218 Solid state

35. (b) LiF is an example of ionic crystal solid, in which constituent

particles are positive (Li  ) and negative (F  ) ions.
36. (a) Amorphous solids neither have ordered arrangement (i.e. no
definite shape) nor have sharp melting point like crystals, but
when heated, they become pliable until they assume the
properties usually related to liquids. It is therefore they are
regarded as super-cooled liquids.
Properties and Types of solids 37. (a) Silicon is a semiconductor because it is a thermal active and its
conductivity increased with increasing temperature.
1. (a) Both gases and liquids possess fluidity and hence viscosity 38. (b) Amorphous solids are isotropic, because of these substances
molecules in the solid state do not have translational motion. show same properties in all directions.
39. (c) Polymorphism is a ability of a substances which show two or
2. (b) It is a characteristic of liquid crystal. more crystalline structure
3. (a) BaTiO3 is a ferroelectric compound. 40. (ac) Amorphous solids neither have ordered arrangement (i.e. no
definite shape) nor have sharp melting point like crystals, but
5. (b) The value of heat of fusion of NaCl is very high due to fcc when heated, they become pliable until they assume the
arrangement of its ions. properties usually related to liquids. It is therefore they are
6. (c) Piezoelectric crystals are used in record player. regarded as super-cooled liquids.
8. (b) NaCl is a ionic solid in which constituent particles are
positive ( Na  ) and negative (Cl  ) ions. Crystallography and Lattice
9. (d) Amorphous solids have short range order but no sharp in
melting point. 1. (b) A crystal system is hexagonal if its unit cell having a  b  c
10. (d) Solids have definite shape, size and rigidity. axial ratio and     90,   120 axial angles.
12. (a) In crystalline solid there is perfect arrangement of the constituent 2. (c) Rhombohedral crystal system
particles only at 0K. As the temperature increases the chance that a a  b  c ,       90 o
lattice site may be unoccupied by an ion increases. As the number
of defects increases with temperature solid change in liquid. ex – NaNO 3 , CaSO 4 , calcite CaCO 3 , HgS
13. (c) Diamond is a covalent solid in which constituent particles are 3. (b) Tetragonal system has the unit cell dimension
atoms. a  b  c,      90 .
14. (c) Solid NaCl is a bad conductor of electricity because ions are 5. (a) Space lattice of CaF2 is face centred cubic.
not free to move.
15. (a) The existence of a substance in more than one crystalline form 6. (a) For body centred cubic arrangement co-ordination number is 8
is known as polymorphism. and radius ratio (r / r ) is 0.732  1.000 .
16. (a) Solids are also non-crystalline in nature. 7. (b) There are 14 Bravais lattices (space lattices).
17. (a) Ice has the lowest melting point out of the given solids, hence 8. (d) Monoclinic sulphur is an example of Monoclinic crystal system.
it has the weakest intermolecular forces. 10. (b) r  0.414 r .
19. (c) All metals and some alloys are metallic crystal.
11. (c) Each unit cell of NaCl contains 4 NaCl units.
20. (c) Iodine crystals are molecular crystals, in which constituent
particles are molecules having interparticle forces are Vander 12. (c) For tetrahedral arrangement co-ordination number is 4 and
Waal’s forces. radius ratio (r / r ) is 0.225  0.414 .
21. (b) Ionic solids have highest melting point due to strong 13. (a) Face-centred cubic lattice found in KCl and NaCl .
electrostatic forces of attraction.
14. (c) Definition of unit cell.
22. (d) For n-type, impurity added to silicon should have more than 4
valence electrons. 16. (b) In NaCl (rock salt) : Number of Na  ions  12 (at edge
23. (d) Glass is an amorphous solid. 1
centers)   1 (at body centre) 1  4 . Number of
25. (a) Crystalline solids have regular arrangement of constituent 4
particles, sharp melting points and are anisotropic. 1 1
Cl  ions  8 (at corners)   6 (at face centre)   4 .
26. (d) Sugar is a crystalline solid while glass, rubber and plastic are 8 2
amorphous solids. Thus 4 formula units per unit cell.
28. (a) MnO2 is antiferromagnetic. 17. (b) Lowest potential energy level provides stable arrangement.
18. (b) The seven basic crystal lattice arrangements are :- Cubic,
29. (d) Graphite is sp 2 hybridised and a covalent crystal. Tetragonal, Orthorhombic, Monoclinic, Hexagonal,
Rhombohedral and Triclinic.
30. (d) Ionic crystals exhibit non-directional properties of the bond.
19. (a) The conditions for monoclinic crystal system.
31. (d) Ice is a molecular crystal in which the constituent units are
molecules and the interparticle forces are hydrogen bonds. 20. (a) High lattice energy of BaSO 4 causes low solubility of
32. (a) Quartz is a covalent crystal having a framework of silicates or BaSO 4 in water.
silica, i.e. a three dimensional network when all the four oxygen 21. (c) 14 kinds of Bravais lattices (space lattices) are possible in a
atoms of each of SiO4 tetrahedron are shared. crystal.
33. (c) Metallic crystals are good conductor of heat and current due to 22. (d) Radius ratio in TlCl is 0.732 – 1.000 and co-ordination number
free electrons in them. is 8 and arrangement is body centred cubic.
34. (a) Silicon is a covalent crystal in which constituent particles are 23. (c) Zinc blende (ZnS ) has fcc structure and is an ionic crystal
atoms. having 4 : 4 co-ordination number.
 Solid state 219

