Chemistry - Solid State Question with Solution | TestHub

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

The packing fraction is given by $\frac{\text{Volume of atoms}}{\text{Total volume}}=\frac{\frac{4}{3}\pi r^3}{a^3}=\frac{\frac{4}{3}\pi r^3}{8r^3}=\frac{\pi }{6}\approx 0.524$.

The fraction of void volume in the unit cell is $1-0.524=0.476$.

Given the void volume is $2.0\times 10^{-23}{\text{cm}}^3$.

Total volume of the unit cell $V=\frac{\text{Void volume}}{\text{Fraction of void volume}}=\frac{2.0\times 10^{-23}}{0.476}$.

$V\approx 4.2\times 10^{-23}{\text{cm}}^3$.

Answer: $4.2\times 10^{-23}$