Q.How would you explain the fact that first ionisation enthalpy of sodium is lower than that of magnesium but its second ionisation enthalpy is higher than that of magnesium?

Concept: Ionisation enthalpy depends on nuclear charge, electron configuration, and the stability of the resulting ion.

First ionisation enthalpy:

Sodium ($\ce{Na}$: $1s^2 2s^2 2p^6 3s^1$) loses one electron to achieve the stable noble-gas configuration $\ce{[Ne]}$. Magnesium ($\ce{Mg}$: $1s^2 2s^2 2p^6 3s^2$) has a higher nuclear charge ($Z = 12$ vs. $11$) and loses an electron from the same $3s$ orbital, but does not immediately reach a noble-gas configuration. The higher nuclear charge in magnesium outweighs the slight pairing energy, so $\text{IE}_1(\ce{Mg}) > \text{IE}_1(\ce{Na})$.

Second ionisation enthalpy: …

Why ionisation energies depend on electron configuration

Ionisation enthalpy measures how tightly an atom holds its outermost electron. The key factors are nuclear charge (more protons pull harder), shielding (inner electrons screen the nucleus), and the stability of the electron configuration before and after removal.

When comparing successive ionisations of two elements, you must ask: which shell is the electron coming from? Removing an electron from a filled, stable inner shell costs far more energy than plucking one from a half-filled or loosely-held valence shell.

Step-by-step comparison

1. Electronic configurations

Write out what we're working with:

2. First ionisation enthalpy: Na < Mg

For sodium, the first ionisation removes the single $3s^1$ electron:

This electron is alone in the $3s$ orbital, experiences relatively weak pairing repulsion, and its removal yields the exceptionally stable neon configuration. The process is comparatively easy.

For magnesium, the first ionisation removes one electron from the paired $3s^2$:

Magnesium has one extra proton (nuclear charge $Z = 12$ vs. $11$), so its $3s$ electrons feel a stronger effective pull. Even though electron–electron repulsion in the $3s^2$ pair slightly raises energy, the higher nuclear charge dominates. Magnesium holds its first electron more tightly.

3. Second ionisation enthalpy: Na > Mg

Now consider removing a second electron.

For sodium, $\text{Na}^+$ has the configuration $1s^2 \, 2s^2 \, 2p^6$ — a closed neon core. The second ionisation must break into this stable, inner $2p$ shell:

The $2p$ electrons are much closer to the nucleus (principal quantum number $n=2$ vs. $n=3$), experience far less shielding, and belong to a completely filled, stable octet. Ripping one out requires enormous energy.

For magnesium, $\text{Mg}^+$ still has one $3s$ electron left:

The second ionisation removes this remaining valence electron:

$\text{Mg}^+ \to \text{Mg}^{2+} + e^- \quad \text{removes } 3s^1$ …