EXERCISE # 1

Q.1 Which of the following is not a characteristic of Q.10 In a face centred cubic cell, an atom at the corner
crystalline solids ? contributes to the unit cell -
(1) They have a regular geometry (1) 1 part (2) 1/2 part
(2) They have sharp melting points (3) 1/4 part (4) 1/8 part
(3) They are isotropic
Q.11 In face centred cubic cell, an atom at the face cen-
(4) They undergo a clean cleavage
tres is shared by -
Q.2 Which of the following is not a crystalline solid ? (1) 4 units cells (2) 2 unit cells
(1) Common salt (2) Sugar (3) One unit cell (4) 6 unit cells
(3) Iron (4) Rubber
Q.12 In a face centred cubic cell, an atom at the face
Q.3 A pseudo solid is - contributes to the unit cell -
(1) glass (2) pitch (1) 1 part (2) 1/2 part
(3) KCl (4) Glass and pitch both (3) 1/4 part (4) 1/8 part

Q.4 Solid CO2 is an example of - Q.13 In a body centred cubic cell, an atom at the body
(1) Ionic crystal (2) Covalent crystal centre is shared by -
(3) Metallic crystal (4) Molecular crystal (1) 1 unit cell (2) 2 unit cell
Q.5 Wax is an example of - (3) 3 unit cell (4) 4 unit cell

(1) Ionic crystal (2) Covalent crystal Q.14 Which of the following type of cubic lattice has
(3) Molecular crystal (4) Metallic crystal maximum number of atoms per unit cell ?

Q.6 a  b  c,  =  = 90°,   90° represents - (1) Simple cubic

(1) tetragonal system (2) Body centred cubic
(2) orthorhombic system (3) Face centred cubic
(3) monoclinic system (4) All have same
(4) triclinic system
Q.15 The number of atoms present in a unit cell of a
Q.7 The most unsymmetrical crystal system is - monoatomic substance (element) of simple cubic
(1) Cubic (2) Hexagonal lattice, body-centred cubic and face centred cubic
(3) Triclinic (4) Orthorhombic respectively are -
(1) 8, 9 and 14 (2) 1, 2 and 4
Q.8 Bravais lattices are of -
(3) 4, 5 and 6 (4) 2, 3 and 5
(1) 10 types (2) 8 types
(3) 7 types (4) 14 types Q.16 Which one of the following is primitive unit cell ?

Q.9 In a simple cubic cell, each point on a corner is (1) Simple cubic

shared by - (2) Body-centred cubic

(1) 2 unit cells (2) 1 unit cell (3) Face-centred cubic

(3) 8 unit cells (4) 4 unit cells (4) Both body-centred and face-centred cubic

115
Q.17 In a body centred cubic unit cell, a metal atom at the
Q.25 The more efficient mode of packing of identical
centre of the cell is surrounded by how many other
atoms in one layer is -
metal atoms -
(1) Square close packing pattern
(1) 8 (2) 6 (3) 12 (4) 4
(2) Hexagonal close packing pattern
Q.18 An alloy of copper, silver and gold is found to have
(3) Both (1) and (2)
copper constituting the fcc lattice. If silver atoms
(4) None of the two
occupy the edge centres and gold is present at body
centre, the alloy has a formula -
Q.26 The ABAB….packing and ABC ABC….packing are
(1) Cu4Ag2Au (2) Cu4Ag4Au
respectively called as -
(3) Cu4Ag3Au (4) CuAgAu
(1) hexagonal close packing(hcp) and cubic close
Q.19 Sodium metal crystallizes in bcc lattice with the cell packing (ccp)
edge a = 42.29 Å. What is the radius of sodium atom ?
(2) ccp and hcp
(1) 1.86 Å (2) 1.90 Å
(3) body centred cubic (bcc) packing and hexago-
(3) 18.3 Å (4) 1.12 Å
nal close packing
Q.20 An element has bcc structure having unit cells (4) hcp and bcc
12.08 × 1023. The number of atoms in these cell is -
(1) 12.08 × 1023 (2) 24.16 × 1023 Q.27 The space occupied in bcc arrangement is -
(3) 48.38 × 1023 (4) 12.08 × 1022 (1) 74 % (2) 70 % (3) 68 % (4) 60.4 %
Q.21 A metal has bcc structure and the edge length of its
unit cell is 3.04 Å. The volume of the unit cell in cm3 Q.28 The vacant space in bcc unit cell is -
will be - (1) 32% (2) 10% (3) 23% (4) 46%
–21 3 –23 3
(1) 1.6 × 10 cm (2) 2.81 × 10 cm
(3) 6.02 × 10 cm –23 3
(4) 6.6 × 10–24 cm3 Q.29 The empty space in the hcp and ccp is about -
(1) 26 % (2) 30 % (3) 35 % (4) 40%
Q.22 A compound having bcc geometry has atomic mass
50. Calculate the density of the unit cell, if its edge
Q.30 Which one of the following is not a close packing ?
length is 290 pm -
(1) hcp (2) ccp (3) bcc (4) fcc
(1) 6.81 g cm–3 (2) 3.40 g cm–3
(3) 13.62 g cm–3 (4) None of these
Q.31 Close packing is maximum in the crystal lattice of -
Q.23 An element, density 6.8 g cm–3 occurs in bcc struc- (1) Simple cubic (2) Face centred
ture with cell edge 290 pm. Calculate the number of (3) Body centred (4) None
atoms present in 200 g of the element.
(1) 2.4 × 1042 (2) 1.2 × 1042 Q.32 Which of the following has hcp structure -
24 24
(3) 1.2 × 10 (4) 2.4 × 10 (1) Al (2) Mg (3) Cu (4) Ni
Q.24 An element A crystallizes in fcc structure. 200 g of
this element has 4.12 × 1024 atoms. The density of A Q.33 If the coordination number of an element in its crys-
is 7.2 g cm–3 Calculate the edge length of the unit tal lattice is 8, then packing is -
cell - (1) fcc (2) hcp
(1) 26.97 × 10–24 cm (2) 299.9 pm (3) bcc (4) None of the above
–12
(3) 5 × 12 cm (4) 2.99 cm

