Ionization enthalpy

Ionization enthalpy ΔᵢH is the energy needed to remove an electron from an isolated gaseous atom in its ground state: X(g) → X⁺(g) + e⁻. It is measured in kJ mol⁻¹ and, unqualified, means the first ionization enthalpy.

It is always positive. The second, X⁺(g) → X²⁺(g) + e⁻, is larger than the first because the electron leaves a positive ion; the third is larger still.

Plotted against Z (up to 60), ΔᵢH peaks at the noble gases (closed shells) and dips at the alkali metals, whose low values match their high reactivity. Generally it rises across a period and falls down a group, the reverse of atomic radius.

Shielding: inner electrons screen the valence electron, so it feels an effective nuclear charge smaller than the full charge. Lithium's 2s electron, screened by 1s², feels much less than +3. Shielding works best when inner shells are complete.

Across a period, electrons join the same shell and shielding barely grows, so rising nuclear charge wins and ΔᵢH rises. Down a group, the electron is farther out and better shielded, so ΔᵢH falls.

Exception 1: ΔᵢH(B) < ΔᵢH(Be). Boron loses a 2p electron, which penetrates less and is more shielded than beryllium's 2s electron.

Exception 2: ΔᵢH(O) < ΔᵢH(N). Nitrogen's three 2p electrons are unpaired in separate orbitals (Hund's rule); in oxygen two 2p electrons share an orbital, and their repulsion makes one easier to remove.

Actual period 2 order: Li < B < Be < C < O < N < F < Ne. In period 3, with Na 496, Mg 737 and Si 786 kJ mol⁻¹, Al should be near 575 kJ mol⁻¹, below Mg, because its 3p electron is shielded by 3s electrons.

Per atom to per mole: hydrogen's ground-state electron has E = −2.18 × 10⁻¹⁸ J, so ΔᵢH = 2.18 × 10⁻¹⁸ × 6.022 × 10²³ ≈ 1.31 × 10⁶ J mol⁻¹.