Solid State-1
Solid State-1
Solid State-1
Contents
Topic Page No.
Theory 01 - 05
Exercise - 1 06 - 15
Exercise - 2 16 - 21
Exercise - 3 22 - 24
Exercise - 4 25 - 26
Answer Key 27 - 28
Syllabus
Solid state: Classification of solids, crystalline state, seven crystal systems
(cell parameters a, b, c, ), close packed structure of solids (cubic), packing
in fcc, bcc and hcp lattices; Nearest neighbours, ionic radii, simple ionic
compounds, point defects.
CUBIC
a
a
a
Simple Face Centred Body Centred
ORTHORHOMBIC
b
a Simple End Centred Body Centred Face Centred
TETRAGONAL MONOCLINIC
c c
a b b
a a
Simple Body Centred End Centred
Simple
c
a c
a b g 120o a
a a b a
a
Corner 1/8
Edge 1/4
Facecenter 1/2
Body Center 1
1
SCC 8 0 0 8× =1
8
1
BCC 8 0 1 8× +1×1 = 2
8
1 1
FCC 8 6 0 8× +6 × =4
8 2
3a
Body centre cubic : atomic radius, r =
4
2a
Face centre cubic/cubic close packed : atomic radius r =
4
4 r 4r
7. Edge of the cube in terms of r : a = 2r a= a=
3 2
3 3
4 r 4 r
8. Total volume of the cube, a3 : (2 r)3
3 2
1 1
= 12 (corners) × + 2(face centres)× + 3 (inside the body) ×1 = 6
6 2
(c) For HCP geometry packing efficiency = 74 %
The ABC ABC ....... peaking has cubic symmetry and is known as cubic close packing (ccp). The cubic
close packing close packing has face centered cubic (fcc) unit cell.
Types of Voids
rvoid rvoid
Triangular : 0.155 Tetrahedral : 0.225 .
rsphere rsphere
rvoid rvoid
Octahedral : 0.414 cubical void : 0.732
rsphere rsphere
ra
Limiting radius ratio Co-ord. No. Shape
rc
Example
(a) Schottky Defects : This type of defect is created when one positive ion and one negative ion are
missing from their respective positions leaving behind a pair of holes. Schottky defects are more common in
ionic compounds with high co-ordination number.
(b) Frenkel Defect – This type of defect is created when an ion leaves its correct lattice site and occupies an
interstitial site. Frenkel defects are common in ionic compounds which have low co-ordination number and in
which there is large difference in size between positive and negative ions.
Non Stoichiometric defects :
Metal excess Defects due to Anion Vacancies. A compound may have excess metal ion if a
negative ion is absent from its lattice site, leaving a ‘hole’, which is occupied by electron to
maintain electrical neutrality.
Metal Deficiency due to cations vacancies. The non-stoichiometric compounds may have metal
deficiency due to the absence of a metal ion from its lattice site. The charge is balanced by an
adjacent ion having higher positive charge.
A-2. Match the solids in Column-I with their constituent particle in Column-II and nature of binding force between
them in Column-III and Identify which is correct for these matching.
Column-I Column-II Column-III
Solid Constituent particle Binding force
(a) Diamond (p) Ion (i) Metallic
(b) Sodium Chloride (q) Atom (ii) Dipole dipole
(c) HCl (r) Kernel (iii) Ionic
(d) Aluminium (s) Molecule (iv) Covalent
(e) H2O(s) (v) H-bonding
(f) I2 (s) (vi) dispersion forces
(A) (a)- (q), (iv) ; (b)- (p), (iii) ; (c) - (s) , (ii) ; (d) - (r) , (i) ; (e) - (s) , (v) ; (f) -(s) , (vi)
(B) (a)- (q), (iv) ; (b)- (p), (iii) ; (c) - (p) , (iii) ; (d) - (r) , (i) ; (e) - (s) , (v) ; (f) -(s) , (vi)
(C) (a)- (q), (iv) ; (b)- (p), (iii) ; (c) - (p) , (iii) ; (d) - (p) , (iii) ; (e) - (s) , (v) ; (f) -(s) , (vi)
(D) (a)- (q), (iv) ; (b)- (p), (iii) ; (c) - (p) , (iii) ; (d) - (r) , (i) ; (e) - (s) , (iv) ; (f) -(s) , (vi)
A-4. Which of the following solids are not correctly matched with the bonds found between the constituent
particles:
(A) Solid CO2 : Vanderwaal's (B) Graphite : Covalent and Vanderwaal
(C) Grey Cast Iron : Ionic (D) Metal alloys : Ions-delocalised electrons
B-2. Which of the following are the correct axial distance and axial angles for rhombohedral system?
(A) a = b = c, = = 900 (B) a = b c, = = = 900
(C) ab c, = = = 90 0
(D) ab c, 900
C-2. In a face centerd lattice of X and Y, X atoms are present at the corners while Y atoms are at face centers.
Then the formula of the compound is :
(A) XY3 (B) X2Y3 (C) X3Y (D) XY
C-3. In a face centerd lattice of X and Y, X atoms are present at the corners while Y atoms are at face centers.
