An element crystallises in bcc type crystal structure with edge length of unit cell $300 \mathrm{pm} .$…

An element crystallises in bcc type crystal structure with edge length of unit cell $300 \mathrm{pm} .$ Calculate radius of element?
  1. $2 \cdot 299 \times 10^{-8} \mathrm{~cm}$
  2. $1 \cdot 299 \times 10^{-8} \mathrm{~cm}$
  3. $6 \cdot 920 \times 10^{-8} \mathrm{~cm}$
  4. $1 \cdot 440 \times 10^{-8} \mathrm{~cm}$

Solution

$a=300 \mathrm{pm}=3 \times 10^{-8} \mathrm{~cm}$ For bcc unit cell, $r=\frac{\sqrt{3} a}{4}$ $\therefore r=\frac{1.732 \times 3 \times 10^{-8} \mathrm{~cm}}{4}=1.299 \times 10^{-8} \mathrm{~cm}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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