Questions - Answers
4 Marks Questions:
1. What is meant by the term co-ordination number? What is the co-ordination number of atoms
a) in a cubic close pack structure?
b) in a body - centered cubic structure?
A: Number of nearest atoms or ions that surround an ion or atom is called co-ordination number.
a) Co-ordination number of an atom in CCP = 12
b) Co-ordination number of an atom in BCC = 8
2. Derive Bragg's equation for X-rays of wave length (λ) and a diffraction angle (θ) for an nth order reflection.
A: Derivation of Bragg's Equation:
A crystal has many planes. Atoms or ions are arranged in systematic geometry in these planes. When X-rays incident on these crystal planes, they undergo diffraction. When the waves are diffracted from these atoms or ions, they may have constructive interference or destructive interference.
From the figure it is very clear that 1st and
2nd X-rays travel the same distance till the wave front AD. Where as 2nd ray travels an extra distance DB + BC (path difference) than that of 1st X-ray.
If the two waves are to present in the same phase (constructive interference), the path difference must be equal to the wave length λ or an integral multiple of wave length.
In ADB triangle, sin θ = 
∴ DB = d sin θ
In ABC triangle, sin θ = 
BC = d sin θ
∴ nλ = DB + BC = 2d sin θ
This relations is known as Bragg's equation
θ Values increases with n values. Knowing the values of θ & λ one can calculate d.
λ = wave length of X-ray
θ = angle of incident X-ray
n = order of diffraction
d = interplaner distance.
3. Write a short notes on a) Schottky defect and b) Frenkel defect.
A: Schottky defect: A stoichiometric, point defect that occurs when the size of the ions are same and small, coordination number is high (6-8), compounds are more ionic if same number of cations and anions are missing from the lattice points. The density of a crystal decreases due to this defect.
e.g.: NaCl, CsCl, AgBr
Frenkel defect: A stoichiometric, point defect that occurs when the size of the cation is small and that occupies interstitial site instead of lattice sites. This defect is seen where the coordination number is low (4-6), compounds are less ionic. The density of the crystal remains the same.
e.g.: AgCl, AgBr
4.
2 Marks Questions:
1. Distinguish between Crystal lattice and Unit Cell.
A: Crystal lattice: Regular three dimensional arrangement of points in space.
Unit Cell: The smallest basic three dimensional repeating unit from which crystal lattice is built.
2. How many lattice points are there in one Unit Cell of
a) Face Centred Cubic lattice?
b) Body Centred Cubic lattice?
A: a) Number of lattice points in FCC = Corners (8) + Face Centers (6) = 8 + 6 = 14
Atoms in FCC Unit Cell = 
+ 
= 1 + 3 = 4
b) Number of lattice points in BCC = Corners (8) + Body (1) = 8 + 1 = 9
Atoms in BCC Unit Cell = + 1 = 1 + 1 = 2
3. What are F centers?
A: The anion vacancies are occupied by the electrons in metal excess defect. These electrons are responsible for colour and paramagnetic nature.
4. A cubic solid is made of 2 elements P and Q, atoms of Q are at the corners of the cube and P at the body centre. What is the formula of the compound? What are the coordination numbers of P and Q?
A: Effective number of P atoms = 1
Effective number of Q atoms = = 1
Formula of the compound = PQ (B.C.C.)
In B.C.C. Coordination number of P = 8
Coordination number of Q = 8
5. If Nickel Oxide has the formula Ni0.98 O1.00. What fraction of Ni exist as Ni2+ and Ni3+ ions?
A: Let us suppose number of Ni+3 ions = x
Number of Ni+2 ions = 0.98 − x
Total charge on oxygen = −2 . 1 = −2
∴ (+3) x + (0.98 − x) (+2) − 2 = 0
∴ x = 0.04
Number of Ni+3 ions = 0.04 (100) = 4
Number of Ni+2 ions = (0.98 − 0.04) 100 = 94
6. Distinguish between Hexagonal and Monoclinic Unit Cells.
A: For Hexagonal Unit Cells:
a = b ≠ c and α = β = 90° ; γ = 120°
For Monoclinic Unit Cells:
a ≠ b ≠ c and α = γ = 90°, β ≠ 90°
7. Distinguish between Face centred and end centred Unit Cells.
A: In Face Centred Unit Cells, all the 8 corners and all the 6 face centers are occupied by atoms.
In End Face Centred Unit Cell, all the 8 corners and any 2 opposite face centres are occupied by atoms.
8. A compound forms hexagonal close - packed structure. What are the total number of voids in 0.5 mole of it?
A: Number of atoms in Unit Cell = 0.5 × 6.023 × 1023
Number of Octahedral Voids = 1 × 0.5 × 6.023 × 1023
Number of Tetrahedral Voids = 2 × 0.5 × 6.023 × 1023
Total number of voids = Number of Octahedral voids + Number of Tetrahedral voids
= (0.5 + 1) × 6 × 1023
= 1.5 × 6 × 1023 voids
9. Mention the Packing Efficiency of
1) Simple Cubic
2) Body - Centred Cubic and
3) Hexagonal Close - Packed lattice
A: Packing efficiency of
1) Simple Cubic lattice = 52%
2) Body Centred lattice = 68%
3) Hexagonal Close Packed lattice = 74%
10. What type of Stoichiometric defect is shown by 1) ZnS 2) AgBr
A: 1) ZnS shows Frenkel defect.
2) AgBr Shows Frenkel & Schottky defects.
11. An element with molar mass 2.7 × 10-2 kg mol-1 forms a Cubic Unit Cell with edge length 405 pm. If its density is 2.7 × 103 kg m-3, what is the nature of the Cubic Unit Cell?
A: d = 2.7 × 103 kg m-3
a = 405 × 10-12m
N0 = 6.023 × 1023
M = 2.7 × 10-2 kg mol-1
Number of atoms (Z) are 4. It could be F.C.C. or C.C.P.
