CHEMISTRY

12th JEE

THE SOLID STATE

(ONLY FOR JEE-ADVANCED)
 VIDYAPEETH Scan for Solution

THE SOLID STATE

DPP-1 (JLC/094)

[Classification of Solids, General Characteristics, Seven crystal

system]
1. A pure amorphous solid 5. How many of the following crystal
(A) contains well-ordered spatial systems have either a = b = c or  = 
distribution of atoms, ions or =  = 90° - Cubic, Tetragonal,
molecules Orthorhombic, Monoclinic,
(B) possess unique melting point (C) Hexagonal, Rhombohedral, Triclinic?
does not contain any short-range
orderorder; only long-range 6. A pure crystalline substance, on being
prevails heated gradually, first forms a turbid
(D) is isotropic liquid at constant temperature and still
TiO2 is a well-known example of at higher temperature, turbidity
2.
(A) triclinic system completely disappears. This behavior is
(B) tetragonal system the characteristic of substances forming-
(C) monoclinic system
(D) cubic system (A) isomeric crystals
(B) liquid crystals
3. Maximum number of Bravais lattices are (C) isomorphous crystals
(D) allotropic crystals
possible for-
(A) cubic
*7. Which of the following is/are pseudo
(B) monoclinic
(C) orthorhombic solids?
(D) hexagonal (A) KCl
(B) Barium chloride dihydrate
4. The metallic solids among the following (C) Rubber
are- (D) Solid cake left after distillation of
NaCl(s), KCl(s), CO2(s), Fe(s), Cu(s), coal tar
SiC(s), K(s), Ca(s)
(A) Fe(s), Cu(s), K(s), Ca(s) 8. Which type of crystals contain more than
(B) NaCl(s), KCl(s) one Bravais lattice?
(C) CO2(s), Fe(s) (A) Hexagonal (B) Triclinic
(D) SiC(s), K(s) (C) Rhombohedral (D) Monoclinic

(2)
9. The total number of elements of 10. The number of solids which are
symmetry in a cubic crystal is- covalent network solid among the
(A) 9 (B) 23 following - S8, Bronze, SiO2,
(C) 13 (D) None of these Diamond, ZnSO4, Si, AlN, SiC, CO2 –
is-
(A) 5
(B) 4
(C) 2
(D) 1

(3)
 DPP-2 (JLC/095)
[Close Packed Structure of Solids, Packing in FCC,
BCC and HCP lattices] Scan for Solution
1. In a multi layered close-packed 5. In a FCC arrangement of given metallic
structure- (A) there are twice as many atom, what is the relative ratio of the sizes
tetrahedral
holes as many close-packed atoms of tetrahedral and octahedral voids?
(B) there are as many tetrahedral holes (A)
as many closed packed atoms 0.543 (B)
(C) there are twice as many octahedral 0.732 (C)
holes as many close-packed atoms 0.414 (D)
(D) there are as many tetrahedral holes 0.637
as many octahedral holes 6. In face centred cubic unit cell, edge length
is-
2. What is the coordination number in a
(A) 4 4
square close packed structure and r (B) r
3 2
hexagonal packed structure in two-
dimensional packing respectively? 3
(C) 2r (D) r
(A) 6, 12 (B) 4, 6 2
(C) 8,12 (D) 6,8
7. What is the volume of an HCP unit cell?
3. In which of the following arrangements, 12 3 16 3
octahedral voids are formed? (A) r (B) r
2 2

(A) HCP (B) BCC (C) 64

(C) 24 2r 3 (D) r3
FCC (D) both HCP & 3 3
FCC
8. Lithium forms body centered cubic
structure. Atomic radius of the lithium
*4. Which of the following statement(s) is 152 pm, then length of the side of
is/are correct? its unit cell is- (A) 75 pm (C) 304 pm
(A) A metal that crystallizes in the fcc (B) 351 pm
structure has coordination number (D) 152 pm
twelve.
(B) Cubic and rhombohedral are two 9. A solid has a BCC structure. If the
primitive crystal systems.
distance of closest approach between the
(C) In orthorhombic crystal system, all
two atoms is 3.46 Å. The edge length of
axial (crystallographic) angles are
unit cell is-
identical.
(A) 2 pm (B) (3 / 2) pm
(D) Number of next nearest neighbors in
the fcc structure is twelve. (C) 400 pm (D) 142.2 pm

(4)
10. Fraction of the total volume occupied by 13. In an fcc unit cell, a cube is formed
atoms in a simple cube is- by joining the centers of all the
tetrahedral voids to generate a new
(A) /6
cube. Then the new cube would
(B) 3 /8 contain voids as effectively-
(C) 2 /6
(D) /3

11. Aluminium crystallises in a cubic close-

(A) 1 full tetrahedral void, 1 full
packed structure. Its metallic radius octahedral void
is 125 pm. What is the edge length of the (B) 1 full tetrahedral void only
unit cell? (C) 8 full tetrahedral voids and 1 full
(A) 3.536 Å octahedral void
(D) 1 full octahedral void only
(B) 1.768 Å
(C) 5.412 Å
*14. What will be the incorrect distance
(D) 2.706 Å between two nearest neighbours (d) in
primitive (or simple cubic), fcc and bcc
Consider a body centered cubic (bcc) unit cell? (a = edge length)
12.
(A) For primitive, d = 0.5a
arrangement, let de, dfd, dbd be the (B) For fcc, d = 0.707 a
distances between successive atoms (C) For bcc, d = 1.732 a
located along the edge, the face-diagonal, (D) For bcc, d = 1.414 a
the body diagonal respectively in a unit In FCC unit cell, what fraction of edge
cell. Their order (of magnitude) is given 15. length is not covered by atoms?
(A) 0.134
by- (B) 0.24
(A) de < dfd < dbd (C) 0.293
(B) dfd > dbd > de (D) None of these
(C) dfd > de > dbd
(D) de = dfd = dbd

(5)
 DPP-3 (JLC/096)
[Density of Solids, Radius Ratio, Structure of Ionic Solids]
Scan for Solution
1. The radius of Ag
+ ion is 126 pm and
6. A metal has a fcc lattice. The edge length
that of I– ion is 216 pm. The co- of the unit cell is 404 pm. The density of
ordination number of Ag+ ion is- (A) 2 the metal is 2.72 g cm–3. The molar mass
(C) 6 (B) 4 of the metal is-
(D) 8 (A) 30 g mol–1
(B) 27 g mol–1
2. An element X with an atomic mass of 60 (C) 20 g mol–1
g/mol has a density of 6.23 g/cm3. If the (D) 40 g mol–1
edge length of the unit cell is 400 pm. The
type of unit cell is- 7. In an ionic solid r+ = 1.6 Å and r– = 1.864
(A) Simple cubic Å . Use the radius ratio rule to determine
(B) BCC the edge length of the cubic unit cell in Å
(C) FCC (in nearest integer value).
(D) Information is not sufficient
8. Lead metal has a density of 11.34 g/cm3
3. An element (atomic mass = 100 g/mole)
and crystallizes in face-centered lattice.
having bcc structure has unit cell edge The atomic radius is- (Atomic mass of
400 pm. The density of the element is
Pb = 207)
(A) 2.144 g/cm3
(A) 150 pm
(B) 5.2 g/cm3
(B) 175 pm
(C) 7. 289 g/cm3
(C) 200 pm
(D) 10.376 g/cm3
(D) 250 pm
4. A metal crystalizes into two cubic phases,
9. In zinc blende structure the coordination
fcc and bcc whose unit cell lengths are
3.5 Å and 3.0 Å respectively. The ratio of number of Zn2+ ion is-
densities of fcc and bcc lattice is- (A) 2
(A) 0.26 (B) 0.56 (B) 4
(C) 1.26 (D) 2.56 (C) 6
(D) 8
5. Polonium
At room temperature,
crystallises in cubic primitive cell. If edge 10. The compound AB crystallizes in a cubic
length is 3.0 Å, calculate the theoretical lattice in which both A and B atoms have
density of Po- coordination numbers of 8. To what
(atomic weight of Po = 207 amu) crystal class does the unit cell belong ?
(A) (25/3) amu/Å3 (A) CsCl structure
(B) (23/3) amu/Å3 (B) NaCl structure
(C) (21/3) amu/Å3 (C) ZnS structure
(D) (27/3) amu/Å3 (D) Al2O3 structure

(6)
*11.Strontium
fluorite chloride has a 15. In a face centered lattice of X and Y,
structure. Which of the following X atoms are present at the corners
statement is/are false for the structure of while Y atoms are at face centers.
strontium chloride? Then the formula of the compound if
(A) The strontium ions are in a body two atoms of X are missing from the
centered cubic arrangement corners would be- (A) X4Y
(B) The strontium ions are in a face (B) X3Y4
centered cubic arrangement (C) XY4
(C) Each chloride ion is at the center of (D) X2Y4
a cube of 8 strontium ions
(D) Each strontium ion is at the center of 16. A mineral having the formula AB2,
a tetrahedron of 4 chloride ions crystallises in the cubic close-packed
lattice, with the A atoms occupying the
12. A solid ‘AB’ having Rock salt structure lattice points. The co-ordination number
has edge length 320 pm. If radius of of the A atoms, that of B atoms and the
cation A+ is 60 pm then the radius of fraction of the tetrahedral sites occupied
anion B– is- by B atoms are most probably-
(A) 144.92 pm (B) 81.96 pm (A) 8, 4, 100%
(C) 100 pm (D) 200 pm (B) 2, 6, 75%
(C) 3, 1, 25%
13. KCl crystallizes in the same type of (D) 6, 6, 50%
r +
lattice as does NaCl. Given that Na = 17. In a compound, oxide ions are arranged
r –
Cl
in cubic close packing arrangement.
r
0.50 and Na+= 0.70, calculate the ratio Cations A occupy one-sixth of the
rK+ tetrahedral voids and cations B occupy
of the side of the unit cell for KCl to that one-third of the octahedral voids. The
of NaCl. formula of the compound is-
(A) 1.143 (B) 1.224 (A) A2BO3 (B) AB2O3
(C) 1.414 (D) 0.875 (C) A2B2O2 (D) ABO3

14. A cubic solid is made by atoms A 18. In a CCP lattice of X and Y, X atoms are
forming close packed arrangement, B present at the corners while Y atoms are
occupying one fourth of tetrahedral voids at face centers. Then the formula of the
and C occupying half of the octahedral compound would be if one of the X atoms
voids. What is the formula of the from a corner is replaced by Z atoms
compound? (having same valency)?
(A) A4B2C2 (B) A3B3C2 (A) X7Y24Z2 (B) X7Y24Z
(C) A4B3C4 (D) AB2C2 (C) X24Y7Z (D) XY24Z

(7)
19. A crystal is made of particles X, Y and 20. A compound MpXq has cubic close
Z. X forms fcc packing. Y occupies all packing (ccp) arrangement of X. Its
the octahedral voids of X and Z unit cell structure is shown below
occupies all the tetrahedral voids of X. then p + q is : (p & q are positive
If all the particles along one body integers).
diagonal are removed, then the
M
formula of the crystal would be (A)
X
XYZ2
(B) X2YZ2
(C) X8Y4Z5
(D) X5Y4Z8

(A) 2 (B) 3
(C) 7 (D) 9

(8)
 DPP-4 ( JLC/097)
[Defects in Ionic Crystals] Scan for Solution
1. In the Schottky defect- *5. Which of the following is/are correct ?
(A) cations are missing from the lattice (A) Schottky defect lowers the density
sites and occupy the interstitial sites (B) Frenkel defect increases the dielectric
(B) cations and anions are missing from constant of the crystals
the lattice in stoichiometric ratio (C) Stoichiometic defects make the
(C) anion are missing and electrons are crystals good electrical conductors
present in their place (D) AgBr shows only Frenkel defect
(D) equal number of extra cations and
electrons are present in the interstitial 6. NaCl shows Schottky defects and AgCl
sites Frenkel defects. Their electrical
conductivity is due to-
2. A neutral crystal of NaCl, which has
(A) motion of ions and not the motion of
sodium ions and chloride ions missing from electrons
the lattice points is said to exhibit-
(B) motion of electrons and not the motion
(A) Surface defect
of
(B) Lattice defect
ions
(C) Frenkel defect
(D) Schottky defect (C) lower co-ordination number of NaCl
(D) higher co-ordination number of AgCl
3. F-centres are-
7. Zinc oxide, white in colour at room
(A) the electrons trapped in anionic
vacancies temperature, acquires yellow colour on
(B) the electrons trapped in cationic heating due to-
vacancies (A) Zn being a transition element.
(C) non-equivalent sites of stoichiometric (B) paramagnetic nature of the compound.
compound (C) trapping of electrons at the site vacated
(D) all of the above by oxide ions.
(D) Both (A) & (B).
*4. Which of the following is a incorrect
statement(s) regarding defects in crystalline8. Experimentally it was found that a metal
solids? oxide has formula M0.98O. Metal M is
(A) Frenkel defect is a dislocation defect. present as M2+ and M3+ in its oxide.
(B) Frenkel defect is a found in halides of Fraction of the metal which exists as M3+
alkaline earth metals. would be-
(C) Schottky defects have no effect on the (A) 7.01%
density of crystalline solids. (B) 4.08%
(D) Frenkel defects decrease the density of (C) 6.05%
crystalline solids. (D) 5.08%

(9)
9. A crystal is made up of metal ions ‘M1’ *10. Identify correct statements
and ‘M2’ and oxide ions. Oxide ions (A) the lattice positions left vacant by
from a ccp lattice structure. The cation anion and occupied by electrons are
‘M1’ occupies 50% of octahedral voids called F-centres.
and the cation (B) the presence of F-centres makes the
lattice electrically neutral and
‘M2’ occupies 12.5% of tetrahedral
diamagnetic.
voids of (C) the presence of F-centres gives colour
oxide lattice. The oxidation numbers of to the crystals.
‘M1’ and ‘M2’ are respectively- (D) F-centres contain unpaired electrons.
(A) +3, + 1
(B) +4, + 2
(C) +1, + 3
(D) +2, + 4

(10)
 DPP-5 (JLC/098)
[Miscellaneous] Scan for Solution

1. KF crystallizes in the NaCl type structure. 5. The theoretical density of ZnS is d

If the radius K+ ion is186 pm and F– ion is g/cm³. If the crystal has 4% Frenkel
2 defect, then the actual density of ZnS
214 should
(A) be.
d g/cm³ (B) 0.04 d
pm, then what is the shortest distance
2 (C) 0.96 d g/cm³ g/cm³ (D) 1.04
between K+ – K+ions (in Å )? d g/cm³
*6. Copper exists in face-centered cubic lattice
2. The packing fraction of diamond structure with unit cell edge of 361 pm. Choose the
is: correct options
(A) 0.74 (B) 0.34 (A) The radius of the largest atom, which
(C) 0.68 (D) 0.52
could fit into octahedral voids is 52.84
*3. SrO crystallizes in rock salt structure while pm
(B) The radius of the largest atom, which
BeO crystallizes in zinc blende structure.
The edge length of SrO lattice is 1.36 times could fit into tetrahedral voids without
the edge length of BeO lattice. If the disturbing the lattice is 18.72 pm.
4 (C) The radius of the largest atom, which
r2 2rBe2 and rBe2 r2–
Sr
3 O could fit into octahedral voids is 32.84
(Atomic mass: Sr = 87.6, Be = 9, O = 16) pm.
Choose the correct options- (D) The radius of the largest atom, which
(A) The ratio of density of SrO to BeO
could fit into tetrahedral voids without
lattice is 2.647
disturbing the lattice is 28.72 pm.
(B) The ratio of packing fractions of the
SrO to BeO lattice is 1.36
(C) The ratio of density of SrO to BeO *7. BaTiO3 crystallizes in the pervoskite
lattice is 1.647 structure. This structure may be described
(D) The ratio of packing fractions of the as a cubic lattice, with barium ions
SrO to BeO lattice is 2.36 occupying the face centers and titanium ion
occupying the center of the unit cell.
4. There are three cubic unit cells A, B and C.
Choose the correct options-
A is FCC and all of its tetrahedral voids are
(A) If titanium is described as occupying
also occupied. B is also FCC and all of its
octahedral voids are also occupied. C is void in the BaO lattice, the void it
simple cubic and all of its cubic voids are occupied is octahedral
also occupied. If voids in all unit cells are (B) Fraction of the octahedral void
occupied by the spheres exactly at their occupied is 1/4
limiting radius, then the order of packing (C) If titanium is described as occupying
efficiency would be void in the BaO lattice, the void it
(A) A < B < C
(B) C < A < B occupied is tetrahedral.
(C) C < B < A (D) Fraction of the tetrahedral void
(D) A < C < B occupied is 1/2.

(11)
*8. 10.
Select the correct statements about three- In the spinel structure, oxide ions are
dimensional hcp system: cubic close packed whereas 1/8th of
(A) The effective number of atoms in hcp tetrahedral voids are occupied by A2+
unit cell is six cations and 1/2 of octahedral voids are
(B) The volume of hcp unit cell is occupied by B3+ cations. The general
24 2r 3 formula of the compound having spinel
structure is-
(C) The empty space in hcp unit cell is
(A) A2B2O4
26%
(B) AB2O4
(D) The base area of hcp unit cell is
(C) A2B4O2
6 3 r2 (D) A4B2O2

9. The density of solid argon is 4/πg/cm³ at

–233ºC. If the argon atoms are assumed
to be spheres of radius 1.5 × 10–8cm,
the approximate percentage of empty
space in solid argon is (Ar = 40)

(12)
 NSEC 2024

EXERCISE #7 (NSEC PYQ)

1. Number of atoms per unit cell for Body Centered Cubic system is: [NSEC-2001]
(A) six (B) four (C) two (D) one

2. Co-ordination number for sodium metal is: [NSEC-2001]

(A) 11 (B) 12 (C) 8 (D) 10

3. Sodium chloride crystallises in a face centred cubic lattice in which each: [NSEC-2003]
(A) sodium ion is tetrahedrally surrounded by 4 chloride ions and each chloride ion is tetrahedrally
surrounded by 4 sodium ions
(B) sodium ion is tetrahedrally by 4 chloride ions and each chloride ion is octahedrally surrounded by 6
sodium ions
(C) sodium ion is octahedrally surrounded by 6 chloride ions and each chloride ion is surrounded by 4
sodium ions
(D) sodium ion is octahedrally surrounded by 6 chloride ions and each chloride ion is octahedrally
surrounded by 6 sodium ions.

4. An element crystallises in a face centered cubic lattice. Hence, its unit cell contains: [NSEC-2004]
(A) 14 atoms of the element and 8 of them belong to the unit cell
(B) 14 atoms of the element and 4 of them belong to the unit cell
(C) 8 atoms of the unit cell and only 1 of them belongs to the cell
(D) 8 atoms of the unit cell and only 2 of them belong to the cell

5. Arsenic is used to dope germanium to obtain [NSEC-2005]

(A) intrinsic semiconductors (B) p-type semiconductors
(C) n-type semiconductors (D) non-conducting germanium.

6. Carborundum is a: [NSEC-2005]
(A) molecular solid (B) covalent solid (C) ionic solid (D) amorphous solid.

7. If a  b  c and  =  = 90°,   90°, the crystal system is called [NSEC-2005]

(A) monoclinic (B) triclinic (C) hexagonal (D) orthorhombic.

