or vice versa.
• The ionic solids having CsCl structure are CsBr, CsI, TlBr.
perovskite Structure
• Perovskite is a mineral with formula CaTiO3
• The Ca2+ ions occupy the corners of the cube, the O2– ions occupy the face centres of the cube and the titanium ion lies at the centre of the cube.
Structure of magnetite (fe3o4)
• The Fe3O4 contains Fe3 + and Fe 2 + ions in the ratio 2:1 and considering the composition of FeO Fe2O3
• In Fe3O4, oxide ions are arranged in ccp and Fe 2 + ions occupy octahedral voids while Fe3 + ions are equally distributed between octahedral and tetrahedral holes.
• Mg Fe O 24 also has the structure similar to magnetite in which Mg 2 + ions are present in place of Fe 2 + ion in Fe O 34
• Magnetite has an inverse spinel structure.
normal Spinel Structure
• Spinel is a mineral (MgAlO24)
• In spinel oxide ions are arranged in ccp with Mg 2 + ions occupying tetrahedral voids and Al3 + ions occupy octahedral voids.
• Ferrites such as ZnFe O 24 also possess spinel structure.
objective questions
57. The tetrahedral voids formed by ccp arrangement of Cl– ions in rock salt structure are (1) vacant (2) occupied by Na + ions (3) occupied by Cl ions (4) occupied by both Na + and Cl ions
58. The number of Cl ions required to form ccp lattice of NaCl structure will be (1) 14 (2) 13 (3) 12 (4) 9
59. The rr +− / value of zinc blende structure is 0.4.This predicts
(1) C.N. 4 with tetrahedral arrangement
(2) C.N. 4 with square planar arrangement
(3) C.N. 8 with b.c.c arrangement
(4) C.N. 6 with octahedral arrangement
60. In fluorite (CaF2) structure all octahedral voids are (1) occupied by Ca 2 + ions (2) vacant (3) occupied by F ions (4) none of these
61. In fluorite (CaF2) structure, the Ca 2 + ions are arranged in (1) bcc type structure (2) fcc type structure (3) hcp type structure (4) none of these
62. Na O 2 has antifluorite structure. The fcc type of lattice will be formed by (1) O 2 ions (2) Na + ions (3) Na + and O 2 ions (4) None of these
63. For an ionic compound of general formula AX and coordination number 6, the value of radius ratio will be
(1) greater than 0.73 (2) in between 0.73 and 0.41 (3) in between 0.41 and 0.22 (4) less than 0.22
64. The positions of Na + ions in NaCl structure are (1) corners of the cube (2) body centre of the cube (3) edge centres of the cube (4) both 2 and 3
65. Space lattice of CaF2 is (1) fcc (2) bcc (3) simple cubic (4) hcp
66. Which of the following statement is not correct? (1) The coordination number of each type of ion in CsCl crystal is 8 (2) A metal crystallizes in bcc structure has a coordination number 12 (3) A unit cell of an ionic crystal shares some of its ions with other unit cells (4) The edge length of the unit cell in NaCl is 552 pm
Rr Na Cl pm pm +− == () 95 181 ,
67. A mineral having the formula AB2 crystallizes in the cubic close-packed lattice with A atoms
Solid State 1.13
occupying the lattice points. What is the coordination number of the B atoms?
(1) 4 (2) 6 (3) 8 (4) 12
68. Antifluorite structure is derived from fluorite structure by
(1) heating fluorite crystal lattice
(2) subjecting fluorite structure of high pressure (3) interchanging the positions of positive and negative ions in the lattice
(4) None of these
69. In a compound XY O 24, Oxide ions are arranged in cubic close-packing arrangement and cations X are present in octahedral voids. Cations Y are equally distributed between octahedral and tetrahedral voids. The fraction of the octahedral voids occupied is
(1) 1 2 (2) 1 4 (3) 1 6 (4) 1 8
70. The coordination numbers of cation occupying a tetrahedral hole and an octahedral hole, respectively, are (1) 4, 6 (2) 6, 4 (3) 8, 4 (4) 4, 8
71. The structure of TlCl is similar to CsCl. What would be the radius ratio in TlCl?
(1) 0.155–0.225 (2) 0.225– 0.414 (3) 0.414–0.732 (4) 0.732–1.00
72. The type of structure assumed by an ionic compound is determined by (1) relative number of each kind of the ions (2) relative sizes of each kind of the ions (3) both 1 and 2 (4) None of these
