Question

An element crystallises in a structure having an $fcc$ unit cell of an edge length $100 \,pm$. If $25 \,g$ of the element contains $25 \times 10^{24}$ atoms, the density of the element is ____ $g \,cm ^{-3}$.

Answer 1

$100 \,pm =100 \times 10^{-10} \,cm$
Volume of unit cell $=\left(100 \times 10^{-10}\right)^{3}$
$=1 \times 10^{-24} \,cm ^{3}$
Mass of an atom $=\frac{25}{25 \times 10^{24}}=1 \times 10^{-24} \,g$
No. of atoms in an fcc unit cell $=4$
Mass of unit cell $=4 \times 1 \times 10^{-24}$
$=4 \times 10^{-24} g $
Density $=\frac{\text { Mass }}{\text { Volume }}$
$=\frac{4 \times 10^{-24}}{1 \times 10^{-24}}=4\, g \,cm ^{-3}$