8. The number of units cells in 117.0 grams of NaCl is approximately [NSEC-2006]

(A) 12 × 1020 (B) 3 × 1023 (C) 6 × 1023 (D) 1 × 10 24

9. In the unit cell of the crystal formed by the ionic compound of X and Y, the corners are occupied by X
and the centers of the faces by Y. The empirical formula of the compound is : [NSEC-2007]
(A) XY (B) X2Y (C) XY3 (D) X8Y6

10. How many nearest neighbours surround each ion in a face-centered cubic lattice of an ionic crystal?
[NSEC-2008]
(A) 4 (B) 6 (C) 8 (D) 12

11. A match box exhibits: [NSEC-2008]

(A) Cubic geometry (B) Monoclinic geometry
(C) Tetragonal geometry (D) Orthorhombic geometry

PW OLYMPIAD WALLAH 60
 NSEC 2024
12. For a face centered cubic lattice, the unit cell content is: [NSEC-2009]
(A) 1 (B) 2 (C) 3 (D) 4

13. Body-centred cubic lattice has a coordination number of : [NSEC-2010]

(A) 8 (B) 10 (C) 6 (D) 4

14. If a  b  c and  =  =  = 90º, the crystal system is: [NSEC-2011]

(A) monoclinic (B) triclinic (C) hexagonal (D) orthorhombic

15. The number of atoms per unit cell and number of the nearest neighbour in a body centred cubic structure
are: [NSEC-2011]
(A) 4, 12 (B) 2, 6 (C) 9, 6 (D) 2, 8

rA+
16. Ionic salt AX grows in face centered cubic lattice with cell length ‘a’. The ratio for this salt will be:
rx−
[NSEC-2014]
(A) 0.155 (B) 0.225 (C) 0.414 (D) 0.732

17. The unit cell of a compound made up of the three elements X, Y and Z is given below.

X
Y
Z
The formula of this compound is: [NSEC-2014]
(A) X2YZ3 (B) XY3Z (C) XYZ3 (D) X3YZ2

18. The metal M crystallizes in a body centered lattice with cell edge 400 pm. The atomic radius of M is.
[NSEC-2015]
(A) 200pm (B) 100pm (C) 173pm (D) 141pm

19. Ice crystallizes in a hexagonal lattice. At ascertain low temperature, the lattice constants are a = 4.53 Å and
c = 7.41 Å. The number of H2O molecules contained in a unit cell (d  0.92 g cm–3 at the given
temperature) is: [NSEC-2015]
(A) 4 (B) 8 (C) 12 (D) 24

20. One mole crystal of a metal halide of the type MX with molecular weight 119 g having face centered
cubic structure with unit cell length 6.58 Å was recrystallized. The density of the recrystallized crystal
was found to be 2.44 g cm–3. The type of defect introduced during the recrystalization is: [NSEC-2015]
(A) additional M+ and X– ions at interstitial sites (B) Schottky defect
(C) F-centre (D) Frenkel defect

21. An ionic solid LaI2 shows electrical conduction due to presence of : [NSEC-2016]
– – – –
2+
(A) La and 2I 3+
(B) La , 2I and e 2+
(C) La , I2 and 2e (D) La , I2 and 3e–
3+

PW OLYMPIAD WALLAH 61
 NSEC 2024
22. In a cubic crystal structure, divalent metal-ion is located at the body-centered position, the smaller
tetravalent metal ions are located at each corner and the O2– ions are located half way along each of the
edges of the cube. The number of nearest neighbour for oxygen is: [NSEC-2016]
(A) 4 (B) 6 (C) 2 (D) 8

23. HgO is prepared by two different methods: one shows yellow colour while the other shows red colour.
The difference in colour is due to difference in: [NSEC-2016]
(A) electronic d-d transitions (B) particle size
(C) Frenkel defect (D) Schottkey defect

24. When NiO is doped with a small quantity of Li2O [NSEC-2017]

(A) both cation and anion vacancies are generated (B) Shottky defects are generated
(C) NiO becomes an n-type semiconductor (D) NiO becomes a p-type semiconductor

25. A crystal of KCl containing a small amount of CaCl2 will have: [NSEC-2018]
(A) vacant Cl– sites
(B) vacant K+ sites and a higher density as compared to pure KCl
(C) vacant K+ sites and a lower density as compared to pure KCl
(D) K+ ions in the interstitial sites

26. A scientist attempts to replace a few carbon atoms in 1.0 g of diamond with boron atoms or nitrogen
atoms in separate experiments. Which of the following is correct? [NSEC-2018]
(A) The resulting material with B doping will be an n-type semiconductor
(B) The resulting material with B doping will be an p-type semiconductor
(C) B doping is NOT possible as B cannot from multiple bonds
(D) The resulting material with N doping will be a p-type semiconductor

27. A solid comprises of three types of elements, 'P', 'Q' and 'R'. 'P' forms an FCC lattice in which 'Q' and 'R'
occupy all the tetrahedral voids and half the octahedral voids respectively. The molecular formula of the
solid is: [NSEC-2019]
(A) P2Q2R (B) PQ2R4 (C) P4Q2R (D) P4QR

28. The crystal defect indicated in the diagram below is: [NSEC-2019]

(A) Frenkel defect (B) Schottky defect

(C) Frenkel and Schottky defects (D) Interstitial defect

PW OLYMPIAD WALLAH 62
 NSEC 2024
29. The unit cell structure of a mineral perovskite crystallizes in cubic unit cell wherein calcium (filled
circles) and oxide (hollow circles) constitute a cubic close packing (ccp) arrangement and titanium ion
(hollow square) occupies an interstitial hole as shown below. (Charges are omitted for simplicity). The
empirical formula of this compound is: [NSEC-2022]

(A) Ca2TiO3 (B) Ca4TiO6 (C) CaTiO3 (D) Ca8TiO6

30. Read carefully all the three statements on defects in solids: [NSEC-2022]
−
(i) In Frenkel defect, interstitial Ag site is surrounded tetrahedrally by four Cl ions and four Ag+ ions,
+

where interstitial Ag+ and Cl− interaction is covalent

(ii) Addition of small amount of SrCl2 in NaCl yields solid solution with a formula of Na1−2x SrxVNaxCl,
where V= valency
(iii) In general, Schottky defect increases the density of the substance
Choose the correct alternative(s):
(A) Statement (i) is correct (B) Statements (ii) and (iii) are correct
(C) Statements (i) and (ii) are correct (D) Statements (i) and (iii) are correct

PW OLYMPIAD WALLAH 63
 NSEC 2024

EXERCISE #7 (NSEC PYQ)

1. (C) 2. (C) 3. (D) 4. (B)
5. (C) 6. (B) 7. (A) 8. (B)
9. (C) 10. (D) 11. (D) 12. (D)
13. (A) 14. (D) 15. (D) 16. (B)
17. (C) 18. (C) 19. (C) 20. (B)
21. (B) 22. (C) 23. (B) 24. (D)
25. (C) 26. (B) 27. (A) 28. (B)
29. (C) 30. (A,C)

PW Web/App - https://smart.link/7wwosivoicgd4
Library- https://smart.link/sdfez8ejd80if

PW OLYMPIAD WALLAH 67
 15 Solid State

SOLVED EXAMPLE

1. The compound A2B has ZnS structure. Its density Sol. a – 2r = 67

is 3.4g / cc. The edge length of unit cell = 5.78 Å,
3a
then find the molecular weight of A2B? a
 67
2
  NA  a3
⇒ a = 496.29 pm
Sol. M 
Z
Z M 2  75
3.4  6.02  1023  (5.78  108 )3 

  98.81 NA  a 3
6.02  10  (496.29  1010 )3
23
4

= 2g / cm3
2. A metal ‘M’ (atomic mass = 31.25) crystallizes in
CCP but it has some vacancy defect. If the edge 5. The approximate percentage of vacant space in a
length of the unit cell is 500 pm and the density silicon cubic cell having crystal structure similar
of the metal is 1.6075 g / cm3, then the number to diamond is
of moles of metal atoms missing per litre of the Sol. Vacant space in diamond is 66%.
crystal is (1 amu = 1.67 × 10–24 g)

It will be the same for silicon
Z M
Sol. Ideal   1.67 g / mL 6. C60 (Buckyball) is cubic closed packed (FCC) in
a3  NA its crystalline form. If you insert potassium atoms
rActual = 1.6075 g / mL into all the tetrahedral holes and octahedral holes
Difference due to Schottky defect = 0.0625 g / mL of the C60 structure the formula would become
KxC60. What is the value of x?
= 2 mol / L
Sol. In CC, there will be 4C 60 and 12 (Eight in
3. The number of hexagonal faces that are present tetrahedral voids and 4 in octahedral voids)
in a truncated octahedron is Hence. formula will be;
Sol. Truncated octahedron is the 14 faced archimedean K12 C60 × 4 = K3 C60∴ x = 3
solid, with 14 total faces; 6 squares and 8 regular
7. Number of Unit cells in 240 gm of element “x”
hexagons.
(Atomic mass 40) which crystallises in BCC in
4. A metal (atomic mass = 75) exist in BCC yN0. What is the value of y?
structure. If the uncovered distance between the
atoms along the edge is equal to 67 pm, then the 240
Sol. 240 gm=x = 6 moles = 6N Atoms.
0
density of crystal (in g / cm3) is 40
(NA = 6 × 1023)_____.
No. of atoms / unit cell = 2
 6N0
Lattice is A8B6
=
∴ No of unit cells = 3N o
2
∴ No. of atoms in lattice = 8 + 6 = 14

Thus, y = 3 10. A solid has a structure in which X atoms are
8. An Element crystallizes into a structure which located at cubic corners of unit cell,
may be described by a cubic type of unit cell O atom are at the edge centers and Y atoms at
having one atom on each corner of the cube. cube center. Then the formula of compound is Xa
Volume of unit cell is 2.4 × 10–23 cm3 and its Yb Oc.
density is 13.82 gm cm–3. The number of atoms
If two atoms of O are missing from any of two
present in 200 gm of element is y × 1023. Find the
value of y. edge centers per unit cell, then the molecular
formula is XxYyOz. Then, find the value of (x + y
200 200 + z) – (a + b + c).
Sol. No. of moles = Atoms = No.
M M
1

Mass of unit cell = d × v = 2.4 × 10−23× 13.82 Sol. (1) Number of X atoms unitCell.
8

No. of atoms in 200 gm of element
Number of Y atoms = 1 / unit cell,number of
200

=  6.029  10 23
= y × 10
23 1
2.4  13.82  1023 O atoms  12   3 / unitCell
4
∴y=6

Formula is: XYO3⇒ Xa Yb Oc
9. Atoms of an Element B form HCP lattice and
(2) Number of O atoms missing from two edge
those of the element A occupy 2/3rdof tetrahedral centers per unit cell
voids. 1 1
 2   / unit cell
How many number of Atoms of A and B (in total) 4 2
are present in the HCP lattice? 1
Sol. No. of atoms in tetrahedral in small cubes of unit Number of O atoms left  3   2.5 / unit
2
cell of B = 4
cell
2 Formula is XYO2.5⇒ X2Y2O5⇒XxYyOz
No. of atoms of A   12  8

3 ∴ Total value of (x + y + z) – (a + b + c)

No. of B-atoms = 6    = (2 + 2 + 5) – (1 + 1 + 3) = 4

EXERCISE

SINGLE CORRECT TYPE QUESTIONS 2. The correct expression for the packing fraction of
(01 TO 47) sodium chloride, if the ions on one face diagonal are
removed is (r+ = radius of Na+& r– = radius of Cl–)
1. Edge length of unit cell of CaF2 having fluorite
type structure is approximately 5.46 Å. Density 4 3 13 3
r  r
16 3 13 3
r  r
of the unit cell is 3 3 3 3
(a) (b)
(a) 3.4 g/cm3 8(r  r )3 8(r  r )3
(b) 4.9 g/cm3 13 3 4 3 13 3 16 3
r  r r  r
(c) 3.2 g/cm3 3 3 3 3
(c) (d)
(d) 3.8 g/cm3 8(r  r )3 8(r  r )3

Solid State 241

 3. A metallic element crystallizes into a lattice 9. With dimensions of a = 100 pm, b = 132 pm and
containing a sequence of layers of ABABAB... c = 160 pm and α = β = γ = 90°, the unit cell will
Identify which of the following statement is true be described as
about such a crystal system. (a) Monoclinic (b) Triclinic
(a) The co-ordination number of a metal (c) Orthorhombic (d) Tetragonal
crystallizing in such a unit cell is 6 10. In a cubic unit cell, A atoms are present on
(b) This type of packing does not leave out voids alternate corners, B atoms are present on alternate
in lattice faces and C atoms are present on alternate edges
and body centre of the cube. The simplest formula
(c) Void fraction in such a unit cell is 0.32
of compound is
(d) The number of atoms in one unit cell of this (a) ABC4 (b) A2BC4 (c) AB2C4 (d) ABC2
type is 6
11. How many unit cells are present in 2 g of Cu if it
4. What is the density of Na2O having antifluorite crystallises in fcc?
type crystal structure, if edge length of cube is 100 (a) 3.3 × 10–21 (b) 4.78 × 1021
pm and what is the effect on density by 0.05%
(c) 4.2 × 1023 (d) 5.3 × 1030
Frenkel defect?
12. Total number of body diagonal planes and body
(a) 205.87 g/cm3, density decreases
diagonal in a cube, respectively, are
(b) 411.75 g/cm3, density decreases (a) 6, 4 (b) 6, 6 (c) 4, 4 (d) 4, 6
(c) 205.87 g/cm3, density remains same
13. 1 mol of NaCl is doped with 10–4 mol of AlCl3.
(d) 411.75 g/cm , density remains same
3
Find the concentration of cationic vacancies
5. A salt AB has rock salt type structure. Find the (a) 6.02 × 1019 mol–1 (b) 1.2 × 1020 mol–1
density of unit cell if distance of closest approach (c) 10–4 mol–1 (d) 2 × 10–4 mol–1
between A+ and B– is 2.4Å. (Molar mass of AB = 14. Total no. of element of symmetry & no. of plane
78) of symmetry in a cubic unit cell respectively are
(a) 4.68 g/cm3 (b) 42.56 g/cm3 (a) 23, 8 (b) 23, 9 (c) 15, 7 (d) 25, 8
(c) 7.98 g/cm3 (d) 10.64 g/cm3 15. Which of the following crystals can show
6. A metal when crystallises in bcc, edge length of Schottky defect?
the cube is found to be 297 pm.The same metal (a) Crystal with 6 : 6 coordination number ratio
when crystallises in fcc, find the edge length of (b) Crystal with 4 : 8 coordination number ratio
cube now (assuming metal atoms are in contact (c) Crystal with 8 :8 coordination number ratio
in both the structures
(d) All can show
(a) 363.75 pm (b) 342.46 pm
16. The γ-form of iron has fcc structure (edge length
(c) 281.89 pm (d) 969.84 pm 386 pm) and β-form has bcc structure (edge
7. In a CsCl structure, the number of Cs+ ions that length 290 pm). The ratio of density in γ-form
occupy second nearest neighbour location of a and β-form is:
Cs+ ion is (a) 0.85 (b) 1.02 (c) 1.57 (d) 0.63
(a) 6 (b) 8 (c) 12 (d) 4 17. Two ionic solids AB and CB crystallise in same
r  r 
8. An ionic compound AB having structure similar to type of lattice. If A and C are 0.40 and 0.70
rock salt. All the ions are removed along one body B
r  r 
B
diagonal plane then the formula of the compound respectively, then the ratio of edge length of AB
will be and CB is:
(a) A5B6 (b) AB (c) A3B2 (d) A2B3 (a) 0.68 (b) 0.78 (c) 0.82 (d) 0.98

242 JEE-Advanced Brahmastra PW

18. A certain sample of cuprous sulphide is found to 23. A transition metal M can exist in two oxidation
have formula Cu1.8S, because of incorporation of states +2 and +3. It forms an oxide whose
Cu2+ ions in the lattice. What is the mole % of experimental formula is given by MxO where x <
Cu2+ in total copper content in this crystal? 1. Then the ratio of metal ions in +3 state to those
(a) 99.8% (b) 11.11% in +2 state in oxide is given by:
(c) 88.88% (d) 13.11% 1 x 1+ 2x
(a) (b)
19. A body centred cubic lattice is made up of hollow 1 x 3x - 2
spheres of B. Spheres of solid A are present in x 2(1 − x )
(c) 1 + (d)
hollow spheres of B. Radius of A is half of radius 2 3x − 2
of B. What is the ratio of total volume of spheres 24. In a f.c.c. crystal, which of the following shaded
of B unoccupied by A in a unit cell and volume planes contains the following type of arrangement
of unit cell? of atoms?
7 3π 7 3
(a) (b)
64 128
7
(c) (d) None of these
24
20. An element X (atomic weight 24 gm/mol) forms
a face centered cubic lattice. If the edge length of
the lattice is 4×10–8 cm and the observed density (a) (b)
is 2.40×103 kg/m3, then the percentage occupancy
of lattice points by element X is (Use NA = 6 ×
1023)
(a) 96 (b) 98 (c) 99.9 (d) 94
(c) (d)
21. A crystal is made of particle X, Y & Z. X forms
FCC packing, Y occupies all octahedral voids of
X and Z occupies all tetrahedral voids of X.If all
the particles along one body diagonal plane are 25. Consider the following statements and arrange in
removed then the formula of the crystal would be the order of true/false as given in the codes.

(a) XYZ2 (b) X2YZ2 S1: One type of unit cell is only possible for the

crystallographic dimensions as a = b ≠ c and α
(c) X8Y4Z5 (d) X5Y5Z8
=β=γ= 90°.
22. Correct statement with respect to hexagonal close
S2: In the configuration shown the size of the

packing of sphere in three dimensions is
 2 
(a) In one unit cell, there are 12 octahedral voids smallest circle is   1 times the size of the
and all are completely inside the unit cell.  3 

(b) In one unit cell, there are six octahedral voids biggest circles.
and all are completely inside the unit cell.
(c) In one unit cell, there are six octahedral void
and of which three are completely inside the
unit cell and other three are partially inside
the unit cell.
(d) In one unit cell, there are 12 tetrahedral voids, S3: Number of next neighbours of Cs+ ion in CsCl

all are completely inside the unit cell. structure is 6 Cs+ ions.

Solid State 243

 S4: A crystal has A3+ ions at the cube corners
32. A metallic element exists as cubic lattice. Each
and B– ions at the edge centres. The coordination edge of the unit cell is 4.0 Å. The density of the
numbers of A and B are respectively 6 and 2. metal is 6.25 g/cm3. How many unit cells will be
(a) TTTT (b) FFTT (c) FTFT (d) FFFF present in 100 g of the metal?
26. KCl crystallizes in the same type of lattice as does (a) 1.5 × 1022
r  r  (b) 2.5 × 1023
NaCl. Given that Na  0.50 and Na  0.70 .
r  r  (c) 5.0 × 1023
Cl K
Calculate the ratio of the side of the unit cell for (d) 2.0 × 1023
KCl to that of NaCl? 33. Is there an expansion or contraction as iron
(a) 1.143 (b) 1.224 (c) 1.414 (d) 0.875 transforms from FCC to BCC? The atomic radius
27. If an Element (At. wt = 50) crystallizes in FCC of iron is 125 pm in FCC but 50 2 pm in BCC.
lattice with a = 0.50 nm. What is the density of (a) Expansion
unit cell if it contains 0.25% schottky defect (NA (b) Contraction
= 6×1023)?
(c) Neither expansion nor contraction.
(a) 2 g/cc (b) 2.66 g/cc
(d) Unpredictable
(c) 3.06 g/cc (d) 1.26 g/cc
34. What is the void space per unit cell for metallic
28. A crystal is made of particles “X” and “Y”. “X” silver crystallizing in the FCC system, the edge
forms FCC packing and “Y” occupies all the length of the unit cell being 5 Å?
octahedral voids. If all the particles along one
body diagonal are removed their formula of the (a) 47.36 Å3 (b) 30.72 Å3
crystal would be (c) 20.48 Å3 (d) 32.50 Å3
(a) X4Y3 (b) X5Y4 (c) X4Y5 (d) X2Y3 35. In FCC unit cell, what fraction of edge is not
29. First three nearest neighbour distance for body covered by atoms?
centred cubic lattice are (a) 0.134 (b) 0.293
a (c) 0.26 (d) 0.32
(a) 2a : a : 3a (b) : 3a : a
2 36. An alkali metal has density 4.5 g/cm3. It has cubic
3a 3a unit cell with edge length 400 pm. The reaction of
(c) : a : 2a (d) : a : 3a 7.68 cm3 chunk of the metal with an excess of HCl
2 2
solution gives a colourless gas which occupies
30. A compound formed by elements X and Y has a
4.54 L at 0°C and 1 bar. The unit cell of metal is
cubic structure in which X atoms are at the corner
of the cube and two atoms (Y) are at each body (a) Simple cubic (b) BCC
diagonal of the cube. If all atoms from one body (c) FCC (d) None of these
diagonal of the cube are removed, then formula
37. A metal crystallizes in such a lattice in which only
of the compound is
70% of the total space of the crystal is occupied
(a) XY2 (b) XY3 (c) XY6 (d) XY8 by the atoms. If the atomic mass of the metal is
31. Analysis show that nickel oxide consists of nickel 32π g/mol and the atomic radius is 0.2 nm, then
ion with 96% ions having d8 configuration and the density of the metal is
4% having d7 configuration. Which amongst (a) 7.0 g/cm3 (b) 3.5 g/cm3
the following best represents the formula of the
(c) 10.5 g/cm3 (d) 14.0 g/cm3
oxide?
(a) Ni1.02 O1.00 (b) Ni0.96 O1.00 38. In a hypothetical solid, ‘C’ atoms form CCP
lattice. ‘A’ atom occupy all tetrahedral voids and
(c) Ni0.98 O0.98 (d) Ni0.98 O1.00 ‘B’ atoms occupy all octahedral voids, without