73. Which one of the following statement is wrong about rock salt type structure?
(1) it has an fcc structure
(2) Na + and Cl ions have a coordination number 6:6
(3) A unit cell of NaCl consists of four NaCl units
(4) All halides of alkali metals have rock-salt type structure
74. Which one of the following statements is wrong about zinc blend-type structure?
(1) Each Zn 2 + ion is surrounded tetrahedrally by four S2 ions and each S2 ion by four Zn 2 + ions
(2) S2 ions form an fcc arrangement
(3) AgBr has zinc blend-type structure
(4) cuprous halides have zinc blende-type structure
75. The number of formula units in unit cell of fluorite is (1) 2 (2) 4 (3) 6 (4) 8
76. Among NaCl, ZnS, CaF2 and CsCl, in which case the cations form ccp structure (1) NaCl (2) ZnS (3) CsCl (4) CaF2
77. In the sphalerite (ZnS) structure S2 ions form face-centred cubic lattice. Then Zn 2 + ions are present on the body diagonal at (1) 1 3 rd of the distance (2) 1 4 th of the distance (3) 1 6 th of the distance (4) 1 8 th of the distance
78. A solid AB+− has the B ions arranged as below. If the A + ions occupy half the tetrahedral sites in the structure, then the formula of solid is
CrySTalloGraphy
• The branch of science which deals with the geometrical properties and structure of crystals and crystalline substances is called crystallography.
• The law of constancy of interfacial angles states that for a given substance the corresponding faces or planes forming the external surface of crystal intersect at a definite angle called interfacial angle and remains always constant no matter how the faces develop.
• Plane of symmetry is an imaginary plane which passes through the centre of a crystal and divides it into two equal portions, such that one part is the exact mirror image of the other.
• Axis of symmetry is a line about a crystal may be rotated such that it presents same appearance more than once during the complete rotation.
• A n-fold (or n-gonal) axis of symmetry is an axis such that when an ideal crystal is rotated around it, the crystal occupies the same position in space by n-times in a complete rotation of 360°.
(1) AB (2) AB2 (3) A2B (4) A3B4
79. For a solid with the following structure, the coordination number of the point B is
(1) 3 (2) 4 (3) 5 (4) 6
80. In a solid AB having the NaCl structure ‘A’ atoms occupy the corners of the cubic unit cell. If all the face-centred atoms along one of the axes are removed, then the resultant stoichiometry of the solid is
(1) AB2 (2) A2B (3) A4B3 (4) A3B4
81. In which of the following crystals alternate tetrahedral voids are occupied (1) NaCl (2) ZnS (3) CaF2 (4) Na2O
answers
(57) 1 (58) 1 (59) 1 (60) 2 (61) 2 (62) 1 (63) 2 (64) 4 (65) 1 (66) 2 (67) 4 (68) 3 (69) 1 (70) 1 (71) 4 (72) 2 (73) 4 (74) 3 (75) 2 (76) 4 (77) 2 (78) 1 (79) 4 (80) 2 (81) 2
• Centre of symmetry is a point in the body of the crystal such that a line drawn through it intersects the opposite faces at equal distances in both directions.
• Only one centre of symmetry is possible for any crystal.
• The total number of planes, axes and centre of symmetry possessed by a crystal is known as elements of symmetry.
• A cube has three rectangular planes of symmetry, six diagonal planes of symmetry, three fourfold axes of symmetry, four threefold axes of symmetry, six twofold axes of symmetry thus the total of symmetry elements is 23.
• The law of rational indices states that intercepts of the planes of a crystal on a suitable set of axes can be expressed by small multiples of unit distances.
• The indices used in practice to denote the direction of a plane of a crystal are called Miller indices.
• For calculating Miller indices, a reference plane known a parametral plane is selected having intercepts a, b and c along x-, y- and z-axes, respectively.
• The intercepts of the unknown plane are given with respect to a, b and c of the parametral plane as
h a x = intercept of the plane along -axis
k b y
l c = = intercept of the plane along -axis
intercept of the p plane along -axis z
• The distance between the parallel planes in crystal is designated as d hkl
• For different cubic lattices, the interplanar spacing is given by the general formula:
objective questions
82. In the Bragg’s equation for the diffraction of X-rays, ‘ n ’ represents (1) number of moles (2) quantum number (3) Avogadro’s number (4) the order of reflection
where ‘ a ’ is the length of the cube side while h, k and l are the Miller indices of the plane.
