Chemistry - Solid State Question with Solution | TestHub

For a simple cubic unit cell, the relation between edge length $a$ and atomic radius $r$ is $a=2r$.

The number of atoms per unit cell is $Z=1$.

Volume of the unit cell, $V=a^3=(3.36\times 10^{-8}{)}^3=37.933\times 10^{-24}{\text{ cm}}^3=3.7933\times 10^{-23}{\text{ cm}}^3$.

Volume occupied by the atom = $\frac{4}{3}\pi r^3=\frac{4}{3}\pi {\left(\frac{a}{2}\right)}^3=\frac{\pi }{6}{a}^3$.

Packing fraction = $\frac{\text{Volume occupied}}{\text{Total volume}}=\frac{\pi }{6}\approx 0.5236$.

Fraction of void volume = $1-0.5236=0.4764$.

Void volume = $0.4764\times V=0.4764\times 3.7933\times 10^{-23}{\text{ cm}}^3\approx 1.807\times 10^{-23}{\text{ cm}}^3$.

Answer: $1.807\times 10^{-23}$ cm${}^3$.