Then the formula of the compound would be if two atoms of X are missing from the corners :
(A) X4Y (B) X3Y4 (C) XY4 (D) X2Y4
C-4. In a cubic structure of compound which is made from X and Y, where X atoms are at the corners of the
cube and Y at the face centers of the cube. The molecular formula of compound is
(A) X2Y (B) X3Y (C) XY2 (D) XY3.
C-5. A solid has a structure in which W atoms are located at the corners of a cubic lattice. O atom at the center
of the edges and Na atom at center of the cube. The formula for the compound is
(A) NaWO2 (B) NaWO3 (C) Na2WO3 (D) NaWO4
C-6. A compound of A and B crystallizes in a cubic lattice in which A atoms occupy the lattice points at the
corners of a cube and two atoms of B occupy the center of each of the cube faces. What is the formula of
this compound?
(A) AB3 (B) AB4 (C) AB2 (D) AB6
C-7. An element (atomic mass = 100 g/mole) having BCC structure has unit cell edge 400 pm. The density of
the element is (no. of atoms in BCC(Z) = 2).
(A) 2.144 g/cm3 (B) 5.2 g/cm3 (C) 7.289 g/cm3 (D) 10.376 g/cm3
D-2. If the radius of a metal atom is 2.00 Å and its crystal structure in cubic close packed (fcc lattice), what is the
volume (in cm3) of one unit cell ?
(A) 8.00 × 10–24 (B) 1.60 × 10–23 (C) 1.80 × 10–22 (D) 2.26 × 10–23
D-4. The fraction of total volume occupied by the atoms in a simple cube is
π π π π
(A) (B) 2 (C) 2 (D)
4 8 6 6
D-5. Platinum crystallizes in a face-centered cubic crystal with a unit cell length 'a'. The distance between
nearest neighbors is :
3 2 2
(A) a (B) a (C) a (D) a
2 2 4
D-7. Metallic gold crystallises in face centered cubic. Lattice with edge-length 4.070 Å. Closest distance between
gold atoms is :
(A) 2.035 Å (B) 8.140 Å (C) 2.878 Å (D) 1.357 Å
D-8. Which of the following shaded plane in fcc lattice contains arrangement of atoms as shown by circles :
D-9. Lithium crystallizes in a body centered cubic lattice. How many next–nearest neighbors does each Li have?
(A) 6 (B) 8 (C) 12 (D) 4
D-10.* The co-ordination number of FCC structure for metals is 12, since
(A) each atom touches 4 others in same layer, 3 in layer above and 3 in layer below.
(B) each atom touches 4 others in same layer, 4 in layer above and 4 in layer below.
(C) each atom touches 6 others in same layer, 3 in layer above and 3 in layer below.
(D) each atom touches 3 others in same layer, 6 in layer above and 6 in layer below.
D-11. An element exists as hexagonal close packed structure as well as cubic closed packed structure. In which
case the element would have higher density ?
(A) ccp (B) hcp (C) same in both (B) unpredictable
D-12. What is the coordination number of atoms in BCC, HCP and CCP and simple lattices.
(A) 8, 12, 12, 6 (B) 6, 12, 12, 8 (C) 12, 6, 8, 12 (D) 12, 12, 8, 6
E-4. Match list- with list-II and select the correct answer by using the codes given below:
List I List II
(Shapes) (Radius ratio)
(A) Planar triangle 1. 0.732
(B) Square planar 2. 0.225
(C) Body centered cubic 3. 0.155
(D) Tetrahedral 4. 0.414
Codes
A B C D A B C D
(A) 3 4 1 2 (B) 3 2 1 4
(C) 2 1 4 3 (D) 1 3 4 2
E-6. A solid is formed and it has three types of atoms X, Y, Z. X forms a FCC lattice with Y atoms occupying all
the tetrahedral voids and Z atoms occupying half the octrahedral voids. The formula of the solid is:
(A) X2Y4Z (B) XY2Z4 (C) X4Y2Z (D) X4YZ2
E-7. The empty space between the shaded balls and hollow balls as shown in the diagram is called
(A) hexagonal void (B) octahedral void (C) tetrahedral void (D) double triangular void
F-2. The radius of Ag+ ion is 126 pm and that of – ion is 216 pm. The co-ordination number of Ag+ ion is.
(A) 2 (B) 4 (C) 6 (D) 8
F-3. The spinal structure (AB2O4) consists of an fcc array of O2– ions in which the :
(A) A cation occupies one-eighth of the tetrahedral holes and B cation occupies one-half of octahedral
holes
(B) A cation occupies one-fourth of the tetrahedral holes and the B cations the octahedral holes
(C) A cation occupies one-eighth of the octahedral hole and the B cation the tetrahedral holes
(D) A cation occupies one-fourth of the octahedral holes and the B cations the tetrahedral holes
F-4. An ionic solid of XY type having anions in CCP lattice and cations in the octahedral voids.Let a be the edge
length of an FCC cube.The radius ratio of cation(R+) to that of anion(R–)is greater than 0.415.Then which
of the following is false:
a a
(A) R+ = (B) R+ + R- =
2 2 2
(C) Anions will not be in contact with each other. (D) Cations will not be in contact with each other.
