$X$-ray diffraction studies show that copper crystallises in an $fcc$ unit cell with cell edge of $3.608 \times 10^{-8} \ cm$. In a separate experiment,copper is determined to have a density of $8.92 \ g / cm^{3}$,calculate the atomic mass of copper.

(N/A) For an $fcc$ lattice,the number of atoms per unit cell is $z = 4$.
The formula for density is $d = \frac{z M}{N_{A} a^{3}}$,where $M$ is the atomic mass.
Rearranging for $M$: $M = \frac{d N_{A} a^{3}}{z}$.
Substituting the given values:
$M = \frac{8.92 \ g \ cm^{-3} \times 6.022 \times 10^{23} \ mol^{-1} \times (3.608 \times 10^{-8} \ cm)^{3}}{4}$.
$M = \frac{8.92 \times 6.022 \times 10^{23} \times 46.97 \times 10^{-24}}{4}$.
$M = \frac{2523.36}{40} \approx 63.1 \ g / mol$.
Thus,the atomic mass of copper is $63.1 \ u$.