24. (d) Na 2 O has antifluorite ( A2 B) type structure. 21. (a) In bcc structure 68% of the available volume is occupied by
spheres. Thus vacant space is 32%.
25. (b) Zinc blende (ZnS ) has fcc structure and is an ionic crystal 22. (c) Number of atoms in the cubic close packed structure = 8.
having 4 : 4 co-ordination number. 1
Number of octahedral voids   8  4 .
1 2
28. (d)  8 (at corners)  1
8 23. (a) Co-ordination number in HCP and CCP arrangement is 12
1 while in bcc arrangement is 8.
 6 (at face centre)  3 24. (d) In NaCl (rock salt) : Number of Na  ions  12 (at edge
2
1
Z  1  3  4 (total no. of atoms) centers)   1 (at body centre) 1  4 . Number of Cl  ions
4
Crystal packing 1 1
 8 (at corners)   6 (at face centre)   4 . Thus 4
8 2
1. (b) Number of tetrahedral voids in the unit cell formula units per unit cell.
25. (b) Co-ordination number in HCP =12
= 2  number of atoms = 2Z.
Co-ordination number in Mg is also = 12
2. (b) The system ABC ABC…… is also referred to as face-centred
cubic or fcc. 26. (a) All are the iso-electronic species but Na  has low positive
3. (d) It represents ccp arrangement. charge so have largest radius.
4. (a) BCC has a coordination number of 8.
5. (b) In rock salt structure the co-ordination number of Na  : Cl  Mathematical analysis of cubic system and
is 6 : 6 . Bragg’s equation
6. (d) The bcc cell consists of 8 atoms at the corners and one atom at
centre. N  mol . wt.( M )
1. (b) Density of unit cell  g cm  3
 1 V ( a 3 )  avogadro no. (N o )
 n  8    1  2 .
 8
1
The fcc cell consists of 8 atoms at the eight corners and one 2. (b) Distance between K  and F    length of the edge
atom at each of the six faces. This atom at the face is shared by 2
two unit cells. 3. (a) There are two atoms in a bcc unit cell.
1  1 So, number of atoms in 12.08  10 23 unit cells
 n  8   6    4 .
8  2  2  12.08  10 23  24.16  10 23 atom .
7. (c) AB2 type of structure is present in CaF2 4. (b) bcc structure has one atom shared by 1 unit cell.
2  2 
 AB2 ⇌ A  2 B ; CaF2 ⇌ Ca  2 F 5. (b) The structural arrangement of co-ordination number ‘6’ is
8. (b) Potassium (K) has bcc lattice. octahedral and its radius ratio is 0.414  0.732 . The
9. (b) Number of atoms per unit cell in bcc system = 2. example of octahedral is KCl and NaCl .
10. (b) In body centred cubic, each atom/ion has a coordination 6. (a) The number of spheres in one body centred cubic and in one
number of 8. face centred cubic unit cell is 2 and 4 respectively.
11. (d) Number of octahedral sites = Number of sphere in the packing. 7. (b) Closest approach in bcc lattice
 Number of octahedral sites per sphere  1 . 1 1 3
12. (c) ABAB …… is hexagonal close packing.  of body diagonal   3 a   4 .3  3 .72 Å .
2 2 2
13. (a) Sodium (Na ) is a body cube.
14. (b) SrF2 has fluorite (CaF2 ) type structure.   a 3  N 0  10 30
10. (a) M
15. (b) In ZnS structure, sulphide ions occupy all FCC lattice points z
while Zn ions are present in alternate tetrahedral voids.
10  (100)  (6 .02  10 23 )  10 30
2+
3
16. (b) MgO contains rock salt (NaCl) structure.   15.05
4
17. (c) CaF2 (fluorite) has fcc structure with 8 : 4 coordination
6.02  1023
number. No. of atoms in 100 g   100  4  1025 .
18. (b) Every constituent has two tetrahedral voids. In ccp lattice 15.05
atoms
1 1 11. (c) Cs  and I  have largest sizes.
8 6  4
8 2 12. (c) 58.5 g NaCl  1 mole  6.02  10 23 Na  Cl units.
 Tetrahedral void  4  2  8 , One unit cell contains 4 Na  Cl  units. Hence number of unit
Thus ratio  4 : 8 :: 1 : 2 .
19. (c) Tetrahedral sites one double comparable to octahedral sites cell present
