1.

THE SOLID STATE

Single Correct Answer Type

1. Which of the following has highest value of energy gap?

a) Aluminum b) Silver

c) Germanium d) Diamond

Which is not the correct statement for ionic solids in which positive and negative ions
are held by strong electrostatic attractive forces?
2.

a) The radius r increases as b) As the difference in size of ions increases,

−¿¿

coordination number increases

+¿/ r ¿

coordination number increases

In ionic solid of the type AX ( ZnS , Wurtzite ) ,
c) When coordination number is eight, the d)
the coordination number of Z n2 +¿¿ and S2−¿¿
ratio lies between 0.225 to 0.414
respectively are 4 and 4
−¿¿
+¿/ r ¿
r
3. The orthorhombic, the value of a , b and c are respectively 4.2 Å , 6.8 A Å and 8.3 Å .Given the
molecular mass of the solute is 155 g mo l−1 and that of density is 3.3g/cc, the number of
formula units per unit cell is
a) 2 b) 3

c) 4 d) 6

A solid has structure in which ‘W’ atoms are located at the corners of a cubic lattice ‘O’
atoms at the centre of edge and Na atoms at the centre of cube. The formula for the
4.

compound is
a) N a W O b) N a W O
2 3 2 2

c) NaW O d) NaW O

The ionic radii of R b and I are 1.46 Å and 2.16 Å . The most probable type of structure
2 3
+¿ ¿ −¿¿
5.
exhibited by it is
a) CsCl type b) ZnS type

c) NaCl type d) Ca F type

Graphite is a
2

6.

a) Molecular solid b) Covalent solid

c) Ionic solid d) Metallic solid

In CsCl type structure the coordination number ofC s and Cl are

+¿ ¿ −¿¿
7.

a) 6, 6 b) 6, 8

c) 8, 8 d) 8, 6

8. In NaCl unit cell, all the ions lying along the axis as shown in the figure are removed.
Then the number of N a and C l ions remaining in the unit cell are
+¿ ¿ −¿ ¿

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 a) 4 and 4 b) 3 and 3

c) 1 and 1 d) 4 and 3

9. The first order reflection (n=1) from a crystal of the X-ray from a copper anode tube
( λ=1.54 Å )occurs at an angle of 45 ° . What is the distance between the set of plane
causing the diffraction?
a) 0.1089 nm b) 0.1089 m

c) 0.905 Å d) −9
1.089 ×10 m
10. Iodine is a

a) Electrovalent solid b) Atomic solid

c) Molecular solid d) Covalent solid

11. A metallic element has a cubic lattice. Each edge of the unit of cell is 2 Å . The density of
the metal is 2.5 g cm−3 . The unit cells in 200 g of metal are
a) 24 b) 20
1 ×10 1 ×10
c) 22 d) 25
1 ×10 1 ×10
12. The number of hexagonal faces that are present in a truncated octahedron is

a) 2 b) 4

c) 6 d) 8

13. In NaCl crystal each C l −¿ ¿ ion is surrounded by

a) 4 N a+¿¿ ions b) 6 N a+¿ ¿ ions

c) 1 N a+¿¿ ion d) 2 N a+¿¿ ions

14. The edge length of a face centred cubic cell of an ionic substance is 508 pm. If the radius
of the cation is 110 pm, the radius of the anions is
a) 288 pm b) 398 pm

c) 618 pm d) 144 pm

For AX ionic crystal to exist in bcc structure, the ratio of radii ( ) should be
15. r cation
r anions
a) Between 0.41 and 0.73 b) Greater then 0.73

c) Less than 0.41 d) Equal to 1.0

16. Which of the following statements about amorphous solids is incorrect?

a) They melt over a range of temperature b) They are anisotropic

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 c) There is no orderly arrangement of d) They are rigid and incompressible
particles
17. A compound of ‘A’ and ‘B’ crystallises in a cubic lattice in which ‘A’ atoms occupy the
lattice points at the corners of the cube. The ‘B’ atoms occupy the centre of each face of
the cube. The probable empirical formula of the compound is
a) A B b) A B
2 3

c) AB d) A B

18. Which set of characteristics of ZnS crystal is correct?

3

a) Coordination number (4 : 4): ccp; Z n b) Coordination number (6 : 6); hcp; Z n ion

2 +¿¿ 2 +¿¿

ion in the alternate tetrahedral voids in all tetrahedral voids

c) Coordination number (6 : 4); hcp; Z n d) Coordination number (4 : 4); ccp; Z n ion
2 +¿¿ 2 +¿¿

ion in all octahedral voids in all tetrahedral voids

19. Which has no rotation of symmetry?

a) Hexagonal b) Orthorhombic

c) Cubic d) Triclinic

20. The coordination number of N a+¿ ¿in NaCl is

a) 6 b) 8

c) 4 d) 1

21. Electrons in a paramagnetic compound are

a) Shared b) Unpaired

c) Donated d) Paired

22. What is the structure of NaCl ?

a) BCC b) FCC

c) Interpenetrating fcc d) None of these

23. In a solid lattice, the cation has left a lattice site and is located at an interstitial position,
the lattice defect is
a) Frenkel defect b) Schottky defect

c) F-centre defect d) Valency defect

24. Schottky defects occurs mainly in electrovalent compounds where

a) Positive ions and negative ions are of b) Positive ions and negative ions are of same
different size size
c) Positive ions are small and negative d) Positive ions are big and negative ions are
ions are big small
25. Which of the following statements is not correct?

