Chemistry - Solid State Question with Solution | TestHub

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

Assuming each atom is a sphere of radius $r$, the volume of one atom is $\frac{4}{3}\pi r^3$.

Total volume of atoms present in the fcc unit cell $=Z\times \frac{4}{3}\pi r^3$.

Total volume $=4\times \frac{4}{3}\pi r^3=\frac{16}{3}\pi r^3$.

Answer: $\frac{16}{3}\pi r^3$