Solid State 9.

CHAPTER

9 Solid State

EXERCISE I (JEE MAIN)

Basics

1. Most crystals show good cleavage because their 5. Constituent particles in quartz are bonded by
atoms, ions or molecules are (a) electrovalent bonds
(a) weakly bonded together. (b) covalent bonds
(b) strongly bonded together. (c) van der Waals forces
(c) spherically symmetrical. (d) metallic bonds
(d) arranged in planes.
6. Ionic solids are characterized by
2. Which of the following is the only incorrect
statement regarding amorphous solids? (a) good conductivity in solid state.
(a) On heating, they may become crystalline at (b) high vapour pressure.
some temperature. (c) low melting point.
(b) They may become crystalline when kept for a (d) solubility in polar solvents.
long time.
(c) Amorphous solids can be moulded by heating. 7. Which of the following is an example of metallic
crystal solid?
(d) They are anisotropic in nature.
(a) C (b) Si
3. A solid melt slightly above 273 K and is a poor
(c) W (d) AgCl
conductor of heat and electricity. To which of the
following categories does it belong?
8. Which of the following is an example of covalent
(a) Ionic solid (b) Covalent solid crystal solid?
(c) Metallic solid (d) Molecular solid (a) SiO2 (b) Al
4. A solid is soft, good conductor of electricity (c) Ar (d) NaF
and has very high melting point. Its one of the
allotropic forms is the hardest known substance. 9. The particles would be stationary in a lattice
EXERCISE I

Hence, the solid is an example of only at

(a) ionic solid (b) covalent solid (a) 0°C (b) 0 K
(c) molecular solid (d) metallic solid (c) 298 K (d) 273 K
 9.2 Chapter 9

10. Iodine molecules are held in the crystal lattice by 16. A lattice is defined as
(a) London forces (a) the amount of energy required per mole to
(b) dipole–dipole interactions separate the ions from their lattice positions to
(c) covalent bonds an infinite distance in the gas phase.
(d) ionic bonds (b) the distance separating the cations and anions.
(c) a set of all points with identical environments
11. The unit cell of highest symmetry is within the crystal.
(a) cubic (b) triclinic (d) the arrangement of electrons in various energy
(c) hexagonal (d) monoclinic levels.

12. The unit cell of lowest symmetry is 17. The axial angles in triclinic crystal system are

(a) cubic (b) triclinic (a) α = β = γ = 90°

(c) hexagonal (d) monoclinic (b) α = γ = 90°, β ≠ 90°
(c) α ≠ β ≠ γ ≠ 90°
13. A match box exhibits ______ geometry. (d) α = β = γ ≠ 90°
(a) cubic (b) orthorhombic
18. TiO2 is a well-known example of
(c) triclinic (d) monoclinic
(a) triclinic system (b) tetragonal system
14. If the three inter-axial angles defining the unit (c) monoclinic system (d) cubic system
cell are all equal in magnitude, the crystal cannot
belong to the ____ system. 19. In a tetragonal crystal,
(a) orthorhombic (b) hexagonal (a) α = β = 90° ≠ γ ; a = b = c
(c) tetragonal (d) cubic (b) α = β = γ = 90°; a = b ≠ c
(c) α = β = γ = 90°; a ≠ b ≠ c
15. In a crystal, the constituent particles are located at
the position of (d) α = β = 90°; γ = 120°; a = b ≠ c

(a) zero potential energy. 20. Which of the following crystalline arrangement
(b) infinite potential energy. will have at least one of the angles equal to 90o
and at least two axial lengths equal?
(c) minimum potential energy.
(d) maximum potential energy. (a) Orthorhombic (b) Rhombohedral
(c) Monoclinic (d) Tetragonal

Analysis of Cubic Crystals

21. An element occurring in the body-centred cubic (a) Cu4Ag2Au (b) Cu4Ag4Au
(BCC) structure has 1.208 × 1023 unit cells. The (c) Cu4Ag3Au (d) CuAgAu
total number of atoms of the element in these cells
24. A solid PQ has rock salt type structure in which Q
will be
atoms are the corners of the unit cell. If the body-
(a) 2.416 × 1023 (b) 3.618 × 1023 centred atoms in all the unit cells are missing, then
(c) 6.04 × 1022 (d) 1.208 × 1023 the resulting stoichiometry will be
(a) PQ (b) PQ2
22. The rank of a cubic unit cell is 4. The type of cell is
(c) P3Q4 (d) P4Q3
(a) body-centred (b) face-centred
25. In a solid AB, having the NaCl structure, A atoms
(c) primitive (d) end-centred
occupy the corners of the cubic unit cell. If all
EXERCISE I

23. An alloy of copper, silver and gold is found to have the face-centred atoms along one of the axes are
copper constituting the face-centred cubic (FCC) removed, then the resulting stoichiometry of the
lattice. If silver atoms occupy the edge centres solid is
and gold is present at body centre, the alloy has a (a) AB2 (b) A2B
formula (c) A4B3 (d) A3B4
 Solid State 9.3

