A metal crystallized in primitive cubic lattice. If the radius of the metal atom is 'r' pm the volume of unit cell 'n pm³ is

In primitive cubic cell the atoms at corners make contact with each other at the centre of side.

$\therefore \text{ side length ' }\mathrm{a}\text{ ' }=2\times \text{ radius of atom }\left(\mathrm{r}\right)$

$\therefore \text{ volume }={\mathrm{a}}^3=(2\mathrm{r}{)}^3=8{\mathrm{r}}^3$