Calculate the density of an element with molar mass $27 \mathrm{~g} \mathrm{~mol}^{-1}$ having 4 atoms in a…

Calculate the density of an element with molar mass $27 \mathrm{~g} \mathrm{~mol}^{-1}$ having 4 atoms in a unit cell with edge length 405 pm
  1. $4.56 \mathrm{~g} \mathrm{~cm}^{-3}$
  2. $2.69 \mathrm{~g} \mathrm{~cm}^{-3}$
  3. $1.53 \mathrm{~g} \mathrm{~cm}^{-3}$
  4. $3.10 \mathrm{~g} \mathrm{~cm}^{-3}$

Solution

We know $\begin{aligned} \mathrm{d} & =\frac{\mathrm{Z}}{\mathrm{V}} \times \frac{\mathrm{M}}{\mathrm{N}_{\mathrm{A}}} \\ & =\frac{4+27}{\left(4.05 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}} \\ \mathrm{~d} & =2.70 \mathrm{~g} / \mathrm{cm}^3\end{aligned}$

Asked in: MHT CET 2022 (07 Aug Shift 1)

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