• The spacings of three planes (100), (110) and (111) of simple cubic lattice can be calculated as follows. d
83. Bragg’s law is given by the equation (1) n λθθ = 2sin (2) ndλθ = 2sin (3) 22ndλθ = sin (4) n d θ θ 22 = sin
84. The second-order Bragg diffraction of X-ray with λ= 10.Å from a set parallel planes in metal occurs at an angle 60° The distance between the scattering planes in the crystal is (1) 057.Å (2) 100.Å (3) 115.Å (4) 200.Å
• The ratio of three planes for a simple cube is
• The d hkl ratio of the face-centred cubic and bodycentred cubic are
85. A crystal plane intercepts the three crystallographic axes at a, 1 2 b and 3 2 c, where a, b and c are the unit lengths along x-, y- and z-axes, respectively. The Miller indices of the plane will be (1) 1:2:0.67 (2) 1:0.5:15 (3) 3:6:2 (4) 2:1:3
86. In a hypothetical solid C atoms are found to form cubical close packed lattice, A atoms occupy all tetrahedral voids B atoms occupy all octahedral voids. A and B atoms are of appropriate size, so that there is no distortion in ccp lattice of C atoms. Now if a plane as shown in the following figure is cut, then the cross section of this plane will look like
deTerminaTion of STruCTure of SolidS by X-ray diffraCTion
• When X-rays are incident on a crystal face, they are reflected by the atoms in different planes.
• Bragg’s equation to calculate the distance between the repeating planes of particles in crystals from the reflected X-rays is ndλθ = 2sin
where n is an integer like 1, 2, 3 and represents order of reflection, λ is the wavelength of the X-rays used and d is the distance between the repeating planes.
87. In an fcc crystal, which of the following shaded planes contains the following type of arrangement of atoms?
• The crystal defects are mainly two types: (i) point defects and (ii) line defects.
• Point defects are due to the irregular arrangement around a point or an atom in a crystalline substance.
• Line defects are the irregularities or deviations from ideal arrangement in the entire rows of lattice points.
Types of point defects
• Point defects are classified into three types: (i) Stoichiometric defects (ii) Impurity defects (iii) Non-stoichiometric defects
(b)
(d)
88. Crystal is made of particles A and B. A forms fcc packing and B occupies all the octahedral voids. If all the particles along the plane as shown in the fig. are removed, then, the formula of the crystal would be:
Stoichiometric defects
• Stoichiometric defects are also known as intrinsic or thermodynamic defects
• The defect due to the vacancy of the lattice sites is called vacancy defect.
• Due to vacancy defect the density of the substances decreases
• Vacancy defects can be developed by heating.
• If constituent particles occupy interstitial site extra to the lattice points, interstitial defects arise.
• Due to interstitial defects, density of substances increases.
• Non-ionic solids exhibit vacancy and interstitial defects.
• The vacancy and interstitial defects exhibited by ionic solids are known as Frenkel and Schottky defects.
(a) AB (b) A5B7 (c) A7B5 (d) None of these answers
(82) 4 (83) 2 (84) 3 (85) 4 (86) 3 (87) 1 (88) 1
imperfeCTionS in SolidS
• The imperfections or defects which arise due to irregularity in the arrangement of atoms or ions
• Schottky defect consists of a pair of holes in the crystalline lattice due to the absence of one positive ion and one negative ion (to maintain electrical neutrality).
• In the case of Schottky defect, the density of solid decreases.
• Schottky defect occurs mainly in the ionic compounds which contain smaller ions of similar size which have high coordination number, for example, NaCl, CsCl, KCl and KBr.
• Frenkel defect is created when an ion occupies an interstitial site instead occupying its correct lattice site.
• The small cations (compared to anions) occupy the interstitial positions thus causing Frenkel defect.
(a)
(c)
• Frenkel defect is favoured when there is large difference in the size between cation and anion and having low coordination number 4 to 6.
• AgCl, AgBr and AgI show Frenkel defect. In these solids Ag+ions occupy the interstitial sites.
• There is no change in density of the solid due to Frenkel defect but the lattice may be distorted and show increase in the unit cell dimensions due to the presence of ions in interstitial positions.
• Impurity defects are due to the occupation of other type of cation in a crystal lattice in the place of normal cations.
• Occupation of Sr 2 + ion in the place NaCl crystal lattice two Na + ions is replaced by one Sr 2 + ion to maintain electrical neutrality, thus creating a site of one Na + ion vacant.
• The cationic vacancies created are equal to the number of M2 + ions, for example, solid solution of Cd Cl 2 and AgCl.
• In non-stoichiometric defects, the ratio of positive ion to negative ion is not exactly one.
• The metal excess defect is due to the absence of a negative ion from its lattice point leaving a hole which is occupied by an electron, thereby maintaining the electrical neutrality.