26. Xenon crystallizes in FCC lattice and the edge of 34. FeO crystallizes in the cubic system, in which there
the unit cell is 620 pm, then the radius of xenon is four formula units in each unit cell. The density
atom is of the crystal is 4.0 g/cm3. The side length of each
(a) 219.20 pm (b) 438.5 pm unit cell is (Fe = 56, NA = 6 × 1023)
(c) 265.5 pm (d) 536.94 pm (a) 4.227 Å (b) 2.424 Å
27. Metallic gold crystallizes in FCC lattice with edge- (c) 4.932 Å (d) 2.974 Å
length 4.07 Å. The closest distance between gold 35. The α-form of iron exists in BCC form and γ-form
atoms is of iron exists in FCC structure. Assuming that
(a) 3.525 Å (b) 5.714 Å the distance between the nearest neighbours is the
(c) 2.857 Å (d) 1.428 Å same in the two forms, the ratio of the density of
γ-form to that of α-form is
28. The distance between two nearest neighbours in
BCC lattice of axial length l, is (a) 4 2 : 3 3 (b) 4 3 : 3 2
3 (c)
(a) l (b) l 3: 2 (d) 2 : 1
2
2 1 36. The number of atoms contained in a FCC unit cell
(c) l (d) l
2 2 of a diatomic molecular solid is

29. Sodium metal crystallizes in BCC lattice with the (a) 8 (b) 2
cell edge a = 4.29 Å. What is the radius of the (c) 4 (d) 6
sodium atom? 37. The packing fraction in simple cubic lattice is
(a) 1.86 Å (b) 2.15 Å
1 2
(c) 4.29 Å (d) 2.94 Å (a) π (b) π
6 6
30. The unit cell of a metallic element of atomic mass
3 1
108 and density 10.5 g/cm3 is a cube with edge (c) π (d) π
length of 409 pm. The structure of the crystal 8 2
lattice is
38. The packing fraction in BCC lattice is
(a) FCC (b) BCC
(c) edge-centred cubic (d) simple cubic 1 2
(a) π (b) π
6 6
31. An element (atomic mass = 100) having BCC
structure has unit cell edge length 400 pm. The 3 3
density of this element will be (NA = 6 × 1023) (c) π (d) π
8 2
(a) 5.2 g/ml (b) 10.4 g/ml
39. The packing fraction in FCC lattice is
(c) 0.42 g/ml (d) 2.6 g/ml
32. Potassium has BCC structure with nearest 1 2
(a) π (b) π
neighbour distance (2.5 × 3) Å. Its density will 6 6
be (K = 39, NA = 6 × 1023)
3 2
(a) 1.040 kg/m3 (b) 104 kg/m3 (c) π (d) π
8 3
(c) 520 kg/m3 (d) 1040 kg/m3
33. Lithium borohydride (LiBH4) crystallizes in an 40. In a BCC packing, the nearest neighbours lie
orthorhombic system with four molecules per unit along the
EXERCISE I

cell. The unit cell dimensions are a = 6.0 Å, b = 4.4 (a) edges of the cube.
Å and c = 7.5 Å. The density of crystals is (Li = 7, (b) face diagonal.
B = 11 NA = 6 × 1023) (c) line joining the two opposite corners of the
(a) 0.74 g/cm3 (b) 1.48 g/cm3 face.
(c) 0.37 g/cm3 (d) 0.90 g/cm3 (d) cube diagonal.
 9.4 Chapter 9

Types of Packing

41. The most malleable metals (Cu, Ag, Au) have (a) ABACABAC….
close-packing of which of the following type? (b) ABCBCABC….
(a) Cubic close packing (CCP) (c) ABCABC….
(b) Simple cubic packing (d) ABBAA….
(c) BCC packing 49. Which of the following has the least void space
(d) Malleability is not related to type of packing. fraction in their structure?
(a) BCC (b) BCC and HCP
42. The number of carbon atoms per unit cell of
(c) HCP (d) FCC and HCP
diamond is
(a) 4 (b) 6 50. The number of tetrahedral and octahedral voids in
hexagonal prismatic unit cell (HCP) is
(c) 8 (d) 12
(a) 8, 4 (b) 2, 1
43. The number of closest neighbours of a carbon
atom in diamond is (c) 12, 6 (d) 6, 12
(a) 2 (b) 4 51. Which of the following void is smallest in close
(c) 6 (d) 8 packing?
(a) Tetrahedral (b) Octahedral
44. The number of closest neighbours of a carbon
atom in graphite is (c) Cubic (d) Square
(a) 2 (b) 3 52. Which of the following interstitial site is formed
(c) 4 (d) 8 when the three closed packed spheres of one layer
is put over three closed packed spheres of the
45. The low density of alkali metals is due to second layer, their positions being inverted with
(a) their BCC structure in which about 32% of the respect to each other?
available space is unfilled. (a) Tetrahedral (b) Octahedral
(b) their HCP structure in which about 74% of (c) Rhombohedral (d) Tetragonal
the available space is unfilled.
(c) their cubic close packed (CCP) structure in 53. In an FCC arrangement of metallic atoms, what
which about 74% of the available space is is the relative ratio of the ideal sizes of tetrahedral
unfilled. and octahedral voids?
(d) their BCC structure in which about 47% of the (a) 0.543 (b) 0.732
available space is unfilled. (c) 0.414 (d) 0.637
46. The coordination number of a metal crystallizing
in a HCP structure is 54. Atoms of the element ‘A’ form HCP and atoms of
element ‘C’ occupy only two-third of octahedral
(a) 12 (b) 4
voids in it, then the general formula of the
(c) 8 (d) 6 compound is
47. A metallic element crystallizes into a lattice (a) CA (b) CA2
containing a sequence of layers of ABABAB…. (c) C2A3 (d) C3A2
Any packing of spheres leaves out voids in the
lattice. Approximately what percentage by volume 55. A solid has three types of atoms , such as X, Y
of this lattice is empty space? and Z. ‘X’ forms a FCC lattice with ‘Y’ atoms
EXERCISE I

