Calculate the density of metal with molar mass $56 \mathrm{~g} \mathrm{~mol}^{-1}$ that crystallises to…

Calculate the density of metal with molar mass $56 \mathrm{~g} \mathrm{~mol}^{-1}$ that crystallises to force bcc structure with edge length $288 \mathrm{pm}$.
  1. $9.8 \mathrm{~g} \mathrm{~cm}^{-3}$
  2. $5.8 \mathrm{~g} \mathrm{~cm}^{-3}$
  3. $8.7 \mathrm{~g} \mathrm{~cm}^{-3}$
  4. $7.8 \mathrm{~g} \mathrm{~cm}^{-3}$

Solution

$\begin{aligned} & \mathrm{d}=\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{V} \times \mathrm{N}_{\mathrm{A}}} \\ & d=\frac{2 \times 56}{\left(2.88 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}} \\ & =7.78 \mathrm{~g} / \mathrm{cm}^3 \\ & \end{aligned}$

Asked in: MHT CET 2022 (05 Aug Shift 2)

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