An element crystallises in bcc type having atomic radius $1 \cdot 33 \times 10^{-8} \mathrm{~cm}$, the edge…

An element crystallises in bcc type having atomic radius $1 \cdot 33 \times 10^{-8} \mathrm{~cm}$, the edge length of unit cell will be
  1. $2 \cdot 17 \times 10^{-8} \mathrm{~cm}$
  2. $2 \cdot 66 \times 10^{-8} \mathrm{~cm}$
  3. $4.08 \times 10^{-8} \mathrm{~cm}$
  4. $3 \cdot 07 \times 10^{-8} \mathrm{~cm}$

Solution

For bcc crystal, $\quad \mathrm{r}=\frac{\sqrt{3}}{4} \mathrm{a}$ $\therefore \quad a=\frac{4 \mathrm{r}}{\sqrt{3}}=\frac{4 \times 1.33 \times 10^{-8} \mathrm{~cm}}{1.732}$ $\therefore \quad a=3.07 \times 10^{-8} \mathrm{~cm} .$

Asked in: MHT CET 2020 (13 Oct Shift 2)

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