F-5. How many units cells are there in 1.00 g cube shaped ideal crystal of AB (Mw = 60) which has a NaCl type
lattice
(A) 6.02 × 1023 (B) 1.00 × 2022 (C) 2.50 × 1021 (D) 6.02 × 1024
F-6. 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
F-7. Which of the following statements is correct in the rock-salt structure of an 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.
F-8. 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
F-10. NH4Cl crystallizes in a body-centered cubic type lattice with a unit cell edge length of 387 pm. The distance
between the oppositively charged ions in the lattice is
(A) 335.1 pm (B) 83.77 pm (C) 274.46 pm (D) 137.23 pm
F-11. The tetrahedral voids formed by ccp arrangement of Cl¯ ions in rock salt structure are
(A) Occupied by Na+ ions (B) Occupied by Cl¯ ions
(C) Occupied by either Na+ or CI¯ ions (D) Vacant
F-12. Which of the following expressions is correct in the case of a sodium chloride unit cell (edge length = a)
(A) rc + ra = a/2 (B) rc + ra = a (C) rc + ra = 2a (D) rc + ra = 21/2 a
F-13. MgO exist in a rock-salt type unit cell. Each Mg+2 ion will be in contact with
(A) 4O–2 ions (B) 6O–2 ions (C) 8O–2 ions (D) 2O–2 ions
+
Na
–
–
e Cl
NaCl Crystal
(A) Frenkle (B) F–centre (C) Metal axcess (D) Edge dislocation
G-3. BaO has a rock-salt type structure. When subjected to high pressure, the ratio of the coordination number
of Ba+2 ion to O–2 changes to
(A) 4 : 8 (B) 8 : 4 (C) 8 : 8 (D) 4 : 4
G-5. The ionic radii of Rb+ and I– are 1.46 and 2.16 Å. The most probable type of structure exhibited by it is
(A) CsCI type (B) NaCl type (C) ZnS type (D) CaF2 type
G-8. A crystal of NaCl, which has sodium ions and chloride ions missing from the lattice point, is said to exhibit
(A) Surface defect (B) Lattice defect (C) Frenkel defect (D) Schottky defect
Comprehensions Type
Comprehension # 1
In HCP or CCP, constituent particles occupy 74% of the available space. The remaining space (26%) in
between the spheres, remains unoccupied and is called interstitial voids or holes. Considering the close
packing arrangement, each sphere in the second layer rests on the hollow space of the first layer, touching
each other. The void created is called tetrahedral void. If R is the radius of the sphere in the close packed
arrangement, then
r (radius of tetrahedral void) = 0.225 R
In a close packing arrangement, the interstitial void formed by the combination of two triangular voids of the
first and second layer is called octahedral void. Thus, double triangular void is surrounded by six spheres.
The centre of these sphere on joining, forms octahedron. If R is the radius of the sphere in a close packed
arrangement, then
r (radius of octahedral void = 0.414 R.
1. If the anions (A) form hexagonal close packing and cations (B) occupy only 2/3rd octahedral voids in it,
then the general formula of the compound is
(A) AB (B) A3B2 (C) A2B (D) AB2
2. If the spinel structure, oxide ions are cubic close whereas 1/8th of tetrahedral voids are occupied by A2+
cations and 1/2 of octahedral voids are occupied by B3+ cations. The general formula of the compound
having spinel structure is :
(A) A2B2 O4 (B) AB2O4 (C) A2B4O2 (D) A4B2O2
(A) simple cubic and face-centred cubic (p) have these cell parameters
a = b = c and = =
(C) cubic and tetragonal (r) have only two crystallographic angles of 90º
(A) 0.866 a (p) Shortest distance between cation & anion in CsCl structure.
(B) 0.707 a (q) Shortest distance between two cation in CaF2 structure.
3a
(B) Zinc Blend structure (q) = r+ + r–
4
(C) Flourite structure (r) Co-ordination number of cation and anion
are same
a
(s) Distance between two nearest anion is
2
15. Statement-1 : Distance between nearest lattice points in BCC is greater than the same in FCC for the
atoms of comparable size.
Statement-2 : FCC has greater packing efficiency than BCC.
(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1
(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement-2 is true.
17. Statement-1 : In Frenkel defect in an ionic crystal, an ion is displaced from its normal site to an interstitial
site.
Statement-2 : There is both a vacancy and an interstitial ion.
(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1
(B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement-2 is true.
20. The minimum void fraction for any unit cell in any shape having only one type of atom and all voids unfilled
is 0.26.
21. The location of tetrahedral voids in FCC unit cell are the centers of 8 minicubes forming a large cube.
22. Effective number of octahedral voids in a unit cell is equal to the effective number of atoms in the unit cell.
23. A metallic element crystallises into a lattice containing a sequence of layers of AB AB AB ...... . Any packing
of spheres leaves out voids in the lattice 26% percent by volume of this lattice is empty space.
24. Number of next neighbours of Cs+ ion in CsCl structure is 6 Cs+ ions.
25. A crystal has A ions at the cube corners and B ions at the edge centers. The coordination numbers of A and
B are respectively 6 and 2.
