Q.Why the first ionisation enthalpy of sodium is lower than that of magnesium while its second ionisation enthalpy is higher than that of magnesium?

Step 1. Sodium's configuration is $[Ne]3s^1$; magnesium's is $[Ne]3s^2$.

Step 2. For IE1: sodium loses its single, comparatively loosely held 3s electron easily, additionally reaching the extra-stable, completely filled Ne configuration in the process -- so Na's IE1 is low. Magnesium, by contrast, must remove one electron from its stable, filled/paired $3s^2$ subshell, which resists losing an electron more -- so Mg's IE1 is higher than Na's.

Step 3. For IE2: sodium's cation Na+ already has the stable, completely filled Ne core, so removing a SECOND electron means breaking into that very stable core -- a much harder, higher-energy step, making Na's IE2 very high. Magnesium's cation Mg+ still has one more ordinary valence electron left in 3s1 (much like sodium's own ground state), so removing it as IE2 is comparatively easy -- keeping Mg's IE2 lower than Na's IE2. …

Track which shell/subshell each successive ionisation removes an electron from for BOTH elements, and identify exactly …

• Explaining only the IE1 comparison (or only the IE2 comparison) without connecting why the two elements …