244 JEE-Advanced Brahmastra PW

 disturbing the crystal. If a unit cell of the crystal voids. The fraction of the octahedral voids
is cut by a plane shown in the figure, then the occupied is
cross section of this plane looks like (a) 1/2 (b) 1/4 (c) 1/6 (d) 1/8
42. Give the correct order of initials T (true) or F
(false) for the following statements.
I. In an anti-fluorite structure, anions form FCC
and cations occupy all the tetrahedral voids.
II. If the radius of cation and anion is 20 and 95
pm, then the coordination number of cation
in the crystal is 4.
III. An atom or ion is transferred from a lattice
(a) (b) site to an interstitial position in Frenkel
defect.
IV. The density of crystal always increases due
to substitutional impurity defect.
(a) TTTT (b) FFFF
(c) (d) (c) FFTT (d) TFTF
43. The theoretical density of ZnS is d g/cm3. If the
crystal has 4% Frenkel defect, then the actual
density of ZnS should be
39. There are three cubic unit cells A, B and C. A
is FCC and all of its tetrahedral voids are also (a) d g/cm3 (b) 0.04 d g/cm3
occupied. B is also FCC and all of its octahedral (c) 0.96 d g/cm3 (d) 1.04 d g/cm3
voids are also occupied. C is simple cubic and all
44. Which of the following oxide shows electrical
of its cubic voids are also occupied. If voids in
properties like metals?
all unit cells are occupied by the spheres exactly
at their limiting radius, then the order of packing (a) SiO2 (b) MgO
efficiency would be (c) SO2 (s) (d) CrO2
(a) A < B < C (b) C < A < B 45. A ferromagnetic substance becomes a permanent
(c) C < B < A (d) A < C < B magnet when it is placed in a magnetic field
40. Spinel is an important class of oxides consisting because
of two types of metal ions with the oxide ions (a) All the domains get oriented in the direction
arranged in CCP pattern. The normal spinel has of magnetic field.
one-eighth of the tetrahedral holes occupied (b) All the domains get oriented in the direction
by one type of metal ion and one-half of the opposite to the direction of magnetic field.
octahedral hole occupied by another type of metal (c) Domains get oriented randomly.
ion. Such a spinel is formed by Zn2+, Al3+ and O2−.
(d) Domains are not affected by magnetic field.
The simplest formula of such spinel is
46. Which of the following is true about the charge
(a) ZnAl2O4 (b) Zn2AlO4 acquired by p-type semiconductor?
(c) Zn2Al3O4 (d) ZnAlO2 (a) Positive
41. In a compound XY 2O 4, the oxide ions are (b) Neutral
arranged in CCP arrangement and cations X are
(c) Negative
present in octahedral voids. Cations Y are equally
distributed between octahedral and tetrahedral (d) Depends on concentration of p impurity

Solid State 245

 47. In a face-centred cubic lattice, atom A occupies 52. Ions of NaCl, which are touched by 1 body
the corner positions and atom B occupies the face diagonal are
centred positions. If one atom of B is missing (a) Cl– ions present at corner of cube
from one of the face points, the formula of the (b) Cl– ions present at face centre of cube
compound is:
(c) Na+ ions present at edge centre of cube
(a) A2B (b) AB2 (c) AB (d) A2B5
(d) Na+ ions present at body centre of cube
MULTIPLE CORRECT TYPE 53. Identical spheres are undergoing two-dimensional
QUESTIONS (48 TO 80) packing in square close packing and hexagonal
close packing, which is correct regarding the
48. In a cubic unit cell, A atoms are present on
spheres?
alternate corners, B atoms are present on alternate
faces and C atoms are present on all edges and (a) Ratio of coordination number for sphere in
body centre of the cube. A diagonal plane is first case to 2nd case is 2 : 3
placed in the cube. All atoms are removed which (b) Packing in 2nd case is more effective
touches the body diagonal plane. Now, the (c) Packing in 1st case is more effective
possible formula of the compound is (d) Stacking of layer on 1 st type packing
(a) AB10 (b) AB2C4 produces simple cubic structure
(c) AC10 (d) AB4C10 54. For which of the following cases answer is 4?
49. For the normal spinel structure (MgAl2O4), the (a) Coordination no. of Zn2+ in Zinc blende
correct statement(s) is/are (b) No. of body diagonal planes in cube
(a) 50% octahedral voids are occupied by ions (c) Formula units in Rock salt structure
(b) Al3+ is equally distributed in tetrahedral and (d) Formula units in CsCl salt structure
octahedral voids
55. In a AB unit cell (Rock salt type) assuming A+
(c) Oxide ions occupy ccp lattice forming FCC and B− are not in contact
(d) 12.5% tetrahedral voids are occupied by ions (a) The nearest neighbour of A+ is six B– ion.
50. If in NaCl crystal, two ‘F-centres’ are present per (b) The nearest neighbour of B– is six A+ion.
unit cell then the possible formula per unit cell is/ (c) The second neighbour of A+ is twelve A+.
are
(d) The packing fraction of AB crystal is 0.79.
(a) Na4Cl3.75 (b) Na4Cl3
56. In the fluorite structure if the radius ratio is
(c) NaCl (d) Na4Cl3.375  3 
51. Which of the following statements are correct?   1 , how many ions can each cation touch?
 2 
(a) 5 th nearest neighbour of Na + in NaCl
(a) 4 anions (b) 12 cations
crystal are present at vertical face center of
neighbouring unit cell (c) 8 anions (d) 8 cations
(b) The nearest distance between two cations in 57. The co-ordination number of FCC structure for
a metals is 12, since
Na2O crystal is (a) Each atom touches 4 others in same layer, 3
2
in layer above and 3 in layer below.
(c) The number of 4thneighbour in CsCl crystal
is 24 (b) Each atom touches 4 others in same layer, 4
in layer above and 4 in layer below.
(d) The nearest distance between two anion is
a (c) Each atom touches 6 others in same layer, 3
rock salt structure is and 5th atom in in layer above and 3 in layer below.
2
(d) Each atom touches 3 others in same layer, 6
CsCl structure separated by 3a in layer above and 6 in layer below.

246 JEE-Advanced Brahmastra PW

58. Select the correct statement(s) related to (c) If X+ is removed from alternate tetrahedral
hexagonal close packing of identical spheres in void, then CN is 4 : 4.
three dimensions: (d) If X+ is removed from alternate tetrahedral
(a) In one unit cell there are 12 octahedral voids void, then CN is 4 : 8.
and all are completely inside the unit cell 62. Which of the following statements is/are correct?
(b) In one unit cell there are six octahedral voids (a) The coordination number of each type of an
and all are completely inside the unit cell. ion in CsCl is 8
(c) In one unit cell there are six octahedral (b) A metal that crystallises in BCC structure
void and out of which three are completely has a coordination number 12
inside the unit cell and other three are from
(c) A unit cell of an ionic crystal shares some of
contributions of octahedral voids which are
its ions with other unit cells
partially inside the unit cell
(d) Co-ordination number of every sphere is 12 (d) The length of the unit cell in NaCl is 2 2
in hcp lattice. times the radius of Cl− ion
59. An excess of potassium ions makes KCl crystals 63. Which of the following statement(s) for crystal
appear violet or lilac in colour since: having Schottky defect is/are correct.
(a) Some of the anionic sites are occupied by an (a) Schottky defect arises due to absence of
unpaired electron cations & anion from positions which they
(b) Some of the anionic sites are occupied by a are expected to occupy.
pair of electrons (b) The density of crystal having Schottky defect
(c) There are vacancies at some anionic sites & is smaller than that of perfect crystal.
some of the sites are occupied by electrons (c) Schottky defect are more common in co-
(d) F-centers are created which impart colour to valent compound with higher co-ordination
number.
the crystals
(d) The crystal having Schottky defect is
60. Which is/are correct statement about zinc blende
electrically neutral as a whole.
structure?
64. The composition of a sample of wurtzite is
(a) The number of first neighbour of S2– is 4
Fe0.93O1.00. Which of the following statements are
a 3 correct related to this compound?
(b) The maximum distance between Zn2+ is
2 (a) The percentage of Fe (III) by mass of total
in a unit cell where ‘a’ = edge length of unit iron content is 15.05%
cell (b) The ratio of Fe (III) to Fe (II) ion is 0.17
(c) If all tetrahedral voids are occupied by Zn2+, (c) The percentage of Fe (II) ion 11.5%
then C.N. of S2– is 8.
(d) The amount of Fe 3+ is 6.5 g in 1.0 g of
(d) If all tetrahedral voids are occupied by Zn2+, wurtzite
then C.N. changes from 4 : 4 to 8 : 8.
65. Which of the following statements is/are false?
61. Compound X2Y have antifluorite structure. Which
(a) Amorphous solids have isotropic nature
is/are correct statement?
(b) Entropy of a crystalline solid is higher than
a that of an amorphous solid.
(a) The minimum distance between X is , +
2
(c) Amorphous solids have definite volume but
where ‘a’ = edge length of unit cell. no definite shape.
(b) The co-ordination number ratio of X+ and (d) Amorphous solids can become crystalline on
Y2– is 8 : 4. slow heating (annealing).

Solid State 247

66. If the three interaxial angles of the unit cell are 71. Which of the following has face-centred Bravais
all equal in magnitude, the crystal cannot belong lattice?
to the (a) Hexagonal (b) Monoclinic
(a) Monoclinic system
(c) Cubic (d) Orthorhombic
(b) Cubic system
72. If the height of HCP unit cell of identical particles
(c) Hexagonal system is h, then the height of tetrahedral voids from the
(d) Triclinic system base is
67. The correct statement(s) regarding defects in 3h 5h h 2h
solids is/are (a) , (b) ,
8 8 3 3
(a) Schottky defect is usually favoured by a very
h 3h h 7h
small difference in the sizes of cation and (c) , (d) ,
4 4 8 8
anion
(b) Frenkel defect increases exponentially with 73. An element exists in two allotropic forms.
temperature One form is CCP and the other form is HCP
arrangement of atoms of the element. If the
(c) Trapping of an electron in the lattice leads
atomic radius of element is same in both the
to the formation of F-center
forms, then both allotropic forms have the same
(d) Solids with F-centre act as semi-conductors
(a) Density
68. Select the correct statements if NaCl is doped by
CaCl2, then the formed solid solution results in (b) Coordination number
(a) Substitutional cation vacancy (c) Fraction of unoccupied space.
(b) Frenkel’s defect (d) Distance between two consecutive layers.
(c) Schottky defect 74. Which of the following information(s) is/ are
(d) Decrease of density incorrect regarding the voids formed in three
dimensional HCP of identical spheres?
69. Which of the following statements is/are correct?
(a) A tetrahedral void is formed when a sphere
(a) Dislocation of ion from lattice site to
of the second layer is present above the
interstitial site is called Frenkel defect
triangular void of the first layer.
(b) Missing of +ve and –ve ions from their
respective position producing a pair of holes (b) All the triangular voids are not covered by
is called Schottky defect the spheres of the second layer.
(c) The presence of ions in the vacant interstitial (c) Tetrahedral voids are formed when the
sites along with lattice point is called triangular voids in the second layer lie above
interstitial defect the triangular voids in the first layer and
(d) Non-stoichiometric NaCl is yellow solid the triangular shapes of these voids do not
overlap.
70. Superconductors are made by cooling metallic
conductors as on cooling (d) Octahedral voids are formed when the
triangular voids in the second layer exactly
(a) Resistance of metal will decrease
overlap with similar voids in the first layer.
(b) Vibrating electrons about their lattice points
will offer least disturbance 75. The crystals in which all tetrahedral voids or none
of the tetrahedral voids are occupied:
(c) Resistance of metal will increase
(d) Vibrating electrons about their lattice point (a) NaCl (b) ZnS
offer maximum disturbance (c) CaF2 (d) Na2O

248 JEE-Advanced Brahmastra PW

76. In a sodium chloride crystal, the unit cell edge NUMERICAL/INTEGER TYPE QUESTIONS
length is a. The option(s) representing the correct (81 TO 98)
combination is/are
Part I :Numerical Type Questions (81 to
Nearest Distance 89)
Number
neighbor Ion from
of ions 81. A crystal of lead (II) sulphide is having NaCl type
of Na+ ion Na+ ion
structure, If the nearest distance between cation
(a) 2nd Na+ 0.707 a 12
and anion is 290 pm, calculate the density of unit
(b) 3rd Cl– 0.866 a 8 cell in g/cm3. (use NA = 6 × 1023)
(c) 4th Na +
a 6 82. An element crystallizes in fcc lattice having edge
(d) 5th Cl– 1.22 a 24 length 432 pm. Calculate the maximum radius (in
77. Potassium hexachloroplatinate (IV), K2[PtCl6] pm) of atom which can be placed in interstitial
adopts anti-fluorite crystal structure. Which of sites without disturbing the structure.
the following information is correct about ideal 83. If SrCl2 crystal is doped with 10–3 mol % of AlCl3.
K2 [PtCl6] crystal? If concentration of cationic vacancies is x × 1018.
(a) K+ ions occupy all the tetrahedral voids. Calculate the value of x. (Use NA = 6.02 × 1023)
(b) The unit cell is FCC with respect to PtCl62− 84. Maximum diagonal plane of symmetry in a cubic
ions. crystal system is _______.
(c) The coordination number of PtCl62− ions is 4. 85. Number of 3-fold axis of symmetry in a cubic
(d) The coordination number of PtCl62− ions is 8. crystal system will be
78. In each of the following ionic solids, the 86. Copper has a face-centred cubic structure with
coordination number of the cation and anion is a unit-cell edge length of 3.61 Å. What is the
same, except size of the largest atom (in Å) which could fit
into the interstices of the copper lattice without
(a) MgO (b) CaF2 (c) Al2O3 (d) CsCl
distorting it?
79. Which of the following statement(s) is/are correct C
regarding the defects in solids?
(a) AgBr crystal show both Schottky and Frenkel
defect.
(b) Impurity defect by doping of arsenic in
silicon results ‘n’-type semiconductor.
A B
(c) Doping in crystal introduces dislocation
defect. 87. Potassium crystallizes with BCC lattice and
(d) Metal deficient defect can occur with extra has a density of 0.856 × 103 kg m–3. What is the
anion present in the interstitial voids. potassium atom radius (in pm) ? (nearest integer)

80. Which of the following is/are correct regarding 88. The density of solid argon is 1.65 g/mL at –233°C.
point defects in solids? If the argon atom is assumed to be sphere of radius
1.54 × 10–8 cm, what percentage of solid argon is
(a) The density of point defect increases with apparently empty space? (Atomic mass of Ar =
the increase in rate of crystallization. 40) (nearest integer)
(b) In the formation of point defects, the entropy
89. A element crystallizes into a structure which may
of system increases but the entropy of
be described by a cubic type of unit cell having
surrounding decreases.
one atom on each corner of the cube and two
(c) The density of point defect increases with atoms on one of its diagonals. If the volume of this
the increase in temperature. unit cell is 24 × 10–24 cm3 and density of element
(d) All point defects result in the decreasing is 7.2 g cm–3, the number of atoms present in 200
density of solid. g of element is x × 1024. Find x.

Solid State 249

Part II :Integer Type Questions (90 to 98) additionally occupied by smaller circles of
relevant size so that the void circles are just
90. A 2B molecule (molar mass = 259.8 g/mol)
contacting their neighbours find the packing
crystallises in a hexagonal lattice as shown. efficiency of the configuration in percent.
Density of crystal is 5g/cm3. If a = 5Å and b =
8Å then number of molecules contained in given 95. In F.C.C. arrangement of identical spheres,
unit cell are: (Use NA = 6 × 1023) distance between two nearest octahedral void
is 8.51 Å. The distance between two nearest
tetrahedral voids (in Å) would be? (nearest
integer)
96. The face diagonal length of FCC cubic cell is
660 2 pm. If the radius of the cation is 110 pm.
What should be the radius of the anion (in pm)
following radius ratio rules
97. A solid cube of edge length = 25.32 mm of an
ionic compound which has NaCl type lattice is
90. NA spheres of radius ‘R’ are melted in x × NA added to 1 kg of water. The boiling point of this
smaller spheres, so that when fcc lattice is solution is found to be 100.52°C (assume 100%
generated from smaller spheres the edge length ionisation of ionic compound). If radius of anion
is formed to be 25/6 R. Find x. of ionic solid is 200 pm then calculate radius of
cation of solid in pm (picometer).
92. An ionic compound MCl is simultaneously doped
with 10–6 mole% NCl2 and 10–7 mole% RCl3. (Kb of water = 0.52 K kg mole–1, Avogadro’s
Calculate the concentration of cationic vacancies number, NA= 6 × 1023, ( 3 75 ) = 4.22)
x 98. Ca crystallizes in FCC unit cell, with a = 0.556
x. Express your answer as × 10 . (Use NA = 6
14
9 nm and density 1.4848 gm cm–3. Percentage of
× 1023) schottky defects in this solid is? (nearest integer)
(Take N & R as divalent & trivalent cations MATRIX TYPE QUESTIONS (99 TO 108)
respectively)
Part I : List Type Questions (99 to 103)
93. Ionic solid B+A– crystallizes in rock salt type of
structure. 1.296 g ionic solid salt (of strong acid 99. Match the following:
and weak base) B+A– is dissolved in water to make List-I List-II
one litre solution. The pH of the solution is
I. Rochelle salt P. Diamagnetic
measured to be 6.0. If the value of face diagonal
II. Barium titanate Q. Ferroelectric
in the unit cell of B+A– be 600 2 pm. Calculate
the density of ionic solid in g/cc. III. Fe3O4 R. Piezoelectric
IV. V2O5 S. Antiferroelectric
[T = 298 K, K b for BOH is 10 –5, (Avogadro
Number = 6.0 × 1023)] T. Ferrimagnetic
94. Consider the arrangement of circles of equal (a) I-Q,R; II-Q,R; III-T; IV-P
radii with their centres arranged as per the
(b) I-T,P; II-Q,R; III-Q; IV-R
2-dimensional lattice defined by a = b, θ= 60°
such that each circle is touching all its nearest (c) I-Q,R; II-Q,R; III-P; IV-R
neighbours. If all the void areas present are (d) I-Q,R; II-P,R; III-T; IV-Q

250 JEE-Advanced Brahmastra PW

100. Match the following 102. Match the following:

List-II List-I List-II

List-I
Distance between
Ionic crystal I. Cubic P. All angles are equal
nearest spheres (in
structure
terms of a) II. Ortho Q. Only two sides have
I. Rock salt P. 0.44 a rhombic equal length

II. Fluorite Q. 0.86 a III. Monoclinic R. Have maximum

elements of
III. CsCl R. 0.5 a symmetry
IV. Aluminium S. 0.7 a IV. Hexagonal S. Contain two Bravais
(Crystallising lattice
in fcc)
(a) I-P, R; II-P; III-S; IV-Q
T.
a
(b) I-R; II-P; III-Q; IV-S
1.16
(c) I-P; II-R; III-Q; IV-S
(a) I-S; II-P; III-Q,T; IV-R
(b) I-P; II-P; III-S,T; IV-R (d) I-P; II-Q; III-R; IV-S
(c) I-R; II-P; III-Q,T; IV-S 103. Match the solids in List-I with the properties
(d) I-R; II-P; III-T,S; IV-Q in List-II.

101. Match the following: List-I List-II

List-I List-II I. Germanium P. A non-conducting
(Type of ionic (Related solid becoming
crystal) information) good conductor on
melting.
I. NaCl type of P. C o o r d i n a t i o n
crystal number of cation II. Potassium Q. A high melting solid
=8 chloride involving covalent
II. CsCl type of Q. C o o r d i n a t i o n bonded atoms.
crystal number of anion III. Sodium R. A solid melting
=4 far below room
III. ZnS type of R. rc + ra= a/2 (lattice temperature and held
crystal (zinc parameter) together by van der
blende) Waal’s forces.
IV. CaF2 type of S. Anions occupy IV. Solid S. A solid having
crystal corners & face methane melting point about
centre 373 K and very
good conductor of
(r c and r a are radius of cation and anion
electricity.
respectively)
(a) I-R; II-P ; III-Q; IV-S (a) I-P; II-R; III-Q; IV-S
(b) I-R,S; II-S; III-P; IV-Q (b) I-Q; II-P; III-S; IV-R
(c) I-R,S; II-P; III-Q,S; IV-P,Q (c) I-R; II-P; III-S; IV-Q
(d) I-R; II-P; III-S; IV-Q (d) I-P; II-S; III-Q; IV-R

Solid State 251

Part II: Matrix Match Questions (104 to 108) IV. A = Alternate corners S. A2B
104. Match the following B = Alternate edge
centres
Column-I Column-II C = Alternate face
Element of symmetry Ions touched (In centres& body centre
(for a cube) NaCl structure)
107. Match Column I with Column II
I. Body diagonal P. Only 2 face
centre ions Column-I Column-II
II. C4 axis Q. Only 2 corner
ions I. For Ionic solid P. Anion – anion
r contact present,
III. Rectangular plane R. Only 2 edge  0.51
cation lies in
centre ions r
octahedral void
IV. Body diagonal S. Body centre
plane ion II. For Ionic solid Q. Anion – anion
r contact missing,
T. Only one  0.414
r cation lies in
octahedral void
tetrahedral void
105. Match the following
III. For Ionic solid R. Anion – anion
Column-I Column-II r contact missing,
 0.4 cation lies in
I. Wurtzite P. Anions occupy F.C.C. r
cubical void
structure lattice
IV. For Ionic solid S. Anion – anion
II. Sphalerite Q. Cations occupy all
r contact missing,
structure tetrahedral voids  0.9
r cation lies in
III. Antifluorite R. Anions occupy HCP octahedral void
structure Lattice
108. Match Column I having different characteristics
IV. Rock salt S. Cations occupy half
with Column II having different type of unit cell.
structure of tetrahedral voids
T. Anions occupy all Column-I Column-II
tetrahedral voids
I. At least two P. Unit cell of
106. Match the following interfacial angles monoclinic
be 90°. sulphur.
Column-I Column-II
(Position of particles) (Formula) II. At least two Q. Unit cell of
I. A = All corners P. AB2 crystallographic diamond.
B = All edge centres axis length be
same.
II. A =fcc Q. AB3
B = Equally distributed III. None of the axial R. Orthorhombic
in octahedral and lengths to be same. crystal.
tetrahedral voids and
octahedral voids are IV. None of the S. Tetragonal
fully occupied interfacial angles crystal.
to be same.
III. A = bcc R. AB2C4
B = Alternate face T. Triclinic
centres crystal.