(a) 74% (b) 26% occupying all the tetrahedral voids and ‘Z’ atoms
(c) 48% (d) 32% occupying half the octahedral voids. The simplest
formula of solid is
48. Which one of the following schemes of ordering
(a) X2Y4Z (b) XY2Z4
close packed sheets of equal-sized spheres do not
generate closest packed lattice? (c) X4Y2Z (d) X4YZ2
 Solid State 9.5

Radius Ratio and Packing of Crystal

56. The ionic radii of Rb+ and I− are 1.46 and 2.16 Å, 64. Sodium oxide has anti-fluorite structure. The
respectively. The most probable type of structure percentage of the tetrahedral voids occupied by
exhibited by it is the sodium ions is
(a) CsCl type (b) NaCl type (a) 12% (b) 25%
(c) ZnS type (d) CaF2 type (c) 50% (d) 100%
57. For an ideal ionic crystal, the simplest formula is
65. CsBr has cubic structure with edge length 4.3 Å.
AX and the coordination number of cation is 6.
The shortest inter ionic distance in between Cs+
The value of radius ratio (rA +:rX −)
and Br− is
(a) must be greater than 0.732.
(a) 3.72 Å (b) 1.86 Å
(b) must lie in between 0.732 and 0.414.
(c) 7.44 Å (d) 4.3 Å
(c) must lie in between 0.414 and 0.225.
(d) must be less than 0.414. 66. In Na2O structure,
58. In the zinc blend structure (ZnS), S2− adopts CCP (a) O2– ions constitute CCP and Na+ ions occupy
arrangement and Zn2+ occupies all the octahedral holes.
(b) O2– ions constitute CCP and Na+ ions occupy
(a) all octahedral voids.
all the tetrahedral holes.
(b) only 50% of octahedral voids.
(c) O2– ions constitute CCP and Na+ ions occupy
(c) only 50% of tetrahedral voids. 50% of tetrahedral holes and 100% octahedral
(d) all tetrahedral voids. holes.
59. The number of next nearest neighbours of Cs+ ion (d) Na+ ions constitute CCP and O2– ions occupy
in CsCl crystal is half of octahedral holes.
(a) 12 (b) 8 67. NaCl crystal is
(c) 6 (d) 4
(a) FCC (b) BCC
60. In calcium fluoride structure, the coordination (c) HCP (d) simple cubic
numbers of calcium and fluoride ions are,
respectively, 68. CsBr has CsCl type structure. Its density is 4.26
g/ml. The side of unit cell is (Cs = 133, Br = 80,
(a) 8 and 4 (b) 6 and 8
NA = 6 × 1023)
(c) 4 and 4 (d) 4 and 8
(a) 5.503 Å (b) 4.368 Å
61. The radius of Ag+ ion is 126 pm while of I− ion is
(c) 3.225 Å (d) 2.856 Å
216 pm. The coordination number of Ag in AgI is
(a) 2 (b) 4 69. A solid contains An+ and Bm− ions. The structure
(c) 6 (d) 8 of solid is FCC for Bm− ions and An+ ions are
present in one-fourth of the tetrahedral voids as
62. A binary solid (A+ B−) has a rock salt structure. If well as in one-fourth of octahedral voids. What is
the edge length is 400 pm and the radius of cation the simplest formula of solid?
is 75 pm, then the radius of anion is
(a) A3B4 (b) A4B3
(a) 100 pm (b) 125 pm (c) AB2 (d) A2B
(c) 250 pm (d) 325 pm
70. An ionic solid is HCP of Q2− ions and Px+ ions
63. MgO exists in a rock salt type unit cell. Each Mg2+
are in half of the tetrahedral voids. The value of x
EXERCISE I

ion will be in contact with

should be
(a) 6 Mg2+ ions (b) 6 O2− ions
(a) 1 (b) 2
(c) 8 O2− ions (d) 4 O2− ions
(c) 4 (d) 1/2
 9.6 Chapter 9

71. In a compound, oxide ions are arranged in CCP with cobalt atoms occupying one-eighth of the
arrangement. Cations A occupy one-sixth of tetrahedral holes and one half of the octahedral
the tetrahedral voids and cations B occupy one- holes in a closest packed array of oxide ions?
third of the octahedral voids. The formula of the (a) Co2O3 (b) Co5O8
compound is
(c) CoO (d) Co3O4
(a) AB2O4 (b) ABO3
74. Caesium chloride, on heating, changes into
(c) ABO2 (d) ABO4
(a) CsCl (g)
72. Sapphire is aluminium oxide. Aluminium oxide (b) NaCl structure
crystallizes with aluminium ions in two-third of
(c) antifluorite structure
the octahedral voids in the closest packed array
of oxide ions. What is the formula of aluminium (d) ZnS structure
oxide? 75. BaO has a rock salt type structure. When subjected
(a) Al2O3 (b) AlO2 to high pressure, the ratio of the coordination
(c) Al3O4 (d) Al3O2 number of Ba2+ ion to O2− ion changes to
73. What is the formula of the magnetic oxide of (a) 4 : 8 (b) 8 : 4
cobalt, used in recording tapes, that crystallizes (c) 8 : 8 (d) 4 : 4

