What is the relation between edge length and total volume occupied by atoms in bec unit cell?

What is the relation between edge length and total volume occupied by atoms in bec unit cell?
  1. $\mathrm{V}=\frac{\pi \mathrm{a}^3}{6}$
  2. $\mathrm{V}=\frac{\sqrt{3} \pi \mathrm{a}^3}{8}$
  3. $\quad \mathrm{V}=\frac{\pi \mathrm{a}^3}{3 \sqrt{2}}$
  4. $\quad \mathrm{V}=\frac{\pi \mathrm{a}^3}{16}$

Solution

The volume occupied by atoms in the $B C C$ unit cell is proportional to $a^3$, and the relation is given by: $V=\frac{\sqrt{3} \pi a^3}{8}$
This matches with Option (2). Correct answer: (2) $V=\frac{\sqrt{3} \pi a^3}{8}$.

Asked in: MHT CET 2024 (09 May Shift 1)

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