116
Q.34 A tetrahedral void in a crystal implies that
Q.43 If the radius ratio is in the range of 0.414 – 0.732
(1) shape of the void is tetrahedral then the co-ordination number will be -
(2) molecules forming the void are tetrahedral in (1) 2 (2) 4 (3) 6 (4) 8
shape
Q.44 In NaCl crystal r / r– ratio is -
(3) the void is surrounded tetrahedrally by four
spheres (1) 0.4 (2) 0.98 (3) 1.0 (4) 0.52
(4) the void is surrounded by six spheres Q.45 The positions of Cl– ions in NaCl structure are -
Q.35 In a closest packed lattice, the number of octahe- (1) Corners of the cube
dral sites as compared to tetrahedral ones will be - (2) Centres of faces of the cube
(1) Equal (2) Half (3) Corners as well as centres of the faces of the
(3) Double (4) None of these cube
(4) Edge centres of the cube
Q.36 The coordination number of a cation occupying an
octahedral hole is - Q.46 The number of NaCl units present in a unit cell of
(1) 4 (2) 6 (3) 8 (4) 12 NaCl are -
(1) 1 (2) 2 (3) 4 (4) 8
Q.37 The size of an octahedral void formed in a closest
packed lattice as compared to tetrahedral void is - Q.47 The tetrahedral voids formed by ccp arrangement
(1) Equal (2) Smaller of Cl– ions in rock salt structure are -
(3) Larger (4) Not definite (1) Occupied by Na+ ions
(2) Occupied by Cl– ions
Q.38 The coordination number of a cation occupying a
(3) Occupied by either Na+ or Cl– ions
tetrahedral hole is -
(4) Vacant
(1) 4 (2) 6 (3) 8 (4) 12
Q.48 A unit cell of CsCl consists of -
Q.39 Number of tetrahedral voids per atom in a crystal
lattice is - (1) one CsCl unit (2) two CsCl unit
(3) four Cscl units (4) eight CsCl units
(1) 1 (2) 2 (3) 4 (4) 8
Q.49 TlCl has structure similar to CsCl. The co-ordina-
Q.40 A compound contains P and Q elements. Atoms Q
tion number of Tl+ is -
are in ccp arrangement while P occupy all tetrahe-
dral sites. Formula of compound is - (1) 4 (2) 6 (3) 10 (4) 8

(1) PQ (2) PQ2 (3) P2Q (4) P3Q Q.50 The co-ordination number of Zn+2 and S2– ions in
the zinc blende (ZnS) type structure is -
Q.41 The limiting radius ratio for tetrahedral shape is -
(1) 4 : 4 (2) 6 : 6
(1) 0 to 0.155 (2) 0.155 to 0.255
(3) 0.225 to 0.414 (4) 0.414 to 0.732 (3) 8 : 8 (4) 4 : 8

Q.42 For an octahedral arrangement the lowest radius Q.51 The number of molecules in a unit cell of fluorite
ratio limit is - is -

(1) 0.155 (2) 0.732 (1) 2 (2) 4 (3) 6 (4) 8

(3) 0.414 (4) 0.225
117
Q.52 4 : 4 Co-ordination is found in - Q.60 At zero Kelvin, most of the ionic crystals posses
(1) ZnS (2) CuCl (1) Frenkel defect
(3) Agl (4) All (2) Schottky defect
Q.53 Antifluorite structure is derived from fluorite struc- (3) Metal excess deffect
ture by - (4) No defect
(1) Heating fluorite crystal lattice
Q.61 As a result of Schottky defect -
(2) Subjecting fluorite structure to high pressure
(1) there is no effect on the density
(3) Interchanging the positions of positive and nega-
(2) density of the crystal increases
tive ions in the lattice
(3) density of the crystal decrease
(4) None of these
(4) any of the above three can happen
Q.54 A binary solid (A+B–) has a zinc blende structure
with B– ions constituting the lattice and A+ ions Q.62 Schottky defect is observed in the crystal of -

occupying 25% tetrahedral holes. The formula of (1) NaCl (2) TlCl
solid is - (3) AgCl (4) MgCl2
(1) AB (2) A2B (3) AB2 (4) AB4 Q.63 Which one of the following is correct ?
Q.55 A solid AB has NaCl type structure. If the radius of (1) Schottky defect lowers the density
the cation A+ is 100 pm, then the radius of the anion (2) Frenkel defect increases the dielectric constant
B– will be - (3) Stoichiometric defects make the crystals good
(1) 192.3 pm (2) 414 pm electrical conductors
(3) 225 pm (4) 44.4 pm (4) All the three

