The $2^{\mathrm{nd}}$ ionization potential of $\mathrm{Mg}$ is less than that of $\mathrm{Na}$ because

none

Atomic size of $\mathrm{Mg}$ is greater than that of $\mathrm{Na}$

$2^{\mathrm{nd}}$ electron removal from $\mathrm{Na}$ occurs from inert gas configuration, while the same for $\mathrm{Mg}$ results in inert gas configuration.

Atomic size of $\mathrm{Mg}$ is less than that of $\mathrm{Na}$