Molar volume from pycnometric density =$\large\frac{M}{2.165\times 10^3}$$m^3$
Molar volume from X-ray density =$\large\frac{M}{2.178\times 10^3}$$m^3$
$\therefore$ Volume occupied =$\large\frac{M}{10^3}\big(\frac{1}{2.165}-\frac{1}{2.178}\big)$$m^3$
$\Rightarrow \large\frac{M}{10^3}\big(\large\frac{0.013}{2.165\times 2.178}\big)$$m^3$
Fraction unoccupied =$\large\frac{\big(\Large\frac{0.013M\times 10^{-3}}{2.165\times 2.178}\big)}{\Large\frac{M\times 10^{-3}}{2.165}}$
$\Rightarrow 5.96\times 10^{-3}$