252 JEE-Advanced Brahmastra PW

COMPREHENSION TYPE QUESTIONS Comprehension-3
(109 TO 137) BaTiO3 crystallizes in the perovskite structure. This
structure may be described as a cubic lattice with
Comprehension-1 barium ions occupying the corners of the unit cell,
Potassium crystallizes in BCC lattice, with a unit cell oxide ions occupying the face centres and titanium ions
length of a = 5.0 Å (K = 39, NA = 6 × 1023). occupying the centres of the unit cells.
109. What is the distance between nearest neighbours? 117. If titanium is described as occupying holes in
(a) 5.0 Å (b) 4.33 Å (c) 3.54 Å (d) 2.5 Å Ba-O lattice, then what type of holes does it
occupy?
110. What is the distance between next nearest
(a) Tetrahedral (b) Octahedral
neighbours?
(c) Cubic (d) Triangular
(a) 5.0 Å (b) 4.33 Å (c) 3.54 Å (d) 7.07 Å
118. What fraction of the holes of this type does it
111. How many nearest neighbours does each K atom
occupy?
have?
(a) 0.25 (b) 0.50 (c) 1.00 (d) 0.75
(a) 8 (b) 6 (c) 4 (d) 12
Comprehension-4
112. How many next nearest neighbours does each K
Silicon carbide (carborundum) (SiC) and diamond are
atom have?
covalent solids which crystallize in cubic structures.
(a) 8 (b) 6 (c) 4 (d) 12 In SiC, carbon atoms occupy lattice points of the FCC
113.What is the theoretical density of crystalline K? lattice and silicon atoms occupy half of the tetrahedral
(a) 1.04 g/cm3 (b) 20.8 g/cm3 voids available. In diamond, the same tetrahedral voids
are occupied by carbon atoms. The densities of SiC and
(c) 1.04 g/cm3 (d) 2.08 g/cm3 diamond are 3.2 and 3.6 g/cm3, respectively (Si = 28,
114. If the metal is melted, the density of molten metal NA = 6 × 1023).
is found to be 0.9 g/cm3. What is the percentage 119. The radius of carbon atom is
of empty space in the molten metal?
(a) 0.76 Å (b) 1.12 Å (c) 3.2 Å (d) 3.6 Å
(a) 58.83% (b) 68.02%
120. The radius of silicon atom is
(c) 41.17% (d) 31.98%
(a) 0.76 Å (b) 1.12 Å (c) 3.2 Å (d) 3.6 Å
Comprehension-2
121. Which of the following will not change the
Titanium crystallizes in a FCC lattice. It reacts with density of solid SiC?
carbon or hydrogen interstitially by allowing atoms
(a) Substitution of some Si-atoms by some
of these elements to occupy holes in the host lattice.
C-atoms.
Hydrogen occupies tetrahedral holes but carbon
(b) Schottky defect
occupies octahedral holes.
(c) Interchange in the position of Si and
115. Predict the formulas of titanium hydride and C-atoms.
titanium carbide formed by saturating the titanium (d) Decrease in the temperature of solid.
lattice with either ‘foreign’ element.
122. If the similar volume of SiC and diamond are
(a) TiH, TiC (b) TiH2, TiC considered, then which of the following is a true
(c) TiH4, TiC (d) TiH2, TiC2 statement?
116. Account for the fact that hydrogen occupies (a) The number of Si-atoms in SiC is 3.75 times
tetrahedral holes while carbon occupies octahedral the number of C-atoms in diamond.
holes. (b) The number of C-atoms in diamond is 3.75
(a) rH = rC times the number of Si-atoms in SiC.
(c) The number of SiC formula units is 3.75
(b) rH < rC
times the number of C-atoms in diamond.
(c) rH > rC (d) The number of C-atoms in diamond is 3.75
(d) Hydrogen is more reactive than carbon. times the total number of atoms in SiC.

Solid State 253

123. Which of the following is incorrect statement?
3
(a) The packing efficiency of SiC is greater than r=
a,
4
that of diamond.
(b) The coordination number of Si and C-atoms Body diagonal = 3a
in SiC is same. Z M
(c) The number of C–C bonds per unit cell in Density;  
a 3  NA
diamond is 16.
Where; M = molar mass, NA= Av. No.
(d) The coordination number of C-atoms in SiC
is half that of C-atoms in diamond. 126. Chromium metal crystallizes with a body centred
cubic lattice. The side of the cube is 287 pm.
Comprehension-5
The atomic radius (r) and density of chromium
In F.C.C. type of lattice structure all the eight corners
in g cm –3; [Atomic mass of Cr = 51.99] are
as well as all the six face centres are occupied by
respectively;
constituents. In a particular face, the face centred atom
will touch all the cornered constituents/atoms present (a) 124.27 pm, 7.31 g cm–3
on the same face but cornered atoms/constituents will (b) 12.427 pm, 9.25 g cm–3
not touch each other. Facial view; (c) 24.25 pm, 8.85 g cm–3
(d) 150.25 pm, 12.85 g cm–3
127. CsCl (d = 3.97 gm cm–3) exists in BCC type lattice
structure, Eight corners are occupied by Cl– but
body centre is occupied by Cs+ ions. Calculate the
distance between Cs+ and Cl–ions, if side of the
cube is 4.13Å?
(a) 3.57 Å (b) 2.15 Å
Face diagonal = 2a
(c) 1.25 Å (d) 2.25 Å
a Comprehension-7
r=
,z=4
2 2 A compound formed by elements X and Y has a cubic
124. Cu-metal crystallizes in FCC Lattice with it’s structure in which X atoms are at the corner of the cube
edge length 3.61, Å. Calculate the radius of the and also at the face centers. Y atoms are present at the
extra atom which can be fitted properly in the body center and at the edge center of the cube.
vacant site on edge without disturbing the whole
128. If all the atoms from the diagonals of one of the
arrangement?
face of the cube are removed, then Zeff is
(a) 1.056 Å (b) 0.53 Å
(a) 3 (b) 4 (c) 7 (d) 8
(c) 5.3 Å (d) 2.5 Å
129. If all the atoms are removed from one of the plane
125. Calculate the Ratio of occupied length and
unoccupied length on the edge (only one) of the passing through the middle of opposite faces of
given Cu lattice? the cube, calculate effective number of atoms left
in the cube,
(a) 2.554 (b) 2.417 (c) 1.25 (d) 3.15
(a) 3 (b) 4 (c) 5 (d) 6
Comprehension-6
In B.C.C. type of lattice structure all the eight corners Comprehension-8
of the cube as well as body centre of the cube are In hexagonal systems of crystals, a frequently
occupied. The no. of atoms/constituents per unit cell encountered arrangement of atoms is described as a
is 2. The atoms or constituents falling on the same hexagonal prism. Here, the top and bottom of the cell
body diagonal are touching each other. If “a” is the side are regular hexagons and three atoms are sandwiched in
Length; then; between them. A space-filling model of this structure,

254 JEE-Advanced Brahmastra PW

called hexagonal close-packed (HCP), is constituted occupied by carbon atoms. Every atom in this structure
of a sphere on a flat surface surrounded in the same is surrounded tetrahedrally by four others. Germanium,
plane by six identical spheres as closely as possible. silicon and grey tin also crystallize in the same way as
Three spheres are then placed over the first layer so that diamond.
they touch each other and represent the second layer. (Given: NA = 6 × 1023, sin 54°44’ = 0.8164).
Each one of these three spheres touches three spheres
132. If edge length of the cube is 3.60 Å, then radius
of the bottom layer. Finally, the second layer is covered
of carbon atom is
with third layer that is identical to the bottom layer in
relative position. Assume radius of every sphere to be (a) 0.78 Å (b) 0.92 Å
‘r’. (c) 0.64 Å (d) 0.35 Å
133. If the edge length is 3.60 Å, density of diamond
crystal is
(a) 3.92 g/cc (b) 2.40 g/cc
(c) 3.37 g/cc (d) 2.58 g/cc
134. Total number of diamond unit cells in 1.2 g of
diamond sample is
(a) 6.0 × 1021 (b) 6.0 × 1022
(c) 7.5 × 1021 (d) 5.0 × 1022
Comprehension-10
The density of any crystal structure can be calculated
by mass contained in unit cell per unit volume. If Z is
130. The volume of this HCP unit cell is: no. of molecules per unit cubic cell of edge length a,
the mass per unit volume of cell is
(a) 12 2 r (b) 24 2 r
3 3
 M 
64 Mass  
Z
(c) 16 2 r (d)
3 3
r  NA 
3 3
ZM
131. In hcp lattice, if a plane is drawn parallel to layers ∴ Density =

c a3 NA
A and B, at a distance above the layer B, it
8 135. Correct expression for density of unit cell of CsCl
passes through centres of x tetrahedral and y in terms of radius of Cs+ (r+) and radius of Cl– (r–)
octahedral voids. A plane parallel to layer A, at a in pm and NA (Avogadro’s number) is (density is
c in g/cm3)
distance just below it passes through centres
8 M CsCl ( 3 )3
(a)
of p tetrahedral and q octahedral voids. Find (x + [2(r  r )]3 N A
y + p + q). c is the cell parameter of hcp lattice,
2M CsCl ( 3 )3
the vertical edge length. (b)
[2(r  r )]3 N A  1030
(a) 10 (b) 9 (c) 6 (d) 14
Comprehension-9 M CsCl ( 3 )3
(c)
Only those atoms which form four covalent bonds [2(r  r )]3 N A  1030
produce a repetitive three dimensional structure using
2M CsCl ( 3 )3
only covalent bonds, e.g., diamond structure. The (d)
latter is based on a FCC lattice where lattice points are [2(r  r )]3 N A

Solid State 255

136. A metal crystallises into 2 crystal unit cells face 137. The number of atoms in 100 g of a bcc crystal with
centred cubic (fcc) and body centre cubic (bcc)
whose unit cell lengths are 2 pm and 2.8 pm density d = 10 g/cm3 and cell edge = 100 pm is
respectively. Ratio of densities of fcc and bcc
(a) 4 × 1025 (b) 2 × 1025
will be
(a) 5.48 (b) 7.23 (c) 6.84 (d) 4.58 (c) 1025 (d) 4 NA

ANSWER KEY
1. (c) 2. (d) 3. (d) 4. (d) 5. (a) 6. (a) 7. (a) 8. (b) 9. (c) 10. (c)
11. (b) 12. (a) 13. (d) 14. (b) 15. (d) 16. (a) 17. (c) 18. (b) 19. (d) 20. (a)
21. (d) 22. (b) 23. (d) 24. (a) 25. (b) 26. (a) 27. (b) 28. (b) 29. (c) 30. (d)
31. (d) 32. (b) 33. (b) 34. (d) 35. (b) 36. (b) 37. (b) 38. (c) 39. (b) 40. (a)
41. (a) 42. (d) 43. (a) 44. (d) 45. (a) 46. (b) 47. (d) 48. (c, d) 49. (a, c, d)
50. (a, b, d) 51. (a, b, c, d) 52. (a, d) 53. (a, b, d) 54. (a, c)
55. (a, b, c) 56. (b, c) 57. (b, c) 58. (b, d) 59. (a, d)
60. (a, b, c) 61. (a, c) 62. (a, c) 63. (a, b, d) 64. (a, b)
65. (b, c) 66. (a, c, d) 67. (a, b, c, d) 68. (a, d) 69. (a, b, c, d)
70. (a, b) 71. (c, d) 72. (a, d) 73. (a, b, c, d) 74. (c, d)
75. (a, c, d) 76. (a, b, c, d) 77. (a, b, d) 78. (b, c) 79. (a, b, d)
80. (a, b, c) 81. (8.17) 82. (63.24) 83. (3.01) 84. (6.00)
85. (4.00) 86. (0.53) 87. (231.00) 88. (62.00) 89. (3.47)
90. (2) 91. (4) 92. (8) 93. (40) 94. (95)
95. (6) 96. (220) 97. (100) 98. (4) 99. (a) 100. (c) 101. (c) 102. (a) 103. (b)
104. I-Q,S,T; II-P,S,T; III-S; IV-P,R,S 105. I-R,S; II-P,S; III-P,Q; IV-P 106. I-Q; II-P; III-S; IV-R
107. I-S; II-P; III-Q; IV– R 108. I-P,Q,R,S; II-Q,S; III-P,R,T; IV-T 109. (b) 110. (a)
111. (a) 112. (b) 113. (c) 114. (c) 115. (b) 116. (b) 117. (b) 118. (a) 119. (a) 120. (b)
121. (c) 122. (b) 123. (d) 124. (b) 125. (b) 126. (a) 127. (a) 128 (c) 129 (b) 130. (b)
131. (c) 132. (a) 133. (c) 134. (c) 135. (c) 136. (a) 137. (b)

256 JEE-Advanced Brahmastra PW

 SOLID STATE

EXERCISE #1
Classification of Solids
1. Classify each of the following solids.
(a) Tetra phosphorus decaoxide (P4O10) (b) Graphite
(c) Brass (d) Ammonium phosphate [(NH4)3 PO4]
(e) SiC (f) Rb
(g) 2 (h) LiBr
(i) P4 (j) Si
(k) Plastic.

Bravais Lattices
2. How many Bravais lattices are possible in 3D?

3. What are the crystallographic parameter of hexagonal, monoclinic and triclinic unit cell respectively.

Metallic Solids
4. A closed packed structure of uniform spheres has the edge length of 534 pm. Calculate the radius of
sphere, if it exists in:
(a) Simple cubic lattice
(b) BCC lattice
(c) FCC lattice

5. Given below are two dimension lattices with nicely shaded regions. You just have to find the
contributions (in fractions) of particles marked to the shaded regions and the total number of particles in
the regions.
(a) (b) (a) (b) (a) (b)
(iv) (a)

(a)

(b)
(i) (ii) (iii) (v)

6. Xenon crystallises in the face-centred cubic lattice and the edge of the unit cell is 620 pm. What is the
nearest neighbour distance and what is the radius of xenon atom?

7. Calculate the perimeter of given plane in HCP unit cell (Given that radius of atoms = R Å).

PHYSICS WALLAH 36
 SOLID STATE
8. How many spherical balls of radii 2 cm can be placed completely inside a cubical box of edge = 8 cm?

9. The effective radius of the iron atom is 1.42 Å. It has FCC structure. Calculate its density (Fe = 56 amu)

10. An element crystallizes in a structure having FCC unit cell of an edge 200 pm. Calculate the density, if
200 g of this element contains 24×1023 atoms.

11. Gold crystallizes in a face centered cubic lattice. If the length of the edge of the unit cell is 407 pm,
calculate the density of gold as well as its atomic radius assuming it to be spherical. Atomic mass of
gold = 197 amu.

12. Iron crystallizes in several modifications. At about 910 ºC, the body-centered cubic ‘a’ form undergoes a
transition to the face-centered cubic ‘’ form. Assuming that the distance between nearest neighbours is
the same in the two forms at the transition temperature. Calculate the ratio of the density of  iron to that
of  iron at the transition temperature.

13. An element crystallizes into a structure which may be described by a cubic type of unit cell having one
atom on each corner of the cube and two atoms on one of its body diagonals. If the volume of this unit
cell is 24×10–24 cm3 and density of element is 7.2 g cm–3, calculate the number of atoms present in 200 g
of element.

14. Following figure shows an FCC unit cell with atoms of radius r marked 1 (corner), 2 (face center),
3(face center). A quadrilateral is also shown by joining the centers of 4 face centered atoms. Find:
(i) The distances between atoms 1 & 2, 2 & 3 and 1 & 3.
(ii) The shape and dimensions of the quadrilateral.
3

15. Iron occurs as bcc as well as fcc unit cell. If the effective radius of an atom of iron is 124 pm. Compute
the density of iron in both these structures.

Voids in Solids
16. In a compound, oxide ions are arranged in cubic close packing arrangement. Cations
A occupy one-sixth of the tetrahedral voids and cations B occupy one-third of the octahedral voids. The
formula of the compound is AxByOz, then find the value of x + y + z.

17. A metal crystallises in bcc. Find the % fraction of edge length not covered and also % fraction of edge
length covered by atom is:

18. What is the number and closest distance between octahedral voids and tetrahedral voids in fcc unit cell?
PHYSICS WALLAH 37
 SOLID STATE
Ionic Solid
19. If the radius of Mg2+ ion, Cs+ ion, O2– ion, S2– ion and Cl– ion are 0.65 Å, 1.69 Å, 1.40 Å, 1.84 Å, and
1.81 Å respectively. Calculate the co-ordination numbers of the cations in the crystals of MgS, MgO and
CsCl.

20. A cubic solid is made up of two elements A and B. Atoms B are at the corners of the cube and A at the
body centre. What is the formula of compound?

21. A cubic solid is made by atoms A forming close pack arrangement, B occupying one-fourth of tetrahedral
void and C occupying half of the octahedral voids. What is the formula of compound?

22. Spinel is a important class of oxides consisting of two types of metal ions with the oxide ions arranged in
CCP pattern. The normal spinel has one-eight of the tetrahedral holes occupied by one type of metal ion
and one half of the octahedral hole occupied by another type of metal ion. Such a spinel is formed by
Zn2+, Al3+ and O2–, with Zn2+ in the tetrahedral holes. Give the formulae of spinel.

23. KF crystallizes in the NaCl type structure. If the radius of K+ ions 132 pm and that of
F– ion is 135 pm, what is the shortest K–F distance? What is the edge length of the unit cell? What is the
closet K–K distance?

24. The two ions A+ and B– have radii 88 and 200 pm respectively. In the closed packed crystal of compound
AB, predict the co-ordination number of A+.
r 1
25. Percentage of void space in AB solid having rock salt structure if + = having cation anion contact.
r– 2
Given  = 3.15.

26. CsCl has the bcc arrangement and its unit cell edge length is 400 pm. Calculate the inter ionic distance in
CsCl.

27. The density of KBr is 2.75 g cm–3. The length of the edge of the unit cell is 654 pm. Find the number of
formula unit of KBr present in the single unit cell.
(N = 6.023 ×1023 mol–1, Atomic mass : K = 39, Br = 80)

28. A crystal of lead (II) sulphide has NaCl structure. In this crystal the shortest distance between Pb +2 ion
and S2– ion is 297 pm. What is the length of the edge of the unit cell in lead sulphide? Also calculate the
unit cell volume.

29. If the length of the body diagonal for CsCl which crystallises into a cubic structure with Cl – ions at the
corners and Cs+ ions at the centre of the unit cells is 7 Å and the radius of the Cs + ion is 1.69 Å, what is
the radius of Cl– ion?

30. Rbl crystallizes in bcc structure in which each Rb+ is surrounded by eight iodide ions each of radius 2.17
Å. Find the length of one side of RbI unit cell.

Defects in Solids
31. The composition of a sample of wurstite is Fe0.93O1.0. What percentage of iron is present in the form of
Fe(III)?

PHYSICS WALLAH 38
 SOLID STATE

32. If NaCl is dopped with 10–3 mol % SrCl2, what is the numbers of cation vacancies per mole of NaCl?

33. AgCl has the same structure as that of NaCl. The edge length of unit cell of AgCl is found to be 555 pm
and the density of AgCl is 5.561 g cm–3. Find the percentage of sites that are unoccupied.

34. A non stoichiometric compound Fe7S8 consist of iron in both Fe+2 and Fe+3 form and sulphur is present as
sulphide ions. Calculate cation vacancies as a percentage of Fe+2 initially present in the sample.
100
[Express your answer as % & fill x in the OMR sheet]
x

PHYSICS WALLAH 39
 SOLID STATE

EXERCISE #2
1. Calculate the density of diamond from the fact that it has face centered cubic structure with two atoms
per lattice point and unit cell edge length of 3.569 Å.

2. What is the percent by mass of titanium in rutile, a mineral that contain Titanium and oxygen, if structure
can be described as a closet packed array of oxide ions, with titanium in one half of the octahedral holes.
What is the oxidation number of titanium? (Ti = 48)

3. A solid A+ and B– had NaCl type closed packed structure. If the anion has a radius of
250 pm, what should be the ideal radius of the cation? Can a cation C+ having a radius of 180 pm be
slipped into the tetrahedral site of the crystal of A+B–, without disturbing the crystal? Give reasons for
your answer.

4. What will be packing fraction of solid in which atoms are present at corners and cubic void is occupied?
The insertion of the sphere into void does not disturb simple cubic lattice.

5. Find packing fraction of unit cell of AAAAA.......type hypothetical arrangement in which hexagonal
packing is taken in layer.

rNa + rNa +
6. KCl crystallizes in the same type of lattice as does NaCl. Given that = 0.5 and = 0.7 Calculate:
rCl− rK +
(a) The ratio of the sides of unit cell for KCl to that for NaCl and
(b) The ratio of densities of NaCl to that for KCl.