Q.56 The radius of Na+ is 95 pm and that of Cl– ion is 181 Q.64 Frenkel defect is generally observed in -
pm. Hence the co-ordination number of Na will + (1) AgBr (2) Agl (3) ZnS (4) All of these
be - Q.65 Frenkel defect is found in crystals in which the ra-
(1) 4 (2) 6 dius ratio is -
(3) 8 (4) unpredictable (1) low (2) 1 . 3
Q.57 The ionic radii of Rb+ and I– are 1.46 and 2.16 Å (3) 1 .5 (4) slightly less than unity
respectively. The most probable type of structure Q.66 F-centres in an ionic crystal are -
exhibited by it is -
(1) lattice sites containing electrons
(1) CsCl type (2) NaCl type
(2) interstitial sites containing electrons
(3) ZnS type (4) CaF2 type
(3) lattice sites that are vacant
Q.58 +
If the distance between Na and Cl ions in NaCl – (4) interstitial sites containing cations
crystal is ‘a’ pm, what is the length of the cell edge ?
Q.67 The correct statement regarding F-centre is -
(1) 2a pm (2) a/2 pm (3) 4a pm (4) a/4 pm
(1) Electrons are held in the lattice sites of crystals
Q.59 Potassium fluoride has NaCl-type structure. What (2) F-centre imparts colour to the crystal
+ – (3) Conductivity of the crystal increases due to F-
is the distance between K and F ions if it’s cell
edge ‘a’ cm ? centre
(1) 2a cm (2) a/2 cm (4) All the three above
(3) 4a cm (4) a/4 cm
118
Q.68 Transition metals, when they form interstitial Q.71 A crystal may have one or more planes and one
compounds, the non-metals (H, B, C, N) are or more axes of symmetry but it possesses -
accomodated in-
(1) Two centres of symmetry
(1) Voids or holes in cubic - packed structure
(2) Tetrahedral voids (2) One centre of symmetry
(3) Octahedral voids (3) No centre of symmetry
(4) All of these (4) None of these
Q.69 Ferrimagnetism is in -
(1)   (2)  Q.72 Structure shown here represents -
(3)  (4) none of these
Q.70 The second order Bragg diffraction of X-rays
with  = 1.0 Å from a set of parallel planes
in a metal occurs at an angle 60º. The distance Cation
between the scattering planes in the Anion
crystals is -
(1) 1.155 Å (2) 1.00 Å
(3) 2.00 Å (4) 1.7 Å
(1) Schottky defect
(2) Frenkel defect
(3) metal excess defect
(4) none of these

119
 EXERCISE # 2
Q.1 A metal (atomic mass = 50) has a body centred Q.8 The co-ordination number of calcium fluorite (CaF2)
cubic crystal structure. The density of metal is 5.96 type structure is -
g cm–3. Find the volume of the unit cell. (1) 1 : 2 (2) 4 : 4 (3) 4 : 8 (4) 8 : 4
–24 3 –24 3
(1) 13.9 × 10 cm (2) 27.8 × 10 cm
Q.9 KF has NaCl structure. What is the distance be-
–24 3
(3) 6.95 × 10 cm (4) 55.6 × 10–24cm3
tween K+ and F– in KF if density is 2.48 g cm–3 ?
Q.2 An element crystallises in BCC structure. The edge
(1) 268.8 pm (2) 537.5 pm
length of its unit cell is 288 pm. If the density of the
(3) 155.3 × 10–24 (4) 5.375 cm
crystal is 7.2 g cm–3, what is the atomic mass of the
element ? Q.10 The shaded plane abcd is referred to as -
Z
(1) 51.8 (2) 103.6 (3) 25.9 (4) 207.2
b
Q.3 The coordination number of hexagonal closest
packed (hcp) structure is ? a
(1) 12 (2) 10 (3) 8 (4) 6
Y
Q.4 The available space occupied by spheres of equal c
size in three demensions in both hcp and ccp ar- d

rangement is - X
(1) rectangular plane of symmetry
(1) 74% (2) 70% (3) 60.4% (4) 52.4% (2) diagonal plane of symmetry
(3) unit plane
Q.5 Which one of the following statements is incorrect
(4) none of these
about rock salt type ?
Q.11 Which of the following defect, if present, lowers
(1) It has fcc arrangement of Cl– the density of the crystal-
(1) Frenkel
(2) Na+ anc Cl– ions have a co-ordination number
(2) Schottky
of 6 : 6 (3) Edge dislocation
(4) Constitution of F-centres.
(3) A unit cell of NaCl consists of four NaCl units
Q.12 The yellow colour of ZnO and conducting nature
(4) All halides of alkali metals have rock-salt type produced in heating is due to -
structure (1) Metal excess defects due to interstitial cation
(2) Extra positive ions present in an interstitial
Q.6 In sodium chloride, Cl– ions form ccp arrangment. site
Which site a Na+ ion will occupy in this structure ? (3) Trapped electrons
(1) Cubic (2) Tetragonal (4) All

(3) Octahedral (4) Trigonal bipyramidal Q.13 How many number of atoms are there in a cube
based unit cell having one atom on each corner
and two atoms on each body diagonal of cube -
Q.7 The NaCl structure can be converted into CsCl (1) 8 (2) 6 (3) 4 (4) 9
structure -
Q.14 In a solid, oxide ions are arranged in CCP.
(1) by application of high pressure Cations A occupy one-sixth of the tetrahedral
voids and cations B occupy one-third of the
(2) by heating to 760 K octahedral voids. The formula of the
(3) both by heat and pressure compound is -
(1) ABO3 (2) AB2O3
(4) the conversion is not possible (3) A2BO3 (4) A2B2O3

120
Q.15 For the structure given below the site marked as
Q.20 A solid ABC has A, B and C arranged as below. The
S is a-
formula of solid is

