Which one of the following relations is correct with respect to first (I) and second (II) ionisation potentials of Na and Mg?

We know that 

Electronic configuration of $\mathrm{Na}=1{ \mathrm{s}}^{2}2{ \mathrm{s}}^{2}2{\mathrm{p}}^{6}3{ \mathrm{s}}^1$

Electronic configuration of $\mathrm{Mg}=1{ \mathrm{s}}^{2}2{ \mathrm{s}}^{2}2{\mathrm{p}}^{6}3{ \mathrm{s}}^2$

 And, Ist Ionization energy of sodium will be less than magnesium.

As we move across the period, the number of valence electrons in an atom increases and also nuclear charge increases which tend to decrease the radius and ionisation energy increases.

When an electron is removed from $\mathrm{Na}$, it acquires a noble gas configuration which is more stable and removing electrons requires more energy.

$\therefore {||{}_{\mathrm{Na}}>||}_{\mathrm{Mg}}$