7. A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge.
(a) What is the empirical formula of the compound?
(b) What is the co-ordination number of the Mn ion?
(c) Calculate the edge length of the unit cell, if the radius of Mn ion is 0.65 Å and that of F– ion is
1.36 Å.

8. Ice crystallizes in a hexagonal lattice. At the low temperature at which the structure was determined, the
lattice constants where a = 4.53 Å, and b = 7.60 Å How many molecules are contained in a given unit
cell? [density (ice) = 0.92 gm/cm3)]

9. Potassium crystallizes in a body-centered cubic lattice with edge length, a = 5.2 Å.

(a) What is the distance between nearest neighbours?
(b) What is the distance between next-nearest neighbours?
(c) How many nearest neighbours does each K atom have?
(d) How many next-nearest neighbours does each K atom have?

10. Prove that void space in fluorite structure per unit volume of unit cell is 0.374.

11. x- ray analysis of a Mn-Si alloy with 75 atomic percent of Mn showed that the unit cell is cubic and the
lattice parameter a = 3.6Å. The density of alloy is 6.85 gram/cc. Find the formula of alloy.

PHYSICS WALLAH 40
 SOLID STATE
12. The olivine series of minerals consists of crystals in which Fe and Mg ions may substitute for each other
causing substitutional impurity defect without changing the volume of the unit cell. In olivine series of
minerals, oxide ion exists as FCC with Si4+ occupying 1/4th of octahedral voids and divalent ions
occupying 1/4th of tetrahedral voids. The density of forsterite (magnesium silicate) is 3.21 g/cc and that
of fayalite (ferrous silicate) is 4.34 g/cc. Find the formula of forsterite and fayalite minerals and the
percentage of fayalite in an olivine with a density of 3.88 g/cc.

13. For ABC ABC ABC .... packing distance between two successive tetrahedral void is X and distance
y 2
between two successive octahedral void is y in an unit cell, then is.
X
2
14. An element 'M' crystallizes in ABAB....type packing if adjacent layer A & B are 10 pm apart, then
3
calculate radius of largest sphere which can be fitted in the void. (in pm) without disturbing the lattice
arrangement (Given: 2 = 1.414 )
Fill your answer as sum of digits (excluding decimal places) till you get the single digit answer.

15. In the 1980’s a class of ceramic materials was discovered that exhibits superconductivity at the
unusually high temperature of 90 K. One such material contains yttrium, barium, copper and oxygen
and is called “YBCO”. It has a nominal composition of YBa2Cu3O7, but its actual composition is variable
according to the formula YBa2Cu3O7- (0 <  < 0.5).
(a) One unit cell of the idealized crystal structure of YBCO is shown below. Identify which circles
correspond to which elements in the structure.

c
b

a
The true structure is actually orthorhombic (a  b  c), but it is approximately tetragonal, with a  b  (c/3).

(b) Estimate the density of this sample of YBCO (with  = 0.25) in g cm–3. Use a = 500 pm and c = 1500 pm.
Ba (137.33), Y (88.91), Cu (63.5), O (16).
PHYSICS WALLAH 41
 SOLID STATE

EXERCISE #3
Classification of Solids
1. How many of the following are covalent network solids?
S8, Bronze, SiO2, Diamond, ZnSO4, Si, AlN, SiC, CO2.
(A) 4 (B) 5 (C) 6 (D) 8

2. Which of the following solids substances will have same refractive index when measured in different
directions?
(A) NaCl (B) Monoclinic sulphur
(C) Rubber (D) Graphite

Bravais Lattices
3. Which of the following are the correct axial distances and axial angles for rhombohedral system?
(A) a = b = c,  =  =   900 (B) a = b  c,  =  =  = 900
(C) a  b = c,  =  =  = 900 (D) a  b  c,       900

4. a  b  c,       900 represents:
(A) tetragonal system (B) orthorhombic system
(C) monoclinic system (D) triclinic system

5. The most unsymmetrical system is:

(A) Cubic (B) Hexagonal (C) Triclinic (D) Orthorhombic

6. A match box exhibits:

(A) Cubic geometry (B) Monoclinic geometry
(C) Tetragonal geometry (D) Orthorhombic geometry

7. The crystal system of a compound with unit cell dimensions, a = 0.387 and b = 0.387 and c = 0.504nm
and  =  = 90º and  = 120º is:
(A) Cubic (B) Hexagonal (C) Orthorhombic (D) Rhombohedral

Metallic Solids
8. If ‘Z’ is the number of atoms in the unit cell that represents the closest packing sequence
---A B C A B C---, the number of tetrahedral voids in the unit cell is equal to:
(A) Z (B) 2Z (C) Z/2 (D) Z/4

9. Which one of the following schemes of ordering closed packed sheets of equal sized spheres generate
crystal of minimum packing fraction.
(A) ABCABC (B) ABACABAC (C) ABBAABBA (D) ABCBCABCBC

10. In a lattice of X and Y atoms, if X atoms are present at corners and Y atoms at the body centre & one X
atom is removed from a corner from each unit cell, then the formula of the compound will be:
(A) X7Y (B) X8Y7 (C) X7Y8 (D) X7Y7

PHYSICS WALLAH 42
 SOLID STATE
11. A 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 figure are removed, then, the formula of the crystal would be:

(A) AB (B) A5B7 (C) A7B5 (D) None of these.

12. Iron has body centred cubic lattice structure. The edge length of the unit cell is found to be 286 pm. What
is the radius of an iron atom?
(A) r = 124 pm (B) r = 128 pm (C) r = 124 Å (D) r = 128 Å

13. A metal crystallizes in a body centered cubic lattice (bcc) with the edge of the unit cell 5.2Å. The
distance between the two nearest neighbours is:
(A) 10.4 Å (B) 4.5 Å (C) 5.2Å (D) 9.0Å

14. The shortest distance between Ist and Vth layer of HCP arrangement is:
2 3 2 3
(A) 8 r (B) 4 r (C) 16 r (D) 8 r
3 2 3 2

15. Volume of HCP unit cell is:

(A) 24 2 r3 (B) 8 2 r3 (C) 16 2 r3 (D) 24 3 r3

Voids in Solids
16. The interstitial hole is called tetrahedral because
(A) It is formed by four spheres.
(B) Partly same and partly different.
(C) It is formed by four spheres the centres of which form a regular tetrahedron.
(D) None of the above three.

17. The size of an octahedral void formed in a closest packed lattice as compared to tetrahedral void is
(A) Equal (B) Smaller (C) Larger (D) Not definite

18. If the anions (A) form hexagonal closest packing and cations (C) occupy only 2/3 octahedral voids in it,
then the general formula of the compound is:
(A) CA (B) CA2 (C) C2A3 (D) C3A2

PHYSICS WALLAH 43
 SOLID STATE
19. In a hypothetical solid C atoms form CCP lattice with A atoms occupying all the Tetrahedral Voids and B
atoms occupying all the octahedral voids. A and B atoms are of the appropriate size such that there is no
distortion in the CCP lattice. Now if a plane is cut (as shown) then type of voids and their numbers which
are present at the cross section would be.
Plane

CCP unit cell

(A) O.V = 3, T.V. = 4 (B) O.V. = 2, T.V. = 4

(C) O.V. = 1, T.V. = 2 (D) O.V. = 0, T.V. = 4

Ionic Solid
20. If x = radius of Na+ & y = radius of Cl– & a is the unit cell edge length for NaCl crystal, then which of the
given relation is correct?
(A) x + y = a (B) 2x + 2y = a (C) x + y = 2a (D) x + y = a 2

21. How many unit cells are there in 1 gram cubic crystal of NaCl:
4  NA NA NA NA
(A) (B) (C) (D)
58.5 58.5 58.5  4 58.5  8

22. In a solid, S2– ions are packed in fcc lattice. Zn2+ occupies half of the tetrahedral voids in an alternating
arrangement. Now if a plane is cut (as shown) then the cross-section would be:

Zn2+
S2–

(A) (B) (C) (D)

23. The density of CaF2 (fluorite structure) is 3.18 g/cm3. The length of the side of the unit cell is
(A) 253 pm (B) 344 pm (C) 546 pm (D) 273 pm

24. The coordination number of cation and anion in Fluorite CaF2 and CsCl are respectively
(A) 8:4 and 6:3 (B) 6:3 and 4:4 (C) 8:4 and 8:8 (D) 4:2 and 2:4

25. A compound XY crystallizes in 8 : 8 lattice with unit cell edge length of 480 pm. If the radius of Y– is
225 pm, then the radius of X+ is
(A) 127.5 pm (B) 190.68 pm (C) 225 pm (D) 255 pm

26. The mass of a unit cell of CsCl corresponds to

(A) 1 Cs+ and 1 Cl– (B) 1 Cs+ and 6 Cl– (C) 4 Cs+ and 4 Cl– (D) 8 Cs+ and 1 Cl–

27. Diamond belongs to the crystal system:

(A) Cubic (B) triclinic (C) tetragonal (D) hexagonal

PHYSICS WALLAH 44
 SOLID STATE
28. An ionic compound AB has ZnS type structure. If the radius A+ is 22.5 pm, then the ideal radius of B–
would be
(A) 54.35 pm (B) 100 pm (C) 145.16 pm (D) none of these

29. Edge length of M+X– (fcc structure) is 7.2 Å. Assuming M+ and X– contact along the cell edge, radius of
X– ion is ( rM+ = 1.6 Å):
(A) 2.0 Å (B) 5.6 Å (C) 2.8 Å (D) 38 Å

30. Choose the correct option/options:

(A) Two adjacent face centre atom doesn't touch each other in fcc unit cell because they are not nearest
atom of face each other in fcc lattice
(B) Number of nearest Na+ ions of another Na+ in Na2O crystal will be 24.
(C) Minimum distance between two cubical voids in simple cube unit cell lattice will be a where a is
length of edge of unit cell
(D) By defects in solids density of solids either remains constant or decreases but it can never increase.

Defects in Solids
31. Which of the following is the most likely to show schottky defect
(A) CaF2 (B) ZnS (C) AgCl (D) CsCl

32. In the Schottky defect, in AB type ionic solids

(A) cations are missing from the lattice sites and occupy the interstitial sites
(B) equal number of cations and anions are missing
(C) anions are missing and electrons are present in their place
(D) equal number of extra cations and electrons are present in the interstitial sites

33. F–centers are

(A) the electrons trapped in anionic vacancies
(B) the electrons trapped in cation vacancies
(C) non-equivalent sites of stoichiometric compound
(D) all of the above

34. Which statements is incorrect about HCP and CCP lattice

(A) Number of tetrahedral voids are twice of octahedral holes
(B) 2 tetrahedral and 1 octahedral voids are present in HCP unit cell per atom.
(C) Coordination number of HCP unit cell is 12
(D) If atom of tetrahedral voids displace into octahedral voids then it is Schottky defect.

35. Strongly heated ZnO crystal can conduct electricity. This is due to
(A) Movement of extra Zn2+ ions present in the interstitial sites
(B) Movement of electrons in the anion vacancies
(C) Movement of both Zn2+ ions and electrons
(D) None of these

PHYSICS WALLAH 45
 SOLID STATE

EXERCISE #4
More than one may be correct
1. Incorrect statement(s) for the packing of identical spheres in two dimensions is/are:
(A) For square close packing, coordination number is 4.
(B) For hexagonal close packing, coordination number is 6.
(C) There is only one void per atom in both, square and hexagonal close packing.
(D) Hexagonal close packing is more efficiently packed than square close packing.

2. Correct statement for ccp is:

(A) Each octahedral void is surrounded by 6 spheres and each sphere is surrounded by 4 octahedral
voids
(B) Each octahedral void is surrounded by 6 spheres and each sphere is surrounded by 6 octahedral
voids
(C) Each octahedral void is surrounded by 6 spheres and each sphere is surrounded by 8 octahedral
voids
(D) Each octahedral void is surrounded by 6 spheres and each sphere is surrounded by 12 octahedral
voids

3. Which of the following statements is correct in the rock-salt structure of ionic compounds?
(A) coordination number of cation is four whereas that of anion is six.
(B) coordination number of cation is six whereas that of anion is four.
(C) coordination number of each cation and anion is four.
(D) coordination number of each cation and anion is six.

4. Which of the following statements is/are correct?

(A) In an anti-fluorite structure anions form FCC lattice and cations occupy all tetrahedral voids.
(B) If the radius of cations and anions are 0.2 Å and 0.95 Å then coordination number of cation in the
crystal is 4.
(C) Each sphere is surrounded by six voids in two dimensional hexagonal close packed layers
(D) 8 Cs+ ions occupy the second nearest neighbour locations of a Cs+ ion

5. Select write statement(s)

(A) Density of crystal always increases due to substitutional impurity defect.
(B) An atom/ion is transferred from a lattice site to an interstitial position in Frenkel defect.
(C) In AgCl, the silver ion is displaced from its lattice position to an interstitial position. Such a defect is
called a Frenkel defect
(D) None

6. Which of the following statement(s) is/are correct –

(A) NaCl is a ‘AB’ crystal lattice that can be interpreted to be made up of two individual fcc unit cells of
A+ and B– fused together in such a manner that the corner of one unit cell becomes the edge centre of
the other.
(B) In a face centred cubic unit cell, the body centre is an octahedral void.
(C) In fcc unit cell, octahedral and tetrahedral voids are equal in number.
(D) Tetrahedral voids = 2 × octahedral voids, is valid for ccp and hcp.

PHYSICS WALLAH 46
 SOLID STATE
7. Select the correct statement (s):
(A) CsCl mainly shows Schottky defect
(B) ZnS mainly shows Frenkel defect
(C) NaCl unit cell contain 4Na+ and 4Cl—
(D) In NaCl one Na+ is surrounded by 6 Cl— then 12 Na+and then 8 Cl–.

8. Which of the following are true:

(A) Ratio of nearest neighbours in simple cubic cell to next nearest neighbours in face cubic centre is 1
(B) Packing efficiency of a unit cell in which atoms are present at each corner and each edge centre is
26 % in metallic crystal.
(C) Distance between two planes in fcc or HCP arrangement is same for a metal exist in both forms.
(D) If number of unit cell along one edge are 'x' then total number of unit cell in cube = x3

Comprehension: (Q. 9 & 10)

Solid balls of radius 17.32 cm crystallises in bcc pattern, during one such crystallisation some oxygen gas
is trapped. This trapped oxygen at 640K creates pressure of 5 atm.
Assume:
(i) BCC arrangement is not disturbed due to trapping of gas.
(ii) Gas is uniformly distributed inside unit cell
[Take R = 0.08 atm-litre/mole-K, NA = 6 × 1023, Mass of a solid ball = 64 g]

9. Calculate number of oxygen molecules present in a unit cell

(A) 24 × 1023 (B) 12 × 1023 (C) 6 × 1023 (D) 3 × 1023

10. Calculate percentage increase in density due to trapping of gas

(A) 16.67 % (B) 33.33 % (C) 100% (D) 50%

Comprehension: (Q. 11 to 14)

Calcium crystallizes in a cubic unit cell with density 3.2 g/cc. Edge-length of the unit cell is 437 pm

11. The type of unit cell is:

(A) Simple cubic (B) BCC (C) FCC (D) Edge-centred

12. The nearest neighbour distance is:

(A) 154.5 pm (B) 309 pm (C) 218.5 pm (D) 260 pm

13. The number of nearest neighbours of a Ca atom are:

(A) 4 (B) 6 (C) 8 (D) 12

14. If the metal is melted, density of the molten metal was found to be 3 g/cc. What will be the percentage of
empty space in the liquid metal?
(A) 31% (B) 36% (C) 28% (D) 49%

PHYSICS WALLAH 47
 SOLID STATE
Comprehension: (Q. 15 & 16)
There is large variety of non-stoichiometric inorganic solids which contain an excess or deficiency of one
of the elements. Such solids showing deviations from the ideal stoichiometric composition form an
important group of solids. For example in the vanadium oxide, VOx, x can be anywhere between 0.6 and
1.3. There are solids which are difficult to prepare in the stoichiometric composition. Thus, the ideal
composition in compounds such as FeO is difficult to obtain (normally we get a composition of Fe0.95 O
but it may range from Fe0.93 O to Fe0.96O). Non-stoichiometric behaviour is most commonly found for
transition metal compounds though are also known for some lanthanides and actinides.
Zinc oxide loses oxygen reversibly at high temperatures and turns yellow in colour. The excess metal is
accommodated interstitially, giving rise to electrons trapped in the neighborhoods. The enhanced
electrical conductivity of the non-stoichiometric ZnO arises from these electrons.
Anion vacancies in alkali halides are produced by heating the alkali halide crystals in an atmosphere of
the alkali metal vapour. When the metal atoms deposit on the surface they diffuse into the crystal and
after ionisation the alkali metal ion occupies cationic vacancy whereas electron occupies anionic vacancy.
Electrons trapped in anion vacancies are referred to as F-centers (from Farbe the German word for
colour) that gives rise to interesting colour in alkali halides. Thus, the excess of potassium in KCl makes
the crystal appear violet and the excess of lithium ions LiCl makes it pink.

15. When LiCI is heated into the vapour of lithium, the crystal acquires pink colour. This is due to:
(A) Schottky defects (B) Frenkel defects
(C) Metal excess defect leading to F-centers (D) Electronic defect

16. AgCl is crystallized from molten AgCl containing a little CdCl2. The solid obtained will have
(A) cationic vacancies equal to number of Cd2+ ions incorporated
(B) cationic vacancies equal to double the number of Cd2+ ions
(C) anionic vacancies
(D) neither cationic nor anionic vacancies

Match the column

17. Match the column
Column I Column II
(A) Tetragonal and Hexagonal (P) are two crystal systems
(B) Cubic and Rhombohedral (Q) a = b  c
(C) Monoclinic and Triclinic (R) a  b  c
(D) Cubic and Hexagonal (S) a = b = c

18. Match the column:

Column I Column II
(A) Rock salt structure (P) Co-ordination number of cation is 4
3a
(B) Zinc Blend structure (Q) = r+ + r–
4
(C) Fluorite structure (R) Co-ordination number of cation and anion are
same
a
(S) Distance between two nearest anion is
2

PHYSICS WALLAH 48
 SOLID STATE
Matching list type
19. Match the column
Column I Column II
(Arrangement of the atoms/ions) (Planes in fcc lattice)

(P) (1)

(Q) (2)

(R) (3)

(S) (4)

Code:
P Q R S
(A) 4 3 1 2
(B) 4 3 2 1
(C) 3 2 1 4
(D) 1 2 4 3

20. Column I Column II

[Distance in terms of edge length of cube (a)]
(P) 0.866 a (A) Shortest distance between cation & anion in CsCl structure.
(Q) 0.707 a (B) Shortest distance between two cation in CaF2 structure.
(R) 0.433 a (C) Shortest distance between carbon atoms in diamond.
(S) 1.414 a (D) the distance at which second nearest neighbour is present in simple cubic
unit cell
Code:
P Q R S
(A) 4 3 1 2
(B) 1 2 3 4
(C) 3 2 1 4
(D) 1 2 4 3

PHYSICS WALLAH 49
 SOLID STATE

EXERCISE #5 (JEE MAIN)

1. The no. of atoms per unit cell in B.C.C. & F.C.C. is respectively: [AIEEE-02]
(A) 8, 10 (B) 2, 4 (C) 1, 2 (D) 1, 3

2. How many unit cells are present in a cube-shaped ideal crystal of NaCl of mass 1.00g ? [AIEEE-03]
(A) 1.28 × 1021 unit cells (B) 1.71 × 1021 unit cells
(C) 2.57 × 1021 unit cells (D) 5.14 × 1021 unit cells

3. What type of crystal defect is indicated in the diagram below? [AIEEE-04]

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

4. Lattice energy of an ionic compound depends upon: [AIEEE-05]

(A) Size of the ion only (B) Charge on the ion only
(C) Charge on the ion and size of the ion (D) Packing of ions only

5. An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the
centres of the faces of the cube. The empirical formula of this compound would be: [AIEEE-05]
(A) A2B (B) AB (C) A3B (D) AB3

6. Total volume of atoms present in a face-centred cubic unit cell of a metal is (r is atomic radius):
[AIEEE-06]
24 3 12 3 16 3 20 3
(A) r (B) r (C) r (D) r
3 3 3 3

7. In a compound, atoms of element Y form ccp lattice and those of element X occupy 2/3rd of
tetrahedral voids. The formula of the compound will be: [AIEEE-08]
(A) X4Y3 (B) X2Y3 (C) X2Y (D) X3Y4

8. Percentages of free space in cubic close packed structure and in body centered packed structure
are respectively: [AIEEE-10]
(A) 48% and 26% (B) 30% and 26% (C) 26% and 32% (D) 32% and 48%

9. The edge length of a face centered cubic cell of an ionic substance is 508 pm. If the radius of the
cation is 110 pm, the radius of the anion is: [AIEEE-10]
(A) 144 pm (B) 288 pm (C) 398 pm (D) 618 pm

10. Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic
radius of the lithium will be: [AIEEE-12]
(A) 152 pm (B) 75 pm (C) 300 pm (D) 240 pm

