Question

The packing efficiency of bcc unit cell is
2
V3
12
6
8
6​

Answer 1

Answer:

68%

Explanation:

In a bcc unit cell, there is 1 atom at the centre and other 1/8 part of other 8 atoms.

Total atoms = 1 + 8(1/8) = 2

Let the edge of the unit cell be 'a'. Then,

Diagonal of the cube = 4r

a√3 = 4r

(√3a/4) = r = radius of atom

Volume of cube = a³

Volume of 2 atom = 2 (4/3 πr³)

Volume of 2 atom = 8/3 (22/7) (√3a/4)³

Volume of 2 atom = 0.68a³

Packing efficiency

= (vol. atom)/vol. cube * 100%

= (0.68a³) / a³ * 100%

= 68%

Packing efficiency of bcc unit cell is 68%.