Q18 / 125 · BITSAT 2011 · Chemistry

The fraction of total volume occupied by the atoms present in a simple cube is

  • A
    $\frac{\pi}{3 \sqrt{2}}$
  • B
    $\frac{\pi}{4 \sqrt{2}}$
  • C
    $\frac{\pi}{4}$
  • Correct answer
    D
    $\frac{\pi}{6}$

Solution

Number of atoms per unit cell $=1$ Atoms touch each other along edges. Hence $r=\frac{a}{2}$ $(\mathrm{r}=$ radius of atom and $\mathrm{a}=$ edge length) Therefore $\%$ $=\frac{\frac{4}{3} \pi r^{3}}{(2 r)^{3}}=\frac{\pi}{6}$

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

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