a) The units of surface tension are dynes b) The units of viscosity coefficient of a liquid
Cm
−1
are ‘poise ‘

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 c) CsCl crystallizes in body centred cubic d) The coordination number of 2−¿¿ in ZnS is 6
type of lattice
S
26. Which one of the following defects in the crystals lowers its density?

a) Frenkel defect b) Schottky defect

c) F-centres d) Interstitial defect

27. The axial angles in triclinic crystal system are

a) α =β=γ =90 ° b) α =γ=90 ° , β ≠ 90 °

c) α ≠ β ≠ γ ≠ 90 ° d) α =β=γ ≠ 90 °

28. In the face centred cubic lattice, atom A occupies the corner positions and atom B
occupies the face centre positions. If one atom of B is missing from one of the face
centred points, the formula of the compound is
a) A B b) A B
2 2

c) A B d) A B

29. If we mix a pentavalent impurity in a crystal lattice of germanium, what type of

2 2 2 5

semiconductor formation will occur?

a) p−¿type b) n−¿type

c) Both (a) and (b) d) None of the two

30. Doping of silicon (Si) with boron (B) leads to

a) n−¿type semiconductor b) p−¿type semiconductor

c) Metal d) Insulator

31. If the radius of K +¿ ¿ and F−¿¿ are 133 pm and 136 pm respectively, the distance between
K and F in KF is
+¿ ¿ −¿¿

a) 269 pm b) 134.5 pm

c) 136 pm d) 3 pm

32. A compound is formed by elements A and B. This crystallises in the cubic structure
where the A atoms are at the corners of the cube and B atoms are at the body centres.
The simplest formula of the compound is
a) AB b) A B
6

c) A B d) A B

33. The radii of N a+¿ ¿and C l −¿ ¿ ions are 95 pm and 181 pm respectively. The edge length of
8 4 6

NaCl unit cell is

a) 276 pm b) 138 pm

c) 552 pm d) 415 pm

34. An ionic compound is expected to have tetrahedral structure if r +¿/ r ¿ lies in the range of

a) 0.414 to 0.732 b) 0.225 to 0.414

−¿¿

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 c) 0.155 to 0.225 d) 0.732 to 1

35. The number of atoms contained in a fcc unit cell of a monoatomic substance is

a) 1 b) 2

c) 4 d) 6

36. The cubic unit cell of Al( molar mass 27 g mol−1 )has an edge length of 405 pm. Its density is
2.7 g cm−3 . The cubic unit cell is
a) Face centred b) Body centred

c) Primitive d) Edge centred

37. Density of a crystal remains unchanged as a result of

a) Ionic defect b) Schottky defect

c) Frenkel defect d) Crystal defect

38. The radius ratio of CsCl is 0.93. The expected lattice structure is

a) Tetrahedral b) Square planar

c) Octahedral d) Body centred cubic

39. KCl crystallises in the same type of lattice as dose NaCl . Given that r Na and
Calculate the ratio of the side of the unit cell for KCl to that of NaCl .
+¿
/ r Cl
−¿
=0.55 ¿
¿

rK
a) 1.123 b) 0.0891
+¿
/ rCl
−¿
=0.74 .¿
¿

c) 1.414 d) 0.414

40. In which of the following crystals alternate tetrahedral voids are occupied?

a) NaCl b) Zns

c) Ca F d) N a O

41. The elements commonly used for making transistors are

2 2

a) C and Si b) Ga and In

c) P and As d) Si and Ge

42. Which element is used for making a transistor?

a) Sn b) Sb

c) Si d) Mg

43. Which of the following statement is true?

a) Some complex metal oxides behave as b) Zinc oxide can act as superconductor
superconductor
c) An impurity of tetravalent germanium d) A Frenkel defect is formed when an ion is
in trivalent gallium creates electron displaced from its lattice site to an
deficiency interstitial site
44. The packing efficiency of the two dimensional square unit cell shown below is
Page|5
 a) 39.27% b) 68.02%

c) 74.05% d) 78.54%

45. What is the number of tetrahedral voids per atom in a crystal?

a) 1 b) 2

c) 6 d) 8

46. What type of crystal defect is indicated in the diagram below?

Na+, Cl-, Na+, Cl-,Na+,Cl-

Cl- Cl- Na+ Na+
Na+ Cl- Cl-, Na+ Cl-
Cl-Na+Cl-Na+ Na+
a) Frenkel defect b) Schottky defect