Defects in Solids
76. Frenkel defect is noticed in defect. The molar ratio of Cu2+ and Cu+ ions in
(a) AgBr (b) Zns the crystal is
(c) AgI (d) All of these (a) 4 : 5 (b) 1 : 12.5
77. Which of the following defect, if present, lowers (c) 1 : 23 (d) 1 : 24
the density of the crystal? 82. NaCl is doped with 2 × 10–3 mole % SrCl2, the
(a) Frenkel concentration of cation vacancies is (NA = 6 × 1023)
(b) Schottky (a) 6.0 × 1018 mol−1 (b) 1.20 × 1019 mol−1
(c) Metal excess defect due to excess cation. (c) 3.0 × 1018 mol−1 (d) 1.20 × 1021 mol−1
(d) Interstitial defect. 83. Each of the following statements is correct except
78. Schottky defect appears in (a) the lattice positions left vacant by anion and
(a) NaCl (b) CsCl occupied by electrons are called F-centres.
(c) AgBr (d) All of these (b) the presence of F-centres makes the lattice
electrically neutral and diamagnetic.
79. The yellow colour of ZnO and conducting nature (c) the presence of F-centres gives colour to the
produced in heating is due to crystals.
(a) metal excess defects due to interstitial cation. (d) F-centres contain unpaired electrons.
(b) extra positive ions present in an interstitial
site. 84. The intrinsic or thermodynamic defect is
(c) trapped electrons. (a) Schottky defect
(d) All of these (b) metal excess defect due to excess cation.
(c) metal excess defect due to anion vacancy.
80. The presence of excess sodium in sodium chloride
(d) metal-deficient defect.
makes the crystal appearance yellow. This is due
to the presence of 85. The only incorrect effect on density by the given
EXERCISE I

(a) Schottky defect (b) Frenkel defect defect in solids is

(c) F-centres (d) interstitial defects (a) density must decrease by vacancy defect.
(b) density must increase by interstitial defect.
81. The composition of a sample of cuprous oxide (c) density must increase by impurity defect.
is found to be Cu1.92O1.00 due to metal deficient (d) density does not change by dislocation defect.
 Solid State 9.7

Properties of Solids

86. Which of the following is a ferromagnetic 89. Addition of arsenic in small amount to pure
substance? germanium will result in the formation of
(a) Fe2O3 (b) Cr2O3 (a) n-type semiconductor
(c) Fe3O4 (d) CrO2 (b) germanium arsenide
(c) p-type semiconductor
87. Which of the following acts as a superconductor
(d) a superconducting alloy
at 4 K?
(a) He (b) Cu 90. Which of the following arrangement shows
schematic alignment of magnetic moments of anti-
(c) K (d) Mg
ferromagnetic substances?
88. Superconductors are substances which (a)
(a) conduct electricity at low temperatures.
(b) conduct electricity at high temperature. (b)
(c) offer very high resistance to the flow of
current. (c)
(d) offer no resistance to the flow of current.
(d)

EXERCISE I
 9.8 Chapter 9

EXERCISE II (JEE ADVANCED)

Section A (Only one Correct)

1. For a certain crystal, the unit cell axial lengths 7. What is the void space per unit cell for metallic
are found to be a = 5.62 Å, b = 7.41 Å and silver crystallizing in the FCC system, the edge
c = 10.13 Å. The three coordinate axes are mutually length of the unit cell being 4 Å?
perpendicular. The crystal system to which the
(a) 47.36 Å3 (b) 30.72 Å3
crystal belongs is
(c) 20.48 Å3 (d) 16.64 Å3
(a) tetragonal (b) orthorhombic
(c) monoclinic (d) cubic 8. A metal exists as FCC crystal. If the atomic radius
is 100 2 pm and the density of metal is 12,500
2. A metallic element exists as cubic lattice. Each
kg/m3, then the metal is (Atomic masses: Ca = 40,
edge of the unit cell is 4.0 Å. The density of the
Co = 58.9, Sn = 119.8, Pb = 207.9 and NA = 6 × 1023)
metal is 6.25 g/cm3. How many unit cells will be
present in 100 g of the metal? (a) Ca (b) Co
(a) 1.0 × 10 22
(b) 2.5 × 10 23 (c) Sn (d) Pb
(c) 5.0 × 1023 (d) 2.0 × 1023 9. A solid element (monoatomic) exists in cubic
3. Aluminium crystallizes in cubic system with unit crystal. If its atomic radius is 1.0 Å and the ratio
cell edge length equal to 4.0 Å. If its density is of packing fraction and density is 0.1 cm3/g, then
45 the atomic mass of the element is (NA = 6 × 1023)
g/cm3, then the atomic radius of Al-atom is
16 (a) 8π (b) 16π
(NA = 6 × 1023, Al = 27) (c) 80π (d) 4π
(a) 1.414 Å (b) 1.732 Å
(c) 4.0 Å (d) 2.0 Å 10. In FCC unit cell, what fraction of edge is not
covered by atoms?
4. Is there an expansion or contraction as iron
(a) 0.134 (b) 0.293
transforms from FCC to BCC? The atomic radius
of iron is 125 pm in FCC but 50 2 pm in BCC. (c) 0.26 (d) 0.32
(a) Expansion 11. The sublimation temperature of a substance is
(b) Contraction −83°C. It exists as cubic close packed structure with
(c) Neither expansion nor contraction. 8
unit cell edge length of 5.0 Å and density g/cm3
(d) Unpredictable 3
at −100°C. What should be the density of
5. Silver (atomic mass = 108) has an atomic radius of substance at 0°C and 1 atm? (NA = 6 × 1023)
144 pm and density 10.6 g/ cm3. To which type of
cubic crystal silver belongs? (a) 50 g/cm3 (b) 2.23 g/cm3
(a) Simple (b) BCC (c) 2.23 g/L (d) 1.86 g/L
(c) FCC (d) End-centred 12. An alkali metal has density 4.5 g/cm3. It has cubic
6. Gold crystallizes with FCC lattice for which the unit cell with edge length 400 pm. The reaction
side length of the unit cell is 5.0 Å. If the density of 7.68 cm3 chunk of the metal with an excess of
of gold is 10.5 g/ cm3, then the value of Avogadro HCl solution gives a colourless gas which occupies
EXERCISE II

number is (Au = 198) 4.54 L at 0°C and 1 bar. The unit cell of metal is
(a) 6.022 × 1023 (b) 6.034 × 1023 (a) simple cubic (b) BCC
(c) 5.966 × 1023 (d) 6.022 × 1022 (c) FCC (d) end-centred
 Solid State 9.9