26. Distance between cation and its next neighbour in ZnS (zinc blande) is 1/4 of the length of body diagonal.
27. In the unit cell of HCP structure the three atoms shown in layer B are completely inside the unit cell.
Layer A
Layer B
Layer A
32. Anions would be in contact with each other only if the cation to anion radius for a given co-ordination
number is_______.
33. The number of tetrahedral voids in hexagonal primitive unit cell is________.
35. For cesium chloride structure, the interionic distance (in terms of edge length, a) is equal to _______.
36. Density of a crystal ___due to Schottky defect and _____due to Frankel defect.
39. A spinal is an important class of oxides consisting of two types of metal ions with the oxides ions arranged
in CCP layers. The normal spinal has one-eighth of the tetrahedral holes occupied by one type of metal ion
and one-half of the octahedral holes occupied by another type of metal ion. Such a spinal is formed by
Zn2+, Al3+ and O2– with Zn2+ in the tetrahedral holes. The formula of the spinal is_______________.
2. Given an alloy of Cu, Ag and Au in which Cu atoms constitute the CCP arrangement.If the hypothetical
formula of the alloy is Cu4Ag3Au. What are the probable locations of Ag and Au atoms.
(A) Ag - all Tetrahedral voids; Au - all Octahedral voids
(B) Ag - 3/8th Tetrahedral voids; Au - 1/4th Octahedral voids
(C) Ag - 1/2 Octahedral voids; Au - 1/2 Tetrahedral voids
(D) Ag - all Octahedral voids; Au - all tetrahedral voids
3. In diamond, carbon atom occupy FCC lattice points as well as alternate tetrahedral voids. If edge length of
the unit cell is 356 pm, then radius of carbon atom is
(A) 77.07 pm (B) 154.14 pm (C) 251.7 pm (D) 89 pm
4. A mineral having the formula AB2, crystallises in the cubic close - packed lattice, with the A atoms occupying
the lattice points. The co-ordination number of the A atoms, that of B atoms and the fraction of the tetrahedral
sites occupied by B atoms are
(A) 8, 4, 100% (B) 2, 6, 75% (C) 3, 1, 25% (D) 6, 6, 50%
6. If the radii of A+ and B– are 95 pm and 181 pm respectively, then the coordination number of A+ will be ?
(A) 12 (B) 8 (C) 6 (D) 4
7. The coordination number of cation and anion in Fluorite CaF2 and Rutile TiO2 are respectively :
(A) 8 : 4 and 6 : 3 (B) 6 : 3 and 4 : 4 (C) 6 : 6 and 8 : 8 (D) 4 : 2 and 2 : 4
8. The distance between adjacent, oppositely charged ions in rubidium chloride is 3.285 Å; in potassium
chloride is 3.139Å; in sodium bromide is 2.981 Å and in potassium bromide is 3.293 Å. The distance
between adjacent oppositely charged ions in rubidium bromide is
(A) 3.147 Å (B) 3.385 Å (C) 3.393 Å (D) 3.439 Å
9. Edge length of M+X– (fcc structure) is 7.2 Å. Assuming M+ – 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
10. The density of KBr is 2.75 g cm–3 and length of the unit cell is 654 pm (K = 39 and Br = 80) then what is true
about the predicted nature of the solid.
(A) Solid has fcc system with Z = 4 (B) Solid has simple cubic system with Z = 4
(C) Solid has bcc system will Z = 3 (D) Solid has bcc system with Z = 2
(A) 6.017 × 1023 (B) 6.023 × 1023 (C) 6.03 × 1023 (D) 6.017 × 1019
12. In NaCl if rNa+ = 100 pm, then maximum size of rCl will be :
(A) 241.5 pm (B) 261.5 pm (C) 251.5 pm (D) 271.5 pm
14. In a solid lattice,the cation has left a lattice site and is located at interstitial position, the lattice defect is :
(A) interstitial defect (B) vacancy defect (C) Frenkel defect (D) Schotlky defect
15. A piece of copper and another of Ge are cooled from room temperature to 80 K. The resistance of:
(A) each of them increases (B) Cu increases and that of Ge decreases
(C) Cu decreases and that of Ge increases (D) each of them decreases
16. Zinc sulphide exists in two different forms-zinc blende and wurtzite. Both occur as 4:4 co-ordination
compounds. Choose the correct option from among the following :
(A) zinc blende has a bcc structure and wurtzite an fcc structure
(B) zinc blende has an fcc structure and wurtzite an hcp structure
(C) zinc blende as well as wurtzite have a hcp structure
(D) zinc blende as well as wurtzite have a cpp structure
17. Choose the correct matching sequence from the possibilities given
(a) Crystal defect (1) AB AB AB ..... type crystal
(b) hcp (2) Covalent crystal
(c) CsCl (3) Frenkel
(d) Diamond (4) Face centered in cube
(e) NaCl (5) Simple cubical lattice
(a) (b) (c) (d) (e) (a) (b) (c) (d) (e)
(A) 3 1 2 5 4 (B) 3 1 5 2 4
(C) 3 5 1 2 4 (D) 5 3 4 2 1
18. In hcp (ABAB...) and ccp (ABCABC...) structures made up of spheres of equal size, the volume
occupied per sphere (including the empty spaces) is (a = radius of sphere) :
(A) 5.66 a3 (B) 1.33 a3 (C) 2.66 a3 (D) 7.40 a3
19. In an f.c.c. crystal, which of the following shaded planes contains the following type of arrangement of
atoms?
