Q49 / 180 · JIPMER 2018 · Chemistry

An atom forms face centred cubic crystal with density $\mathrm{d}=8.92 \mathrm{~g} / \mathrm{mL}$ and edge length $\mathrm{a}=3.6 \times 10^{-8} \mathrm{~cm}$. The molecular mass of atom in amu is

  • A
    $98 amu$
  • Correct answer
    B
    $63 amu$
  • C
    $32 amu$
  • D
    $93 amu$

Solution

Given, Density $(\mathrm{d})=8.92 \mathrm{~g} / \mathrm{mL}$ Edge length $(\mathrm{a})=3.6 \times 10^{-8} \mathrm{~cm}$ $\mathrm{Z}=4$ (fcc) The molecular mass of atom in a lattice can be calculated by using the formula $\begin{aligned} & \mathrm{d}=\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{N}_0 \mathrm{a}^3} \\ & \therefore \quad \mathrm{M}=\frac{\mathrm{dN}_0 \mathrm{a}^3}{\mathrm{Z}} \\ & M=\frac{8.92 \times 6.023 \times 10^{23} \times(3.6)^3 \times\left(10^{-8}\right)^3}{4} \\ & M=62.6 \approx 63 \mathrm{amu} \\ & \end{aligned}$

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

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