Chemistry - Solid State Question with Solution | TestHub

Number of atoms in hcp is 6 per unit cell.

Packing fraction$=\frac{6\times \frac{4}{3}{\text{πr}}^3}{\text{Base area}\times \text{C}}$

Base area$=6\times \frac{\sqrt{3}}{4}\left(\text{4}{\text{r}}^2\right)$

$\mathrm{C}=\text{4r}\sqrt{\left(\frac{2}{3}\right)}$

Packing fraction$=\frac{\mathrm{\pi }}{3}\sqrt{2}=0.\text{74}$

Void %$=\left(1-0.\text{74}\right)\times 100=\text{26}\mathrm{\%}$