13. The densities of ice and water at 0°C and 1 bar are 18. Packing fraction in 2D-hexagonal arrangement of
0.96 and 0.99 g/cm3, respectively. If the percentage identical spheres is
of occupied space in ice is x, then the percentage π π
of empty space in water is (a) (b)
3 2 3 3
32 33
(a) x (b) x π π
33 32 (c) (d)
33 32 2 3 6
(c) 100 − x (d) 100 − x
32 33 19. A close packing consists of a base of spheres,
followed by a second layer where each sphere
14. A metal crystallizes in such a lattice in which only
rests in the hollow at the junction of four spheres
70% of the total space of the crystal is occupied by
below it and the third layer then rests on these in
the atoms. If the atomic mass of the metal is 32π
an arrangement which corresponds exactly to that
g/ mol and the atomic radius is 0.2 nm, then the
in the first layer. This packing is known as
density of the metal is
(a) 7.0 g/cm3 (b) 3.5 g/cm3 (a) HCP (b) CCP
(c) 10.5 g/cm 3
(d) 14.0 g/cm3 (c) square close packing (d) BCC packing

15. The number of octahedral voids per unit BCC 20. If the height of HCP unit cell of identical particles
cell is is h, then the height of octahedral voids from the
(a) 1.0 (b) 2.0 base is
(c) 1.5 (d) 0 h h 2h
(a) (b) ,
16. In a hypothetical solid, ‘C’ atoms form CCP 2 3 3
lattice. ‘A’ atoms occupy all tetrahedral voids and
h 3h h 7h
‘B’ atoms occupy all octahedral voids, without (c) , (d) ,
disturbing the crystal. If a unit cell of the crystal 4 4 8 8
is cut by a plane shown in the figure, then the cross
section of this plane looks like 21. If the volume occupied by a unit cell of NaCl is
4.7 × 10–23 ml, then the volume of a crystal of
NaCl weighing 1.0 g is
(a) 2.13 × 1022 ml (b) 8.03 × 10−25 ml
(c) 0.48 ml (d) 0.12 ml

22. If the unit cell length of sodium chloride crystal is

600 pm, then its density will be
(a) (b)
C B C C C C (a) 2.165 g/cm3 (b) 3.247 g/cm3
A
B B B B B B (c) 1.79 g/cm3 (d) 1.082 g/cm3
A
C B C C C C 23. The inter-metallic compound LiAg crystallizes
in cubic lattice in which both Li and Ag have
(c) (d) co-ordination number of 8. The class of
C C C C C C
A A A A crystal is
B B B BABAB
A A (a) simple cubic (b) BCC
C C C C C C (c) FCC (d) end-centred cubic
24. A mineral having the formula AB2 crystallizes in
EXERCISE II

17. A metal having atomic mass 60.22 g/ mole

crystallizes in ABCABC…. type packing. The the CCP lattice with the A atoms occupying the
density of each metal atom if the edge length of lattice points. What is the coordination number of
unit cell is 10 Å is (NA = 6.022 × 1023) the B atoms?
(a) 0.4 g/cm3 (b) 40 g/cm3 (a) 4 (b) 6
(c) 0.54 g/cm 3
(d) 54 g/cm3 (c) 8 (d) 12
 9.10 Chapter 9

