Chemistry - Solid State Question with Solution | TestHub

The packing efficiency of a face-centered cubic (fcc) unit cell is $74\%$, meaning the particles occupy $0.74$ of the total volume.

Total volume occupied by all particles in the unit cell $=0.74\times V$

Substituting $V=1.6\times 10^{-23}{\mathrm{cm}}^3$:

Total occupied volume $=0.74\times 1.6\times 10^{-23}=1.184\times 10^{-23}{\mathrm{cm}}^3$

An fcc unit cell contains $4$ particles.

Volume occupied by one particle $=\frac{1.184\times 10^{-23}}{4}=0.296\times 10^{-23}{\mathrm{cm}}^3$

Volume occupied by one particle $=2.96\times 10^{-24}{\mathrm{cm}}^3$

Answer: $2.96\times 10^{-24}{\mathrm{cm}}^3$