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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
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Verified Answer
The correct answer is:
$2.69 \mathrm{~g} \mathrm{~cm}^{-3}$
We know
$\begin{aligned} \mathrm{d} & =\frac{\mathrm{Z}}{\mathrm{V}} \times \frac{\mathrm{M}}{\mathrm{N}_{\mathrm{A}}} \\ & =\frac{4+27}{\left(4.05 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}} \\ \mathrm{~d} & =2.70 \mathrm{~g} / \mathrm{cm}^3\end{aligned}$
$\begin{aligned} \mathrm{d} & =\frac{\mathrm{Z}}{\mathrm{V}} \times \frac{\mathrm{M}}{\mathrm{N}_{\mathrm{A}}} \\ & =\frac{4+27}{\left(4.05 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}} \\ \mathrm{~d} & =2.70 \mathrm{~g} / \mathrm{cm}^3\end{aligned}$
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