• NaCl/Na; KCl/K shows metal excess defect.
• The non-stoichiometric NaCl/Na is yellow in colour.
• In metal excess defect, the anion site occupied by an electron is called F-Centre.
• The solids having F-centres have colour and the intensity of the colour increases with an increase in the number of F-centres.
• Solids containing F-centres are paramagnetic since the electrons occupying the vacant sites are unpaired.
• When materials with F-centres are irradiated with light become photoconductors.
• Metal excess defects also occur when an extra positive ion occupies an interstitial position in the lattice and to maintain electrical neutrality one electron is included in an interstitial position for example, ZnO, CdO, Cr2O3 and Fe2O3.
• The solids with metal excess defect contain free electrons and behave as n-type semiconductors.
• ZnO is white at low temperature but yellow at high temperature because it loses oxygen reversibly at high temperature and forms a non-stoichiometric defect with metal excess.
• Metal deficiency defect is due to the absence of a positive ion from its lattice point and the charge can be balanced by an adjacent metal ion having an extra positive charge, for example, FeO, NiO, FeS and CuI.
• If one Fe2+ ion is missing from its lattice site in FeO then there must be two Fe3+ ions somewhere in the lattice to balance the electrical charges.
• Crystals with metal deficiency defects are p-type semiconductors
objective questions
89. In Schottky defect (1) some of the lattice sites are vacant (2) an ion occupies interstitial position between lattice points (3) a lattice point is occupied by electron (4) the radius ratio rr +− / is low
90. Schottky defect generally appears in (1) NaCl (2) KCl (3) CsCl (4) All
91. Frenkel defect generally appears in (1) AgBr (2) AgI (3) ZnS (4) All
92. In a solid lattice the cation has left a lattice site and is located at an interstitial position, the lattice defect is (1) interstitial defect (2) valency defect (3) Frenkel defect (4) Schottky defect
93. Ionic solids with Schottky defects contain in their structure (1) equal number of cation and anion vacancies (2) anion vacancies and interstitial anions (3) cation vacancies (4) cation vacancies and interstitial cations
94. Due to Frenkel defect, the density of ionic solids (1) increases (2) decreases (3) does not change (4) changes
95. Point defects are present in (1) ionic solids (2) molecular solids (3) amorphous solids (4) liquids
96. Schottky defects in crystal is observed when (1) unequal number of cations and anions are missing from the lattice (2) equal number of cations and anions are missing from the lattice
(3) an ion leaves its normal sites and occupies an interstitial site (4) density of crystal is increased
97. Which of the following solid will not show the Schottky defect?
(1) NaCl (2) CsCl (3) KBr (4) AgBr
98. In which of the following solids, the Frenkel defects are common?
(1) covalent solids with high coordination number (2) covalent solids with low coordination number (3) ionic solids with low coordination number (4) ionic solids with high coordination number
99. In stoichiometric defects, the ratio of positive and negative ions as indicated by chemical formula of the compound (1) decreases (2) increases (3) remains the same (4) cannot be predicted
100. In the Schottky defect (1) cations are missing from the lattice sites and occupy the interstitial sites (2) equal number of cations and anions are missing (3) anions are missing and electrons are present in their place (4) equal number of extra cations and electrons are present in the interstitial sites
101. As a result of Schottky defect (1) there is no effect on the density (2) density of the crystal increases (3) density of the crystal decreases (4) any of the above three can happen
102. Frenkel defect is found in crystals in which the radius ratio is (1) low (2) 1.3 (3) 1.5 (4) slightly less than unity