c) Interstitial defect d) Frenkel and Schottky defects

47. Which of the following statements is correct?

a) Silicon doped with boron is an n−¿type b) Silicon doped with arsenic is a p−¿type
semiconductor semiconductor
c) Metals are good conductors of d) Electrical conductivity of semiconductors
electricity decreases with increasing temperature
48. Copper crystallises in fcc with a unit cell length of 361 pm. What is the radius of copper
atom?
a) 108 pm b) 127 pm

c) 157 pm d) 181 pm

49. A metal crystallises in a bcc lattice. Its unit cell edge length is about 300 pm and its
molar mass about 50 g mol−1 . What would be the density of the metal( ¿ g cm−3 ) ?
a) 3.1 b) 6.2

c) 9.3 d) 12.4

50. The limiting radius ratio for tetrahedral shape is

a) 0 to 0.155 b) 0.255 to 0.414

c) 0.155 to 0.225 d) 0.414 to 0.732

51. Which is the wrong statement regarding a crystal containing Schottky defect?

a) Electrical neutrality of the crystal is b) Entropy of the crystal increases

maintained

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 c) The density of the overall crystal d) The density of the overall crystal reduces
remains the same
52. How many number of atoms are there in a cube based unit cell having one atom on each
corner and two atoms on each body diagonal of cube
a) 8 b) 6

c) 4 d) 9

53. The crystalline structure of NaCl is

a) Hexagonal close packing b) Face centred cubic

c) Square planar d) Body centred cubic

54. If the distance between N a+¿ ¿ and C l −¿ ¿ ions in sodium chloride crystal is X pm, the
length of the edge of the unit cell is
a) 4 X pm b) X/4 pm

c) X/2 pm d) 2 X pm

55. The radius ratio ¿ of an ionic solid ¿ is 0.69. What is the coordination number of B−¿? ¿

a) 6 b) 8

c) 2 d) 10

56. In a cubic structure of diamond which is made from X and Y, where X atoms are at the
corners of the cube and Y at the face centres of the cube. The molecular formula of the
compound is
a) X Y b) X Y
2 3

c) X Y d) X Y

57. The maximum proportion of available volume that can be filled by hard spheres in
2 3

diamond is
a) 0.52 b) 0.34

c) 0.32 d) 0.68

58. In an antifluorite structure, cations occupy

a) Octahedral voids b) Centre of cube

c) Tetrahedral voids d) Corners of cube

59. Coordination number of Zn in ZnS (zinc blende) is

a) 6 b) 4

c) 8 d) 12

60. The flame colours of metal ions are due to

a) Frenkel defect b) Schottky defect

c) Metal deficiency defect d) Metal excess defect

61. A metal has bcc structure and the edge length of its unit cell is 3.04 Å . The volume of the

Page|7
 unit cell in c m3 will be
a) −21 3 b) −23 3
1.6 ×10 cm 2.81 ×10 cm
c) −23 3 d) −24 3
6.02 ×10 cm 6.6 ×10 cm
62. For a crystal, the angle of diffraction ( 2. θ ) is 90 ° and the second order line has a d value
of 2.28 Å . The wavelength ( ¿ Å ) of X-rays used for Bragg’s diffraction is
a) 1.612 b) 2.00

c) 2.28 d) 4.00

63. How many unit cells are present in a cube shaped ideal crystal of NaCl of mass 1.00g?
[ Atomic masses : Na=23 ,Cl=35.5 ]
a) 21 b) 21
2.57 ×10 5.14 × 10
c) 21 d) 21
1.28 ×10 1.71 ×10
64. A solid metal has ccp or fcc structure. The relation of side of cube ( a )and radius of atom
(r ) will be
a) a=2 r b)
a=2 √ 2 r
c) a= 4 r
√3
d)
a=
√ 3
r
65. Number of atoms in the unit cell of Na(bcc type crystal) and Mg(fcc type crystal ) are
2

respectively
a) 4,4 b) 4,2

c) 2,4 d) 1,1

66. Sodium metal crystallises at room temperature in a body centred cubic lattice with a cell
edge a=4.29 Å . The radius of sodium atom is
a) 1.40 b) 2.65

c) 1.85 d) 2.15

67. Which one of the following is a covalent crystal?

a) Rock salt b) Ice

c) Quartz d) Dry ice

68. An ion leaves its regular site occupy a position in the space between the lattice sites is
called
a) Frenkel defect b) Schottky defect

c) Impurity defect d) Vacancy defect

69. The lattice points of a crystal of hydrogen iodide are occupied by

a) HI molecules b) H atoms and I atoms

c) H +¿¿ cations and I −¿¿ anions d) H ❑ molecules and I molecules

70. The ability of a given substance to assume two or more crystalline structure is called
2 2

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 a) Amorphism b) Isomorphism

c) Polymorphism d) Isomerism

71. 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, the alloy has a
formula
a) Cu Ag Au b) C u A g Au
4 2

