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

The electronic congiguration of Na is `[Ne] 3s ^(1)` and that of Mg is `[Ne] 3s ^(2).` The configuration of Mg is more stable (being completely filled) than that of Na. Therefore, first ionization enthalpy of Mg is more than that of Na. After the loss of an electron from Na, it acquires the electronic configuration of noble gas, Ne, i.e., `1s ^(2) 2s ^(2)2p^(6).` On the other hand, in case of Mg atom, the elctronic configuration becomes `[Ne]3s ^(1).` Thus, the elctronic congiguration of `Na ^(+)` is more stabe than `Mg ^(+)` and hence the second ionization enthalpy of Na is much larger than that of Mg.
`Ne([Ne]3s ^(1)) overset(IE_(1))toNa ^(+) ([Ne])overset(IE _(2))toNa ^(2+) (1s ^(2) 2s ^(2)2p ^(5))`
`Mg ([Ne]3s ^(2)) overset(IE _(2))toMg ^(2+) ([Ne]3s ^(1))overset(IE_(2))toMg ^(2+) ([Ne])`
`IE _(1) (NA) lt IE _(1) (Mg) " "IE_(2) (Na) gt IE _(2) (Mg)`