25. There are three cubic unit cells A, B and C. A (a) ZnAl2O4 (b) Zn2AlO4
is FCC and all of its tetrahedral voids are also (c) Zn2Al3O4 (d) ZnAlO2
occupied. B is also FCC and all of its octahedral
voids are also occupied. C is simple cubic and all 31. An ionic crystalline solid MX3 has a cubic unit
of its cubic voids are also occupied. If voids in cell. Which of the following arrangement of the
all unit cells are occupied by the spheres exactly ions is consistent with the stoichiometry of the
at their limiting radius, then the order of packing compound?
efficiency would be (a) M3+ ions at the corners and X− ions at the face
(a) A < B < C (b) C < A < B centres.
(c) C < B < A (d) A < C < B (b) M3+ ions at the corners and X− ions at the
body centres.
26. In a cubic closest packed structure of mixed oxides,
(c) X− ions at the corners and M3+ ions at the face
the lattice is made up of oxide ions. Tetrahedral
centres.
voids are occupied by divalent X2+ ions and
octahedral voids are occupied by trivalent Y3+ (d) X− ions at the corners and M3+ ions at the
ions. If only 50% of the octahedral voids are body centres.
occupied, then the percentage of tetrahedral voids 32. In a compound XY2O4, the oxide ions are
occupied is arranged in CCP arrangement and cations X are
(a) 50% (b) 12.5% present in octahedral voids. Cations Y are equally
(c) 25% (d) 40% distributed between octahedral and tetrahedral
voids. The fraction of the octahedral voids
27. The distance between adjacent oppositely charged occupied is
ions in rubidium chloride is 328.5 pm, in potassium (a) 1/2 (b) 1/4
chloride is 313.9 pm, in sodium bromide is 298.1
(c) 1/6 (d) 1/8
pm and in potassium bromide is 329.3 pm. The
distance between adjacent oppositely charged ions 33. Give the correct order of initials T (true) or
in rubidium bromide is F (false) for the following statements.
(a) 314.7 pm (b) 338.5 pm I. In an anti-fluorite structure, anions form FCC
(c) 339.3 pm (d) 343.9 pm and cations occupy all the tetrahedral voids.
28. Solid AB has a rock salt type structure. If the II. If the radius of cation and anion is 20 and 95
radius of the cation is 200 pm, then what is the pm, then the coordination number of cation
maximum possible radius of the anion? in the crystal is 4.
(a) 483.1 pm (b) 273.6 pm
III. An atom or ion is transferred from a lattice
(c) 200 pm (d) 400 pm site to an interstitial position in Frenkel
29. The simplest formula of a solid having CCP defect.
arrangement for ‘A’ atoms in which alternate face- IV. The density of crystal always increases due to
centres are occupied by ‘B’ atoms and alternate substitutional impurity defect.
edge centres are occupied by ‘C’ atom, is
(a) TTTT (b) FFFF
(a) ABC (b) A4BC
(c) FFTT (d) TFTF
(c) A2BC (d) A4B2C
34. The crystalline structure of a solid is CCP for ‘X’
30. Spinel is an important class of oxides consisting atoms. If ‘Y’ atoms occupy all the octahedral voids
of two types of metal ions with the oxide ions and ‘Z’ atoms occupy all the tetrahedral voids,
EXERCISE II

arranged in CCP pattern. The normal spinel without any distortion in the CCP arrangement
has one-eighth of the tetrahedral holes occupied of ‘X’ atoms, then the fraction of body diagonal
by one type of metal ion and one-half of the not covered by the atoms is
octahedral hole occupied by another type of metal
ion. Such a spinel is formed by Zn2+, Al3+ and O2−. (a) 0.26 (b) 0.24
The simplest formula of such spinel is (c) 0.76 (d) 0.81
 Solid State 9.11

35. In an ionic solid AB2O4, the oxide ions form CCP. (a) 76.8 (b) 176.8
‘A’ and ‘B’ are metal ions in which one is bivalent (c) 33.8 (d) 23.8
and another is trivalent (not necessarily in given
38. Which of the following oxide shows electrical
order). If all the bivalent ions occupy octahedral
properties like metals?
holes and the trivalent ions occupy tetrahedral
and octahedral voids in equal numbers, then the (a) SiO2 (b) MgO
fraction of octahedral voids unoccupied is (c) SO2(s) (d) CrO2
1 3 39. Which kind of defects is introduced by doping in
(a) (b)
2 4 silicon crystal?
1 7 (a) Dislocation defect (b) Schottky defect
(c) (d)
4 8 (c) Frenkel defect (d) Electronic defect
36. The theoretical density of ZnS is d g/cm3. If the 40. A ferromagnetic substance becomes a permanent
crystal has 4% Frenkel defect, then the actual magnet when it is placed in a magnetic field
density of ZnS should be because
(a) d g/cm3 (b) 0.04d g/cm3 (a) all the domains get oriented in the direction of
(c) 0.96d g/cm3 (d) 1.04d g/cm3 magnetic field.
37. In a crystal at 827°C one out of 1010 lattice site is (b) all the domains get oriented in the direction
found to be vacant but at 927°C, one out of 2 × 109 opposite to the direction of magnetic field.
lattice sites is found to be vacant. The enthalpy of (c) domains get oriented randomly.
vacancy formation in kJ/mol is (d) domains are not affected by magnetic field.

Section B (One or More than one Correct)

1. Which of the following solid substance(s) will (a) the distance between nearest octahedral and
have the same refractive index when measured in 3a
different directions? tetrahedral void is .
4
(a) Rubber (b) NaCl
(b) the distance between two nearest octahedral
(c) Plastic (d) Graphite a
void is .
2. Which of the following is/are amorphous solid(s)? 2
(a) NaCl (b) CaF2 (c) the distance between two nearest tetrahedral
(c) Glass (d) Plastic 3a
void is .
3. Which of the following has face-centred Bravais 2
lattice? (d) the distance between successive A and B layers
(a) Hexagonal (b) Monoclinic 2
is 2r. .
(c) Cubic (d) Orthorhombic 3
4. If the height of HCP unit cell of identical particles
is h, then the height of tetrahedral voids from the 6. An element exists in two allotropic forms. One form
base is is CCP and the other form is HCP arrangement
3h 5h h 2h of atoms of the element. If the atomic radius
(a) , (b) , of element is same in both the forms, then both
8 8 3 3
EXERCISE II

allotropic forms have the same

h 3h h 7h
(c) , (d) , (a) density
4 4 8 8
(b) coordination number.
5. The correct information regarding a solid element
(atomic radius = r) having ABCABC…. type (c) fraction of unoccupied space.
packing (FCC unit cell edge length = a) is (d) distance between two consecutive layers.
 9.12 Chapter 9

