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Question:

The ratio of number of atoms present in a simple cubic, body-centred cubic and face-centred cubic structure are, respectively:

1:2:4

4:2:3

8:1:6

4:2:1

Solution:

Correct option is A. 1:2:4
ZSC = 8 × 1/8 = 1 [Atoms are only at the corners]
ZBCC = 8 × 1/8 + 1 = 1 + 1 [Atoms are at the corners and at the body centre]
ZFCC = 8 × 1/8 + 6 × 1/2 = 1 + 3 = 4 [Atoms are at the corners and at the face centres]
Here, Z = effective number of atoms in the unit cell.
Now, ZSC : ZBCC : ZFCC = 1:2:4