Question

Percentage of free space in a body centred cubic unit cell is :

• A. 30%
• B. 32%
• C. 34%
• D. 28%

Answer 1

Answer: (B)

Packing efficiency $=$

$\frac{\text{ Volume occupied by two atoms in unit cell }}{\text{ Volume of the unit cell }}\times 100$

For bcc, packing efficiency $=$

$\frac{2\times \frac{4}{3}\times \pi r^3}{{\left(\frac{4r}{\sqrt{3}}\right)}^3}\times 100=\frac{\sqrt{3}\pi }{8}\times 100=68\%$

$\therefore$ Volume occupied $=68\%$ and volume vacant $=$ $100-68=32\%$