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Question: Answered & Verified by Expert
A metal with an atomic radius of $141.4 \mathrm{pm}$ crystallizes in the face centred cubic structure. The volume of the unit cell in pm is-
ChemistrySolid StateKVPYKVPY 2010 (SB/SX)
Options:
  • A $2.74 \times 10^{7}$
  • B $2.19 \times 10^{7}$
  • C $6.40 \times 10^{7}$
  • D $9.20 \times 10^{7}$
Solution:
1575 Upvotes Verified Answer
The correct answer is: $6.40 \times 10^{7}$
$\quad \mathrm{r}=\frac{\mathrm{a}}{2 \sqrt{2}}=141.4 \mathrm{pm}$
$$
\begin{array}{l}
\mathrm{a}=2 \times \sqrt{2} \times 141.4 \\
\therefore \mathrm{V}=\mathrm{a}^{3}=(2 \times \sqrt{2} \times 141.4)^{3}
\end{array}
$$

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