(1) Tetrahedral void (2) Cubic void

(3) Octahedral void (4) None of these
(1) ABC (2) AB2C2
(3) A2BC (4) AB8C2
Q.16 In Corundum, oxide ions are arranged in hcp
arrangement and aluminium ion occupy two third
Q.21 In a cubic close packed structure of mixed oxides,
of the octahedral holes. Its formula is -
the lattice is made up of oxide ions, one eighth of
(1) Al2O3 (2) Al2O4
tetrahedral voids are occupied by divalent (X2+)
(3) Al3O4 (4) AlO2.
ions, While one-half of the octahedral voids are
occupied by trivalent ions (Y3+), then the formula
Q.17 NH4Cl crystallizes in bcc lattice with edge length of
of the oxide is -
unit cell equal to 387 pm. If radius of Cl– is 181 pm,
(1) XY2O4 (2) X2YO4
the radius of NH4 will be - (3) X4Y5O10 (4) X5Y4O10
(1) 174 pm (2) 154 pm
(3) 116 pm (4) 206 pm Q.22 Titanium crystallizes in a face centred cubic lattice.
It reacts with carbon or hydrogen interstitially by
Q.18 Pink colour in non stoichiometric LiCl is due to- allowing atoms of these elements to occupy holes
(1) Cl– ions in lattice (2) Li+ ions in lattice in the host lattice. Hydrogen occupies tetrahedral
–
(3) e in lattice (4) Both A and B holes but carbon occupies octahedral holes the
formula of titanium carbide and hydride are
Q.19 A solid with formula ABC3 would probably have - (1) TiC2, TiH4 (2) TiC, TiH2
(1) A at body centre, B at face centres and C at (3) Ti3C, TiH2 (4) TiC2, TiH
corners of the cube
(2) A at corners of cubes, B at body centre, C at face
centre
(3) A at corners of hexagon, B at centres of the
hexagon and C inside the hexagonal unit cell
(4) None of these

121
 EXERCISE # 3 (A)
Q.1 How many Cl– ions are there around Na+ ion in NaCl Q.9 The edge length of face centred unit cubic cell is
crystal - 508 pm. Then the radius of that atom will be -
[NCERT 78, 89, AIPMT-88, BHU-82, 87 AMU-04] [AIPMT-98]
(1) 3 (2) 4 (3) 6 (4) 8 (1) 179.6 pm (2) 288 pm
(3) 618 pm (4) 398 pm
Q.2 The number of atoms contained in a fcc unit cell of
a monoatomic substance is - Q.10 Zn convert its molten state to its solid state, it has
[AIPMT-86,89, MP-CEE-93,AMU- 03] h.c.p structure then find out number of nearest
atoms - [AIPMT-2001]
(1) 1 (2) 2 (3) 4 (4) 6
(1) 6 (2) 8 (3) 12 (4) 4
Q.3 An octahedral void is surrounded by how many
Q.11 In a bcc unit cell, the number of atom is -
spheres ? [AIPMT-90]
[AIPMT-2002]
(1) 6 (2) 4 (3) 8 (4) 1 2
(1) 1 (2) 2 (3) 4 (4) 6
Q.4 Most crystals show good cleavage because their
Q.12 The pykometric density of sodium chloride crystal
atoms, ions or molecules are - [AIPMT-93]
is 2.165 × 103 kg m–3 while its X-ray density is
(1) weakly bonded together 2.178 × 103 kg m–3. The fraction of unoccupied sites
(2) strongly bonded together in sodium chloride crystal is - [AIPMT-2003]
(3) spherically symmetrical
H int : Fraction of unoccupied sites 
(4) arranged in planes  X - ray density – pyknometric density 
 
Q.5 For orthorhombic system axial ratio are a  b  c and  X  ray density 
the axial angles are [AIPMT-91]
(1) 5.96 (2) 5.96 0 × 10–2
(1)  =  =   90º (2)  =  =  = 90º
(3) 5.96 × 10–1 (4) 5.96 × 10–3
(3)    =  = 90º (4)      = 90º
Q.13 What is the co-ordination number of sodium in
Q.6 In the fluorite structure, the co-ordination number Na2O - [AIIMS-2003]
of Ca2+ ion is - [AIPMT-93] (1) 6 (2) 4 (3) 8 (4) 2
(1) 4 (2) 6 (3) 8 (4) 3
Q.14 A compound formed by element X and Y crystal-
lizes in a cubic structure in which the X atoms are at
Q.7 The number of atoms in 100 g of an FCC crystal
the corners of a cube and the Y atoms are at
with density d = 10g cm–3 and cell edge as 200 pm is the face-centres. The formula of the compound
equal to - [AIPMT-94] is - [AIPMT-2004]
(1) X3Y (2) XY (3) XY2 (4) XY3
(1) 3 × 1025 (2) 0.5 × 1025
Q.15 The crystal system of a compound with unit cell
(3) 1 × 1025 (4) 2 × 1025 dimensions a = 0.387, b = 0.387 and c = 0.504 nm and
 =  = 90º and  = 120º is - [AIIMS- 2004]
Q.8 When electrons are trapped into the crystal in (1) Cubic (2) Hexagonal
anion vacancy, the defect is known as [AIPMT-94] (3) Orthorhombic (4) Rhomhombic
(1) Schottky defect (2) Frenkel deferct
(3) Stoichiometric defect (4) F-centres
122
Q.16 In a NaCl type crystal distance between Na+ and Cl– Q.24 Percentage of free space in a body centred cubic
ion is 2.814 Å and the density of solid is 2.167 g unit is -
–3
cm then find out the value of Avogadro constant. (1) 32 % (2) 34 % (3) 28 % (4) 30 %
[AIPMT-2004]
(1) 6.05 × 1023
(2) 3.02 × 1023 Q.25 If ‘a’ stands for the edge length of the cubic
(3) 12.10 × 10 23
(4) None systems : simple cubic, body centred cubic and face
centred cubic, then the ratio of radii of the spheres in
these system will be respectively. [AIPMT-2008]
Q.17 If ‘Z’ is the number of atoms in the unit cell that
1 1 1 3 2
represents the closest packing sequence ---A B C A (1) a: 3a: a (2) a : a: a
B C ----, the number of tetrahedral voids in the unit 2 2 2 2 2
cell is equal to - [AIIMS-2005] 1 3 1
(1) Z (2) 2 Z (3) Z/2 (4) Z/4 (3) 1a : 3 a : 2a (4) a: a: a
2 4 2 2
Q.18 In a face-centered cubic lattice, an unit cell is shared Q.26 Which of the following statement/s is /are not
equally by how many unit cells : [AIPMT-2005] correct ? [AIPMT-2008]
(1) 4 (2) 2 (3) 6 (4) 8 (1) Molecular solids are generally volatile
(2) The numbers of carbon atoms in an unit cell of
Q.19 Density of Li atom is 0.53 g cm–3. The edge length of Li diamond is 4
is 3.5 Å. Find out the number of Li atoms in an unit cell. (3) The number of Bravais lattices in which a crystal
(Na = 6.023 × 1023), (M = 6.94 g mol–1) [AIPMT-2005] can be categorized is14
(1) 2 (2) 8 (3) 4 (4) 6 (4) The fraction of the total volume occupied by the
atoms in a primitive cell is 0.48
Q.20 The Ca2+ and F– are located in CaF2 crystal, respectively at
face centred cubic lattice pointsand in - [AIIMS-2006] Q.27 Cupper crystallizes in a face-centred cubic lattice
(1) Tetrahedral voids (2) Half of tetrahedral voids with a unit cell length of 361 pm. What is the radius
(3) Octahedral void (4) half of octahedral voids of cupper atom in pm ? [AIPMT-2009]
(1) 128 (2) 157 (3) 181 (4) 108