c) C u A g Au d) C u A g Au

72. The 8 : 8 type of packing is present in

4 3 4 4

a) Mg F b) CsCl

c) KCl d) NaCl
2

73. Number of atoms per unit cell of bcc is

a) 1 b) 2

c) 8 d) 4

74. What is the coordination number of body centred cube?

a) 8 b) 6

c) 4 d) 12

75. A fcc unit cell of aluminium contains the equivalent of how may atoms?

a) 1 b) 2

c) 3 d) 4

76. A solid compound contains X , Y and Z atoms in a cubic lattice with X atom occupying the
corners. Y atoms in the body centred positions and Z atoms at the centres of faces of the
unit cell. What is the empirical formula of the compound?
a) X Y Z b) XY Z
2 3 3

c) X Y Z d) X Y Z

77. Possible number of different type of crystal lattice present in all types of crystals, is
2 2 3 8 6

a) 23 b) 7

c) 230 d) 14

78. Which kind of defect is shown by the given crystal?

−¿ ¿
−¿ K +¿ C l ¿¿
+¿ Cl ¿
−¿K ¿
+¿C l ¿
K
−¿ ¿ +¿ □¿
+¿ ¿
Cl □ C l −¿ K ¿
K
−¿ ¿
−¿ K+¿ C l ¿¿
−¿□C l ¿
+¿C l ¿
K
+¿ ¿
−¿ K+¿ □ K ¿¿
+¿C l ¿
−¿ K ¿

a) Schottky defect b) Frenkel defect

Cl

c) Schottky and Frenkel defects d) Substitution disorder

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79. The coordination number of Al in the crystalline state of AlC l 3is

a) 2 b) 4

c) 6 d) 8

80. Silver (atomic weight ¿ 108 g mol−1 ) has a density of 10.5 g c m−3 . The number of silver
atoms on a surface of area 10−12 m 2 can be expressed in scientific notation as y ×10 x . The
value of x is
a) 3 b) 5

c) 7 d) 9

81. The unit cell with dimensions α =β=γ =90 ° ,a=b ≠ c is

a) Cubic b) Triclinic

c) Hexagonal d) Tetragonal

82. Which one of the following is a covalent crystal?

a) Rock salt b) Ice

c) Quartz d) Dry ice

83. Total volume of atoms present in a face centred cubic unit cell of a metal is
(r=atomic radius )
a) 20 π r 3 b) 24 π r 3
3 3
c) 12 π r 3 d) 16 π r 3

84. For a crystal system a=b=c and α =β=γ ≠ 90 °

3 3

a) Tetragonal b) Hexagonal

c) Rhombohedral d) Monoclinic

85. Percentage of free space in cubic close packed structure and in body centred packed
structure are respectively
a) 30% and 26% b) 26% and 32%

c) 32% and 48% d) 48% and 26%

86. Copper crystallises in fcc lattice with a unit cell edge of 361 pm. The radius of copper
atom is
a) 181 pm b) 108 pm

c) 128 pm d) 157 pm

87. A solid is made of two elements X and Z . The atoms Z are in ccp arrangement while the
atom X occupy all the tetrahedral sites. What is the formula of the compound?
a) XZ b) X Z
2

c) X Z d) X Z

88. In a compound, atoms of element Y form ccp lattice and those of element X occupy 2/3rd
2 2 3

of tetrahedral voids. The formula of the compound will be

P a g e | 10
 a) X Y b) X Y
4 3 2 3

c) X Y d) X Y

89. Schottky defect generally appears in

2 3 4

a) NaCl b) KCl

c) CsCl d) All of these

90. If a crystal lattice of a compound, each corner of a cube is enjoyed by sodium, each edge
of a cube has oxygen and centre of a cube is enjoyed by tungsten (W), then give its
formula
a) N a W O b) NaW O
2 4 3

c) N a W O d) N a W O

91. Arrangement of sulphide ions in zinc blende is

3 3 2 3

a) Simple cubic b) hcp

c) bcc d) fcc

P a g e | 11
 1.THE SOLID STATE

: ANSWER KEY :

1) d 2) c 3) c 4) d 49) b 50) b 51) c 52) d

5) c 6) b 7) c 8) a 53) b 54) d 55) a 56) d
9) c 10) c 11) d 12) d 57) b 58) c 59) b 60) d
13) b 14) d 15) b 16) b 61) b 62) a 63) a 64) b
17) d 18) a 19) d 20) a 65) c 66) c 67) b 68) a
21) b 22) b 23) a 24) b 69) a 70) c 71) c 72) b
25) d 26) b 27) c 28) d 73) b 74) a 75) d 76) b
29) b 30) b 31) a 32) a 77) d 78) a 79) c 80) c
33) c 34) b 35) c 36) a 81) d 82) c 83) d 84) c
37) c 38) d 39) a 40) b 85) b 86) c 87) c 88) a
41) d 42) c 43) d 44) d 89) d 90) b 91) d
45) b 46) b 47) c 48) b

P a g e | 12
 1.THE SOLID STATE

: HINTS AND SOLUTIONS :

Diamond has the highest value of energy

1 (d) rc +¿

∴ ¿
gap as it is a insulator.
1.46
ra =
−¿ =0.676 ¿
∴ It will have coordination number 6 and
2.16

structure will be same as of NaCl.

