Sodium crystallizes in bcc structure with radius $1 \cdot 86 \times 10^{-8} \mathrm{~cm}$. What is the edge…
Sodium crystallizes in bcc structure with radius $1 \cdot 86 \times 10^{-8} \mathrm{~cm}$. What is the edge length of unit cell of sodium?
- $4 \cdot 3 \times 10^{-8} \mathrm{~cm}$
- $3 \cdot 72 \times 10^{-8} \mathrm{~cm}$
- $7 \cdot 44 \times 10^{-8} \mathrm{~cm}$
- $5 \cdot 26 \times 10^{-8} \mathrm{~cm}$
Solution
$\begin{aligned}
r &=1.86 \times 10^{-8} \mathrm{~cm} \\
a &=?
\end{aligned}$
For bcc structure, $r=\frac{\sqrt{3}}{4} a$
$\begin{array}{l}
\therefore \sqrt{3} \mathrm{a}=4 \mathrm{r} \\
\therefore a=\frac{4 \mathrm{r}}{\sqrt{3}}=\frac{4 \times 1.86 \times 10^{-8} \mathrm{~cm}}{\sqrt{3}} \quad \therefore a=4.3 \times 10^{-8} \mathrm{~cm}
\end{array}$
Asked in: MHT CET 2020 (12 Oct Shift 1)
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