Question

Match the type of unit cell given in Column I with the features given in Column II.

Column I	Column II
(i) Primitive cubic unit cell	(a) Each of the three perpendicular edges compulsorily have the different edge length i.e; a ≠ b ≠ c.
(ii) Body centred cubic unit cell	(b) Number of atoms per unit cell is one.
(iii) Face centred cubic unit cell	(c) Each of the three perpendicular edges compulsorily have the same edge length i.e; a = b = c.
(iv) End centred orthorhombic cell	(d) In addition to the contribution from unit cell the corner atoms the number of atoms present in a unit cell is one.
	(e) In addition to the contribution from the corner atoms the number of atoms present in a unit cell is three.

Answer 1

Column I	Column II
(i) Primitive cubic unit cell	(b) Number of atoms per unit cell is one.
	(c) Each of the three perpendicular edges compulsorily have the same edge length i.e; a = b = c.
(ii) Body-centred cubic unit cell	(c) Each of the three perpendicular edges compulsorily have the same edge length i.e; a = b = c.
	(d) In addition to the contribution from unit cell the corner atoms the number of atoms present in a unit cell is one.
(iii) Face centred cubic unit cell	(c) Each of the three perpendicular edges compulsorily have the same edge length i.e; a = b = c.
	(e) In addition to the contribution from the corner atoms the number of atoms present in a unit cell is three.
(iv) End-centred orthorhombic cell	(a) Each of the three perpendicular edges compulsorily have the different edge length i.e; a ≠ b ≠ c.
	(d) In addition to the contribution from unit cell the corner atoms the number of atoms present in a unit cell is one.

Explanation:

(i)

For primitive unit cell, a = b = c

Total number of atoms per unit cell = `1/8 xx 8` = 1

Here, `1/8` is due to contribution of each atom present at comer.

(ii)

For body centered cubic unit cell, a = b = c.

This lattice contains atoms at comer as well as body centre.

Contribution due to atoms at comer = `1/8 xx 8` = 1

Contribution due to atoms at body centre = 8

(iii)

For face centred unit cell, a = b = c

Total constitutent ions per cell present at corners = `1/8 xx 8` = 1

Total constitutent ions per unit cell present at face centre = `1/2 xx 6` = 3

(iv)

For end centred orthorhombic unit cell, a ≠ b ≠ c

Total contribution of atoms present at corner = `1/8 xx 8` = 1

Total constibution of atoms present at end centre = `1/2 xx 2` = 1