When coordination number is eight, the
2 (c)

radius ratio −¿ ¿ lies between 0.732 to

+¿
r
Graphite is an example of covalent solid.
6 (b)

1.000.
r ¿

The coordination number is 8 : 8 in

7 (c)
3 (c)
V ×N ×d Cs+¿ :Cl
−¿¿
¿

The coordination number is 6 : 6 in

Z=
m
−21 23
4.2 ×8.6 × 8.3× 10 × 6.023 ×10 ×3.3 Na
+¿: Cl
−¿ ¿
¿
¿
155

Since, in a unit cell of NaCl crystal, the

¿ 3.14 8 (a)

ions are arranged in the following

≈4

manner.
In a unit cell, W atoms at the corner
4 (d)

1
¿ × 8=1
O-atoms at the centre of edge
8

1
¿ ×12=3
W : O : Na = 1 : 3 : 1
4

Hence, formula ¿ NaW O3 When all the ions lying along the shown
axis, the remaining unit cell contains
4 N a and 4 Cl ions.
5 (c) +¿¿ −¿¿

Radius Coor Exam

ratio dinat ple 9 (c)
ion nλ=2 d sinθ
no
0.155 −¿ 3
1 ×1.54=2 d sin 45 °

0.225
B2 O 3 1 ×1.54=2 d × 0.850

0.225 – 4
1.54
2 d= =0.905 Å
0.414
ZnS 0.850
0.414 – 6
0.732
NaCl 11 (d)

0.732 – 1 8 Number of unit cells ¿

mass of metal
In ionic solids the shape of crystal
CsCl
Given, edge length of unit cell
mass of one unit cell
depends upon relative size of ions.
Given, r c ¿ ¿
−8

Mass of metal ¿ 200 g

+¿
¿ 2 Å=2 ×10 cm

Density of metal ¿ 2.5 g cm−3

ra −¿
¿¿

P a g e | 13
 Volume of unit cell 2 ¿ edge length
−8 3 2¿
So, r −¿=114 pm ¿
¿ ( edge length ) =( 2 ×10 )
3

−24 3

Mass of one unit cell ¿ volume ×density

¿ 8 ×10 cm

For body centred cubic (bcc) structure,

15 (b)
−24
¿ 8 ×10 × 2.5
the ratio of radii (r +¿/ r ¿ ) lies in between
−24

∴ No. of unit cells in 200 g metal

¿ 20 ×10
0.732−¿1.00.
−¿¿

mass of metal ∴ The ratio of radii for bcc is greater

than 0.73.
¿
mass of one unit cell
200
¿
A occupies corners, thus number of A
20× 10
−24 17 (d)

atoms per unit cell

24 25
¿ 10 ×10 =1.0× 10

The truncated octahedron is the 14-faced

12 (d) 1
¿ 8 × =1
Archimedean solid, with 14 total faces : 6 B occupies face centres, thus number of
8

squares and 8 regular hexagons. B atoms per unit cell

The truncated octahedron is formed by
removing the six right square pyramids
1
¿ 6 × =3
one from each point of a regular ∴ The empirical formula of the compound
2

octahedron as : is A B3 .

ZnS has zinc blende type structure (i .e . ,

18 (a)

ccp structure). The S2−¿¿ ions are present

at the corners of the cube and at the
centre of each face. Zinc ions occupy half
Truncated Octachedron of the tetrahedral sites. Each zinc ion is
surrounded by four sulphide ions which
are disposed towards the corner of
regular tetrahedron. Similarly, S2−¿¿ ion is
surrounded by four Z n2 +¿¿ ions.

In triclinic lattice, the eight lattice points

19 (d)

are located, one each at the corners of

Truncated octahedron unf olded in

triclinic lattice. Also a ≠ b ≠ c and α ≠ β ≠ γ .

two dimensions

There is no planes and no axes. Thus,

In NaCl crystal, C l ions adopt cubic
13 (b)
triclinic lattice has no rotation of
−¿ ¿

close packed arrangement and N a ions symmetry.

+¿ ¿

occupy all the octahedral sites. Therefore,

Na and Cl have 1 : 1 stoichiometry. In
In sodium chloride, each Na ion is
20 (a)
other words, each Na ion is surrounded
+¿¿

surrounded by six Cl ions and Cl ion

+¿¿

by six Cl ions which are disposed

−¿¿ −¿¿

is surrounded by six Na ions. Thus, both

−¿¿

towards the corners of a regular

+¿¿

octahedron. Similarly, each Cl

−¿¿
ion is the ions have coordination number six.
surrounded by six Na ions.
+¿¿

NaCl has fcc arrangement of ions. The

22 (b)

For fcc arrangement

14 (d)

P a g e | 14
 coordination number of C l as well as
−¿ ¿

N a ion is six. Therefore, it is termed 6 :

+¿ ¿

6 coordination crystal.

