Q48 / 180 · KCET 2020 · Chemistry
A metal crystallises in face centred cubic structure with metallic radius $\sqrt{2} Å$. The volume of the unit cell (in $\mathrm{m}^{3}$ ) is
- A$4 \times 10^{-10}$
- Correct answerB$6.4 \times 10^{-29}$
- C$4 \times 10^{-9}$
- D$6.4 \times 10^{-30}$
Solution
In fcc, $4 r=\sqrt{2} a$
$\begin{aligned}
\text { Volume of unit cell } &=a^{3}=\left(\frac{4 r}{\sqrt{2}}\right)^{3}=\frac{64}{2 \sqrt{2}} \times(\sqrt{2})^{3} Å \\
&=\frac{64}{2 \sqrt{2}} \times 2 \sqrt{2} Å \\
&=64 \times 10^{-30} \mathrm{~m}^{3} \\
&=6.4 \times 10^{-29} \mathrm{~m}^{3}
\end{aligned}$
Hence, the correct answer is option: 'B'.