21. The number of atoms in 100 g of an FCC crystal with density d = 10 gcm–3 and cell edge of 200 pm is equal
to :
(A) 3 × 1025 (B) 5 × 1024 (C) 1 × 1025 (D) 2 × 1025
22. In a face centerd lattice of X and Y, X atoms are present at the corners while Y atoms are at face centers.
Then the formula of the compound would be if one of the X atoms is missing from a corner in each unit cell
(A) X7Y24 (B) X24Y7 (C) XY24 (D) X24Y
23. Aluminum metal has a density of 2.72g/cm3 and crystallizes in a lattice with an edge length of 404 pm.Which
of the following alternatives are correct
(A) it forms a base centered cubic unit cell (B) it forms a face centered cubic unit cell
(C) its coordination number is 8 (D) its coordination number is 6
24. Consider a Body Centered Cubic(BCC) arrangement, let de, dfd, dbd be the distances between successive
atoms located along the edge, the face-diagonal, the body diagonal respectively in a unit cell.Their order is
given by:
(A) de < dfd < dbd (B) dfd > dbd > de (C) dfd > de > dbd (D) dbd > de > dfd,
25. Figure shows a cube of unit cell of CCP arrangement with face centered atoms marked 1, 2, 3.Which of the
following statements is true.
3
1
(A) Atom 3 is twice as far from 1 as from 2 (B) Atom 2 is equidistant from atoms 1 & 3.
(C) Atom 2 is nearer to 1 than to 3. (D) All atoms lie on a right angled triangle.
26. Consider a cube 1 of Body Centered Cubic unit cell of edge length a now atom at the body center can be
viewed to be lying on the corner of another cube 2.Find the volume common to cube 1 and cube 2.
a3 a3 a3 a
3
(A) (B) (C) (D)
27 64 2 2 8
27. You are given 6 identical balls.What is the maximum number of square voids and triangular voids(in sepa-
rate arrangements) that can be created (balls are to be arranged in one plane)?
(A) 2 , 4 (B) 4 , 2 (C) 4 , 3 (D) 3 , 4
28. MgAl2O4, is found in the Spinal structure in which O 2 ions constitute CCP lattice, Mg2+ ions occupy 1/8th of
the Tetrahedral voids and Al3 ions occupy 1/2 of the Octahedral voids.
Find the total +ve charge contained in one unit cell.
(A) +7/4 electronic charge (B) +6 electronic charge
(C) +2 electronic charge (D) +8 electronic charge
29. Which of the following statements are correct in context of point defects in a crystal ?
(A) AgCl has anion Frenkel defect and CaF2 has Schottky defects
(B) AgCl has cation Frenkel defects and CaF2 has anion Frenkel defects
(C) AgCl as well as CaF2 have anion Frenkel defects
(D) AgCl as well as CaF2 has Schottky defects
31. There are three ionic compounds, first compound has fcc lattice of anions and cations are present in all
tetrahedral voids, second compound has fcc lattice of anions and cations are present in all octahedral
voids and third compound has simple cubical lattice in which cubical void is occupied by cation, then the
order of packing efficiency of these will be
(A) > > (B) > > (C) > > (D) > >
32. Strontium chloride has a fluorite structure, which of the following statement is true for the structure of
strontium chloride ?
(A) the strontium ions are in a body–centered cubic arrangement
(B) the strontium ions are in a face–centered cubic arrangement
(C) each chloride ion is at the center of a cube of 8 strontium ions
(D) each strontium ion is at the center of a tetrahedron of 4 chloride ions
33. Zinc Oxide, white in colour at room temperature, acquires yellow colour on heating due to:
(A) Zn being a transition element
(B) paramagnetic nature of the compound
(C) trapping of electrons at the site vacated by Oxide ions
(D) Both (A) & (B)
34. NaCl shows Schottky defects and AgCl Frenkel defects. Their electrical conductivity is due to :
(A) motion of ions and not the motion of electrons
(B) motion of electrons and not the motion of ions
(C) lower co-ordination number of NaCl
(D) higher co-ordination number of AgCl
36. The ionic radii of Cs and Cl are 0.165 nm and 0.181nm respectively. Their atomic weights are 133 and
35.5. Then,
(A) the lattice parameter (a) is 0.4 nm
(B) the lattice parameter can not be determined from this data
(C) the density of CsCI is 4.37 × 103 kg/m3
(D) the CsCI structure has a fcc structure on the basis of given information.
40. Which statements is/are true about HCP and CCP lattice
(A) Number of tetrahedral voids are twice of octahedral holes
(B) 12 tetrahedral and 6 octahedral voids are present in one HCP unit cell
(C) C.N. of HCP unit cell is 12
(D) If atom of tetrahedral voids displace into octahedral voids then it is Schootky defect.