When an ion (generally cation due to its

23 (a)

small size) is missing from its normal Thus, formula is A1 B 5/ 2= A2 B5

position and occupy an interstitial site
between the lattice points, the lattice
defect obtained is known as Frenkel On adding a pentavalent impurity with
29 (b)

defect. germanium, we get n−¿type of

semiconductors because excess of
electrons is responsible for conduction.
When equal number of cations or anions
24 (b)

are missing from their lattice sites (to

maintain electrical neutrality), then the Doping of silicon with boron leads to p−¿
30 (b)

defect is called Schottky defect. The type semiconductor.

defect is observed in highly ionic
compounds which have cations and
Distance between K and F in KF
31 (a)
anions of similar size e . g . , NaCl, KCl etc.
+¿ ¿ −¿¿

¿rK +¿
+rF −¿
=133+ 136=269 pm ¿
¿

Zinc blende (ZnS) has ccp arrangement

25 (d)

Since A atoms are present at the corners

32 (a)
of S2−¿¿ and Z n2 +¿¿ in alternative
tetrahedral sites. The coordination of the cube,
number of Z n2 +¿=4 ¿ and S2−¿=4 ¿ in ZnS Number of A atoms per unit cell ¿ 8 × =1
1

Number of B atoms per unit cell = 1

8

Schottky defects - This defect is due to

26 (b)

vacancy at a cation site accompanied by

( ∵ Present at the body centre of the cube )
Hence, the formula of the compound ¿ AB
vacancy at an anion site so that the
electrical neutrality of the system is
NaCl has fcc structure.
33 (c)
maintained. Due to this defect, density
decreases. In fcc lattice
a
−¿= ¿
2
+¿+r ¿

Where, a=¿ edge length

r
The axial angles in triclinic crystal system
27 (c)

are different and none is perpendicular to

−¿=181 pm¿

r +¿=95 pm , r ¿

any of the others i .e . , α ≠ β ≠ γ ≠ 90 ° . Edge length ¿ 2 r +¿+2 r

−¿ ¿
¿

¿ ( 2 ×95+ 2×181 ) pm

Number of atoms ( A ) per unit cell

28 (d)
¿ 190+362=552 pm

1 34 (b)
¿ 8 × =1
Radius ratio¿ Structure
8
Number of atoms (B) per unit cell
¿ 0.155 linear
planar
1 5
triangular
¿ ( 6−1 ) × = 0.155−0.225
(One atom B is missing)
2 2
tetrahedr
al
0.225−0.414

octahedra
l
0.414−0732

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 0.732−1 bcc r +¿ rCl −¿
¿
K + ¿

In fcc→ contribution of each atom

35 (c) r +¿
Na + rCl−¿ =
1.74
=1.1226¿
¿
1.55

present at the corner ¿

In ZnSstructure, sulphide ions occupy all
1 40 (b)

Contribution of each atom at the face (fcc) lattice points while Z n2 +¿¿ ions are
8

present in alternate tetrahedral sites.

centre ¿
1
Therefore, there is one Z n2 +¿¿ ion for
Hence, the total number of atoms in fcc
2
every S2−¿¿ ion.

( 18 )+(6 × 12 )=1+3=4
¿ 8×
Si and Ge are used for making
41 (d)

36 (a) transistors.

Density(ρ)=
Z ×M

Silicon is used for making a transistor.

3 42 (c)
a ×N0
Z ×27
2.7= 3
( 405 ×10−10) × 6.023× 1023
Frenkel defect is formed by displacement
43 (d)

of ion from its lattice to interstitial state.

3 −30 23
2.7 × ( 405 ) ×10 × 6.023× 10
Z= =4
For face centred cubic unit cell, number
27

of atoms are 4.
44 (d)
a=( √2 2 r )Packing fraction
2 2

Due to Frenkel defect, density of a

37 (c) 2× π r 2π r
¿ =
crystal remains unchanged.
2 2
( √2 2 r ) 8r
π 3.14
¿ = =0.78 54
4 4
The radius ratio of CsCl is 0.93 hence, its
38 (d)
¿ 78.54 %
structure is body centred cubic.
In the close packing of ‘ n ’ atoms, the
45 (b)

number of tetrahedral voids are ‘ 2 n ’.

39 (a)
Given, r Na
Hence, their number per atom is 2.
+¿
/ r Cl
−¿
=0.55 ¿
¿

rK +¿
/ r Cl
−¿
=0.74 ¿
¿

When equal number of cations and anions

r KCl 46 (b)
=?
(such, that charges are equal) are
r NaCl

missing ¿
r Na +¿

¿
It is a case of Schottky defect.
r Cl =0.55 ¿
−¿

r Na +¿

¿
In fcc unit cell
r Cl +1=0.55+1 ¿
−¿ 48 (b)
r r ¿
√ 2 a=4 r ⇒ r = √
+¿ Cl
−¿

Na + ¿
rCl =1.55 … ( i ) ¿
−¿ 2a
rK +¿ 4
¿
¿√
r Cl =0.74 ¿ 2 ×361
−¿
=127 pm
rK +¿
4
¿
r Cl +1=0.7 4+ 1¿
Given,
−¿
49 (b)
¿
Molar mass, M =¿ 50g/mol
r +¿ r Cl
−¿

