Chemistry - Solid State Question with Solution | TestHub

The mass of one unit cell is given by $\rho \times a^3=1.728\times 10^{-22}\mathrm{g}$.

For an fcc crystal structure, the number of atoms per unit cell is $Z=4$.

The number of unit cells in $1\mathrm{g}$ of the metal is $\frac{1}{\rho \times a^3}$.

The total number of atoms in $1\mathrm{g}$ of the metal is $Z\times \frac{1}{\rho \times a^3}$.

Substituting the given values:

Number of atoms $=\frac{4}{1.728\times 10^{-22}}$

Number of atoms $=2.3148\times 10^{22}\approx 2.315\times 10^{22}$

Answer: $2.315\times 10^{22}$