41. Given that interionic distance in Na+ F– crystal is 2.31Å and rF = 1.36Å, which of the following predictions
will be right
(A) rNa rF 0.7
(B) coordination number of Na+ = coordination nunber of F– = 6
(C) Na+ F– will have rock salt type crystal structure
(D) effective nuclear charge for Na+ and F– are equal
1. Silver crystallizes in cubic lattice. The density is found to be 10.7 kg/dm3. If the unit cell length is 4.06Å, find
the unit cell type.
2. A compound formed by elements X & Y, Crystallizes in a cubic structure, where X is at the corners of the
cube and Y is at six face centers. What is the formula of the compound? If side length is 5Å, estimate the
density of the solid assuming atomic weight of X and Y as 60 and 90 respectively.
3. The metal nickel crystallizes in a face centred cubic structure. Its density is 8.9 gm/cm3. Calculate
(a) the length of the edge of the unit cell.
(b) the radius of the nickel atom. [Atomic weight of Ni = 58.89]
4. Four identical spheres of radius r are arranged such that centers of three of them form an equilateral
triangle and the fourth one rests symmetrically above the triangle touching all of them. Find :
(i) The area of the triangle thus formed.
(ii) Perpendicular distance between the triangle and the center of the fourth atom.
(iii) Are all the balls identical in the arrangement ?
5. Consider a corner atom of Ist layer of an HCP unit cell showing alternate AA layers. Find
(i) Find identical atoms (III layer) with respect to the distances from the atom 1.
(ii) Arrange the distances in ascending order.
e d
Layer A
f g c
a b
Layer A
Atom 1
7. 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.
8. A solid A+B– has NaCl type close packed structure. If the anion has a radius of 241.5 pm, what should be
the minimum radius of the cation ? Can a cation C+ having radius of 50 pm be fitted into the tetrahedral
hole of the crystal A+B– ?
9. In a crystalline solid, anions B are arranged in a cubic close packing. Cations A are equally distributed
between octahedral and tetrahedral voids. If all the octahedral voids are occupied, what is the formula of
the solid ?
10. In corundum, oxide ions are arranged in hexagonal close packing and aluminium ions occupy two–third
of the octahedral voids. What is the formula of corundum ?
11. The two ions A+ and B– have radii 88 and 200 pm respectively. In the close packed crystal of compound AB,
predict the co–ordination number of A+.
12. A small sphere of radius 10Å was found to fit perfectly in the largest void of Simple Cubic arrangement.Find
the location of the sphere and the volume of the unit cell.
13. A spinal is an important class of oxides consisting of two types of metal ions with the oxides ions arranged
in CCP layers. The normal spinal has one-eighth of the tetrahedral holes occupied by one type of metal ion
and one-half of the octahedral holes occupied by another type of metal ion. Such a spinal is formed by
Zn2+, Al3+ and O2– with Zn2+ in the tetrahedral holes. Give formula of the spinal.
Face centres
14. In Rock Salt type structure cations(radius r) occupy Octahedral holes in the FCC
of anions(radius R) such that there is no distortion in the FCC lattice. Find the
perimeter of the shaded region.
16. Given that is the ratio of the observed to the theoretical densities of a solid.Can one give the idea about
the value of for the following.
(i) Schottky defects are present in the solid.Find fraction of the missing units.
(ii) Interstitial defects are present in the solid.
(iii) Frenkel defects are present.
17. Calculate the concentration of cation vacancies if NaCl is doped with 10–3 mole % of SrCl2.
18. The edge length of the unit cube of diamond is 356.7 pm and this cube contains 8 carbon atoms. Calculate:
(a) the distance dC–C between carbon atoms, assuming them to be spheres in contact;
(b) the fraction of the total volume that is occupied by carbon atoms.
2. 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 :
[JEE-2001, 1/35]
(A) AB2 (B) A2B (C) A4B3 (D) A3B4
3. A substance Ax By crystallizes in a face centered cubic lattice in which atoms ‘A’ occupy each corner of the
cube and atoms ‘B’ occupy the centers of each face of the cube . Identify the correct composition of the
substance Ax By . [JEE-2002, 3/90]
(A) AB3 (B) A4 B3
(C) A3 B (D) composition cannot be specified
4. Marbles of diameter 10 mm each are to be arranged on a flat surface so that their centers 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, 2/60]
5. A binary salt AB (formula weight = 6.023 Y amu, where Y is an arbitrary number) has rock salt structure with
1 : 1 ratio of A to B. The shortest A-B distance in the unit cell is Y1/3 nm. [JEE-2004, 4/60]
–3
(a) Calculate the density of the salt in kg m .
(b) Given that the measured density of the salt is 20 kg m–3, specify the type of point defect present in the
crystal.
