Calculate the volume occupied by all atoms in bcc unit cell if the volume of unit cell is $1.5 \times…

Calculate the volume occupied by all atoms in bcc unit cell if the volume of unit cell is $1.5 \times 10^{-22} \mathrm{~cm}^3$.
  1. $2.40 \times 10^{-22} \mathrm{~cm}^3$
  2. $3.51 \times 10^{-22} \mathrm{~cm}^3$
  3. $1.56 \times 10^{-22} \mathrm{~cm}^3$
  4. $1.02 \times 10^{-22} \mathrm{~cm}^3$

Solution

BCC unit cell contains 2 particles. Hence, volume occupied by particles in bcc unit cell $\begin{aligned} & =2 \times \frac{\sqrt{3} \pi \mathrm{a}^3}{16} \\ & =\frac{\sqrt{3} \pi \mathrm{a}^3}{8} \\ & =0.68 \times 1.5 \times 10^{-22}=1.02 \times 10^{-22} \mathrm{~cm}^3 \end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 1)

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