MHT CET · Chemistry · Solid State
What is the percentage efficiency of packing in BCC structure?
- A \(32 \%\)
- B \(74 \%\)
- C \(26 \%\)
- D \(68 \%\)
Answer & Solution
Correct Answer
(D) \(68 \%\)
Step-by-step Solution
Detailed explanation
Packing efficiency:
\(\text {P.E. }=\frac{\mathrm{z} \times \frac{4}{3} \pi \mathrm{r}^3}{V}=\frac{2 \times \frac{4}{3} \times \pi\left(\frac{\sqrt{3} \mathrm{a}}{4}\right)^3}{\mathrm{a}^3}\) \(=\frac{\sqrt{3} \mathrm{a}}{8}=0.68\)
\({\left[\because \mathrm{z}=2, \mathrm{r}=\frac{\sqrt{3} \mathrm{a}}{4}, V=\mathrm{a}^3\right]}\)
In B.C.C., \(68 \%\) of total volume is occupied by atoms or ions.
\(\text {P.E. }=\frac{\mathrm{z} \times \frac{4}{3} \pi \mathrm{r}^3}{V}=\frac{2 \times \frac{4}{3} \times \pi\left(\frac{\sqrt{3} \mathrm{a}}{4}\right)^3}{\mathrm{a}^3}\) \(=\frac{\sqrt{3} \mathrm{a}}{8}=0.68\)
\({\left[\because \mathrm{z}=2, \mathrm{r}=\frac{\sqrt{3} \mathrm{a}}{4}, V=\mathrm{a}^3\right]}\)
In B.C.C., \(68 \%\) of total volume is occupied by atoms or ions.
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