Solid State Test - 17

14 types of three-dimensional Bravais lattices (primitive and centred unit cells

Lattice sites always contain atoms/molecules/ions. If atom is replaced by electron, then imperfection arises in the crystal and it would not be pure crystal

Ionic compounds are held by electrostatic forces of attraction between anions and cations.  These compounds form an extensive a 3 dimensional network where the boundaries between molecules are difficult to determine. The formula of ionic compounds are the empirical formula and are called the formula units.

The number of Na+ ions present in one unit cell = 12×1/4 + 1 =4 atoms per unit cell.

The number of Cl- ions present in one unit cell = 6×1/2 + 8×1/8 = 4 atoms per unit cell.

So, each unit cell has 4 atoms of each Na+ and Cl-. Hence there are total 4 molecules of NaCl in each unit cell.

Hence B

(c) By Bragg's equation, spacing between two planes is given by

For first-order diffraction, n =1

∴             
If d = λ, then 2 sin θ =1

if d = λ/2, then 
sin θ = 1 => θ = 90^o

In a unit cell W atoms at the corner 

O-atoms at the centre of edges = 
Na-atoms at the centre of the cube = 1
W:O:Na = 1:3:1
Hence, formula is NaWO₃

 (b) Number of atoms in the unit cell

where, n_c = number of atoms at the corners n_f = number of atoms at the faces n_i = number of atoms inside 

(c) By using Bragg’s equation,
nλ = 2d sin θ
where, n =2  
(second order diffraction)
λ = d sin θ
or
log λ = log d + log sin θ
d is constant (distance between two planes) as θ changes, X also changes.
When θ = 90°, sin 90° =1, hence log sin 90°= 0

(i) Triclinic, a b c and α β γ = 90° Thus, (i)→ (r)

(ii) Hexagonal, a = b c, α = β = 90°,γ = 120° Thus, (ii) → (s)

(iii) C u b ic ,a = b = c , α = β =γ = 90° Thus, (iii) → (p)

(iv) Tetragonal, a = b c, α = β =γ = 90^o 

Thus, (iv) → (q)