Which is the volume of unit cell of a metal (at. mass $25 \mathrm{~g} \mathrm{~mol}^{-1}$ ) having BCC…
Which is the volume of unit cell of a metal (at. mass $25 \mathrm{~g} \mathrm{~mol}^{-1}$ ) having BCC structure and density $3 \mathrm{~g} \mathrm{~cm}^{-3}$ ?
$3.64 \times 10^{-23} \mathrm{~cm}^3$
$1.56 \times 10^{-24} \mathrm{~cm}^3$
$2.76 \times 10^{-23} \mathrm{~cm}^3$
$1.88 \times 10^{-24} \mathrm{~cm}^3$
Solution
$\begin{aligned}
& \text { Density }=\frac{\text { mass of atomsin unitcell }}{\text { Volume of unitcell }} \\
& \text { mass of atoms in unit cell }=\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{N}_{\mathrm{A}}}=\frac{2 \times 25}{6.023 \times 10^{23}} \\
& \text { Volume of unit cell }=\frac{2 \times 25}{6.02 \times 10^{23} \times 3}=2.76 \times 10^{-23} \mathrm{~cm}^3
\end{aligned}$