7. The correct statement(s) for the packing of 9. Which of the following statement(s) is (are)
identical spheres in two dimensions is/ are correct?
(a) For square close packing, the coordination (a) The coordination number of each type of ions
number is 4. in CsCl crystal is 8.
(b) For HCP, the coordination number is 6. (b) A metal that crystallizes in BCC structure has
(c) There is only one void per sphere in both, a coordination number of 12.
square and HCP. (c) A unit cell of an ionic crystal shares some of
(d) HCP is more efficiently packed than square its ions with other unit cells.
close packing. (d) The length of the unit cell in NaCl is 552 pm.
8. Which of the following information(s) is/ are ( rNa+ = 95 pm, rCl− = 181 pm).
incorrect regarding the voids formed in three
dimensional HCP of identical spheres? 10. In which of the following crystals, alternate
tetrahedral voids are occupied?
(a) A tetrahedral void is formed when a sphere of
the second layer is present above the triangular (a) NaCl (b) ZnS
void of the first layer. (c) CaF2 (d) Na2O
(b) All the triangular voids are not covered by the 11. Which of the following statement(s) is/ are correct
spheres of the second layer. with respect to zinc blende structure?
(c) Tetrahedral voids are formed when the
(a) Zn2+ ions are present at the corners and at the
triangular voids in the second layer lie above
centres of each face.
the triangular voids in the first layer and
the triangular shapes of these voids do not (b) Only alternate tetrahedral holes are occupied
overlap. by Zn2+ ions.
(d) Octahedral voids are formed when the (c) The coordination number of Zn2+ and S2− is 4
triangular voids in the second layer exactly each.
overlap with similar voids in the first layer. (d) The number of ZnS units in a unit cell is 4.

12. In a sodium chloride crystal, the unit cell edge length is a. The option(s) representing the correct combination
is/are
Options Nearest neighbour of Na+ ion Ion Distance from Na+ ion Number of ions
nd +
(a) 2 Na 0.707a 12
(b) 3rd Cl– 0.866a 8
th +
(c) 4 Na a 6
th
(d) 5 Cl– 1.12a 24

13. A quantity of 80.0 g of a salt (XY) of strong acid and (a) C3– ions form CCP, A+ ions occupy all
weak base is dissolved in water to form 2.0 L aqueous octahedral voids and B2+ ions occupy half of
solution. At 298 K, the pH of the solution is found the tetrahedral voids.
to be 5.0. If XY forms CsCl type crystal and the (b) B2+ ions form HCP, A+ ions occupy all
radius of X+ and Y– ions are 160 pm and 186.4 pm, octahedral voids and C3– ions occupy half of
respectively, then the correct information is (Given: the tetrahedral voids.
Kb of XOH = 4 × 10−5, NA = 6 × 1023, 3 = 1.732 )
(c) A+ ions occupy alternate corners of a simple
(a) molar mass of the salt is 100 g/mol. cube, B2+ ions occupy the other corners of the
the degree of hydrolysis of salt is 2.5 × 10−5.
EXERCISE II

(b) cube and C3– ions occupy body centre of the

(c) unit cell edge length of XY crystal is 400 pm. cube.
(d) density of solid XY is 2.6 g/cm3. (d) B2+ ions form CCP, C3– ions occupy all the
14. An ionic compound consists of only A+, B2+ and tetrahedral voids and A+ ions occupy all the
C3− ions. Which of the following option(s) is/are octahedral voids.
correct with respect to their possible structure?
 Solid State 9.13

15. Potassium hexachloroplatinate (IV), K2[PtCl6] 21. Which of the following is/are correct regarding
adopts anti-fluorite crystal structure. Which of point defects in solids?
the following information is correct about ideal
(a) The density of point defect increases with the
K2[PtCl6] crystal ?
increase in rate of crystallization.
(a) K+ ions occupy all the tetrahedral voids.
(b) In the formation of point defects, the entropy
(b) The unit cell is FCC with respect to PtCl62− of system increases but the entropy of
ions. surrounding decreases.
(c) The coordination number of PtCl62− ions is 4.
(c) The density of point defect increases with the
(d) The coordination number of PtCl62− ions is 8. increase in temperature.
16. In each of the following ionic solids, the (d) All point defects results in the decreasing
coordination number of the cation and anion is density of solid.
same, except
(a) MgO (b) CaF2 22. Which of the following is/are correct statement(s)
about Fe3O4 crystal?
(c) Al2O3 (d) CsCl
(a) Fe2+ ions occupy octahedral voids only.
17. Which of the following defects in the crystals may
(b) Fe3+ ions occupy tetrahedral voids only.
lower the density?
(c) Fe3+ ions occupy octahedral as well as
(a) Interstitial defect (b) Vacancy defect tetrahedral voids.
(c) Schottky defect (d) Impurity defect
(d) O2− ions are present at the corner as well as the
18. Which of the following may have Frenkel defect? centre of alternate faces.
(a) Sodium chloride (b) Zinc sulphide 23. Which of the following statement(s) is/are true
(c) Silver bromide (d) Diamond regarding the electrical properties of solids?
19. Which of the following statement(s) is/are (a) (Conductivity) metals << (Conductivity)
incorrect regarding the defects in solids? insulators < (Conductivity) semiconductors.
(a) AgBr crystal show both Schottky and Frenkel (b) Depending upon the temperature, TiO3 can
defect. behave as insulator or conductor.
(b) Impurity defect by doping of arsenic in silicon (c) I2(s) is non-conducting.
results ‘n’-type semiconductor.
(d) n-type semiconductor will have conductivity
(c) Doping in crystal introduces dislocation less than pure semiconductor.
defect.
24. Which of the following solids is not an electrical
(d) Metal deficient defect can occur with extra
conductor?
anion present in the interstitial voids.
(a) Mg(s) (b) TiO(s)
20. Which of the following statement is correct (c) I2(s) (d) H2O(s)
regarding defects in solid?
25. Which of the following oxides behave as
(a) Frenkel defect is usually favoured by a very a conductor or an insulator depending on
small difference in the sizes of cation and temperature?
anion.
(a) TiO (b) SiO2
(b) Frenkel defect is a dislocation defect.
(c) TiO3 (d) VO
(c) Trapping of an electron in the lattice leads to
the formation of F-centre.
EXERCISE II

