Calculate the edge length of bcc unit cell if radius of metal atom is $227 \mathrm{pm}$.

Calculate the edge length of bcc unit cell if radius of metal atom is $227 \mathrm{pm}$.
  1. $4.54 \times 10^{-8} \mathrm{~cm}$
  2. $5.24 \times 10^{-8} \mathrm{~cm}$
  3. $6.42 \times 10^{-8} \mathrm{~cm}$
  4. $1.135 \times 10^{-8} \mathrm{~cm}$

Solution

For bcc unit cell, $r=\frac{\sqrt{3}}{4} \mathrm{a}$ $\begin{aligned} \therefore \quad \mathrm{a}=\frac{4 \mathrm{r}}{\sqrt{3}}=\frac{4 \times 227}{1.73} & =524.85 \mathrm{pm} \\ & =524.85 \times 10^{-10} \mathrm{~cm} \\ & =5.24 \times 10^{-8} \mathrm{~cm} \end{aligned}$

Asked in: MHT CET 2023 (14 May Shift 2)

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