The percentage of free space in a BCC unit cell is ___ ?

In a BCC, in addition to the corners of a cube, an atom is placed at the centre of the cube. They touch each other by the body diagonal.

$\sqrt{3}a = 4 r$

Packing efficiency is

$$\begin{gathered} \frac{volume occupied}{volume available}\times 100 \\ =\frac{\left({\displaystyle \frac{4}{3}}\pi r^3\right)\times 2}{{\displaystyle \frac{a^3}{1}}}\times 100 \\ =68 \% \end{gathered}$$

Thus, percentage of empty space is 32 %