PHYSICS WALLAH 50
 SOLID STATE
11. Among the following the incorrect statement is: [JEE Main-2012]
(A) Density of crystals remains unaffected due to Frenkel defect
(B) In BCC unit cell the void space is 32%
(C) Electrical conductivity of semiconductors and metals increases with increase in temperature
(D) Density of crystals decreases due to Schottky defect

12. A solid has 'bcc' structure. If the distance of nearest approach between two atoms is 1.73 Å, the edge
length of the cell is: [JEE Main-2012]
(A) 314.20 pm (B) 216 pm (C) 200 pm (D) 1.41 pm

13. Ammonium chloride crystallizes in a body centred cubic lattice with edge length of unit cell of 390 pm.
If the size of chloride ion is180 pm, the size of ammonium ion would be: [JEE Main-2012]
(A) 158 pm (B) 174 pm (C) 142 pm (D) 126 pm

14. The radius of a calcium ion is 94 pm and of the oxide ion is 146 pm. The possible crystal structure of
calcium oxide will be: [JEE Main-2012]
(A) Octahedral (B) Tetrahedral (C) Pyramidal (D) Trigonal

15. Experimentally it was found that a metal oxide has formula M0.98O. Metal M, is present as M2+ and M3+ in
its oxide. Fraction of the metal which exists as M3+ would be: [JEE Main-2013]
(A) 7.01% (B) 4.08% (C) 6.05% (D) 5.08

16. An element having an atomic radius of 0.14 nm crystallizes in an fcc unit cell. What is the length of a
side of the cell? [JEE Main-2013]
(A) 0.96 nm (B) 0.4 nm (C) 0.24 nm (D) 0.56 nm

17. Which one of the following statements about packing in solids is incorrect? [JEE Main-2013]
(A) Void space in ccp mode of packing is 26%
(B) Coordination number in hcp mode of packing is 12
(C) Void space in hcp mode of packing is 32%
(D) Coordination number in bcc mode of packing is 8

18. In a face centred cubic lattice, atoms of A form the corner points and atoms of B form the face centred
points. If two atoms of A are missing from the corner points, the formula of the ionic compound is:
[JEE Main-2013]
(A) AB2 (B) AB3 (C) AB4 (D) A2B5

19. Copper crystallises in fcc with a unit length of 361pm. What is the radius of copper atom?
[JEE Main -2013]
(A) 181pm (B) 128pm (C) 157pm (D) 108pm

20. CsCl crystallises in body centred cubic lattice. If 'a' is its edge length then which of the following
expression is correct: [JEE Main-2014]
3 3a
(A) rCs+ + rCl− = a (B) rCs+ + rCl− = 3a (C) rCs+ + rCl− = 3a (D) rCs+ + rCI− =
2 2
PHYSICS WALLAH 51
 SOLID STATE
21. In a face centered cubic lattice atoms A are at the corner points and atoms B at the face centered points. If
atom B is missing from one of the face centered points, the formula of the ionic compound is:
[JEE Main-2014]
(A) AB2 (B) A2B3 (C) A5B2 (D) A2B5

22. The appearance of colour in solid alkali metal halides is generally due to:
(A) Frenkel defect (B) F-centres (C) Schottky defect (D) Interstitial position

23. In a monoclinic unit cell, the relation of sides and angles are respectively: [JEE Main-2014]
(A) a  b  c and       90º (B) a  b  c and  =  = 90º  
(C) a = b  c and  =  =  = 90º (D) a  b  c and  =  =  = 90º

24. The total number of octahedral void(s) per atom present in a cubic close packed structure is:
[JEE Main-2014]
(A) 1 (B) 2 (C) 3 (D) 4

25. Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29Å. The
radius of sodium atom is approximately: [JEE Main-2015]
(A) 5.72Å (B) 0.93Å (C) 1.86Å (D) 3.022Å

26. Which of the following compounds is metallic and ferromagnetic? [JEE Main-2016]
(A) CrO2 (B) VO2 (C) MnO2 (D) TiO2

27. A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the
closest approach between two atoms in metallic crystal will be: [JEE Main-2017]
a
(A) 2 a (B) (C) 2a (D) 2 2 a
2

28. Which type of 'defect' has the presence of cations in the interstitial sites? [JEE Main-2018]
(A) Schottky defect (B) Vacancy defect
(C) Frenkel defect (D) Metal deficiency defect

29. Which of the following arrangements shows the schematic alignment of magnetic moments of
antiferromagnetic substance? [JEE Main-2018]
(A) (B)
(C) (D)

30. A compound of formula A2 B3 has the hcp lattice. Which atom forms the hcp lattice and what
fraction of tetrahetral voids is occupied by the other atoms: [JEE Main-2019]
2 1
(A) hcp lattice-A, Tetrahedral voids-B (B) hcp lattice-A, Tetrahedral voids-B
3 3
2 1
(C) hcp lattice -B, Tetrahedral voids-A (D) hcp lattice-B, Tetrahedral voids-A
3 3

PHYSICS WALLAH 52
 SOLID STATE
31. An element has a face-centred cubic (fcc) structure with a cell edge of a. The distance between
the centres of two nearest tetrahedral voids in the lattice is: [JEE Main-2019]
a 3
(A) 2a (B) a (C) (D) a
2 2

32. An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance
between the centres of two nearest octahedral voids in the crystal lattice is: [JEE Main-2020]
a a
(A) (B) a (C) 2a (D)
2 2

[JEE Main 2020-21]

33. The incorrect statement about the imperfections in solids is:
(A) Schottky defect decreases the density of the substance.
(B) Interstitial defect increases the density of the substance.
(C) Frenkel defect does not alter the density of the substance.
(D) Vacancy defect increases the density of the substance.

34. A hard substance melts at high temperature and is an insulator in both solid and in molten state. This
solid is most likely to be a/an:
(A) Ionic solid (B) Molecular solid (C) Metallic solid (D) Covalent solid

35. In a binary compound, atoms of element A form a hcp structure and those of element M occupy 2/3 of
the tetrahedral voids of the hcp structure. The formula of the binary compound is:
(A) M2A3 (B) M4A3 (C) M4A (D) MA3

36. The parameters of the unit cell of a substance are a = 2.5, b = 3.0, c = 4.0,  = 90°,  = 120°  = 90°.
The crystal system of the substance is:
(A) Hexagonal (B) Orthorhombic (C) Monoclinic (D) Triclinic

37. Given below are two statements.

Statement-I: Frenkel defects are vacancy as well as interstitial defects.
Statement-II: Frenkel defect leads to colour in ionic solids due to presence of F-centres.
Choose the most appropriate answer for the statements from the options given below:
(A) Statement I is false but Statement II is true (B) Both Statement I and Statement II are true
(C) Statement I is true but Statement II is false (D) Both Statement I and Statement II are false

2
38. Atoms of element X form hcp lattice and those of element Y occupy of its tetrahedral voids. The
3
percentage of element X in the lattice is_________ (Nearest integer)

39. The distance between Na+ and Cl– ions in solid NaCl of density 43.1 g cm–3 is ________ × 10–10m.
(Nearest Integer) (Given: NA = 6.02 × 1023 mol–1)

40. In a solid AB. A-atoms are in ccp arrangement and B atoms occupy all the octahedral sites. If two atoms
from the opposite faces are removed, then the resultant stoichiometry of the compound is AxBy. The
value of x is_______. [nearest integer]

PHYSICS WALLAH 53
 SOLID STATE
41. Metal deficiency defect is shown by Fe0.93O. In the crystal, some Fe2+ cations are missing and loss of
positive charge is compensated by the presence of Fe3+ ions. The percentage of Fe2+ ions in the Fe0.93O
crystals is ________. (Nearest integer)

42. An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the
element is 6.0 g cm–3. The number of atoms present in 180 g of the element is ______ × 1023
(Nearest integer)

43. Metal M crystallizes into a FCC lattice with the edge length of 4.0×10–8 cm. The atomic mass of the
metal is ______ g/mol. (Nearest integer).
(Use: NA = 6.02 × 1023 mol–1, density of metal, M = 9.03 g cm–3)

44. Ionic radii of cation A+ and anion B– are 102 and 181 pm respectively. These ions are allowed to
crystallize into an ionic solid. This crystal has cubic close packing for B–. A+ is present in all octahedral
voids. The edge length of the unit cell of the crystal AB is _____ pm. (Nearest Integer)

45. The coordination number of an atom in a body centered cubic structure is _______.
[Assume that the lattice is made up of atoms.]

46. The unit cell of copper corresponds to a face centered cube of edge length 3.596 Å with one copper atom
at each lattice point. The calculated density of copper in kg/m3 is _______.
[Molar mass of Cu: 63.54 g; Avogadro Number = 6.022 × 1023]

47. The number of octahedral voids per lattice site in a lattice is _____.(Rounded off to the nearest integer)

48. Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in
0.581 g of Ga is _______ × 1021. (Round off to the Nearest Integer).

49. KBr is doped with 10–5 mole percent of SrBr2. The number of cationic vacancies in 1 g of KBr crystal is
_____1014. (Round off to the Nearest Integer).
[Atomic Mass: K : 39.1 u, Br : 79.9 u, NA = 6.023 × 1023]

50. Diamond has a three-dimensional structure of C atoms formed by covalent bonds. The structure of
diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon
atoms. The number of carbon atoms present per unit cell of diamond is _______.

51. A copper complex crystallising in a CCP lattice with a cell edge of 0.4518 nm has been revealed by
employing X-ray diffraction studies. The density of a copper complex is found to be 7.62 g cm–3. The
molar mass of copper complex is ______ g mol–1. (Nearest integer)
[Given: NA = 6.022 × 1023 mol–1]

52. A certain element crystallises in a bcc lattice of unit cell edge length 27 Å. If the same element under the
same conditions crystallises in the fcc lattice, the edge length of the unit cell in Å will be ________.
(Round off to the Nearest Integer).
[Assume each lattice point has a single atom] [Assume 3 = 1.73, 2 = 1.41]

PHYSICS WALLAH 54
 SOLID STATE
53. The empirical formula for a compound with a cubic close packed arrangement of anions and with cations
occupying all the octahedral sites in AxB. The value of x is _______. (Integer answer)

[JEE Main-2023]
54. Which of the following represents the lattice structure of A0.95 O containing A2+, A3+ and O2– ions:

(1) (2)

(3)

(A) 1 and 2 only (B) 2 and 3 only (C) 2 only (D) 1 only

55. A metal M crystallizes into two lattices: face centred cubic (fcc) and body centred cubic (bcc) with unit
cell edge length of 2.0Å and 2.5Å respectively. The ratio of densities of lattices fcc to bcc for the metal
M is: (Nearest integer)

56. A cubic solid is made up of two elements X and Y . Atoms of X are present on every alternate corner
1
and one at the center of cube. Y is at rd of the total faces. The empirical formula of the compound is:
3
(A) X2.5Y (B) X2Y1.5 (C) X1.5Y2 (D) XY2.5

57. A metal M forms hexagonal close-packed structure. The total number of voids in 0.02 mol of it
is________ 1021 (Nearest integer).
(Given NA = 6.02 1023 )

PHYSICS WALLAH 55
 SOLID STATE

EXERCISE #6 (JEE ADVANCED)

1. A metal cryatallises into two cubic phases, FCC and BCC whose unit cell lengths are 3.5 and 3.0 Å
respectively. Calculate the ratio of densities of FCC and BCC. [JEE-1999]

2. The figures given below show the location of atoms in three crystallographic planes in FCC lattice. Draw
the unit cell for the corresponding structure and identify these planes in your diagram. [JEE-2000]

3. In a solid “AB” having 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: [JEE-2000]
(A) AB2 (B) A2B (C) A4B3 (D) A3B4

4. In any ionic solid [MX] with schottky defects, the number of positive and negative ions are same. [T/F]
[JEE-2000]

5. The coordination number of a metal crystallising in a hcp structure is: [JEE-2000]

(A) 12 (B) 4 (C) 8 (D) 6

6. A substance AxBy crystallises in a FCC lattice in which atoms “A” occupy each corner of the cube and
atoms “B” occupy the centres of each face of the cube. Identify the correct composition of the substance
AxBy. [JEE-2002]
(A) AB3 (B) A4B3
(C) A3B (D) composition cannot be specified

7. Marbles of diameter 10 mm each are to be arranged on a flat surface so that their centres lie within the
area enclosed by four lines of length each 40 mm. Sketch the arrangement that will give the maximum
number of marbles per unit area, that can be enclosed in this manner and deduce the expression to
calculate it. [JEE 2003]

8. (i) AB crystallizes in a rock salt structure with A : B = 1 : 1. The shortest distance between A and B is
Y1/3 nm. The formula mass of AB is 6.023 Y amu where Y is any arbitrary constant. Find the density
in kg m–3. [JEE–2004]
(ii) If measured density is 20 kg m-3. Identify the type of point defect.

9. An element crystallises in FCC lattice having edge length 400 pm. Calculate the maximum diameter
which can be placed in interstitial sites without disturbing the structure. [JEE 2005]

10. Which of the following FCC structure contains cations in alternate tetrahedral voids? [JEE 2005]
(A) NaCl (B) ZnS (C) Na2O (D) CaF2

11. The edge length of unit cell of a metal having atomic weight 75 g/mol is 5 Å which crystallizes in cubic
lattice. If the density is 2 g/cc then find the radius of metal atom. (NA = 6 × 1023). Give the answer in pm.
[JEE 2006]

PHYSICS WALLAH 56
 SOLID STATE
12. Match the crystal system / unit cells mentioned in Column I with their characteristic features mentioned
in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 × 4 matrix given in the
ORS. [JEE 2007]
Column-I Column-II
(A) simple cubic and face-centred cubic (P) have these cell parameters a = b = c and  =  = 
(B) cubic and rhombohedral (Q) are two crystal systems
(C) cubic and tetragonal (R) have only two crystallographic angles of 90°
(D) hexagonal and monoclinic (S) belong to same crystal system.

Paragraph for Question No. 13 to 15

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a
hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are
sandwiched in between them. A space-filling model of this structure, called hexagonal close-packed
(HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as
closely as possible. Three spheres are then placed over the first layer so that they touch each other and
represent the second layer. Each one of these three spheres touches three spheres of the bottom layer.
Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative
position. Assume radius of every sphere to be ‘r’.

13. The number of atoms in this HCP unit cells is: [JEE 2008]
(A) 4 (B) 6 (C) 12 (D) 17

14. The volume of this HCP unit cell is: [JEE 2008]
64 3
(A) 24 2r3 (B) 16 2r3 (C) 12 2r3 (D) r
3 3

15. The empty space in this HCP unit cell is: [JEE 2008]
(A) 74% (B) 47.6 % (C) 32% (D) 26%

16. The correct statement(s) regarding defects in solid is (are): [JEE 2009]
(A) Frenkel defect is usually favoured by a very small difference in the sizes of cation and anion.
(B) Frenkel defect is a dislocation defect
(C) Trapping of an electron in the lattice leads to the formation of F-center.
(D) Schottky defects have no effect on the physical properties of solids.

17. The packing efficiency of the two-dimensional square unit cell shown below is: [JEE-2010]

(A) 39.27% (B) 68.02% (C) 74.05% (D) 78.54%

18. The number of hexagonal faces that present in a truncated octahedron is: [JEE-2011]

PHYSICS WALLAH 57
 SOLID STATE
19. A compound MpXq has cubic close packing (ccp) arrangement of X. Its unit cell structure is shown
below. The empirical formula of the compound is: [JEE-2012]

M=
M=

(A) MX (B) MX2 (C) M2X (D) M5X14

20. The arrangement of X– ions around A+ ion in solid AX is given in the figure (not drawn to scale). If the
radius of X– is 250 pm, the radius of A+ is - [JEE-2013]

X-

A+

(A) 104 pm (B) 125 pm (C) 183 pm (D) 57 pm

21. If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of
octahedral holes occupied by aluminum ions and n fraction of tetrahedral holes occupied by magnesium
ions m and n respectively, are: [JEE-2015]
1 1 1 1 1 1 1
(A) , (B) 1, (C) , (D) ,
2 8 4 2 2 4 8

22. The CORRECT statement(s) for cubic close packed (ccp) three-dimensional structure is (are): [JEE-2016]
(A) The number of the nearest neighbours of an atom present in the topmost layer is 12
(B) The efficiency of atom packing is 74%
(C) The number of octahedral and tetrahedral voids per atom are 1 and 2, respectively
(D) The unit cell edge length is 2 2 times the radius of the atom

23. A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If
the density of the substance in the crystal is 8 g cm-3, then the number of atoms present in 256 g of the
crystal is N × 1024. The value of N is [JEE-2017]

24. Consider an ionic solid MX with NaCl structure. Construct a new structure (Z) whose unit cell is
constructed from the unit cell of MX following the sequential instructions given below. Neglect the
charge balance. [JEE-2018]
(i) Remove all the anions (X) except the central one
(ii) Replace all the face centered cations (M) by anions (X)
(iii) Remove all the corner cations (M)
(iv) Replace the central anion (X) with cation (M)
 number of anions 
The value of   in Z is _____.
 number of cations 
PHYSICS WALLAH 58
 SOLID STATE
25. The cubic unit cell structure of a compound containing cation M and anion X is shown below. When
compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s). (2020 Adv.)

(A) The empirical formula of the compound is MX.

(B) The cation M and anion X have different coordination geometries.
(C) The ratio of M–X bond length of the cubic unit cell edge length is 0.866.
(D) The ratio of the ionic radii of cation M to anion X is 0.414.

26. For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only
one face are shown for clarity), the packing fraction is approximately (packing fraction
packing efficiency
= ) (2021 Adv.)
100

(A) 0.74 (B) 0.63 (C) 0.52 (D) 0.48

27. Atom X occupies the fcc lattice sites as well as alternate tetrahedral voids of the same lattice. The
packing efficiency (in %) of the resultant solid is closest to: (2022 Adv.)
(A) 25 (B) 35 (C) 55 (D) 75

28. Atoms of metals x, y and z form face-centred cubic (fcc) unit cell of edge length L x, body-centred cubic
(bcc) unit cell of edge length Ly, and simple cubic unit cell of edge length Lz, respectively. If
3 8 3
rz = ry ; ry = rx ; Mz = M y and M z = 3M x , then the correct statement(s) is(are): [Given: Mx, My,
2 3 2
and Mz are molar masses of metals x, y and z, respectively. rx, ry and rz are atomic radii of metals x, y,
and z, respectively.] (2023 Adv.)
(A) Packing efficiency of unit cell of x > Packing efficiency of unit cell of y > Packing efficiency of unit
cell of z
(B) Ly > Lz
(C) Lx > Ly
(D) Density of x > Density of y

PHYSICS WALLAH 59
 SOLID STATE

EXERCISE #7 (NSEC PYQ)

1. Number of atoms per unit cell for Body Centered Cubic system is: [NSEC-2001]
(A) six (B) four (C) two (D) one

2. Co-ordination number for sodium metal is: [NSEC-2001]

(A) 11 (B) 12 (C) 8 (D) 10

3. Sodium chloride crystallises in a face centred cubic lattice in which each: [NSEC-2003]
(A) sodium ion is tetrahedrally surrounded by 4 chloride ions and each chloride ion is tetrahedrally
surrounded by 4 sodium ions
(B) sodium ion is tetrahedrally by 4 chloride ions and each chloride ion is octahedrally surrounded by 6
sodium ions
(C) sodium ion is octahedrally surrounded by 6 chloride ions and each chloride ion is surrounded by 4
sodium ions
(D) sodium ion is octahedrally surrounded by 6 chloride ions and each chloride ion is octahedrally
surrounded by 6 sodium ions.

4. An element crystallises in a face centered cubic lattice. Hence, its unit cell contains: [NSEC-2004]
(A) 14 atoms of the element and 8 of them belong to the unit cell
(B) 14 atoms of the element and 4 of them belong to the unit cell
(C) 8 atoms of the unit cell and only 1 of them belongs to the cell
(D) 8 atoms of the unit cell and only 2 of them belong to the cell

5. Arsenic is used to dope germanium to obtain [NSEC-2005]

(A) intrinsic semiconductors (B) p-type semiconductors
(C) n-type semiconductors (D) non-conducting germanium.

6. Carborundum is a: [NSEC-2005]
(A) molecular solid (B) covalent solid (C) ionic solid (D) amorphous solid.

7. If a  b  c and  =  = 90°,   90°, the crystal system is called [NSEC-2005]

(A) monoclinic (B) triclinic (C) hexagonal (D) orthorhombic.

