Ionisation energy

Definition. Ionisation energy (or ionisation enthalpy) is the minimum energy needed to remove the most loosely bound electron from the valence shell of an isolated, neutral, gaseous atom in its ground state:

where $IE_1$ is the first ionisation energy.

Successive ionisation energies. The minimum energy needed to remove an electron from the resulting unipositive cation is the second ionisation energy, $M^+_{(g)} + IE_2 \rightarrow M^{2+}_{(g)} + e^-$, and third, fourth, and so on ionisation energies are defined the same way. Because a cation has fewer electrons than the neutral atom but the same nuclear charge, its effective nuclear charge is higher, so each successive electron is held more tightly than the last:

Trend across a period: ionisation energy generally increases, with a few exceptions. Moving left to right, the valence electrons keep being added to the same shell even as protons are added to the nucleus, so the growing nuclear charge pulls the valence electrons in more tightly and more energy is needed to remove one.

The Be/B and N/O exceptions (Figure 3.2). Boron is expected to have a higher ionisation energy than beryllium (it has one more proton), yet the measured values are Be = 899 kJ mol-1 and B = 800 kJ mol-1 -- the reverse of the naive expectation. The reason is stability, not nuclear charge: beryllium's configuration $1s^2\,2s^2$ has a completely filled 2s subshell, which is more stable (harder to disturb) than boron's partially filled $2s^2\,2p^1$, so it takes relatively less energy to remove boron's single, higher-energy 2p electron. Similarly, nitrogen ($1s^2\,2s^2\,2p^3$, IE = 1402 kJ mol-1) has a higher ionisation energy than oxygen ($2p^4$, IE = 1314 kJ mol-1): nitrogen's exactly half-filled 2p3 subshell is extra-stable, whereas removing one electron from oxygen's paired 2p4 actually relieves some electron-electron repulsion and leaves oxygen with the same stable half-filled configuration nitrogen already has -- so it is comparatively easier to pull an electron off oxygen. …