What is the volume of one particle in BCC structure if 'a' is edge length?

What is the volume of one particle in BCC structure if 'a' is edge length?
  1. $\frac{\pi \mathrm{a}^3}{3 \sqrt{2}}$
  2. $\frac{\pi \mathrm{a}^3}{12 \sqrt{2}}$
  3. $\frac{\sqrt{3} \pi \mathrm{a}^3}{16}$
  4. $\frac{\sqrt{3} \pi \mathrm{a}^3}{8}$

Solution

For bec unit cell, $r=\frac{\sqrt{3}}{4} a$ $\therefore \quad$ Volume of one particle $=\left(\frac{4}{3} \pi \mathrm{r}^3\right)=\left(\frac{4}{3} \pi\right)\left(\frac{\sqrt{3} \mathrm{a}}{4}\right)^3=\frac{\sqrt{3} \pi \mathrm{a}^3}{16}$

Asked in: MHT CET 2024 (15 May Shift 2)

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