Question

Assuming that atoms are touching each other, calculate the efficiency of packing in case of a crystal for simple cubic metal?

Answer 1

Let $a$ be the edge length of the sphere and $r$ be the atomic radius. The atoms are touching each other. Hence, $a=2r$. The volume of unit cell is $V=a^3=(2r{)}^3=8r^3$. The volume of one atom is $v=\frac{4}{3}\pi r^3$.
A simple cubic unit cell contains only one atom per unit cell. The packing efficiency $=\frac{v}{V}\times 100=\frac{\frac{4}{3}\pi r^3}{8r^3}\times 100=\frac{4\times 3.1416}{3\times 8}\times 100=52.4$ %