Question
An element with molar mass $27\ g\ mol^{–1}$ forms a cubic unit cell with edge length $ 4.05 \times 10^{–8}\ cm$. If its density is $2.7\ g\ cm^{–3}$, what is the nature of the cubic unit cell?
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Answer
$\text{d}=\frac{\text{z}\times\text{M}}{\text{a}^{3}\text{N}_{A}}$
$\text{z}=\frac{\text{d a}^{3}\text{N}_{A}}{\text{M}}$
$\text{z}=\frac{\text{2.7g cm}^{-3}\times\text{6.022}\times\text{10}^{23}\text{mol}^{-1}\times\text{(4.05}\times\text{10}^{-8}\text{cm)}^{3}}{\text{27 g mol}^{-1}}$
$=3.999 \approx 4$
Face centered cubic cell/fcc.
$\text{z}=\frac{\text{d a}^{3}\text{N}_{A}}{\text{M}}$
$\text{z}=\frac{\text{2.7g cm}^{-3}\times\text{6.022}\times\text{10}^{23}\text{mol}^{-1}\times\text{(4.05}\times\text{10}^{-8}\text{cm)}^{3}}{\text{27 g mol}^{-1}}$
$=3.999 \approx 4$
Face centered cubic cell/fcc.
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