Ans: As the name suggests, packing efficiency is the proportion of the crystal (or unit cell) that is actually taken up by the atoms themselves.
Packing efficiency is calculated by.
$$
\text { Packing efficiency }=\frac{\text { Volume occupied by the atoms in the unit cell }}{\text { Total volume of the unit cell }} \times 100
$$
For BCC (Body centered cubic cell), volume occupied by the atoms in the unit cell is: $\frac{8}{3} \pi r^{3}$
Total volume of the BCC unit cell is:
$$
\frac{64 r^{3}}{3 \sqrt{3}}
$$
Now, putting the values:
Packing efficiency $=\frac{\frac{8}{3} \pi r^{3}}{\frac{64 r^{3}}{3 \sqrt{3}}} \times 100=6896$