8. The number of units cells in 117.0 grams of NaCl is approximately [NSEC-2006]

(A) 12 × 1020 (B) 3 × 1023 (C) 6 × 1023 (D) 1 × 10 24

9. In the unit cell of the crystal formed by the ionic compound of X and Y, the corners are occupied by X
and the centers of the faces by Y. The empirical formula of the compound is : [NSEC-2007]
(A) XY (B) X2Y (C) XY3 (D) X8Y6

10. How many nearest neighbours surround each ion in a face-centered cubic lattice of an ionic crystal?
[NSEC-2008]
(A) 4 (B) 6 (C) 8 (D) 12

11. A match box exhibits: [NSEC-2008]

(A) Cubic geometry (B) Monoclinic geometry
(C) Tetragonal geometry (D) Orthorhombic geometry

PHYSICS WALLAH 60
 SOLID STATE
12. For a face centered cubic lattice, the unit cell content is: [NSEC-2009]
(A) 1 (B) 2 (C) 3 (D) 4

13. Body-centred cubic lattice has a coordination number of : [NSEC-2010]

(A) 8 (B) 10 (C) 6 (D) 4

14. If a  b  c and  =  =  = 90º, the crystal system is: [NSEC-2011]

(A) monoclinic (B) triclinic (C) hexagonal (D) orthorhombic

15. The number of atoms per unit cell and number of the nearest neighbour in a body centred cubic structure
are: [NSEC-2011]
(A) 4, 12 (B) 2, 6 (C) 9, 6 (D) 2, 8

rA+
16. Ionic salt AX grows in face centered cubic lattice with cell length ‘a’. The ratio for this salt will be:
rx−
[NSEC-2014]
(A) 0.155 (B) 0.225 (C) 0.414 (D) 0.732

17. The unit cell of a compound made up of the three elements X, Y and Z is given below.

X
Y
Z
The formula of this compound is: [NSEC-2014]
(A) X2YZ3 (B) XY3Z (C) XYZ3 (D) X3YZ2

18. The metal M crystallizes in a body centered lattice with cell edge 400 pm. The atomic radius of M is.
[NSEC-2015]
(A) 200pm (B) 100pm (C) 173pm (D) 141pm

19. Ice crystallizes in a hexagonal lattice. At ascertain low temperature, the lattice constants are a = 4.53 Å and
c = 7.41 Å. The number of H2O molecules contained in a unit cell (d  0.92 g cm–3 at the given
temperature) is: [NSEC-2015]
(A) 4 (B) 8 (C) 12 (D) 24

20. One mole crystal of a metal halide of the type MX with molecular weight 119 g having face centered
cubic structure with unit cell length 6.58 Å was recrystallized. The density of the recrystallized crystal
was found to be 2.44 g cm–3. The type of defect introduced during the recrystalization is: [NSEC-2015]
(A) additional M+ and X– ions at interstitial sites (B) Schottky defect
(C) F-centre (D) Frenkel defect

21. An ionic solid LaI2 shows electrical conduction due to presence of : [NSEC-2016]
– – – –
2+
(A) La and 2I 3+
(B) La , 2I and e 2+
(C) La , I2 and 2e (D) La , I2 and 3e–
3+

PHYSICS WALLAH 61
 SOLID STATE
22. In a cubic crystal structure, divalent metal-ion is located at the body-centered position, the smaller
tetravalent metal ions are located at each corner and the O2– ions are located half way along each of the
edges of the cube. The number of nearest neighbour for oxygen is: [NSEC-2016]
(A) 4 (B) 6 (C) 2 (D) 8

23. HgO is prepared by two different methods: one shows yellow colour while the other shows red colour.
The difference in colour is due to difference in: [NSEC-2016]
(A) electronic d-d transitions (B) particle size
(C) Frenkel defect (D) Schottkey defect

24. When NiO is doped with a small quantity of Li2O [NSEC-2017]

(A) both cation and anion vacancies are generated (B) Shottky defects are generated
(C) NiO becomes an n-type semiconductor (D) NiO becomes a p-type semiconductor

25. A crystal of KCl containing a small amount of CaCl2 will have: [NSEC-2018]
(A) vacant Cl– sites
(B) vacant K+ sites and a higher density as compared to pure KCl
(C) vacant K+ sites and a lower density as compared to pure KCl
(D) K+ ions in the interstitial sites

26. A scientist attempts to replace a few carbon atoms in 1.0 g of diamond with boron atoms or nitrogen
atoms in separate experiments. Which of the following is correct? [NSEC-2018]
(A) The resulting material with B doping will be an n-type semiconductor
(B) The resulting material with B doping will be an p-type semiconductor
(C) B doping is NOT possible as B cannot from multiple bonds
(D) The resulting material with N doping will be a p-type semiconductor

27. A solid comprises of three types of elements, 'P', 'Q' and 'R'. 'P' forms an FCC lattice in which 'Q' and 'R'
occupy all the tetrahedral voids and half the octahedral voids respectively. The molecular formula of the
solid is: [NSEC-2019]
(A) P2Q2R (B) PQ2R4 (C) P4Q2R (D) P4QR

28. The crystal defect indicated in the diagram below is: [NSEC-2019]

(A) Frenkel defect (B) Schottky defect

(C) Frenkel and Schottky defects (D) Interstitial defect

PHYSICS WALLAH 62
 SOLID STATE
29. The unit cell structure of a mineral perovskite crystallizes in cubic unit cell wherein calcium (filled
circles) and oxide (hollow circles) constitute a cubic close packing (ccp) arrangement and titanium ion
(hollow square) occupies an interstitial hole as shown below. (Charges are omitted for simplicity). The
empirical formula of this compound is: [NSEC-2022]

(A) Ca2TiO3 (B) Ca4TiO6 (C) CaTiO3 (D) Ca8TiO6

30. Read carefully all the three statements on defects in solids: [NSEC-2022]
−
(i) In Frenkel defect, interstitial Ag site is surrounded tetrahedrally by four Cl ions and four Ag+ ions,
+

where interstitial Ag+ and Cl− interaction is covalent

(ii) Addition of small amount of SrCl2 in NaCl yields solid solution with a formula of Na1−2x SrxVNaxCl,
where V= valency
(iii) In general, Schottky defect increases the density of the substance
Choose the correct alternative(s):
(A) Statement (i) is correct (B) Statements (ii) and (iii) are correct
(C) Statements (i) and (ii) are correct (D) Statements (i) and (iii) are correct

PHYSICS WALLAH 63
 SOLID STATE

Answer Key
Do yourself-1
1. (B) 2. (C) 3. (D) 4. (C)
5. (A)-(q); (B)-(p); (C)-(s); (D)-(r) 6. (A) 7. (B)
8. (C) 9. (C)

Do yourself-2
1. (C) 2. (B) 3. (D) 4. (A)
5. (D) 6. (D)

Do yourself-3
1. (C) 2. (A) 3. (D) 4. (C)
5. (A) 6. (A) 7. (A) 8. (C)

Do yourself -4
1. (D) 2. (B) 3. (A) 4. (D)
5. (D) 6. (D) 7. (A,B,D)

EXERCISE #1

1. Ionic – LiBr, (NH4)3PO4; Metallic – Brass, Rb; Molecular – P4O10, 2, P4

Network – SiC, Graphite, Si, Amorphous – Plastic
2. 14
3. Crystal System Features Unit cell found Examples
Monoclinic abc S, EC Monoclinic sulphur, PbCrO4 ,
α = γ = 90°; Na2SO4.10H2O, Na2B4O7.10H2O.
β  120°,  90°,  60°
Hexagonal a=bc S Graphite, ZnO, CdS, Mg, PbI2, SiC.
α = β = 90°, γ = 120°
Triclinic abc S K2Cr2O7, CuSO4.5H2O, H3BO3.
α  β  γ  90°
4. (a) 267 pm, (b) 231.2 pm, (c) 188.8 pm
5. Ques. (a) (b) Total particles
(i) 1/4 1 2
(ii) 1/2 1/4 2
(iii) 1/6 1/2 2
(iv) 1/6 – 1/2
(v) 1/3 1/6 1
6. 438.5 pm, 219.25 pm
2  4 2R
7. Perimeter of plane is = 2C + 8R = + 8R = 6.437 R
3
8. 8 9. 5.74 g cm–3 10. 41.67 g cm–3 11. 19.4g/cm3, 143.9 pm
12. 1.09 13. 3.48 × 1024 atoms 15. 7.922 g/cc, 8.625 g/cc
a a
16. 5 (ABO3) 17. 86.6% 18. 4, 8, , 19. 4, 6, 8
2 2

PHYSICS WALLAH 64
 SOLID STATE
20. A, B 21. A2BC 22. ZnAl2O4 23. 267 pm, 534 pm, 378 pm
24. (6) 25. 30% 27. 4
28. a =5.94×10–8cm, V=2.096 × 10–22 cm–3 29. 1.81Å 30. 4.34 Å

31. 15.05 32. 6.02 × 1018 33. 0.24 34. 8

EXERCISE #2

1. 3.5 g cm–3 2. 60%, +4 3. 103.4 pm, No 4. 0.7285

5. 0.605 6. (a) 1.143, (b) 1.172
7. (a) MnF3, (b) 6, (c) 4.02Å 8. 4 molecules of H2O
3
9. (a) 4.5 Å, (b) 5.2 Å, (c) 8, (d) 6, (e) 0.92 g/cm
10. Not Available 11. Mn3Si1, Si at corners and Mn at face centre
12. Mg2SiO4, Fe2SiO4, 66.32% 13. 2 14. 2.07
15. (a)

= Cu

=O

= Ba

=Y

c
b

a
(b) density = 5.90 g cm–3

EXERCISE #3

1. (B) 2. (C) 3. (A) 4. (D)

5. (C) 6. (D) 7. (B) 8. (B)
9. (C) 10. (C) 11. (A) 12. (A)
13. (B) 14. (A) 15. (A) 16. (C)
17. (C) 18. (C) 19. (A) 20. (B)
21. (C) 22. (B) 23. (C) 24. (C)
25. (B) 26. (A) 27. (A) 28. (B)
29. (A) 30. (C) 31. (D) 32. (B)
33. (A) 34. (D) 35. (B)

PHYSICS WALLAH 65
 SOLID STATE

EXERCISE #4
1. (C) 2. (B) 3. (D) 4. (A,C)
5. (BC) 6. (ABD) 7. (ABCD) 8. (ABCD)
9. (B) 10. (D) 11. (C) 12. (B)
13. (D) 14. (A) 15. (C) 16. (A)
17. (A)→P,Q; (B)→P,S; (C)→P,R; (D)→P 18. (A)→R,S; (B)→P,Q,R,S; (C)→Q
19. (A) 20. (B)

EXERCISE #5 (JEE MAIN)

1. (C) 2. (B) 3. (B) 4. (C)
5. (C) 6. (A) 7. (A) 8. (A)
9. (C) 10. (B) 11. (A) 12. (C)
13. (C) 14. (A) 15. (A) 16. (B)
17. (B) 18. (C) 19. (C) 20. (C)
21. (A) 22. (D) 23. (B) 24. (B)
25. (A) 26. (B) 27. (C) 28. (C)
29. (D) 30. (D) 31. (C) 32. (A)
33. (D) 34. (D) 35. (B) 36. (C)
37. (C) 38. (43) 39. (1) 40. (3)
41. (85) 42. (22) 43. (87) 44. (512 or 566)
45. (8) 46. (9077) 47. (1) 48. (15)
49. (5) 50. (8) 51. (106) 52. (33)
53. (1) 54. (D) 55. (4) 56. (A)
57. (36)

EXERCISE #6 (JEE ADVANCED)

1. (1.259)
2.

3. (D) 4. (True) 5. (A) 6. (A)

7. (18)
8. (i) = 5 kg m–3
(ii) There is huge difference in theoretically calculated density and observed density. It is only
possible if some foreign species occupies interstitial space i.e. substitution defect.
9. (117.1 pm) 10. (B) 11. (216.5 pm)
12. (A)-P,S; (B)-P,Q; (C)-Q; (D)-Q,R 13. (B) 14. (A)
15. (D) 16. (B,C) 17. (D) 18. (8)
19. (B) 20. (A) 21. (A) 22. (B,C,D)
23. (2) 24. (C) 25. (A,C) 26. (B)
27. (B) 28. (A,B,D)

PHYSICS WALLAH 66
 SOLID STATE

EXERCISE #7 (NSEC PYQ)

1. (C) 2. (C) 3. (D) 4. (B)
5. (C) 6. (B) 7. (A) 8. (B)
9. (C) 10. (D) 11. (D) 12. (D)
13. (A) 14. (D) 15. (D) 16. (B)
17. (C) 18. (C) 19. (C) 20. (B)
21. (B) 22. (C) 23. (B) 24. (D)
25. (C) 26. (B) 27. (A) 28. (B)
29. (C) 30. (A,C)

PW Web/App - https://smart.link/7wwosivoicgd4
Library- https://smart.link/sdfez8ejd80if

PHYSICS WALLAH 67
 Lakshya JEE (2025)
Solid State
Revision Practice Sheet

1. Most crystals show good cleavage because their 8. The axial angles in triclinic crystal system are
atoms, ions or molecules are (1) α = β = γ = 90°
(1) weakly bonded together. (2) α = γ = 90°, β  90°
(2) strongly bonded together. (3) α  β  γ  90°
(3) spherically symmetrical. (4) α = β = γ  90°
(4) arranged in planes.
9. In a tetragonal crystal,
2. Which of the following is the only incorrect (1) α = β = 90°  γ; a = b = c
statement regarding amorphous solids? (2) α = β = γ = 90°; a = b  c
(1) On heating, they may become crystalline at (3) α = β = γ = 90°; a  b  c
some temperature. (4) α = β = 90°; γ = 120°; a = b  c
(2) They may become crystalline when kept for a
long time. 10. Which of the following crystalline arrangement
will have at least one of the angles equal to 90° and
(3) Amorphous solids can be moulded by heating.
at least two axial lengths equal?
(4) They are anisotropic in nature.
(1) Orthorhombic (2) Rhombohedral
(3) Monoclinic (4) Tetragonal
3. Constituent particles in quartz are bonded by
(1) electrovalent bonds 11. An element occurring in the body-centred cubic
(2) covalent bonds (BCC) structure has 1.208 × 1023 unit cells. The
(3) van der Waals forces total number of atoms of the element in these cells
(4) metallic bonds will be
(1) 2.416 × 1023 (2) 3.618 × 1023
22
4. Which of the following is an example of metallic (3) 6.04 × 10 (4) 1.208 × 1023
crystal solid?
(1) C (2) Si 12. An alloy of copper, silver and gold is found to have
(3) W (4) AgCl copper constituting the face-centred cubic (FCC)
lattice. If silver atoms occupy the edge centres and
gold is present at body centre, the alloy has a
5. The particles would be stationary in a lattice only at
formula
(1) 0°C (2) 0 K
(1) Cu4Ag2Au (2) Cu4Ag4Au
(3) 298 K (4) 273 K (3) Cu4Ag3Au (4) CuAgAu

6. The unit cell of highest symmetry is 13. In a solid AB, having the NaCl structure, A atoms
(1) cubic occupy the corners of the cubic unit cell. If all the
(2) triclinic face-centred atoms along one of the axes are
(3) hexagonal removed, then the resulting stoichiometry of the
(4) monoclinic solid is
(1) AB2 (2) A2B
7. In a crystal, the constituent particles are located at (3) A4B3 (4) A3B4
the position of
(1) zero potential energy. 14. Metallic gold crystallizes in FCC lattice with edge-
length 4.07 Å. The closest distance between gold
(2) infinite potential energy.
atoms is
(3) minimum potential energy.
(1) 3.525 Å (2) 5.714 Å
(4) maximum potential energy.
(3) 2.857 Å (4) 1.428 Å
 2

15. Sodium metal crystallizes in BCC lattice with the 23. The low density of alkali metals is due to
cell edge a = 4.29 Å. What is the radius of the (1) their BCC structure in which about 32% of the
sodium atom? available space is unfilled.
(1) 1.86 Å (2) 2.15 Å (2) their HCP structure in which about 74% of the
(3) 4.29 Å (4) 2.94 Å available space is unfilled.
(3) their cubic close packed (CCP) structure in
16. Potassium has BCC structure with nearest which about 74% of the available space is
neighbour distance (2.5 × 3 ) Å. Its density will unfilled.
be (K = 39, NA = 6 × 1023) (4) their BCC structure in which about 47% of the
(1) 1.040 kg/m3 available space is unfilled.
(2) 104 kg/m3
(3) 520 kg/m3 24. A metallic element crystallizes into a lattice
(4) 1040 kg/m3 containing a sequence of layers of ABABAB….
Any packing of spheres leaves out voids in the
17. The packing fraction in simple cubic lattice is lattice. Approximately what percentage by volume
1 2 of this lattice is empty space?
(1)  (2) 
6 6 (1) 74% (2) 26%
3 1 (3) 48% (4) 32%
(3)  (4) 
8 2
25. Which one of the following schemes of ordering
18. The packing fraction in BCC lattice is close packed sheets of equal-sized spheres do not
generate closest packed lattice?
1 2
(1)  (2)  (1) ABACABAC…. (2) ABCBCABC….
6 6
(3) ABCABC…. (4) ABBAA….
3 3
(3)  (4) 
8 2 26. Which of the following void is smallest in close
packing?
19. The packing fraction in FCC lattice is
(1) Tetrahedral (2) Octahedral
1 2 (3) Cubic (4) Square
(1)  (2) 
6 6
3 2 27. In an FCC arrangement of metallic atoms, what is
(3)  (4) 
8 3 the relative ratio of the ideal sizes of tetrahedral and
octahedral voids?
20. In a BCC packing, the nearest neighbours lie along (1) 0.543 (2) 0.732
the (3) 0.414 (4) 0.637
(1) edges of the cube.
(2) face diagonal. 28. Atoms of the element ‘A’ form HCP and atoms of
(3) line joining the two opposite corners of the element ‘C’ occupy only two-third of octahedral
face. voids in it, then the general formula of the
(4) cube diagonal. compound is
(1) CA (2) CA2
21. The number of carbon atoms per unit cell of
(3) C2A3 (4) C3A2
diamond is
(1) 4 (2) 6
29. A solid has three types of atoms, such as X, Y and
(3) 8 (4) 12
Z. ‘X’ forms a FCC lattice with ‘Y’ atoms
22. The number of closest neighbours of a carbon atom occupying all the tetrahedral voids and ‘Z’ atoms
in graphite is occupying half the octahedral voids. The simplest
(1) 2 (2) 3 formula of solid is
(3) 4 (4) 8 (1) X2Y4Z (2) XY2Z4
(3) X4Y2Z (4) X4YZ2
 3

30. The ionic radii of Rb+ and I− are 1.46 and 2.16 Å, 36. A solid contains An+ and Bm− ions. The structure of
respectively. The most probable type of structure solid is FCC for Bm− ions and An+ ions are present
exhibited by it is in one-fourth of the tetrahedral voids as well as in
(1) CsCl type one-fourth of octahedral voids. What is the
(2) NaCl type simplest formula of solid?
(3) ZnS type (1) A3B4 (2) A4B3
(4) CaF2 type (3) AB2 (4) A2B

31. For an ideal ionic crystal, the simplest formula is 37. An ionic solid is HCP of Q2− ions and Px+ ions are
AX and the coordination number of cation is 6. The in half of the tetrahedral voids. The value of x
value of radius ratio (r + : r − ) should be
A X
(1) must be greater than 0.732. (1) 1 (2) 2
(3) 4 (4) ½
(2) must lie in between 0.732 and 0.414.
(3) must lie in between 0.414 and 0.225.
38. Sapphire is aluminium oxide. Aluminium oxide
(4) must be less than 0.414.
crystallizes with aluminium ions in two-third of the
octahedral voids in the closest packed array of oxide
32. In the zinc blend structure (ZnS), S2− adopts CCP
ions. What is the formula of aluminium oxide?
arrangement and Zn2+ occupies
(1) Al2O3 (2) AlO2
(1) all octahedral voids.
(3) Al3O4 (4) Al3O2
(2) only 50% of octahedral voids.
(3) only 50% of tetrahedral voids.
39. BaO has a rock salt type structure. When subjected
(4) all tetrahedral voids.
to high pressure, the ratio of the coordination
number of Ba2+ ion to O2− ion changes to
33. A binary solid (A+ B−) has a rock salt structure. If
(1) 4 : 8 (2) 8 : 4
the edge length is 400 pm and the radius of cation (3) 8 : 8 (4) 4 : 4
is 75 pm, then the radius of anion is
(1) 100 pm 40. Which of the following defect, if present, lowers
(2) 125 pm the density of the crystal?
(3) 250 pm (1) Frenkel
(4) 325 pm (2) Schottky
(3) Metal excess defect due to excess cation.
34. CsBr has cubic structure with edge length 4.3 Å. (4) Interstitial defect.
The shortest inter ionic distance in between Cs+ and
Br− is 41. Schottky defect appears in
(1) 3.72 Å (2) 1.86 Å (1) NaCl (2) CsCl
(3) 7.44 Å (4) 4.3 Å (3) AgBr (4) All of these

35. In Na2O structure, 42. The yellow colour of ZnO and conducting nature
(1) O2– ions constitute CCP and Na+ ions occupy produced in heating is due to
all the octahedral holes. (1) metal excess defects due to interstitial cation.
(2) O2– ions constitute CCP and Na+ ions occupy (2) extra positive ions present in an interstitial site.
all the tetrahedral holes. (3) trapped electrons.
(4) All of these
(3) O2– ions constitute CCP and Na+ ions occupy
50% of tetrahedral holes and 100% octahedral
43. The presence of excess sodium in sodium chloride
holes.
makes the crystal appearance yellow. This is due to
(4) Na+ ions constitute CCP and O2– ions occupy
the presence of
half of octahedral holes.
(1) Schottky defect (2) Frenkel defect
(3) F-centres (4) interstitial defects
 4