103. What type of crystal defect is indicated in the diagram given below?
(1) Frenkel and Schottky defects (2) Schottky defect (3) Interstitial defect (4) Frenkel defect
104. Metal deficiency defects are shown by (1) alkaline earth metals (2) alkali metals
(3) transition metals (4) None of these
105. The electrons trapped in anion vacancies in metal excess defects are called (1) mobile electrons (2) trapped electrons (3) valence electrons (4) F-centres
106. The correct statement regarding F-centre is (1) electrons are held in the voids of crystals (2) F-centre imparts colour to the crystals (3) conductivity of the crystal increased due to F-centre
(4) All the above three
107. Non-stoichiometric form of NaCl is (1) yellow (2) red (3) lilac (4) blue
108. Non-stoichiometric metal deficiency is shown in the salts of (1) all metals (2) alkali metals only (3) alkaline earth metals only (4) transition metals only
109. ZnO is white when cold and yellow when hot. It is due to the development of (1) Frenkel defect (2) Schottky defect (3) metal excess defect (4) metal deficiency defect
110. When NaCl crystal is doped with MgCl2, the nature of the defect produced is (1) interstitial defect (2) Schottky defect (3) Frenkel defect (4) None of these
111. Mark the false statement in the below: (1) CsCl crystal shows Schottky defect
(2) Crystals having F-centres are coloured and paramagnetic
(3) Photosensitivity of AgBr is due to the presence of Frenkel defect in its crystals (4) None of these
answers
(89) 1 (90) 4 (91) 4 (92) 3 (93) 1 (94) 3 (95) 1 (96) 2 (97) 4 (98) 3 (99) 3 (100) 2 (101) 3 (102) 1 (103) 2 (104) 3 (105) 4 (106) 4 (107) 1 (108) 4 (109) 3 (110) 4 (111) 4
properTieS of SolidS
electrical properties
• Good conductors are those which allow the maximum current to flow through them and their conductivity is of the order 1081 1 Ω cm .
• Metallic conductors allow the current to pass through them without undergoing any chemical change.
• In metallic conductors, the conductance is due to the movement of electrons under the influence of an applied electric potential. The stream of electrons constitutes the current.
• Electrolytic conductors allow the electricity to pass through them by undergoing chemical change.
• The conductivity of electrolytic conductors is due to the movement of ions in their molten state or in their aqueous solution.
• Semiconductors are the solids whose conductivity lies between those of typical metallic conductors and insulators. Their conductivity range is 10 6 to 10 41 1 Ω cm .
• Insulators are those which do not allow electricity to flow through them. Their conductivity is 10-22W-1cm-1
electrical Conductivity in metals
• According to molecular orbital (MO) theory, in a metal crystal the orbitals of valence shell of all atoms combine to form a large number of MOs around all the atoms in that metal crystal.
• Since a large number of MOs having almost equal energy are formed, they are very close to each other and form as a band of MOs.
• Depending upon different types of atomic orbitals which overlap, different energy bands are formed.
• The arrangement of electrons in the different energy bands determines the characteristics of a metal.
• The energy bands formed from different atomic orbital may overlap or be separated from each other.
• The highest occupied energy band is called the valence band while the lowest unoccupied energy band is called conduction band.
• In the case of metals, the valence band may be half filled or there may be an overlapping between the valence band and conduction bands which makes it possible for the electrons to go in to vacant bands and hence responsible for electrical conductivity.
• In the case of insulators, the energy gap is intermediate between those of metals and insulators. The increase in temperature gives thermal energy for some electrons in valence band to move into the conduction band and hence their electrical conductivity increases with increase in temperature
• Semiconductors are perfect insulators at absolute zero.
• Silicon and germanium which crystallize in diamond type network lattice are semiconductors.
• At room temperature the conductivity of silicon and germanium is extremely low but at high temperature the bonds begin to break down emitting the electrons and hence conductivity increases.
• The conduction introduced in the crystal without adding an external substance is called intrinsic conduction.
• Doping is a process of mixing pure silicon or germanium with an impurity.
• Doping enhances the conductivity and the products are called extrinsic semiconductors.
• n-type semiconductors (‘n’ stands for ‘negative’) are obtained due to metal excess defect or by adding trace amounts of V or 15th group elements (P, As) to pure silicon or germanium.
• When P or As is added to silicon or germanium, some of the Si or Ge atoms in the crystal are replaced by P or As atoms and 4 out 5 electrons of P and As atom will be used for bonding with Si or Ge atoms while the fifth electron serves to conduct electricity.
• P-type semiconductors (‘p’ stands for ‘positive’) are obtained due to metal deficiency defect or by doping with impurity atoms containing less electrons (i.e. atoms of III or 13th group).
• When B, Ga or In is added to silicon or germanium, some of the Si or Ge atoms in the crystal are replaced by B, Ga or In atoms and only three valencies of Si or Ge are satisfied leaving an electron at Si or Ge because B, Ga or In have one electron less.
• Due to the shortage of electrons when Si or Ge is doped with B, Ga or In electron, vacancies commonly known as positive holes arises in p-type semiconductors.
1.20 Objective Chemistry - Vol. II
• When electric field is applied to p-type semiconductors, flow of current takes place due to migration of positive holes due to the movement of electrons from adjacent site into positive hole.
• Unlike metals the conductivity of semiconductors increases with increase in temperature because the weakly bound extra electron or positive hole becomes free by the increased temperature and can be used for conduction.
• A superconductor is that whose electrical resistance is zero.