Q.21 CsBr crystallises in a body centred cubic lattice.

Q.28 Lithium metal crystallises in a body centred cubic
The unit cell length is 436.6 pm. Given that the
atomic mass of Cs = 133 and that of Br = 80 amu and crystal. If the length of the side of the unit cell of
Avogadro number being 6.023 × 1023 mol–1, the lithium is 351pm, the atomic radius of lithium will
density of CsBr is - [AIPMT-2006] be : [AIPMT-2009]
(1) 42.5 g cm–3 (2) 0.425 g cm–3 (1) 240.8 pm (2) 151.8 pm
(3) 8.25 g cm–3 (4) 4.25 g cm–3 (3) 75.5 pm (4) 300.5 pm

Q.22 NaCl is doped with 10–4 mol% SrCl2, the concentra-

tion of cation vacancies is - [AIPMT-2007] Q.29 AB crystallizas in a body centred cubic lattice with
edge length ‘a’ equal to 387 pm. The distance be-
 10 – 4  tween two oppositively charged ions in the lattice
 H int : Concentrat ion of vacancies  NA 
 100  is : [AIPMT-2010]
(1) 6.02 × 1015 mol–1 (2) 6.02 × 1016 mol–1 (1) 335 pm (2) 250 pm
(3) 200 pm (4) 300 pm
(3) 6.02 × 1017 mol–1 (4) 6.02 × 1014 mol–1
Q.30 A solid compound XY has NaCl structure. If the
radius of the cation is 100 pm, the radius of the
Q.23 The fraction of total volume occupied by the atoms anion (Y–) will be- [AIPMT MAINS-2011]
present in a simple cube is - (1) 165.7 pm (2) 275.1 pm

  (3) 322.5 pm (4) 241.5 pm

 
(1) (2) (3) (4)
6 3 2 4 2 4
123
 EXERCISE # 3 (B)
Q.1 The 8 : 8 type of packing is present in Q.10 Which of the following is not a crystalline solid ?
[EAMCET- 84] [KCET- 95]
(1) NaCl (2) KCl (3) CsCl (4) MgF2 (1) KCl (2) CsCl
(3) Glass (4) Rhombic S
Q.2 The number of spheres in contact with a tetrahedral
Q.11 A metallic crystal crystallizes into a lattice contain-
void is : [MLNR- 90]
ing a sequence of layers AB AB AB...... Any pack-
(1) 3 (2) 6 (3) 4 (4) 8
ing of spheres leaves out voids in the lattice. What
Q.3 Which of the following has hcp crystal structure ? percentage of volume of this lattice is empty
space ? [AFMC- 95]
[KCET- 90]
(1) 74 % (2) 26 %
(1) NaCl (2) CsCl (3) Zn (4) RbCl
(3) 50 % (4) None of these
Q.4 Co-ordination number of Cu is - [AMU- 90]
Q.12 A solid has sturcture in which W atoms are located
(1) 1 (2) 6 (3) 8 (4) 12 at the corners of a cubic lattice, O atoms at the
centre of edges and Na atom at centre of the cube.
Q.5 Space lattice of CaF2 is - [MP PMT- 93]
the formula of the compound is ?
(1) fcc (2) bcc [Kurukshetra CEE- 93]
(3) simple cubic (4) hcp (1) NaWO2 (2) NaWO3
(3) Na2WO3 (4) NaWO4
Q.6 A match box exhibits [MP CEE - 93]
(1) Cubic geometry Q.13 Cu have f.c.c. unit cell and edge length 362 pm than

(2) Monoclinic geometry density of copper is - [RPMT-2001]

