An element with molar mass $2.7 \times 10^{-2} \mathrm{~kg} \mathrm{~mol}^{-1}$ forms a cubic unit cell with edge length $405 \mathrm{pm}$. If its density is $2.7 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$, what is the nature of the cubic unit cell?

Question

An element with molar mass $2.7 \times 10^{-2} \mathrm{~kg} \mathrm{~mol}^{-1}$ forms a cubic unit cell with edge length $405 \mathrm{pm}$. If its density is $2.7 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$, what is the nature of the cubic unit cell?,

MARKS App · Accepted Answer

$d=\frac{Z \times M}{a^3 N_A}$ Given: $\quad$ Density, $d=2.7 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ $a=405 \mathrm{pm}$ $\begin{aligned} &=405 \times 10^{-12} \mathrm{~m} \ M &=2.7 \times 10^{-2} \mathrm{~kg} \mathrm{~mol}^{-1} \end{aligned}$ $\Rightarrow Z=\frac{d a^3 N_A}{M}$ $\begin{aligned} &=\frac{\left(2.7 \times 10^3\right)\left(405 \times 10^{-12}\right)^3\left(6.022 \times 10^{23}\right)}{2.7 \times 10^{-2}} \ &=4.004 \simeq 4 \end{aligned}$ Therefore, it is a $f c c$ unit cell.

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