6. In which of the following compounds the cations are present in alternate tetrahedral voids:[JEE-2005,3/84]
(A) NaCl (B) ZnS (C) CaF2 (D) Na2O
7. In a FCC lattice of a metal edge length is 400 pm. Find the maximum diameter of an atom which can be
accommodated in an interstitial gap in this lattice without causing any distortion. [JEE-2005, 2/60]
8. For a unit cell edge length = 5Å, the element is of atomic mass 75, has density of 2gm/cc. Calculate atomic
radius of the element. [JEE-2006, 6/184]
9. Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in
Column II. [JEE-2007, 6/162]
Column I Column II
(A) simple cubic and face-centerd cubic (p) have these cell parameters
a = b = c and = =
(C) cubic and tetragonal (r) have only two crystallographic angles of 90º
10. The number of atoms in the HCP unit cell is [JEE-2008, 4/81]
(A) 4 (B) 6 (C) 12 (D) 17
12. The empty space in this HCP unit cell is [JEE-2008, 4/81]
(A) 74% (B) 47.6% (C) 32% (D) 26%
13.* The correct statement(s) regarding defects in solids is(are) : [JEE-2009, 4/80]
(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.
14. The packing efficiency of the two dimensional square unit cell shown below is : [JEE-2010, 5/79]
15. The number of hexagonal faces that are present in a turncated octahedron is. [JEE-2011s, 4/80]
16. A compound MpXq has cubic close packing (ccp) arrangement of X. Its unit cell structure is show below.
The empirical formula of the compound is- [JEE-2012, 5/210]
1. Na and Mg crystallize in BCC and FCC type crystals respectively, then the number of atoms of Na and Mg
present in the unit cell of their respective crystal is [AIEEE-2002]
(1) 4 and 2 (2) 9 and 14 (3) 14 and 9 (4) 2 and 4
2. How many unit cells are present in a cube-shaped ideal crystal of NaCl of mass 1.00g?
[Atomic masses : Na = 23, Cl = 35.5] [AIEEE-2003]
(1) 2.57 × 1021 (2) 5.14 × 1021 (3) 1.28 × 1021 (4) 1.71 × 1021.
4. An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centers of
the faces of the cube. The empirical formula for this compound would be [AIEEE-2005]
(1) AB (2) A2B (3) AB3 (4) A3B
5. Total volume of atoms present in a face-center cubic unit cell of a metals (r is atomic radius)
[AIEEE-2006]
20 3 24 3 12 3 16 3
(1) r (2) r (3) r (4) r
3 3 3 3
6. 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 - 2008, 3/105]
(1) X2Y3 (2) X2Y (3) X3Y4 (4) X4Y3
7. Copper crystallises in fcc with a unit cell length of 361 pm. What is the radius of copper atom ?
[AIEEE - 2009, 8/144]
(1) 127 pm (2) 157 pm (3) 181 pm (4) 108 pm
8. The edge length of a face centred cubic cell of an ionic substance is 508 pm. If the radius of the cation is
110 pm, the radius of the anion is : [AIEEE - 2010, 4/144]
(1) 288 pm (2) 398 pm (3) 618 pm (4) 144 pm
9. Percentages of free space in cubic close packed structure and in body centered packed structure are
respectively. [AIEEE - 2010, 4/144]
(1) 30% and 26% (2) 26% and 32% (3) 32% and 48% (4) 48% and 26%
10. In a face centred cubic lattice, atom A occupies the corner position and atom B occupies the face centre
positions. If one atom of B is missing from one of the face centred points, the formula of the compound is:
[AIEEE - 2011]
(1) A2B (2) AB2 (3) A2B3 (4) A2B5
11. 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 - 2012]
(1) 75 pm (2) 300 pm (3) 240 pm (4) 152 pm
2. What makes a glass different from a solid such as quartz? Under what conditions could quartz be con-
verted into glass?
3. Classify each of the following solids as ionic, metallic, molecular, network (covalent) or amorphous.
(i) Tetra phosphorus decoxide (P4O10) (ii) Ammonium phosphate (NH4)3PO4
(iii) SiC (iv) I2
(v) P4 (vi) Plastic
(vii) Graphite (viii) Brass
(ix) Rb (x) LiBr
(xi) Si
5. How can you determine the atomic mass of an unknown metal if you know its density and the dimension of
its unit cell? Explain.
6. 'Stability of a crystal is reflected in the magnitude of its melting points'. Comment. Collect melting points of
solid water, ethyl alcohol, diethyl ether and methane from a data book. What can you say about the
intermolecular forces between these molecules?
8. How many lattice points are there in one unit cell of each of the following lattice?
(i) Face-centred cubic
(ii) Face-centred tetragonal
(iii) Body-centred
9. Explain
(i) The basis of similarities and differences between metallic and ionic crystals.
(ii) Ionic solids are hard and brittle.
11. Silver crystallises in fcc lattice. If edge length of the cell is 4.07 × 10–8 cm and density is 10.5 g cm–3,
calculate the atomic mass of silver.
13. Niobium crystallises in body-centred cubic structure. If density is 8.55 g cm –3, calculate atomic radius of
niobium using its atomic mass 93 u.
14. If the radius of the octahedral void is r and radius of the atoms in closepacking is R, derive relation between
r and R.
15. Copper crystallises into a fcc lattice with edge length 3.61 × 10–8 cm. Show that the calculated density is in
agreement with its measured value of 8.92 g cm–3.
