The percentage of free space in a body centred cubic unit cell is

Options

A. 0.3
B. 0.32
C. 0.34
D. 0.28

Answer

B

Explanation

In bcc unit cell , the number of atoms = 2
Thus, volume of atoms in unit cell `(v) = 2 xx 4/3 pi r^3`
For bcc structure `( r) = (sqrt3)/(4) a`
`(V) = 2 xx 4/3 pi ( (sqrt3)/(4) a)^3 = (sqrt3)/(8) pi a^2`
Volume of unit cell `(V) =a^3`
Percentage of volume occupied by unit cell
` ( (sqrt3)/(8) pi a^3 )/(a^3) xx 100 = (sqrt3)/(8) pi xx 100 = 68%`
Hence the free space in bcc in unit cell
100 - 68 = 32%