Chemistry - Solid State Question with Solution | TestHub

Number of particles in BCC unit cell $(Z)=2$ Relation between edge length and radius, $$\begin{array}{rl}& \sqrt{3}\mathrm{a}=4\mathrm{r}\\ & \mathrm{r}=\frac{\sqrt{3}\mathrm{a}}{4}\end{array}$$ Volume occupied by particles in BCC $=2\times$ Volume of one atom $$\begin{array}{rl}& =2\times \frac{4}{3}\pi {\mathrm{r}}^3\\ & =2\times \frac{4}{3}\pi {\left(\frac{\sqrt{3}\mathrm{a}}{4}\right)}^3\\ & =\frac{2\times 4}{3}\times \pi \times \frac{3\sqrt{3}{\mathrm{a}}^3}{64}\\ & =\frac{\sqrt{3}\pi {\mathrm{a}}^3}{8}\end{array}$$