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?
  1. $4 \cdot 3 \times 10^{-8} \mathrm{~cm}$
  2. $3 \cdot 72 \times 10^{-8} \mathrm{~cm}$
  3. $7 \cdot 44 \times 10^{-8} \mathrm{~cm}$
  4. $5 \cdot 26 \times 10^{-8} \mathrm{~cm}$

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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