Question

The vacant space in bcc lattice unit cell is

• A. 48%
• B. 23%
• C. 32%
• D. 26%

Answer 1

The correct option is C

32%

For BCC, Z=2
$r=\frac{\sqrt{3}a}{4}$
Packing fraction = $\frac{Zeff\times Volumeofoneparticle}{Volumeofunitcell}=\frac{2\times [\frac{4}{2}\times \pi \times r^3]}{a^3}=\frac{\sqrt{3}\pi }{8}=0.68$
Packing efficiency $=68\%$
$\Rightarrow$ Empty space $=100-68=32\%$