(d) Schottky defect have no effect on the physical

properties of solids.
 Solid State 9.23

13. The density of solid argon is 4/π g/cm3 at −233°C. 15. The structure of crystalline macromolecules may
If the argon atoms are assumed to be spheres of be determined by X–ray diffraction techniques
radius 1.5 × 10−8 cm, the approximate percentage using method similar to those for smaller
of empty space in solid argon is (Ar = 40) molecules. Fully crystalline polyethylene has its
chain aligned in an orthorhombic unit cell of
14. An element (atomic mass = 125) crystallizes in dimensions 667 pm × 500 pm × 280 pm. There
simple cubic structure. If the diameter of the are two repeating CH2CH2 units per unit cell. The
largest sphere which can be placed in the crystal theoretical density of fully crystalline polyethylene
without disturbing the crystal is 366 pm and the (in kg/m3) is (NA = 6 × 1023)
density of crystal is ‘d ’ g/cm3, then the value of
‘300 d ’ is (NA = 6 × 1023)

Answer Keys Exercise I

Basics
1. (d) 2. (d) 3. (d) 4. (b) 5. (b) 6. (d) 7. (c) 8. (a) 9. (b) 10. (a)
11. (a) 12. (b) 13. (b) 14. (b) 15. (c) 16. (c) 17. (c) 18. (b) 19. (b) 20. (d)

Analysis of Cubic Crystals

21. (a) 22. (b) 23. (c) 24. (c) 25. (d) 26. (a) 27. (c) 28. (b) 29. (a) 30. (a)
31. (a) 32. (d) 33. (a) 34. (c) 35. (a) 36. (a) 37. (a) 38. (c) 39. (b) 40. (d)

Types of Packing
41. (a) 42. (c) 43. (b) 44. (b) 45. (a) 46. (a) 47. (b) 48. (d) 49. (d) 50. (c)
51. (a) 52. (b) 53. (a) 54. (c) 55. (a)

Radius Ratio and Packing of Crystal

56. (b) 57. (b) 58. (c) 59. (c) 60. (a) 61. (c) 62. (b) 63. (b) 64. (d) 65. (a)
66. (b) 67. (a) 68. (b) 69. (a) 70. (b) 71. (b) 72. (a) 73. (d) 74. (b) 75. (c)

Defects in Solids
76. (d) 77. (b) 78. (d) 79. (c) 80. (c) 81. (c) 82. (b) 83. (b) 84. (a) 85. (c)

Properties of Solids
86. (d) 87. (a) 88. (d) 89. (a) 90. (d)
ANSWER KEYS
 9.24 Chapter 9

Answer Keys Exercise II

Section A (Only one Correct)
1. (b) 2. (b) 3. (a) 4. (b) 5. (c) 6. (b) 7. (d) 8. (c) 9. (a) 10. (b)
11. (c) 12. (b) 13. (c) 14. (b) 15. (d) 16. (c) 17. (c) 18. (b) 19. (b) 20. (c)
21. (d) 22. (c) 23. (a) 24. (a) 25. (b) 26. (b) 27. (d) 28. (a) 29. (b) 30. (a)
31. (a) 32. (a) 33. (d) 34. (b) 35. (a) 36. (a) 37. (b) 38. (d) 39. (d) 40. (a)

Section B (One or More than one Correct)

1. (a), (c) 2. (c), (d) 3. (c), (d) 4. (a), (d)
5. (a), (b), (d) 6. (a), (b), (c), (d) 7. (a), (b), (d) 8. (c), (d)
9. (a), (c), (d) 10. (b) 11. (b), (c), (d) 12. (a), (b), (c), (d)
13. (a), (b), (c), (d) 14. (a), (b) 15. (a), (b), (d) 16. (b), (c)
17. (b), (c), (d) 18. (b), (c) 19. (c) 20. (b), (c)
21. (a), (b), (c) 22. (a), (c) 23. (b), (c) 24. (c), (d)
25. (c), (d)

Section C
Comprehension I Comprehension VII
1. (b) 2. (a) 3. (a) 4. (b) 5. (c) 19. (a) 20. (a) 21. (c) 22. (b)
6. (c)
Comprehension VIII
Comprehension II
23. (c) 24. (b) 25. (b) 26. (a)
7. (d) 8. (a)
Comprehension IX
Comprehension III
27. (b) 28. (b) 29. (c)
9. (a) 10. (b) 11. (c) 12. (c)
Comprehension X
Comprehension IV
30. (a) 31. (b)
13. (b) 14. (b)
Comprehension V Comprehension XI

15. (a) 16. (b) 32. (b) 33. (d)

Comprehension VI Comprehension XII

17. (b) 18. (a) 34. (a) 35. (b) 36. (c) 37. (d) 38. (d)

Section D (Assertion – Reason)

1. (c) 2. (d) 3. (a) 4. (a) 5. (a) 6. (a) 7. (d) 8. (a) 9. (c) 10. (a)
11. (a) 12. (b) 13. (a) 14. (b) 15. (a) 16. (a) 17. (b) 18. (a) 19. (b) 20. (b)
ANSWER KEYS