–3 –3
(1) 8.90 g cm (2) 2.23 g cm
(3) Tetragonal geometry
–3
(3) 6.29 g cm (4) 4.45 g cm–3
(4) Orthorhombic geometry
Q.14 The co-ordination number of bcc, scc and fcc is :
Q.7 In CsCl structure, each Cs+ ions is surrounded by ?
[RPMT-2001]
[MP CEE - 93]
(1) 8, 6, 12 (2) 6, 8, 12
(1) 4 Cl– ions (2) 6 Cl– ions
(3) 6, 6, 12 (4) 8, 12, 12
(3) 8 Cl– ions (4) 12 Cl– ions
Q.15 In ionic crystal an increase in temperature :
Q.8 Which of the following is an example of body
[AMU-2002]
centred cube ? [Pb. CET - 94]
(1) Increases the coordination no.
(1) Mg (2) Zn (3) Cu (4) Na
(2) Lowers the co-ordination no.
Q.9 In crystal structure of sodium chloride, the (3) Causes no change in the structure
arrangement of Cl– ions is - [BHU- 95] (4) Causes no change in co-ordination no.
(1) fcc (2) bcc Q.16 What is the % of volume occupied by atom in BCC
(3) Both fcc and bcc (4) None of these [RPMT-2007]
(1) 58 % (2) 68 % (3) 78 % (4) 88 %

124
Q.17 Co-ordination number in HCP is ? [RPMT-2007] Q.24 Alternate tetrahedral void in FCC are occupied in -
[IIT - 2005]
(1) 6 (2) 8 (3) 12 (4) 18 (1) NaCl (2) ZnS
(3) CaF2 (4) Na2O
Q.18 Structure of Mg is : [RPMT-2007]
(1) Hexagonal (HCP) (2) CCP Q.25 The edge length of a face centred cubic cell of an
(3) BCC (4) FCC ionic substance is 508 pm. If the radius of the cation
is 110 pm, the radius of the anion is -
Q.19 The lattice structure of group I elements is ?
[AIEEE-2010]
[RPMT-2007] (1) 144 pm (2) 288 pm
(1) FCC (2) BCC (3) HCP (4) CCP (3) 398 pm (4) 618 pm

Q .20 What type of crystal defect is indicated in the Q.26 Percentages of free space in cubic close packed
diagram below ? [AIEEE-2004] structure and in body centered packed structure
Na+ Cl– Na+ Cl– Na+ Cl– are respectively. [AIEEE-2010]
Cl– Cl– Na+ Na+ (1) 48 % and 26 % (2) 30 % and 26 %
Na+ Cl– Cl– Na+ Cl– (3) 26 % and 32 % (4) 32 % and 48 %
Cl– Na+ Cl– Na+ Na+
(1) Frenkel defect Q.27 In a face centred cubic lattice, atom A occupies the
(2) Schottky defect corner positions and atom B occupies the face cen-
(3) Interstitial defect
tre positions. If one atom of B is missing from one
(4) Frenkel and Schottky defects.
of the face centred points, the formula of the com-
Q.21 Total volume of atoms present in a face-centred
pound is: [AIEEE-2011]
cubic unit cell of a metal is (r is atomic radius)
[AIEEE 2006] (1) A2B (2) AB2
24 3 12 3 (3) A2B3 (4) A2B5
(1) r (2) r Q.28 Copper crystallizes in fcc lattice with a unit cell edge
3 3
16 3 20 3 of 361 pm. The radius of copper atom is -
(3) r (4) r
3 3 [AIEEE-2011]
Q.22 In a compound, atoms of element Y form ccp lattice (1) 108 pm (2) 128 pm
and those of element X occupy 2/3rd of tetrahedral (3) 157 pm (4) 181 pm
voids. The formula of the compound will be -
[AIEEE 2008]
(1) X2Y3 (2) X2Y
(3) X3Y4 (4) X4Y3

Q.23 In a solid AB having the NaCl structure, A atoms

occupy the corners of the cubic unit cell. If all the
face centered atoms along one of the axes are
removed, then the resultant stoichiometry of the
solid is - [IIT - 2001]

