Q33 / 150 · MHT CET 2021 (21 Sep Shift 1) · Chemistry

Which is the volume of unit cell of a metal (at. mass $25 \mathrm{~g} \mathrm{~mol}^{-1}$ ) having BCC structure and density $3 \mathrm{~g} \mathrm{~cm}^{-3}$ ?

  • A
    $3.64 \times 10^{-23} \mathrm{~cm}^3$
  • B
    $1.56 \times 10^{-24} \mathrm{~cm}^3$
  • Correct answer
    C
    $2.76 \times 10^{-23} \mathrm{~cm}^3$
  • D
    $1.88 \times 10^{-24} \mathrm{~cm}^3$

Solution

$$ \begin{aligned} & \text { Density }=\frac{\text { mass of atomsin unitcell }}{\text { Volume of unitcell }} \\ & \text { mass of atoms in unit cell }=\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{N}_{\mathrm{A}}}=\frac{2 \times 25}{6.023 \times 10^{23}} \\ & \text { Volume of unit cell }=\frac{2 \times 25}{6.02 \times 10^{23} \times 3}=2.76 \times 10^{-23} \mathrm{~cm}^3 \end{aligned} $$

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

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