Q77 / 200 · NEET 2007 · 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 $r=\frac{a}{2}$ $\begin{aligned} & \text {Therefore % fraction }=\frac{\frac{4}{3} \pi r^3}{(2 r)^3}=\frac{\pi}{6} \\ & =0.52 \end{aligned}$

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

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