• The electrical resistance of a material usually becomes zero near absolute zero.
• The temperature at which a substance starts behaving like a super conductor is called transition temperature.
maGneTiC properTieS
• Diamagnetic solids contain paired electrons (↑↓) and repel the external magnetic field.
• Paramagnetic solids contain unpaired electrons and are attracted into the applied magnetic field.
• In ferromagnetic solids there occurs magnetic interactions between the neighbouring centres (domains) and the electrons in these centres interact in parallel direction (↑↑↑↑↑). This interaction leads to an increase in magnetic moment. Iron, cobalt and nickel are examples of ferromagnetic substances.
• In anti-ferromagnetic solids, there occurs magnetic interaction between the neighbouring centres and the electrons in these centres interact in an antiparallel (↑↓↑↓↑↓ ) direction, which leads to a decrease in magnetic moment, for example, [Cu(CH3COO)2 H2O], VO(CH3COO)2, MnO, MnO2, Mn2O3]
• In ferrimagnetic solids there occurs magnetic interactions between the neighbouring centres and the electrons in these centres interact in such a way which leads to the presence of uncompensated spins (↑↑↓↑↑↓) in the opposite direction resulting some magnetic moment, for example, magnetite Fe O 34 () ; Ferrite MFeO 4 (where MMgCuZn++ = + 22 2 ,, , etc.)
dieleCTriC properTieS
• A dielectric substance is that which may not allow electric current throughout it but charges are induced on its faces by the application of electric field.
• When electric field is applied, displacement of charges takes place and dipoles are created which results in polarization.
• Crystals in which dipoles may align to produce a net dipole moment are called piezoelectrics
• When piezoelectric crystals are subjected to pressure or mechanical stress, electricity is produced due to displacement of ions and this is known as piezoelectricity
• In some piezoelectric crystals, the dipoles are spontaneously aligned in a definite direction even in the absence of electric field and are called ferroelectric substances and this phenomenon is called ferroelectricity
• Potassium hydrogen phosphate (KH PO 24), barium titanate (BaTiO3) and potassium sodium tartrate (KNa CH OH O 44 62 4 Rochelle salt) are ferroelectric substances.
• The crystals in which alternate dipoles are in opposite direction and have net dipole moment equal to zero are called anti-ferroelectric substances, for example, lead zirconate (Pb ZrO 2).
• The polar crystals which attain charges on opposite faces and produce a small electric current on heating are called pyroelectric substances and this phenomenon is called pyroelectricity.
objective questions
112. Germanium and silicon become semiconductors due to (1) Schottky defect (2) Chemical impurity (3) Frenkel defect (4) Schottky defect
113. On adding a little phosphorous to silicon, we get a/an (1) p-type semiconductor (2) n-type semiconductor (3) insulator (4) metallic conductor
114. On adding a little indium to germanium we get (1) rectifier (2) insulator (3) n-type semiconductor (4) p-type semiconductor
115. Which of the following possess zero resistance at 0 K? (1) insulators (2) semiconductors (3) conductors (4) superconductors
116. Which of the following magnetism arises due to spontaneous alignment of magnetic moment of ions or atoms in the same direction?
(1) diamagnetism (2) paramagnetism (3) ferromagnetism (4) ferrimagnetism
117. Doping of silicon with P or Al increases the conductivity. The difference in the two cases is
(1) P is non-metal whereas Al is a metal (2) P is poor conductor while Al is good conductor (3) P gives rise to extra electron while Al gives rise holes
(4) P gives rise to holes while Al gives rise to extra electrons
118. Ferromagnetism is maximum in (1) Fe (2) Ni (3) Co (4) None
119. Anti-ferromagnetic substances possess (1) low magnetic moment (2) large magnetic moment (3) zero magnetic moment (4) any value of magnetic moment
120. Which of the following substances shows antiferromagnetism?
(1) ZrO 2 (2) CdO (4) CrO 2 (4) Mn O 23
121. A diode used a rectifier is (1) n-type semiconductor (2) p-type semiconductor (3) a combination of the above two types (1) None of the above
