Q7 / 150 · JEE Main 2006 · Chemistry

Total volume of atoms present in a face-centre cubic unit cell of a metal is ( $r$ is atomic radius)

  • A
    $\frac{20}{3} \pi r^3$
  • B
    $\frac{24}{3} \pi r^3$
  • C
    $\frac{12}{3} \pi r^3$
  • Correct answer
    D
    $\frac{16}{3} \pi r^3$

Solution

$\begin{aligned} V & =n \times\left(\frac{4}{3} \pi r^3\right) \\ & =4 \times\left(\frac{4}{3} \pi r^3\right) \\ & =\frac{16}{3} \pi r^3\end{aligned}$

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

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