Chemistry - Solid State Question with Solution | TestHub

The mass of one unit cell is given by $\rho \times a^3$.

Given that $\rho \times a^3=7.2\times 10^{-22}\text{ g}$.

For a face-centered cubic (fcc) structure, the number of atoms per unit cell is $Z=4$.

Mass of one atom = $\frac{\text{Mass of one unit cell}}{Z}=\frac{7.2\times 10^{-22}}{4}=1.8\times 10^{-22}\text{ g}$.

Number of atoms in $5.4\text{ g}$ of the metal = $\frac{\text{Total mass}}{\text{Mass of one atom}}$

Number of atoms = $\frac{5.4}{1.8\times 10^{-22}}=3.0\times 10^{22}$

Answer: $3.0\times 10^{22}$