Chemistry - Solid State Question with Solution | TestHub

The distance between nearest neighbours is same in both forms means ' 2r ' is same in both and hence the unit cell edge length, i.e., cell constant, a , is different in both.

${\mathrm{a}}_{\alpha }=\frac{4\mathrm{r}}{\sqrt{3}}$ and ${\mathrm{a}}_{\beta }=\frac{4\mathrm{r}}{\sqrt{2}}$

The distance between next nearest neighbours in both form is ' a ', which is different. Void space in BCC $=32\%$, $\mathrm{FCC}=26\%$

In both forms, the required diameter of largest spheres $=(a-2r)$ and ' $a$ ' is different $2{\mathrm{r}}_{\mathrm{c}}=\left(\frac{\mathrm{a}\sqrt{3}}{4}\right)$