(i) Identify the type of defect shown in the following figure:
What type of substances show this defect?
(ii) A metal crystallizes in a body centred cubic structure. If ‘a’ is the edge length of its unit cell, ‘r’ is the radius of the sphere. What is the relationship between ‘r’ and ‘a’?
(iii) An element with molar mass 63 g / mol forms a cubic unit cell with edge length of 360.8 pm. If its density is 8.92 g/ cm3. What is the nature of the cubic unit cell?
(i) The type of defect show in the figure is Schottky defect. If in ionic crystal of the type A+B- equal number of cations and anions are missing from their lattice sites so that the electrical neutrality is maintained, it is called Schottky defect.
This type of defect shown by the highly ionic compounds which have:
⇒ high coordination number
⇒ small differences in the size of cations and anions.
Note: Coordination number of any constituent particle in a crystal is the number of its nearest neighbours.
(ii) For body centered cubic structure:
r = 
(iii) Given :
Molar mass (M) = 63 g/mol
Edge length (a) = 360.8 pm = 360.8 × 10-8
Density (ρ) = 8.92 g/ cm3
First we will calculate the no. of atoms in per unit cell by applying the formula:
ρ = 
where NA (Avogadro’s number) = 6.022 × 1023 mol-1
We can also write,
Z = 
⇒ Z = 
⇒ Z = 4
Thus, it is a face-centered cubic lattice.
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