K + ¿

Eq (ii) devide by Eq (i)

rCl =1.74 … ( ii ) ¿
−¿

P a g e | 16
 N A =6.02 ×10
23
coordination number
Z=2 (for bcc crystal)
Coordinati
Edge length a=300 pm on number
rc

0.155 −¿ 3
−8 ra
¿ 3 ×10 cm
Z×M 0.225
0.225−¿ 4
d= 3

0.414
NA×a

0.414 6
2 ×50
¿
0.732
−8 3 −¿
6.02× 10 × ( 3× 10 )
23

¿ 6.15 0.732 −¿1 8

≈ 6.2 56 (d)

Number of atoms at corner ¿ 8 × =1

1
For tetrahedral shape, limiting radius
50 (b)
8
ratio is 0.225 −¿ 0.414. Number of atoms at face centres ¿ 6 × =3
1
2
∴ The formula of the compound is X Y 3 .
When equal number of cations and anions
51 (c)

are missing from their position in a

In diamond,
57 (b)
crystal lattice so that electrical neutrality
is maintained, the defect is called the maximum proportion of available
Schottky defect. Due to missing of ions, volume that can be filled by hard spheres
the overall density of the crystal π √3
decreases. Moreover, defect leads to
¿ =0.34
16
randomness, thus entropy also increases.
In antifluorite structure, the anions are
58 (c)

There are four body diagonals. Atoms on oxide ions. The oxide ions form a face
52 (d)

the body diagonals are not shared by any centred cubic array and the metal ion
other unit cell. (cation) fill half of the tetrahedral voids.
Contribution by atoms on corners e . g ., - Na2 O .
1
¿ 8 × =1∧¿
In ZnS each sulphide ion is tetrahedrally
59 (b)

Contribution by atoms on body diagonal

8
surrounded by four zinc ions and each
zinc ion is surrounded by four sulphide
¿ 2 ×4=8
Hence, total number of atoms = 9
ions. Thus, zinc sulphide possesses 4 : 4
coordination.
Sodium chloride ( NaCl ¿has face centred
53 (b)

cubic structure. It contains 4 N a and 4

Flame colours are due to metal excess
+¿ ¿ 60 (d)

C l in the unit cell. Each Na is

defect. What happens that in some ionic
−¿ ¿ +¿¿

surrounded by 6 C l ions and vice−versa. crystals, there becomes an excess of

−¿ ¿

metal atom, which by loosing e−¿ ,¿ change

In NaCl ,the length of the edge of the unit into ions. These electrons can absorb
54 (d)

cell is energy and go into excited states from

¿ 2 ×distance between N a and C l ions ground state. Thus, the absorption of
certain wavelength of light takes place
+¿ ¿ −¿ ¿

hence, a=2 X pm .
and crystal becomes coloured according
to complementary colour. The spaces
Relation between radius ratio and
55 (a)
occupied by extra e are called F-
−¿¿

P a g e | 17
 centres.
Frenkel defects arises when an ion is
68 (a)

missing from its normal position and

Edge length α =3.04 Å
61 (b)
occupies an interstitial site between the
lattice points.
−8
¿ 3.04 × 10 cm
Volume of bcc (cubic) cell ¿ a 3

The phenomenon by which a certain

−8 3 70 (c)
¿ ( 3.04 × 10 )
crystalline compound exists in two or
−23 3
¿ 2.81 ×10 cm
more different crystalline forms, is called
Given, angle of diffraction ( 2 θ )=90° polymorphism e.g., CaC O3 occurs in two
62 (a)

polymorphic forms, i .e . , calcite

(rhombohedral) and aragonite
θ=45 °
Distance between two planes, d=2.28 Å
n=2 ¿ Second order diffraction] (orthorhombic).
Bragg’s equation is 71 (c)

Number of Cu atoms at corners ¿ 8 × =1

nλ=2 d sinθ 1
2 × λ=2 ×2.28 ×sin 45 °
Number of Ag atoms at edge centres
8
λ=1.612
1
¿ 12 × =3
Mass of one unit-cell (m)
63 (a)

Number of Au atoms at body centre

4
= volume × density
¿ 1 ×1=1
∴ Formulais Cu4 Ag3 Au.
3 3 MZ MZ
¿ a × d=a × =
N0 a
3
N0
58.5 × 4
The 8:8 type of packing is present in
72 (b)
m= 23
g

caesium chloride (CsCl). In this structure

6.02 ×10
∴ Number of unit cells in 1 g ¿
each C s ion is surrounded by 8 C l
1
+¿ ¿ −¿ ¿

ions and each C l ion is also

m
−¿ ¿

surrounded by 8 C s ions.
23
6.02× 10
¿ +¿ ¿
58.5 × 4
21
¿ 2.57 ×10
For bcc unit cell, number of atoms at
73 (b)

In case of ccp or fcc structure corners

64 (b)

(per unite cell)¿

4r 1
4 r= √ 2 a ⇒ a= × 8=1
Number of atoms at body centre =1
√2 8

Total number of atoms = 1 + 1 = 2

∴ a=2 √2 r

Number of atoms in unit cell of Na are 2 74 (a)

65 (c)

(bcc). Number of atoms in unit cell of Mg The unit cell of body centred cube has
(fcc) are 4. one atom at each of the eight corners and
one atom at the centre of the body. Thus,
the atom at centre remains in contact
For a body centred cubic lattice radius,
66 (c)
with 8 corner atoms. Hence, the
(r ) coordination number of bcc is 8.

