How would you explain the fact that the first ionisation enthalpy of sodium is lower than that of magnesium but its second ionisation enthalpy is higher than that of magnesium?
First ionisation enthalpy of sodium is lower than that of magnesium because the
electron to be removed in both the cases is from 3s-orbital but the nuclear charge is lower in the Na than that of magnesium
(IE ∝ 1/ Atomic size)
After the removal of first electron Na+ acquires inert gas (Ne) configuration (Na+ =${{1s}^{2}}$, ${{2s}^{2}}$, ${{2p}^{6}}$) and hence, removal of second electron from sodium is difficult. While in case of magnesium, after the removal of first electron, the electronic configuration of Mg+ is ${{1s}^{2}}$, ${{2s}^{2}}$, ${{2p}^{6}}$,${{3s}^{1}}$.
In this case, ${{3s}^{1}}$ electron is easy to remove in comparison to remove an electron from inert gas configuration. Therefore, ${ IE }_{ 2 }$ of Na is higher than that of Mg.