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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. |
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Solution
| 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
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