Explain quantitatively the order of magnitude difference between the diamagnetic susceptibility of ${N_2} \left( { \sim 5 \times {{10}^{ - 9}}} \right)$ (at $STP$) and ${Cu} \left( { \sim {{10}^{ - 5}}} \right)$.

(A) Magnetic susceptibility $\chi$ is proportional to the number of atoms per unit volume,which is directly related to the density $\rho$ of the substance.
Density of $N_2$ at $STP$:
$\rho_{N_2} = \frac{28 \text{ g}}{22.4 \text{ L}} = \frac{28 \text{ g}}{22400 \text{ cm}^3} \approx 1.25 \times 10^{-3} \text{ g/cm}^3$.
Density of Copper $(Cu)$:
$\rho_{Cu} \approx 8.9 \text{ g/cm}^3$.
Ratio of densities:
$\frac{\rho_{N_2}}{\rho_{Cu}} = \frac{1.25 \times 10^{-3}}{8.9} \approx 1.4 \times 10^{-4}$.
Since susceptibility $\chi$ is proportional to the number density of atoms,the ratio of susceptibilities should be of the same order as the ratio of densities:
$\frac{\chi_{N_2}}{\chi_{Cu}} \approx \frac{5 \times 10^{-9}}{10^{-5}} = 5 \times 10^{-4}$.
The difference in order of magnitude arises because $N_2$ is a gas at $STP$ with a very low atomic density compared to the solid metal $Cu$.