44. The composition of a sample of cuprous oxide is 52. Which of the following arrangement shows
found to be Cu1.92O1.00 due to metal deficient schematic alignment of magnetic moments of anti-
defect. The molar ratio of Cu2+ and Cu+ ions in the ferromagnetic substances?
crystal is (1)
(1) 4 : 5 (2) 1 : 12.5
(2)
(3) 1 : 23 (4) 1 : 24
(3)
45. NaCl is doped with 2 × 10–3 mole % SrCl2, the
(4)
concentration of cation vacancies is (NA = 6 × 1023)
(1) 6.0 × 1018 mol−1 (2) 1.20 × 1019 mol−1
One or More Than One Correct Type Question
(3) 3.0 × 1018 mol−1 (4) 1.20 × 1021 mol−1 53. Which of the following is/are amorphous solid(s)?
(1) NaCl
46. The intrinsic or thermodynamic defect is (2) CaF2
(1) Schottky defect (3) Glass
(2) metal excess defect due to excess cation. (4) Plastic
(3) metal excess defect due to anion vacancy.
(4) metal-deficient defect. 54. Which of the following has face-centred Bravais
lattice?
47. The only incorrect effect on density by the given (1) Hexagonal
defect in solids is (2) Monoclinic
(1) density must decrease by vacancy defect. (3) Cubic
(2) density must increase by interstitial defect. (4) Orthorhombic
(3) density must increase by impurity defect.
55. If the height of HCP unit cell of identical particles
(4) density does not change by dislocation defect.
is h, then the height of tetrahedral voids from the
base is
48. Which of the following is a ferromagnetic substance?
3h 5h h 2h
(1) Fe2O3 (2) Cr2O3 (1) , (2) ,
8 8 3 3
(3) Fe3O4 (4) CrO2
h 3h h 7h
(3) , (4) ,
4 4 8 8
49. Which of the following acts as a superconductor at
4 K? 56. The correct information regarding a solid element
(1) He (2) Cu (atomic radius = r) having ABCABC… type
(3) K (4) Mg packing (FCC unit cell edge length = a) is
(1) the distance between nearest octahedral and
50. Superconductors are substances which 3a
(1) conduct electricity at low temperatures. tetrahedral void is .
4
(2) conduct electricity at high temperature. (2) the distance between two nearest octahedral
(3) offer very high resistance to the flow of current. a
(4) offer no resistance to the flow of current. void is .
2
(3) the distance between two nearest tetrahedral
51. Addition of arsenic in small amount to pure
3a
germanium will result in the formation of void is .
2
(1) n-type semiconductor
(4) the distance between successive A and B
(2) germanium arsenide
2
(3) p-type semiconductor layers is 2r. .
3
(4) a superconducting alloy
 5

57. Which of the following information(s) is/are (4) B2+ ions form CCP, C3– ions occupy all the
incorrect regarding the voids formed in three tetrahedral voids and A+ ions occupy all the
dimensional HCP of identical spheres? octahedral voids.
(1) A tetrahedral void is formed when a sphere of
the second layer is present above the triangular 61. Potassium hexachloroplatinate (IV), K2[PtCl6]
void of the first layer. adopts anti-fluorite crystal structure. Which of the
(2) All the triangular voids are not covered by the following information is correct about ideal
spheres of the second layer. K2[PtCl4] crystal?
(3) Tetrahedral voids are formed when the (1) K+ ions occupy all the tetrahedral voids.
triangular voids in the second byer lie above (2) The unit cell is FCC with respect to PtCl62− ions.
the triangular voids in the first linyer and the (3) The coordination number of PtCl62− ions is 4.
triangular shapes of these voids do not overlap (4) The coordination number of PtCl62+ ions is 8.
(4) Octahedral voids are formed when the
triangular voids in the second layer exactly 62. In each of the following ionic solids, the
overlap with similar voids in the first layer. coordination number of the cation and anion is
same, except
58. Which of the following statement(s) is/are correct (1) MgO
with respect to zinc blende structure?
(2) CaF2
(1) Zn2+ ions are present at the comers and at the
(3) Al2O3
centres of each face.
(4) CsCl
(2) Only alternate tetrahedral holes are occupied
by Zn2+ ions.
63. Which of the following statement(s) is/are
(3) The coordination number of Zn2+ and S2– is 4
incorrect regarding the defects in solids?
each.
(1) AgBr crystal show both Schottky and Frenkel
(4) The number of ZnS units in a unit cell is 4.
defect.
59. In a sodium chloride crystal, the unit cell edge (2) Impurity defect by doping of arsenic in silicon
length is a. The option(s) representing the correct results 'n'-type semiconductor.
combination is/are (3) Doping in crystal introduces dislocation
defect.
Options Nearest Ion Distance Number
(4) Metal deficient defect can occur with extra
neighbour from Na+ of ions
anion present in the interstitial voids.
of Na+ ion ion

(1) 2nd Na+ 0.707 a 12 64. Which of the following is/are correct statement(s)
about Fe3O4 crystal?
(2) 3rd Cl– 0.866 a 8 (1) Fe2+ ions occupy octahedral voids only.
(3) 4th Na+ a 6 (2) Fe3+ ions occupy tetrahedral voids only.
(3) Fe3+ ions occupy octahedral as well as
(4) 5th Cl– 1.12 a 24 tetrahedral voids.
(4) O2– ions are present at the corner as well as the
60. An ionic compound consists of only A+, B2+ and centre of alternate faces.
C3– ions. Which of the following option(s) is/are
(1) C3– ions form CCP, A+ ions occupy all 65. Which of the following statement(s) is/are true
octahedral voids and B2+ ions occupy half of regarding the electrical properties of solids?
the tetrahedral voids. (1) (Conductivity) metals << (Conductivity)
(2) B2+ ions form HCP, A+ ions occupy all insulators < (Conductivity) semiconductors.
octahedral voids and C3– ions occupy half of (2) Depending upon the temperature, THO3 can
the tetrahedral voids. behave as insulator or conductor.
(3) A+ ions occupy alternate corners of a simple (3) I2(s) is non-conducting.
cube, B2+ ions occupy the other corners of the (4) n-type semiconductor will have conductivity
cube and C3– ions occupy body centre of the less than pure semiconductor.
cube.
 6

66. Which of the following oxides behave as a 73. A metal (atomic mass = 75) exist in BCC structure.
conductor or an insulator depending on If the uncovered distance between the atoms along
temperature? the edge is equal to 67 pm, then the density of
(1) TiO (2) SiO2 crystal (in g/ cm3) is (NA = 6 × 1023, 3 = 1.732)
(3) TiO3 (4) VO
PREVIOUS YEAR QUESTION MAINS
Integer Type Question 74. Select the correct statements.
67. Methane crystallizes in a cubic unit cell with edge (A) Crystalline solids have long range order.
(B) Crystalline solids are isotropic
length 0.6 nm. The density of solid CH4 is only
(C) Amorphous solids are sometimes called
slightly greater than the density of liquid CH4. If
Pseudo solids
the density of liquid CH4 is 0.5 g/cm3, then the (D) Amorphous solids soften melt over a range of
number of CH4 molecules per unit cell is temperatures
(E) Amorphous solids have a definite heat of
68. Ice crystallizes in a hexagonal lattice. At low fusion.
temperatures at which the structure was determined, Choose the most appropriate answer from the
the lattice constants were a = 4.53 Å and b = 7.41 option given below.
Å as shown in the figure. How many H2O (1) (A), (C), (D) only
molecules are contained in an unit cell? (2) (C), (D) only
(Given that density of ice = 0.92 g/cm3) (3) (B), (D) only
(4) (A), (B), (E) only

75. The one that is extensively used as a piezoelectric

material is
(1) Tridymite (2) Amorphous silica
(3) Quartz (4) Mica

76. A cubic solid is made up of two elements X and Y.

69. X-ray diffraction analysis of crystalline C60
Atoms of X are present on every alternate corner
(Buckminsterfullerene) shows that the crystal
1
structure at 300 K can be regarded as FCC with a and one at the center of cube. Y is at of the total
3
one-molecule basis and unit cell edge length of 2
faces. The empirical formula of the compound is
nm. The molecules are orientationally disordered
(1) X2Y1.5 (2) X2.5Y
due to rotation. The centre-to-centre distance (in
(3) XY2.5 (4) X1.5Y2
nm) between the nearest neighbour C60 molecules
in the solid at 300 K is 77. Which of the following expressions is correct in
case of a CsCl unit cell (edge length ‘a’)?
70. KF crystallizes in the NaCl type structure. If the a
(1) r + + r − = (2) rCs + + rCl− = a
186 214 Cs Cl
radius of K+ ion is pm and F– ion is pm , 2
2 2 3 a
(3) r +r = (4) r * + r − =
then what is the shortest distance between K+ – K+ Cs + Cl− 2 Cs Cl 2
ions (in Å)?
78. Iron oxide FeO, crystallises in a cubic lattice with
71. A metal ‘M’ (atomic mass = 31.25) crystallizes in a unit cell edge length of 5.0Å. If density of the FeO
CCP but it has some vacancy defect. If the edge in the crystal is 4.0 g cm–3, then the number of FeO
length of the unit cell is 500 pm and the density of units present per unit cell is ________.
the metal is 1.6075 g/cm3, then the number of (Nearest Integer)
moles of metal atoms missing per litre of the crystal (Given:
is (1 amu = 1.67 × 10−24 g) Molar mass of Fe and O is 56 and 16 g mol–1
respectively.)
NA = 6.0 × 1023 mol–1
72. The number of hexagonal faces that are present in
a truncated octahedron is Z = 4.166  4
 7

79. Sodium metal crystallizes in a body centred cubic 87. In a solid AB, A atoms are in ccp arrangement and
lattice with unit cell edge length of 4Å. The radius B atoms occupy all octahedral sites.
of sodium atom is × 10–1 Å (Nearest Integer) If two atoms from the opposite faces are removed,
then the resultant stoichiometry of the compound is
80. The parameters of the unit cell of a substance are a AxBy. The value of x is ________ (Nearest Integer)
= 2.5, b = 3.0, c = 4.0, α = 90°, β = 120° and γ =
90°. The crystal system of the substance is 88. Metal M crystallizes into a fcc lattice with the edge
(1) Monoclinic (2) Hexagonal
length of 4.0 × 10–8 cm. The atomic mass of the
(3) Orthorhombic (4) Triclinic
metal is ________ g / mol. (Nearest Integer)
81. In a binary compound, atoms of element A form a (Use: NA = 6.02 × 1023 mol–1, density of metal,
hcp structure and those of element M occupy 2/3 of M = 9.03 g cm–3).
the tetrahedral voids of the hcp structure. The
formula of the inary compound is 89. A copper complex crystallising in a CCP lattice
(1) M2A3 (2) MA3 with a cell edge of 0.4518 nm has been revealed by
(3) M4A (4) M4A3 employing X-ray diffraction studies. The density of
a copper complex is found to be 7.62 g cm–3. The
82. The coordination number of an atom in a body molar mass of copper complex in g mol–1 is
centred cubic structure is _________. (Nearest Integer)
[Assume that the lattice is made up of atoms] (Given : NA = 6.022 × 1023 mol–1)

83. An element has a face-centred cubic (fcc) structure

90. Diamond has a three dimensional structure of C
with a cell edge of a. The distance between the
atoms formed by covalent bonds. The structure of
centres of two nearest tetrahedral voids in the
diamond has face centred cubic lattice where 50%
lattice is:
(1) a/2 (2) a of the tetrahedral voids are also occupied by carbon
(3) 3a/2 (4) 2a atoms The number of carbon atoms present per unit
cell of diamond is _________.
84. A compound is formed by two elements X and Y.
The element Y forms cubic close packed 91. A solid having density of 9 × 103 kg m–3 forms face
arrangement and those of element X occupy one centred cubic crystal of edge length 200 2 pm.
third of the tetrahedral voids. What is the formula What is the molar mass of the solid?
of the compound?
[Avogadro constant ≅ 6 × 1023 mol–1, π ≅ 3]
(1) X2Y3 (2) X3Y
(1) 0.0432 kg mol–1 (2) 0.0216 kg mol–1
(3) X3Y (4) XY3
(3) 0.0305 kg mol–1 (4) 0.4320 kg mol–1
85. The correct relationship between unit cell edge
length ‘a’ and radius of sphere ‘r’ for face–centred 92. Consider the bcc unit cells of the solids 1 and 2 with
and body centred cubic structures respectively are: the position of atoms as shown below. The radius
of atom B is twice that of atom A. The unit cell
(1) r = 2 2a and 3r = 4a
edge length is 50% more in solid 2 than in 1. What
(2) r = 2 2a and 4r = 3a is the approximate packing efficiency in solid 2?
(3) 2 2r = a and 4r = 3a
(4) 2 2r = a and 3r = 4a

86. An atomic substance A of molar mass 12 g mol–1

has a cubic crystal structure with edge length of 300
pm. The no. of atoms present in one unit cell of A
(1) 45% (2) 65%
is _____. (Nearest Integer)
(3) 90% (4) 75%
Given the density of A is 3.0 g mL–1 and NA = 6.02
× 1023 mol–1
 8

93. Which of the following represents the lattice 96. Given below are two statements:
structure of A 0.95 Ocontaining A2+, A3+ and O2– Statement-I: Frenkel defects are vacancy as well
ions? as interstitial defects.
Statement-II: Frenkel defect leads to colour in
ionic solid due to presence of F-centres.
Choose the most appropriate answer for the
(A) statements from the option given below.
(1) Both statement-I and Statement-II are true
(2) Statement-I is false but Statement-II is true
(3) Both statement-I and Statement-II are false
(4) Statement-I is true but statement-II is false

97. KBr is doped with 10–5 mole percent of SrBr2. The

(B) number of cationic vacancies in 1 g of KBr crystal
is _________1014.
(Round off the Nearnest Integer.)
(Atomic mass : K : 39.1 u, Br : 79.9 u,
NA = 6.023 × 1023)

98. Which of the following compounds is likely to

show both Frenkel and Schottky defects in its
(C) crystalline form?
(1) CsCl (2) KBr
(3) AgBr (4) ZnS

(1) B and C only (2) B only 99. Given below are two statements.
(3) A and B only (4) A only Statement-I: O2, Cu2+, and Fe3+ are weakly
attracted by magnetic field and are magnetized in
94. When Fe0.93O is heated in presence of oxygen, it the same direction as magnetic field.
converts to Fe2O3. The number of correct Statement-II: NaCl and H2O are weakly
statement/s from the following is _________. magnetized in opposite direction to magnetic field.
(1) The equivalent weight of Fe0.93O is In the light of the above statements, choose the
Molecular weight most appropriate answer from the options given
.
0.79 below.
(2) The number of moles of Fe2+ and Fe3+ in 1 (1) Both Statement-I and Statement-II are correct.
mole of Fe0.93O is 0.79 and 0.14 respectively. (2) Both Statement-I and Statement-II are incorrect.
(3) Fe0.93O is metal deficient with lattice (3) Statement-I is correct but Statement-II is
comprising of cubic closed packed incorrect.
arrangement of O2– ions. (4) Statement-I is incorrect but Statement-II is
(4) The % composition of Fe2+ and Fe3+ in correct.
Fe0.93O is 85% and 15% respectively.
PREVIOUS YEAR QUESTION ADVANCE
95. The incorrect statement about the imperfections in
100. Silver (atomic weight = 108 g mol–1) has a density
solid is:
(1) Schottky defect decreases the density of the of 10.5 g cm–3. The number of silver atoms on a
substances. surface of area 10–12 m2 can be expressed in
(2) Interstitial defect increases the density of the scientific notation as y × 10x. The value of x is
substance.
(3) Frenkel defect does not alter the density of the 101. The number of hexagonal faces that are present in
substance. a truncated octahedron is
(4) Vacancy defect increases the density of the
substance.
 9

102. The arrangement of X– ions around A+ ion in solid

AX is given in the figure (not drawn to scale). If
the radius of X– is 250 pm, the radius of A+ is

(1) 104 pm (2) 125 pm

(3) 183 pm (4) 57 pm (1) The empirical formula of the compound is
MX.
103. If the unit cell of a mineral has cubic close packed (2) The cation M and anion X have different
(ccp) array of oxygen atoms with m fraction of coordination geometries.
octahedral holes occupied by aluminium ions and (3) The ratio of M–X bond length of the cubic unit
n fraction of tetrahedral holes occupied by cell edge length is 0.866.
magnesium ions, m and n respectively, are (4) The ratio of the ionic radii of cation M to anion
1 1 1 X is 0.414.
(1) , (2) 1,
2 8 4
108. Atoms of metals x, y and z form face-centred cubic
1 1 1 1
(3) , (4) , (fcc) unit cell of edge length Lx, body-centred cubic
2 2 4 8
(bcc) unit cell of edge length Ly, and simple cubic
104. The correct statement(s) for cubic close packed unit cell of edge length Lz, respectively.
(ccp) three dimensional structure is (are) 3 8 3
If rz = ry ;ry = rx ;M z = M y and Mz =
(1) The number of the nearest neighbours of an 2 3 2
atom present in the topmost layer is 12 3Mx, then the correct statement(s) is (are)
(2) The packing efficiency of atom is 74% [Given : Mx, My and Mz are molar masses of metals
(3) The number of octahedral and tetrahedral
x, y and z, respectively.
voids per atom are 1 and 2, respectively
rx, ry and rz are atomic radii of metals x, y and z,
(4) The unit cell edge length is 2 2 times the respectively.]
radius of the atom (1) Packing efficiency of unit cell of x > Packing
efficiency of unit cell of y > Packing
105. A crystalline solid of a pure substance has a face- efficiency of unit cell of z.
centred cubic structure with a cell edge of 400 pm. (2) Ly > Lz
If the density of the substance in the crystal is
(3) Lx > Ly
8 g cm–3, then the number of atoms present in
(4) Density of x > Density of y
256 g of the crystal is N × 1024. The value of N is
109. Atom X occupies the fcc lattice as well as alternate
106. Consider an ionic solid MX with NaCl structure. tetrahedral voids of the same lattice. The packing
Construct a new structure (Z) whose unit cell is efficiency (in %) of the resultant solid is closest to
constructed from the unit cell of MX following the (1) 25 (2) 35
sequential instruction given below. Neglect the (3) 55 (4) 75
charge balance.
(i) Remove all the anions (X) except the central 110. For the given close packed structure of a salt made
one of cation X and anion Y shown below (ions of only
(ii) Replace all the face centered cations (M) by one face are shown for clarity), the packing fraction
anions (X) is approximately
(iii) Remove all the corner cations (M) Packing efficiency
(iv) Replace the central anion (X) with cation (M) (Packing fraction = )
100
 Number of anions 
The value of   in Z is ____
 Number of cations 

107. The cubic unit cell structure of a compound

containing cation M and anion X is shown below.
When compared to the anion, the cation has smaller
ionic radius. Choose the correct statement(s). (1) 0.74 (2) 0.63
(3) 0.52 (4) 0.48
 ANSWER KEY
1. (4) 38. (1) 75. (2)
2. (4) 39. (3) 76. (*)
3. (2) 40. (2) 77. (2)
4. (2) 41. (4) 78. (4)
5. (2) 42. (3) 79. (17)
6. (1) 43. (2) 80. (1)
7. (3) 44. (2) 81. (4)
8. (3) 45. (2) 82. (8)
9. (2) 46. (1) 83. (1)
10. (4) 47. (2) 84. (1)
11. (1) 48. (4) 85. (2)
12. (3) 49. (1) 86. (4)
13. (4) 50. (4) 87. (3)
14. (2) 51. (1) 88. (87)
15. (1) 52. (4) 89. (106)
16. (4) 53. (3, 4) 90. (8)
17. (1) 54. (3, 4) 91. (2)
18. (3) 55. (1, 4) 92. (2)
19. (2) 56. (1, 2, 4) 93. (4)
20. (4) 57. (3, 4) 94. (4)
21. (3) 58. (2, 3, 4) 95. (4)
22. (2) 59. (1, 2, 3, 4) 96. (2)
23. (1) 60. (1, 2) 97. (5)
24. (2) 61. (1, 2, 4) 98. (2)
25. (4) 62. (2, 3) 99. (1)
26. (1) 63. (3) 100. (7)
27. (1) 64. (1, 3) 101. (8)
28. (2) 65. (2, 3) 102. (1)
29. (1) 66. (3, 4) 103. (1)
30. (2) 67. (4) 104. (2, 3, 4)
31. (2) 68. (4) 105. (2)
32. (2) 69. (1) 106. (3)
33. (2) 70. (4) 107. (1, 3)
34. (1) 71. (2) 108. (1, 2, 4)
35. (2) 72. (8) 109. (2)
36. (1) 73. (2) 110. (2)
37. (2) 74. (1)

PW Web/App - https://smart.link/7wwosivoicgd4
Library- https://smart.link/sdfez8ejd80if