then ratio of X and Z respectively 2 : 1 since formula of the 6 .02  10 23
compound X 2 Z .   1.5  10 23 .
4
20. (c) A atoms are at eight corners of the cube. Therefore, the no. of
1
8 13. (a)  6.023  10 23  1.029  10 22
A atoms in the unit cell =  1 . B atoms are at the face 58.5
8
centre of six faces. Therefore, its share in the unit cell = A unit cell contains 4 Na  ion and 4 Cl  ions
6
 3 . The formula is AB . 1 .029  10 22
2
3
Unit cell   2.57  10 21 unit cell.
4
 220 Solid state
14. (b) Bragg’s equation is n  2d sin 4. (a) A atoms are at eight corners of the cube. Therefore, the
where n is an integer i.e. 1, 2, 3, 4 etc. 8
number of A atoms in the unit cell   1 , atoms B per unit
15. (d) Face centred cubic structure contribute of 1/8 by each atom 8
present on the corner and 1/2 by each atom present on the cell = 1. Hence the formula is AB.
face. 5. (d) Co-ordination number for Cu is 12.
16. (c) As CsCl is body-centred, d  3a / 2 . 6. (b) Each Cs  in CsCl is surrounded by eight Cl  and each
3a 3  4 .29 Cl  in CsCl is surrounded by eight Cs  .
17. (a) Radius of Na (if bcc lattice)   7. (d) X atoms are at eight corners of the cube. Therefore, the
4 4
8
number of X atoms in the unit cell   1 .
 1.8574 Å  1.8574  10 8 cm 8
18. (b) The crystals in which radius ratio value is found between Y atoms are at the face centre of six faces. Therefore, its share
0.225  0.414 shows tetrahedral crystal structure. 6
in the unit cell   3 . The formula is XY 3 .
3 2d 2  4.52 2
19. (d) For bcc, d  a or a    5.219 Å  522 pm 8. (a) Let the units of ferrous oxide in a unit cell  n , molecular weight
2 3 1.732
of ferrous oxide (FeO)  56  16  72 g mol 1 ,
ZM 2  39
  72  n
a 3  N 0  10 30 (522)3  (6 .023  10 23 )  10 30 weight of n units 
6 .023  10 23
 0.91 g / cm 3  910 kg m 3
Volume of one unit  (lengthof corner )3
20. (c) The value of ionic radius ratio is 0.52 which is between
0.414  0.732, then the geometrical arrangement of ions in  (5 Å)3  125  10 24 cm 3
crystal is octahedral. wt.of cell 72  n
Density  , 4.09 
21. (c) The number of atoms present in sc, fcc and bcc unit cell are 1, volume 6.023  10 23  125  10 24
4, 2 respectively.
3079.2  10 1
22. (b) The number of atoms present in sc, fcc and bcc unit cell are 1, n  42.7  10 1  4.27  4
4, 2 respectively. 72
23. (d) Cl  Na  Cl  9. (b) In NaCl crystal Na  ions has coordination number 6.
10. (b) Cl  ions in CsCl adopt BCC type of packing.
x 11. (d) There were 6 A atoms on the face-centres removing face-
centred atoms along one of the axes means removal of 2 A
a a = 2x atoms.
a 620 Now, number of A atoms per unit cell
24. (a) r ; r  219.25 Pm
1 1
2 2 2 2  8  4 3
V  N0 d 8 2
(face  centred)
25. (c) Z (corners )
M Number of B atoms per unit cell
4 .2  8 .6  8 .3  10 24  6 .023  10 23  3.3  12 
1
+ 14
  3.84  4 4
155 (edge centred) ( body centred )
26. (b) Volume of unit cell  a 3 Hence the resultant stoichiometry is A3 B4
 (3.04  10 8 cm)3  2.81  10 23 cm 3 12. (a) In Cs  Cl  crystal co-ordination number of each ion is 8.
27. (b) In FCC 180
13. (b) r / r   0 .962 which lies in the range of
4 r  2a 187
4r 0.732  1.000 , hence co-ordination number = 8 i.e. the
a
2 structure is CsCl type.
14. (a) In diamond, C-atoms are arranged in a regular tetrahedral
structure.
Crystal structure and Coordination number 15. (b) In hcp, co-ordination no. is 12.
1 16. (c) Mg has 6 co-ordination number (fcc structure).
1. (b) In a unit cell, W atoms at the corner  8 1
8 17. (d) In NaCl crystal every Na  ion is surrounded by 6 Cl  ion and

