Calculate the volume of unit cell if an element having molar mass $180 \mathrm{~g} \mathrm{~mol}^{-1}$ forms…
Calculate the volume of unit cell if an element having molar mass $180 \mathrm{~g} \mathrm{~mol}^{-1}$ forms fcc unit cell. $\left[\rho \cdot \mathrm{N}_{\mathrm{A}}=120 \times 10^{21} \mathrm{~g} \mathrm{~cm}^{-3} \mathrm{~mol}^{-1}\right]$
$6.00 \times 10^{-21} \mathrm{~cm}^3$
$5.00 \times 10^{-21} \mathrm{~cm}^3$
$4.00 \times 10^{-21} \mathrm{~cm}^3$
$7.00 \times 10^{-21} \mathrm{~cm}^3$
Solution
Volume of unit cell $=\mathrm{a}^3=$ ?
Density $(\rho)=\frac{M \times n}{a^3 \times N_A}$
$\mathrm{a}^3=\frac{\mathrm{M} \times \mathrm{n}}{\rho \times \mathrm{N}_{\mathrm{A}}}=\frac{180 \times 4}{120 \times 10^{21}}=6.00 \times 10^{-21} \mathrm{~cm}^3$