(1) AB2 (2) A2B

(3) A4B3 (4) A3B4

125
 EXERCISE # 4
(ASSERTION & REASON TYPE)
These questions consist of two statements each, Q.6 Assertion : Metals are generally good conductors
printed as Assertion and Reason. While of electricity.
answering these Question you are required to Reason : Eletrical conductivity of metals is due
choose any one of the follwonig four responses. to schottky defect.
(A) If both Assertion & Reason are True & the (1) A (2) B (3) C (4) D
Reason is a correct explanation of the Q.7 Assertion : Na2O adopts structure similar to that
Assertion. of CaF2 but positions of positive and negative
(B) If both Assertion & Reason are True but ions are reversed.
Reason is not a correct explanation of the Reason : The structure of Na2O is also called
Assertion. inverse spinel struture.
(C) If Assertion is True but the Reason is False. (1) A (2) B (3) C (4) D
(D) If both Assertion & Reason are False.
Q.8 Assertion : The number of tetrahedral void is
Q.1 Assertion : Due to Frenkel defect the density of double the number of octahedral voids.
solid decrease. Reason : The size of the tetrhedral void is half
Reason : In Frenkel defect cation or anion is of that of the octahedral void.
present leaving lattice sites vacant. (1) A (2) B (3) C (4) D
(1) A (2) B (3) C (4) D Q.9 Assertion : Graphite is an example of tetragonal
Q.2 Assertion : By increasing the temperature C.N. crystal system.
of CsCl changes from 8 : 8 to 6 : 6. Reason : For a tetragonal system a = b  c,
Reason : Temperature also influences the C.N. of  =  = 90º,  = 120º
solid. (1) A (2) B (3) C (4) D
(1) A (2) B (3) C (4) D Q.10 Assertion : In NaCl structure, the interionic
Q.3 Assertion : Solid having more F-centers have distance is a/2. (a = Unit cell edge legth)
intense colour. Reason : NaCl form face centered Cubic Unit
Reason : Excess of Na+ in NaCl solid having F- Cell.
centers make it appears to pink. (1) A (2) B (3) C (4) D
(1) A (2) B (3) C (4) D Q.11 Assertion : The co-ordination number of CaF2 is
Q.4 Assertion : Close packing of atoms in cubic 8 : 4.
structure is in order of : fcc > bcc > sc Reason : Ca2+ ions occupy ccp lattice while F–
Reason : Packing efficiency ions occupy 50 % octahedral voids & 50 %
tetrahedral voids.
 vol. of sphere in an unit cell 
=   (1) A (2) B (3) C (4) D
 a3 
Q.12 Assertion : The number of spheres are equal to
(1) A (2) B (3) C (4) D the number of octahedral void as well as tetrahedral
Q.5 Assertion : In CsCl crystal, the Co-ordination void.
number of Cs+ ions is 6. Reason : Octahedral void & tetrahedral void has
Reason :Cl– ion in CsCl, adopt body centred equal size.
cubic arrangement (1) A (2) B (3) C (4) D
(1) A (2) B (3) C (4) D
126
Q.13 Assertion : In Schottky defect, density of crystal Q.14 Assertion : If a tetrad axis is passed through the
decreases. unit cell of NaCl & all ions are removed which
Reason : Equal number of cations & anions are are touching to tetrad axis than the formula of
missing in Schottky defect. NaCl becomes Na3 Cl4.
(1) A (2) B (3) C (4) D Reason : Only one Na+ is removed not the
Cl–.
(1) A (2) B (3) C (4) D

127
 EXERCISE # 5
(NCERT QUESTIONS)
1. Explain -
(a) Unit cell is not simply a cube of four sodium 4. Niobium crystallizes in body centred cubic struc-
ions and four chloride ions. ture. If density is 8.55 g cm–3, calculate atomic ra-
(b) Can be cube consisting of Na+ and Cl– ions at dius of niobium. (MW of niobium = 93) -
alternate corners serve as a satisfactory unit Sol. Given that Crystal density = 8.55 g cm–3
cell for the sodium chloride lattice ? for BCC, n = 2
Sol. (a) A unit cell has its atoms on the edges and lattice MW of niobium = 93
point also shared by other unit cells. The atom
n  MW
does not singly belong to any particular unit  Crystal density =
V  NA
cell and a unit cell actually exists as part of a
lattice and not as individual cell. 2  93
V= = 3.6 × 10–23 cm3
8.55  6.023  10 23
(b) No, NaCl consists of two half way
or a3 = 36 × 10–24 cm3
interpenetrating fcc lattices, one composed
entriely of Na+ ions and the other composed  a = 3.3 ×10–8 cm
entirely of Cl– ions. for BCC 4r = 3 a

1.732  3.3  10 –8
2. Silver crytallises in fcc lattice. If edge length of the r=
4
cell is 4.077 × 10–8 cm and density is 10.5 g cm–3,
r = 1.43 × 10–8 cm.
calculate the atomic mass of silver.
Sol. Given that a = 4.077 × 10–8 cm
5. If the radius of an octahdral void is r and the radius
Crystal density = 10.5 gm cm–3 of the atom in close packing is R, derive the relation
for fcc, n = 4 between r and R ?
n  MW Sol. In the triangle ABC
 Crystal density =
V  NA

4  MW
10.5 =
(4.077 10–8 )3  6.0231023 A

10.5  67.76  10 –24  6.023  10 23

MW = B C
4
= 107.14
BC2 = AB2 + AC2
3. A cubic solid is made up of two elements P and Q. 4R2 = 2(R + r)2
Atoms Q are present at the corners of the cube and
R+r= 2R
atoms P at the body centre. What is the formula of
the compound ? What are the co-ordination num- Rr
= 2
ber of P and Q ? -
R

