Q36 / 150 · MHT CET 2024 (03 May Shift 1) · Chemistry

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

  • A
    $2.40 \times 10^{-22} \mathrm{~cm}^3$
  • B
    $3.51 \times 10^{-22} \mathrm{~cm}^3$
  • C
    $1.56 \times 10^{-22} \mathrm{~cm}^3$
  • Correct answer
    D
    $1.02 \times 10^{-22} \mathrm{~cm}^3$

Solution

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

Hence, the correct answer is option: 'D'.

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