How many number of unit cells are present in $100 \mathrm{~g}$ of an element with fcc crystal having density…
How many number of unit cells are present in $100 \mathrm{~g}$ of an element with fcc crystal having density $10 \mathrm{~g} / \mathrm{cm}^{3}$ and edge length $100 \mathrm{pm}$ ?
$3 \times 10^{25}$
$2 \times 10^{25}$
$4 \times 10^{25}$
$1 \times 10^{25}$
Solution
$\begin{aligned} \text { Vol. of unit cell } &=(100 \mathrm{pm})^{3}=\left(100 \times 10^{-10} \mathrm{~cm}\right)^{3} \\ &=10^{-24} \mathrm{~cm}^{3} \end{aligned}$
Vol. of $100 \mathrm{~g}$ of an element $=\frac{\text { Mass }}{\text { Density }}=\frac{100 \mathrm{~g}}{10 \mathrm{~g} \mathrm{~cm}^{-3}}=10 \mathrm{~cm}^{3}$
No. of unit cells in $100 \mathrm{~g}$ of an element $=\frac{\text { Total volume }}{\text { Volume of one unit cell }}$
$=\frac{10 \mathrm{~cm}^{3}}{10^{-24} \mathrm{~cm}^{3}}=1 \times 10^{25}$ unit cells.