Sol. PQ, 8 , 8 r r r
1+ = 2 ; R = 1.414 – 1 or R = 0.414
R
128
  Ni2+ = 0.959, Ni3+ = 0.041
6. Copper crystallises into a fcc lattice with edge length
The percentage of Ni2+ is 95.9%  96%and that of
3.61 × 10–8 cm. Show that the calculated density is Ni3+ = 4%
in agreement with its measured value of 8.92 g cm–3.
9. The compound CuCl has ZnS structure. Its density
Sol. Given that a = 3.61 × 10–8 cm
is 3.4 g cm–3. What is the length of the edge of the
for fcc, n = 4
unit cell ?
MW fo Cu = 63.5
Sol. ZnS has f.c.c. structure and thus CuCl has f.c.c.
n  MW
 Crystal density = structure, thus n = 4
V  NA
Density avogadro number Volume
4  63.5 Formula mass =
 Crystal density = n
(3.6110–8 )3 6.0231023
Crystal density = 8.96 gcm–3 3.4  6.023  10 23  Volume
97 =
4
It is agreement with measured value 8.92 g cm–3
7. Formula mass of NaCl is 58.45 g mol–1 and density  Volume = 189 × 10–22 cm3
of its pure form is 2.167 g cm–3. The average dis-
tance between adjacent sodium and chloride ions  Edge length a = 3
V = 3
(1.89  10 –22 )
in the crystal is 2.814 ×10–8 cm. Calculate Avogadro = 5.75 × 10–8 cm
constant - = 575 pm
Sol. Given that MW = 58.45 g mol–1 10. If the radius of the bromide ion is 0.182 nm, how
for fcc, n = 4 large a cation can fit in each of the tetrahedral
–3
Crystal density (C.D.) = 2.167 g cm hole ?
a r
= 2.814× 10–8 cm Sol. for tetrahedral hole = 0.225
2 r–
 a = 5.628 × 10–8 cm  r = 0.225 ×0.182 nm
 V = a3 = (5.628 × 10–8)3 cm3 = 0.4095 nm.
n  MW
 C.D. = 11. The first order diffaction of X-rays from a certain
V  NA
set of crystal planes occurs at an angle of 11.8º from
4  58.45
 NA = the planes. If the planes are 0.281 nm apart, what is
2.167  (5.628 10–8 )3
the wavelength of X-rays ?
NA = 6.025 × 1023
Sol. According to Bragg equation,
n = 2d sin
8. Analysis shows that nickel oxide has formula Ni0.98
2d sin 
O1.00. What fractions of the nickel exist as Ni2+ and or  =
n
Ni3+ ions ?
2 = 11.8º
Sol. Ni0.98 O1.00 and  = 5.9 º, n =1 (first order diffraction)
Let Ni2+ be a and Ni3+ be (1 – a), the average oxida- d = 0.281 nm = 0.281 ×10–9 m
tion no. of Ni.
2  (0.281 10 –9 m)(sin 5.9º )
=
2 1.00 1
a × 2 + (1 – a) × 3 =
0.98 = 2 × (0.281 ×10–9 m) × 0.146 = 0.584 × 10–10 m
 a = 0.959 = 0.0584 ×10–9 m or 0.0584 nm

129
12. Ferric oxide crystallises in a hexagonal close packed 14. Gold (atomic radius 0.144 nm) crystallises in a face
array to oxide ions with two out of every three octa- centred cubic unit cell. What is the length of the
hedral holes occupied ferric ions. Derive the for- side (edge) of the unit cell ?
mula of the ferric oxides. Sol. For a face centred cubic unit cell (fcc)
Sol. Hexagonal close packing having array of oxide ions a
with two out of three octahedral holes occupied by Radius of gold atom (r) =
2 2
Fe3+ ions has one octahedral void or holes corre-
sponding to each atom constituting the close pack-  a = 0 .144 × 2 2

ing. In iron oxide only 2/3 of octahedral holes are = 0.144 × 2 × 1.414 = 0.407 nm
3+
occupied by Fe ions. It means corresponding to 15. Aluminium crystallises in a cubic close-packed
3+
each oxide ion,there are 2/3 Fe ions. Thus, mo- structure. Its metallic radius is 125 pm
lecular formula of iron oxide is Fe2O3 . (a) What is the length of the side of the unit cell ?
13. Thallium choride, TiCl crystallises in either a simple (b) How many unit cells are there in 1.00 cm3 of
–
cubic lattice or a face centred cubic lattice of Cl aluminium ?
ions with TI+ ions in the holes. If the density of the Sol. Given that r = 125 pm
solid is 9.00 g cm–3 and edge of the unit cell is
for fcc n = 4
3.85×10–8 cm. what is the unit cell geometry ?
(a) 4r = 2a
Sol. Given that crystal density = 9.00 g cm–3
a = 3.85 × 10–8 cm 4r 4  125  10 –10
a= = = 3.53 × 10–8 cm
2 1.414
M W of TC = 204.38 + 35.3 = 239.9
a = 3.53 × 10–8 cm
n  MW
 Crystal density (C.D.) =
V  NA (b) No. of unit cell = Total volume/Volume of unit cell
1.00
9  (3.85 10–8 )3  6.0231023 =
n= V
239.9
1
n = 12.89 × 10–1 = 1.3 ~ 1 = [ V = a3]
So, lattice is simple cubic. (3.53  10 –8 )3
= 2.27 × 1022

130
 ANSWER KEY

EXERCISE # 1

Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ans. 3 4 4 4 3 3 3 4 3 4 2 2 1 3 2
Q.No. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Ans. 1 1 3 3 2 2 1 4 2 2 1 3 1 1 3
Q.No. 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
Ans. 2 2 3 3 2 2 3 1 2 3 3 3 3 4 3
Q.No. 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Ans. 3 4 1 4 1 2 4 3 3 1 2 2 1 2 4
Q.No. 61 62 63 64 65 66 67 68 69 70 71 72
Ans. 3 1 4 4 1 1 4 4 3 1 2 1

EXERCISE # 2
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ans. 2 1 1 1 4 3 1 4 1 2 2 4 4 1 3
Q.No. 16 17 18 19 20 21 22
Ans. 1 2 3 2 1 1 2

EXERCISE # 3 (A)

Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ans. 3 3 1 4 2 3 2 4 1 3 2 4 2 4 2
Q.No. 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Ans. 1 2 3 1 1 4 3 1 1 4 4 1 2 1 4

131
 EXERCISE # 3 (B)
Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Ans. 3 3 3 4 1 4 3 4 1 3 2 2 1 1 2
Q.No. 16 17 18 19 20 21 22 23 24 25 26 27 28
Ans. 2 3 1 2 2 3 4 4 2 1 3 4 2

EXERCISE # 4
Q.N o. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Ans . 4 1 3 1 4 3 2 3 4 2 3 4 1 4

132