Calculate the volume of unit cell if an element having molar mass $56 \mathrm{~g} \mathrm{~mol}^{-1}$ that…
Calculate the volume of unit cell if an element having molar mass $56 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms bcc unit cells.
$\left[\rho . \mathrm{N}_{\mathrm{A}}=4: 8 \times 10^{24} \mathrm{~g} \mathrm{~cm}^{-3} \mathrm{~mol}^{-1}\right]$
$1.17 \times 10^{-23} \mathrm{~cm}^3$
$4.79 \times 10^{-23} \mathrm{~cm}^3$
$3.31 \times 10^{-23} \mathrm{~cm}^3$
$2.33 \times 10^{-23} \mathrm{~cm}^3$
Solution
$\begin{aligned} & \text { Density of unit cell }=\rho=\frac{M n}{a^3 N_A} \\ & \text { Volume of unit cell }\left(a^3\right)=\frac{M n}{\rho N_A} \\ & =\frac{56 \mathrm{~g} \mathrm{~mol}^{-1} \times 2}{4.8 \times 10^{24} \mathrm{~g} \mathrm{~cm}^{-3} \mathrm{~mol}^{-1}} \\ & =2.33 \times 10^{-23} \mathrm{~cm}^3 \\ & \end{aligned}$