Calculate the edge length of unit cell of metal which crystallises to bcc structure. (Radius of metal atom…

Calculate the edge length of unit cell of metal which crystallises to bcc structure. (Radius of metal atom $=173 \mathrm{pm}$ )
  1. $5.01 \times 10^{-8} \mathrm{~cm}$
  2. $4.00 \times 10^{-8} \mathrm{~cm}$
  3. $4.5 \times 10^{-8} \mathrm{~cm}$
  4. $5.5 \times 10^{-8} \mathrm{~cm}$

Solution

For bcc unit cell, $r=\frac{\sqrt{3}}{4} \mathrm{a}$ $\begin{aligned} \therefore \quad \mathrm{a}=\frac{4 \mathrm{r}}{\sqrt{3}}=\frac{4 \times 173}{1.73} & =400 \mathrm{pm} \\ & =400 \times 10^{-10} \mathrm{~cm} \\ & =4.00 \times 10^{-8} \mathrm{~cm} \end{aligned}$

Asked in: MHT CET 2023 (10 May Shift 1)

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