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Solid State — Chemistry STD 12 — Question

Tamilnadu BoardEnglish MediumSTD 12ChemistrySolid State2 Marks
Question
An element with molar mass $2.7 \times 10^{-2} kg mol ^{-1}$ forms a cubic unit cell with edge length 405 pm. If the density is $2.7 \times 10^3 kg m ^{-3}$, what is the nature of the cubic unit cell?
✓

Answer

Density
$
\begin{aligned}
d & =\frac{ z \times M }{ a ^3 \times N _{ A }} \quad(\rho)=\frac{ n M }{a^3 N _{ A }} \\
n & =\frac{\rho^{\times} a ^3 \times N _{ A }}{ M }=\frac{\left(2.7 \times 10^3 kg m ^{-3}\right)\left(4.05 \times 10^{-10} m \right)^3\left(6.022 \times 10^{23} mol ^{-1}\right)}{\text { } 2.7 \times 10^{-2} kg mol ^{-1}} \\
& =3.99=4
\end{aligned}
$
Thus, there are 4 atoms of elements present per unit cell, hence, the cubic unit cell must be facecentred or cubic close - packed (cep).

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