Question

The void space in a primitive unit cell is:

• A. 48% void space
• B. 24% void space
• C. 96% void space
• D. 50% void space

Answer 1

Answer: (A)

$a = 2r $
Volume of the cube $=a^{3}=\left(2 r\right)^{3}=8r^{3}$
Packing fraction $=\frac{\text{Volume of one atom}}{\text{Volume of the cube}}$
$=\frac{\left(\frac{4}{3} \, \pi r^{3}\right)}{8 r^{3}}=\frac{\pi }{6}=0.52$
Void fraction $= \, 1 \, - \, 0.52 \, = \, 0.48$
Void space $=48 \, \%$