What is the percentage efficiency of packing in BCC structure?

What is the percentage efficiency of packing in BCC structure?
  1. $32 \%$
  2. $74 \%$
  3. $26 \%$
  4. $68 \%$

Solution

Packing efficiency: $\begin{aligned} & \text { P.E. }=\frac{\mathrm{z} \times \frac{4}{3} \pi \mathrm{r}^3}{V}=\frac{2 \times \frac{4}{3} \times \pi\left(\frac{\sqrt{3} \mathrm{a}}{4}\right)^3}{\mathrm{a}^3}=\frac{\sqrt{3} \mathrm{a}}{8}=0.68 \\ & {\left[\because \mathrm{z}=2, \mathrm{r}=\frac{\sqrt{3} \mathrm{a}}{4}, V=\mathrm{a}^3\right]} \end{aligned}$ In B.C.C., $68 \%$ of total volume is occupied by atoms or ions.

Asked in: MHT CET 2021 (21 Sep Shift 1)

Practice more Solid State questions on Aicharya