Question

Percentage of free space in body centred cubic unit cell is

Options

• 34%

• 28%

• 30%

• 32%

Answer 1

32%

Explanation:

In bcc unit cell, the number of atoms = 2

Thus, volume of atoms in unit cell (v) = `2 xx 4/3 pir^3`

For bcc structure (r) = `sqrt(3)/4 a`

(V) = `2 xx 4/3 pi (sqrt(3)/4 a)^3 = sqrt(3)/8 pia^3`

Volume of unit cell (V) = a³

Percentage of volume occupied by unit cell = `"Volume of the atoms in unit cell"/"Volume of unit cell"`

= `(sqrt(3)/8 pia^3)/a^3 xx 100 = sqrt(3)/8 pi xx 100` = 68%

Hence, the free space in bcc unit cell = 100 – 68 = 32%.