Chemistry - Solid State Question with Solution | TestHub

Radius of the atom, $r=100\text{ pm}=100\times 10^{-12}\text{ m}=10^{-8}\text{ cm}$

In a face-centered cubic (fcc) unit cell, the effective number of atoms is $Z=4$.

Volume occupied by the particles (atoms) in the unit cell is given by:

$V=Z\times \frac{4}{3}\pi r^3$

Substituting the values:

$V=4\times \frac{4}{3}\times \frac{22}{7}\times (10^{-8}{)}^3$

$V=\frac{352}{21}\times 10^{-24}{\text{ cm}}^3$

$V\approx 16.76\times 10^{-24}{\text{ cm}}^3$

$V\approx 1.677\times 10^{-23}{\text{ cm}}^3$

Answer: $1.677\times 10^{-23}{\text{cm}}^3$