MHT CET · Chemistry · Solid State
What is the percentage of unoccupied volume in BCC structure?
- A \(32 \%\)
- B \(74 \%\)
- C \(26 \%\)
- D \(68 \%\)
Answer & Solution
Correct Answer
(A) \(32 \%\)
Step-by-step Solution
Detailed explanation
Packing efficiency
\(\text {P.E. }=\frac{z \times \frac{4}{3} \pi \mathrm{r}^3}{V}=\frac{2 \times \frac{4}{3} \times \pi\left(\frac{\sqrt{3} a}{4}\right)^3}{a^3}\) \(=\frac{\sqrt{3} \pi}{8}=0.68\)
\({\left[\because z=2, r=\frac{\sqrt{3} a}{4}, V=a^3\right]}\)
In B.C.C., \(68 \%\) of total volume is occupied by atoms or ions.
And \(100-68=32 \%\) of total volume is unoccupied.
\(\text {P.E. }=\frac{z \times \frac{4}{3} \pi \mathrm{r}^3}{V}=\frac{2 \times \frac{4}{3} \times \pi\left(\frac{\sqrt{3} a}{4}\right)^3}{a^3}\) \(=\frac{\sqrt{3} \pi}{8}=0.68\)
\({\left[\because z=2, r=\frac{\sqrt{3} a}{4}, V=a^3\right]}\)
In B.C.C., \(68 \%\) of total volume is occupied by atoms or ions.
And \(100-68=32 \%\) of total volume is unoccupied.
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