Chemistry - Solid State Question with Solution | TestHub

The edge length of the unit cell is $a=390\text{ pm}=3.9\times 10^{-8}\text{ cm}$.

The total volume of the unit cell is $V=a^3=(3.9\times 10^{-8}{)}^3{\text{ cm}}^3=59.319\times 10^{-24}{\text{ cm}}^3=5.932\times 10^{-23}{\text{ cm}}^3$.

For a face-centered cubic (fcc) unit cell, the packing efficiency is $74\%$.

The percentage of void space in the fcc unit cell is $100\%-74\%=26\%$.

The void volume of the unit cell is $0.26\times V$.

Substituting the value of $V$, we get $0.26\times 5.932\times 10^{-23}{\text{ cm}}^3=1.542\times 10^{-23}{\text{ cm}}^3$.

Answer: $1.542\times 10^{-23}$ ${\text{cm}}^3$