122. Which one among the following is an example of ferroelectric substance?
(1) Quartz (2) Lead chromate (3) Barium titanate (4) Semiconductor
123. Which arrangement of electrons decides ferrimagnetism?
(1) ↑↑↑↑↑ (2) ↑↓↑↓ (3) ↑↑↑↓↓ (4) None of these
124. Which arrangement of electrons leads to ferromagnetism?
(1) ↑↑↑↑↑ (2) ↑↓↑↓ (3) ↑↑↑↓↓ (4) None of these
125. Which arrangement of electrons leads to antiferrimagnetism?
(1) ↑↑↑↑↑ (2) ↑↓↑↓ (3) ↑↑↑↓↓ (4) None of these
126. Some of the polar crystals on heating produce a small electric current called (1) anti-ferroelectricity (2) ferroelectricity (3) piezoelectricity (4) pyroelectricity
127. Crystals where dipoles may align themselves in an ordered manner so that there is a net dipole moment exhibit
(1) pyroelectricity (2) piezoelectricity (3) ferroelectricity (4) anti-ferroelectricity
128. The electricity produced on applying stress on the crystals is called (1) pyroelectricity (2) piezoelectricity (3) ferroelectricity (4) anti-ferroelectricity
129. On heating some polar crystals, weak electric current is produced. It is termed as (1) piezo electricity (2) pyroelectricity (3) photoelectric current (4) superconductivity
130. Which of the following statement is true? (1) piezoelectricity is due to net dipole moment (2) ferroelectricity is due to alignment of dipoles in the same direction (3) pyroelectricity is due to heating polar crystals (4) All are correct
answers
(112) 2 (113) 2 (114) 4 (115) 4 (116) 3 (117) 3 (118) 1 (119) 2 (120) 4 (121) 3 (122) 3 (123) 3 (124) 1 (125) 2 (126) 4 (127) 2 (128) 2 (129) 2 (130) 4
practice exercise level-i
1. Which of the following statement is false?
(1) The unit cell of highest symmetry is hexagonal (2) The unit cell of lowest symmetry is triclinic (3) The number of planes of symmetry in cubic crystal is 9 (4) The number of axes of symmetry in cubic crystal is 13
2. Most crystals show good cleavage because their atoms, ions or molecules are (1) arranged in planes (2) weakly bonded together (3) strongly bonded together (4) spherically symmetrical
3. In a crystal the atoms are located at the position of (1) zero potential energy (2) infinite potential energy (3) minimum potential energy (4) Maximum potential energy
4. A big red spherical balloon (radius = 6a) is filled up with gas. On the balloon six small green spherical balloons (radius = a) are stuck on the surface in a specific manner. As red balloon is slowly deflated, a point comes when all these six green balloons touch and green balloons arrange themselves in a 3D closed packing arrangement. At that stage the radius of the red balloon would have reduced by approximately (1) 14.5 times (2) 1.414 times (3) 6.0 times (4) 2.42 times
5. An element occurring in the bcc structure has 12 08 10 23 × unit cells. The total number of atoms of the element in these cells will be (1) 24 16 10 23 . × (2) 36 18 10 23 . × (3) 60410 23 . × (4) 12 08 10 23 . ×
6. Copper metal has a face centred cubic structure with the unit cell length equal to 0.361 nm. The apparent radius of a copper ion is (1) 0.128 pm (2) 1.42 nm (3) 3.2 nm (4) 4.2 nm
7. A solid PQ has rock salt type structure in which Q atom are at the corners of the unit cell. If the body-centred atoms in all unit cells are missing, the resulting stoichiometry will be (1) PQ (2) PQ 2 (3) PQ34 (4) PQ43
8. Gold crystallizes in fcc lattice with edge length 407.Å . The closest distance between gold atoms is (1) 2 035 .Å (2) 814.Å (3) 2 878 .Å (4) 1 357 .Å
9. Which of the following is wrong?
(1) packing fraction in simple cubic lattice is 2 6 π (2) packing fraction in body centred cubic lattice is 3 8 π
(3) packing fraction in face centred cubic lattice is 2 6 π
(4) The distance between the two nearest neighbours in simple cubic lattice of axial length ‘l’ is also ‘l’
10. An element (atomic weight = 100) having bcc structure has unit cell edge length 400 pm. The density of this element will be (1) 5.188 g/mL (2) 16.37 g/mL (3) 7.29 g/mL (4) 2.14 g/mL
11. A metallic element exists in bcc lattice. Each edge of the unit cell is 288.Å The density of the metal is 720 1 .g cm . How many unit cells will be present in 100 g of the metal?