O atoms at the centre of edges 

1
 12  3 every chloride ion is surrounded by 6 Na  ion.
4 18. (d) Crystals show good cleavage because their constituent particles
Na atoms at the centre of the cube = 1 are arranged in planes.
W : O : Na  1 : 3 : 1, hence formula  NaW O3 19. (b) Fe3 O4 is a non-stoichiometric compound because in it the
2. (d) For bcc lattice, co-ordination number is 8. ratio of the cations to the anions becomes different from that
3. (b) Body centered cubic lattice has a co-ordination number 8. indicated by the chemical formula.
20. (d) The radius ratio for co-ordination number 4, 6 and 8 lies in
between the ranges [0.225  0.414], [0.414  0.732] and
[0.732  1] respectively.
 Solid state 221
21. (c) The radius ratio for co-ordination number 4, 6 and 8 lies in 16. (c) AgBr exhibits Frenkel defect due to large difference in the
between the ranges [0.225  0.414], [0.414  0.732] and
size of Ag  and Br  ions.
[0.732  1] respectively. 17. (c) Both are stoichiometric crystalline defects.
22. (b) In Na 2 O, each oxide ions (O 2 ) is co-ordinated to 8 Na  18. (c) Brass, Cu  80%, Zn  20% substitutional alloy.
ions and each Na  ion to 4 oxide ions. Hence it has 4 : 8 co- Steel is an interstitial alloy because it is an alloy of Fe with C, C
ordination. atoms occupy the interstitial voids of Fe crystal.
23. (b) When radius ratio between 0.732  1, then co-ordination 19. (d) In metal excess defect when holes created by missing of anions
are occupied by electrons, there sites are called F-centres and
number is 8 and structural arrangement is body-centred cubic. are responsible for colour in the crystal.
24. (c) Each Cs  is surrounded by eight Cl  ions in CsCl crystal 20. (c) KBr exhibits Schottky defect and not Frenkel defect.
lattice because its co-ordination number is 8 : 8. 21. (c) When cation shifts from lattice to interstitial site, the defect is
25. (a) NaCl has fcc arrangement of ions. called Frenkel defect.
26. (c) Each Na  is surrounded by six Cl  ions in NaCl crystal 22. (d) F-centres are the sites where anions are missing and instead electrons
lattice because its co-ordination number is 6 : 6. are present. they are responsible for colour.
27. (b) Zinc blende (ZnS ) has fcc structure and is an ionic crystal Critical Thinking Questions
having 4 : 4 co-ordination number.
30. (d) In a simple cubic structure 1. (c) Amorphous solids neither have ordered arrangement (i.e. no
1 definite shape) nor have sharp melting point like crystals, but
z   8 (atoms one at a corners) when heated, they become pliable until they assume the
8
properties usually related to liquids. It is therefore they are
z 1 regarded as super-cooled liquids.
31. (a) Co-ordination number in hcp structure is 12.
2. (c) Silicon due to its catenation property form network solid.
32. (acd) A metal that crystallizes in bcc structure has a co-ordination
number of 8. 3. (c) Orthorhombic geometry has abc and
33. 
(a) In sodium chloride, each Na ion is surrounded by six Cl        90 . The shape of match box obey this
geometry.
ions and each Cl  ion is surrounded by six Na  ions. Thus,
both the ions have coordination number six. 4. (d) In a triclinic crystal has no notation of symmetry.
34. (b) The Ca 2  ions are arranged in (ccp) arrangement, i.e. Ca 2  5. (a) In NH 3 molecule, the original appearance is repeated as a
ions are present at all corners and tat the centre of each face of result of rotation through 120 o . Such as axis is said to be an
the cube. the fluoride ions occupy all the tetrahedral sites. This axis of three-fold symmetry or a triad axis.
is 8 : 4 arrangement i.e., each Ca 2  ion is surrounded by
6. (a) Na 2 O has antifluorite ( A2 B) type structure.
8 F  ions and each F  ion by four Ca 2  ions.
7. (b) Cationic radius increases down the group and decreases along
the period.
Defects in crystal
8. (c) Distance between centres of cation and anion
d 508
1. (c) When polar crystal is subjected to a mechanical stress,    254 pm
electricity is produced – a case of piezoelectricity. Reversely, if 2 2
electric field is applied, mechanical stress is developed.
rc  ra  254 pm or 110  ra  254 or ra  144 pm
Piezoelectric crystal acts as a mechanical electrical transductor.
2. (b) More is the Schottky defect in crystal more is the decrease in nM
density. 9. (b) 
a 3  N 0  10  30
3. (d) All the given statements are correct about F-centres.
5. (a) As each Sr 2 ion introduces one cation vacancy, therefore 2  100
  5.188 g/cm 3
concentration of cation vacancies = mol % of SrCl 2 added. (400)  (6 .02  10 23 )  10 30
3