16. Analysis shows that nickel oxide has the formula Ni0.98O1.00. What fractions of nickel exist as Ni2+ and Ni3+
ions?
17. What is a semiconductor? Describe the two main types of semiconductors and contrast their conduction
mechanism.
18. Non-stoichiometric cuprous oxide, Cu2O can be prepared in laboratory. In this oxide, copper to oxygen
ratio is slightly less than 2:1. Can you account for the fact that this substance is a p-type semiconductor?
19. Ferric oxide crystallises in a hexagonal close-packed array of oxide ions with two out of every three octahedral
holes occupied by ferric ions. Derive the formula of the ferric oxide.
20. Classify each of the following as being either a p-type or a n-type semiconductor :
(i) Ge doped with In (ii) Si doped with B.
21. Gold (atomic radius = 0.144 nm) crystallises in a face-centred unit cell. What is the length of a side of the
cell?
24. Aluminium crystallises in a cubic close-packed structure. Its metallic radius is 125 pm.
(i) What is the length of the side of the unit cell?
(ii) How many unit cells are there in 1.00 cm3 of aluminium?
25. If NaCl is doped with 10–3 mol % of SrCl2, what is the concentration of cation vacancies?
A-1 (A) A-2. (A) A-3. (C) A-4. (C) B-1. (A) B-2. (A) B-3. (B)
B-4. (C) C-1. (A) C-2. (A) C-3. (C) C-4. (D) C-5. (B) C-6. (D)
C-7. (B) D-1. (B) D-2. (C) D-3. (A) D-4. (D) D-5. (C) D-6. (C)
D-7. (C) D-8. (C) D-9. (A) D-10.* (B*C) D-11. (C) D-12. (A) E-1. (C)
E-2. (A) E-3. (D) E-4. (A) E-5. (C) E-6. (A) E-7. (B) F-1. (C)
F-2. (C) F-3. (A) F-4. (A) F-5. (C) F-6. (C) F-7. (D) F-8. (C)
F-9. (B) F-10. (A) F-11. (D) F-12. (A) F-13. (B) F-14.* (ABD) F-15.* (AB)
G-1. (B) G-2. (B) G-3. (C) G-4. (B) G-5. (B) G-6. (B) G-7. (B)
G-8. (D) G-9. (A)
PART - II
1. (B) 2. (B) 3. (C) 4. (D) 5. (D) 6. (A) 7. (C)
8. (B) 9. (A) 10. (C) 11. (A) p, s (B) p, q (C) q (D) q, r
12. (A) p (B) q, s (C) r 13. (A) r, s (B) p, q, r, s (C) q 14. (C) 15. (A)
16. (B) 17. (A) 18. F 19. T 20. T 21. T
22. T 23. T 24. T 25. T 26. F 27. F 28. F
3a
32. least or minimum 33. 12 34. 0.732 35.
2
36. decreases, remains constant 37. 23 38. simple cubic
39. ZnAl2O4
Exercise # 2
PART - I
22. (A) 23. (B) 24. (C) 25. (B) 26. (D) 27. (A) 28. (D)
29. (B) 30. (A) 31. (C) 32. (B) 33. (C) 34. (A) 35. (AC)
36. (AC) 37. (ACD) 38. (ABC) 39. (ABD) 40. (ABC) 41. (ABC)
PART - II
1. Z = N0a3/M = 10.7 × 103 × 6.023 × 1023 × (4.06 × 10–10)3/(108 × 10–3) = 4
Thus there are 4 atoms per unit cell. Hence it is FCC.
2. XY3, 4.38 g/cm3
3. (a) 3.52 Å,(b) 1.24 Å
4. (i) r 2 3 ; (ii) 2r 2 / 3 ; (iii) Yes, of course
5. (i) b, f, g are identical; c, e are identical. (ii) da < [db = df = dg]< [dc = de]< dd
15. (i) Zn2+ ions occupy alternate Tetrahedral holes ; (ii) Anti-Flourite: Anions in FCC and Cations in Tetrahedral
holes, Fluorite: Cations in FCC and Anions in Tetrahedral holes
16. (i) < 1, fraction = ( 1 - ); (ii) > 1 ;(iii) = 1. 17. 6.02 × 1018
Exercise # 3
PART - I
9. (A) p, s ; (B) p, q ; (C) q ; (D) q, r 10. (B) 11. (A) 12. (D) 13.* (BC)
Exercise # 4
4. (i) The number of nearest neighbours of any constituent particle present in the crystal lattice is called its
coordination number.
(ii) The coordination number of atoms
(a) in a cubic close-packed structure is 12, and
(b) in a body-centred cubic structure is 8
8. (i) There are 14 (8 from the corners + 6 from the faces) lattice points in face-centred cubic.
(ii) There are 14 (8 from the corners + 6 from the faces) lattice points in face-centred tetragonal.
(iii) There are 9 (1 from the centre + 8 from the corners) lattice points in body-centred cubic.
24. (i) 354 pm (approximately) (ii) 2.27 × 1022 25. 6.022 × 1018 mol–1