(1) 68510 2 . × (2) 58210 23 . × (3) 437105 × (4) 21210 6 ×
12. The unit cell of a metallic element of atomic mass 108 and density 10.5 g/cm3 is a cube with edge length of 409 pm. The structure of the crystal lattice is (1) fcc (2) bcc (3) hcp (4) simple cubic
13. α-form of iron exists in bcc form and γ -form of iron exist in fcc structure. Assuming that the distance between the nearest neighbours is the same in the two forms, the ratio of the density of γ -form to that of α-form is (Atomic weight of Fe = 56) (1) 1.089 (2) 1.25 (3) 0.89 (4) 2.2
14. The most malleable metals (Cu, Ag, Au) have close-packing of the type (1) hexagonal close-packing (2) cubic close packing (3) body-centred cubic packing (4) simple cubic
15. The anions (A) form hexagonal closest packing and atoms (C) occupy 2/3 of octahedral voids in it, then the general formula of the compound is (1) CA (2) CA2 (3) C2A3 (4) C3A2
16. The number of tetrahedral and octahedral voids in hexagonal primitive unit cell is (1) 8, 4 (2) 2, 1 (3) 12, 6 (4) 6, 12
17. The number of octahedral voids per unit body centred cubic structure is (1) 12 (2) 4 (3) 8 (4) 6
18. Transition metals, when they form interstitial compounds, the non-metal (H, B, C) are accommodated in (1) voids or holes in cubic close packed structure (2) tetrahedral voids (3) octahedral voids (4) all of these
19. In a body-centred cubic packing, the nearest neighbours lie along (1) edges of the cube (2) face diagonal (3) line joining the two opposite corners of the face (4) cube diagonal
20. A mineral having the formula AB2 crystallizes in cubic close packed lattice, with the A atoms occupying the lattice points. What is the coordination number of the B atoms?
(1) 4 (2) 6 (3) 8 (4) 12
21. Copper has a face-centred cubic lattice with unit cell edge length of 0.361 nm. What is the size of the largest atom that could be fit into octahedral holes of the lattice without disturbing the lattice? (1) 0.09 nm (2) 0.187 nm (3) 0.106 nm (4) 0.053 nm
22. The ionic radii of Rb+ and I– are 1.46 and 216.Å The most probable type of structure exhibited by it is (1) CsCl type (2) NaCl type (3) ZnS type (4) CaF2 type
23. Sapphire is aluminium oxide. Aluminium oxide crystallizes with aluminium ions in two-third of the octahedral voids in the closest packed array of oxide ions. What is the formula of aluminium oxide? (1) Al O 23 (2) AlO 2 (3) Al O 34 (4) Al O 32
24. What is the formula of magnetic oxide of cobalt used in recording tapes, that crystallizes with cobalt atoms occupying one-eighth of the tetrahedral holes and one half of the octahedral holes in a closest packed array of oxide ions?
(1) Co O 23 (2) Co O 58 (3) CoO (4) Co O 34
25. Caesium chloride on heating to 760 K changes into (1) CaCl (g) (2) NaCl structure (3) antifluorite structure (4) ZnS structure
Solid State 1.23
26. BaO has rock salt type structure. When subjected to high pressure, the ratio of the coordination number of Ba 2 + ion to O 2 ion changes to (1) 4:8 (2) 8:4 (3) 8:8 (4) 4:4
27. An ionic solid is hexagonal close packing of Q2–ions and PX+ ions are in half of the tetrahedral voids. The value of X should be (1) 1 (2) 2 (3) 4 (4) 0.5
28. A solid X melts slightly above 273 K and is a poor conductor of heat and electricity. To which of the following categories does it belong (1) Ionic solid (2) Covalent solid (3) Metallic solid (4) Molecular solid
29. The particles would be stationary in a lattice only at (1) 273 K (2) 0 K (3) 298 K (4) 373 K
30. An ionic crystalline solid MX3, has a cubic unit cells which of the following arrangement of the ions is consistent with the stoichiometry of compound?
(1) M3 + ions at the corners and X ions at the body centres (2) M3 + ions at the corners and X ions at the face centres
(3) X ions at the corners and M3 + ions at the body centres (4) X ions at the corners and M3 + ions at the face centres
answers
(1) 1 (2) 1 (3) 3 (4) 1 (5) 1 (6) 1 (7) 3 (8) 3 (9) 1 (10) 1 (11) 4 (12) 1 (13) 1 (14) 2 (15) 3 (16) 3 (17) 1 (18) 4 (19) 4 (20) 1 (21) 4 (22) 2 (23) 1 (24) 4 (25) 2 (26) 3 (27) 2 (28) 4 (29) 2 (30) 1
practice exercise level-ii
1. In a compound XY O 24, oxide ions are arranged in ccp and cations X are present in octahedral voids. Cations Y are equally distributed between octahedral and tetrahedral voids. The fraction of the octahedral voids occupied is (1) 1 2 (2) 1 4 (3) 1 8 (4) 1 6