High pressure
6. (c) Yellow colour on heating NaCl in presence of Na is due to 10. (a) NaCl structure CsCl structure
(6 : 6 co.  ord. ) 760 K (8 : 8 co.  ord. )
presence of electrons in anion vacancies (F-centres).
7. (d) Frenkel’s defect is due to shift of an ion from the normal lattice
site (Creating a vacancy) and occupy interstitial spaces. 11. (a) Difference  2.178  10  2.165  10 3  0.013  10 3
3

8. (c) AgBr exhibits Frenkel defect due to large difference in the 0 .013  10 3
Fraction unoccupied   5.96  10 3
size of Ag  and Br  ions. 2 .178  10 3
9. (d) Schottky defects occurs in highly ionic compounds which have 12. (c) CsBr3 consist of Cs  and Br3 ions.
high co-ordination number ex. NaCl, KCl, CsCl .
10. (d) Schottky defect is due to missing of equal number of cations 13. (a) Each Cs  is surrounded by eight Cl  ions in CsCl crystal
and anions. lattice because its co-ordination number is 8 : 8.
11. (a) Schottky defect is due to missing of equal number of cations 14. (b) In each CaF2 each calcium cation is surrounded by eight
and anions. fluoride anions in a body centred cubic arrangement. Each
12. (a) Impurity present in a crystal does not establish thermal fluoride ion is in contact with four calcium ions. Thus CaF2
equilibrium.
13. (c) Since no ions are missing from the crystal as a whole, there is has 8 : 4 co-ordination number.
no effect on density. 15. (c) The radius ratio for co-ordination number 4, 6 and 8 lies in
15. (b) On adding non-metal in metal the metal becomes less tensile. between the ranges [0.225  0.414], [0.414  0.732] and
[0.732  1] respectively.

O O

Si O

O
 222 Solid state
16. (b)

17. (b) In this diagram, equal number of cations ( Na  ) and anions

(Cl  ) are missing, so it, shows schottky defect.
18. (c) Zeolite is a three dimensional silicate because of in the silicates
all the four oxygen atoms at (SiO4 )4 tetrahedra are shared
with other tetrahedra, vesulting in a three dimensional
network.

Assertion & Reason

1. (b) It is true that in the dimond structure, carbon atoms are

arranged in tetrahedrally ( sp 3 hybridized) but it is not the
correct explanation of assertion.
2. (d) Tetrahedral holes are smaller in size than octahedral
holes. Cations usually occupy less space than anions.
3. (d) Crystalline solids have regular arrangement of constituent
particles and are anisotropic whereas amorphous solids have no
regular arrangement and are isotropic.
4. (a) Schottky defect is due to missing of equal number of cations and
anions.
5. (b) Space or crystal lattice is a regular repeating arrangement of
points in space and forms the basis of classification of all
structures.
6. (c) Tetrahedral void is so called because it is surrounded by four
spheres tetrahedrally while octahedral void is so called because
it is surrounded by six spheres octahedrally.
7. (c) Two corners per tetrahedron one shared in both the cases.
8. (b) When an atom or an ion is missing from its normal lattice site,
a lattice vacancy or defect is created, which is called schottky
defect. Due to missing density of crystal will be lowered.
9. (b) On heating, the metal atoms deposit on the surface and finally
they deffuse into the crystal and after ionisation the alkali metal
ion occupies cationic vacancy where as electron occupies
anionic vacancy.
10. (a) In case of semiconductors, the gap between valence band and
the conduction band is small and there fore some of the
electrons may jump from valence band to conduction band and
thus on increasing temperature conductivity is also increased.
11. (a) All magnetically ordered solids (ferromagnetic and
antiferromagnetic solids) transform to the paramagnetic state
at high temperature due to the randomisation of spins.
12. (c) In piezoelectric crystals, the dipoles may align them selves in an
ordered manner such that there is a net dipole moment in the
crystal.