¿ √ a=0.433 a
3
In fcc atoms are present at faces and
75 (d)
4
Therefore, radius of N a+¿=0.433× 4.29=1.8575¿
corners.

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 Number of atoms in fcc = atoms at So, number of silver atoms in given area
corners
+ atoms at faces of
−12 8
10 10
¿ =
unit cell.
−29 3 2 /3 π ×2
( 0.407 ×10 m )
= (no. of corners × contribution by one
7 x

So, x=7
¿ 1.6 ×10 = y × 10
atom)
+ (no. of faces × contribution by
one atom) The unit cell with dimensions
81 (d)

a=b ≠ c , α= β=γ =90 is tetragonal.

¿ 8×( 18 )+(6 × 12 )=1+3=4
82 (c)
Quartz ( SiO2 ) is a covalent crystal.
Since atom X is present at corner and
76 (b)

one corner is shared by eight unit cells, 83 (d)

Number of X atoms per unit cell ¿ Volume of an atom ¿

1 4 3
× 8=1 πr
In fcc, number of atoms per unit cell = 4
3
Atom Y is present at body centred
8

position and used by only one unit cell. ∴ Volume of total atoms ¿ 4 ×
4 3
So, number of Y atoms per unit cell = 1
πr
3
Atom Z is present at the center of each 16 2
face, so shared by two unit cells,
¿ πr
3
Thus, number of Z atoms per unit cell
84 (c)
1
Crystal Axial Axial
¿ ×6=3
2
Hence, the formula of compound ¿ XY Z 3 system distanc angle
es
Tetragonal a=b ≠ c α =β=γ =90 °
Hexagonal
In the given crystal equal number of
78 (a)
a=b ≠ c α ≠ β=90° , γ =120 °
Rhombohed
cations and anions are missing (two K ral
+¿ ¿ a=b=c α =β=γ ≠ 90 °

and two Cl from their normal lattice Monoclinic a ≠ b ≠ c α =γ=90 , β ≠ 90 °

−¿¿

sites and the crystal maintains electrical 85 (b)

neutrality. Hence, this is Schottky defect. Packing fraction of ccp ¿
π
=0.74 ⇒ 74 %
3 √2
79 (c) % free space in ccp = 26%
Coordination number of Al in AlC l 3 in
Packing fraction of bcc ¿
π √3
(solid) crystalline state is 6.
=0.68 ⇒ 68 %
% free space in bcc = 32%
8

Volume of one mole of silver atoms

80 (c)

Copper crystallises in fcc lattice.

86 (c)
108
If, r = radius
3
¿ cm /mol
Volume of one silver atom
10.5
a=¿ edge length
Then r =
108 1 3 a
361
¿ × cm pm =
10.5 6.022 ×10 23
2 √2 2 √2
So, π r =
4 3 108 1 −23 ¿ 127.633 pm ≈ 128 pm
× =1.708 ×10
3 10.5 6.022× 10 23

Given, A solid has two elements ¿ X ∧Z

3 −23 3 −29 3 87 (c)

Area of each silver atom,

r =0.407 ×10 cm =0.407 × 10 m
Z are in ccp arrangement and X occupy
all tetrahedral sites.
3 2 /3
π r =π ( 0.407 ×10 m )
2 −29

Let the number of atoms of Z in ccp

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 arrangement = 100
∴ Number of atoms of tetrahedral sites =
200
∴ Number of atoms of X =200 ¿They
occupy all
tetrahedral sites)
∴ Ratio of X : Z=200 :100
¿ 2 :1
∴ The formula of compound is X 2 Z .

Suppose atoms of element Y in ccp

88 (a)

= 100
Number of tetrahedral voids ¿ 2 ×100

Number of atoms of element X = ×200

2
3
400
¿
3
X 400
=
Y 300
Formula ¿ X 4 Y 3

Schottky defect arises when equal

89 (d)

number of a cations and anions are

missing from their sites. This defect is
generally found in ionic compounds like
NaCl, KCl, CsCl, etc.

No. of Na atoms present at each corner

90 (b)

1
¿ 8 × =1
No. of O atoms present at the centre of
8

edges ¿ 12 × =3
1

No. of W atoms present at the centre of

4

cube = 1
Formula of the compound ¿ NaW O3

Arrangement of sulphide ions ¿ in zinc

91 (d)

blende (ZnS) is fcc while Z n2 +¿¿ ions

occupy alternate tetrahedral voids.

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