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?

Explanation

From the electronic configuration of Na and Mg, it is evident that in both the atoms,t he valence electrons enters the 3s orbital. However, nuclear charge of Mg atom (+12) is greater than that of Na atom (+11). again the 3s orbital Mg atom being completely filled is more stable than half-filled 3s-orbital of Na atom. thus, first ionisation enthalpy of sodium is lower than that of magnesium.
On the other hand, removal of one electron from the valence shell of Na atom leads to the formation of `Na^(+) ` ion whose electronic configuration is highly stable (similar to inert gas, neon). so high amount of energy is required to remove the second electron because it distrurbs the stble electronic configuration. however, electronic configuration of `Mg^(+)` is not as stable as that of `Na^(+)`, but electronic configuration of `Mg^(2+)` is more stable as it is similar in the electronic configuration of inert gas, neonl. so, less amount of energy is required to remove an electron from `Mg^(+)`. thus, second ionisation enthalpy of sodium is higher than that of magnesium.