Electron Configurations and Ionization Energy

Evidence: emission spectra

When excited electrons fall back to lower levels they emit photons of fixed energy, $E=hf$. The spectrum is therefore a set of discrete lines, not a continuum — direct evidence that electron energy is quantised. Within a series the lines converge at higher energy; the convergence limit corresponds to $n=\infty$, i.e. removal of the electron, so it gives the ionization energy directly.

Filling the orbitals

Order of filling: $\text{1s }\text{2s }\text{2p }\text{3s }\text{3p }\text{4s }\text{3d }\text{4p}$. Hund's rule: fill degenerate orbitals singly with parallel spins before pairing. Chromium and copper are the two exceptions in period 4: $\ce{Cr}=[\ce{Ar}]\,\text{3d}^5\text{4s}^1$ and $\ce{Cu}=[\ce{Ar}]\,\text{3d}^{10}\text{4s}^1$.

The rule that catches everyone: for a transition-metal cation, electrons are removed from 4s first, because once 3d is occupied the 3d orbitals drop below 4s in energy. So $\ce{Fe^{2+}}=[\ce{Ar}]\,\text{3d}^6$, not $[\ce{Ar}]\,\text{3d}^4\text{4s}^2$.

(HL) Successive ionization energies

Each successive energy is larger, because the electron is pulled from an increasingly positive ion. A large jump appears when the next electron must come from a shell closer to the nucleus — so the number of electrons removed before the jump equals the number of valence electrons, which identifies the group.

Across a period the first ionization energy generally rises, with two dips: $\ce{Al}<\ce{Mg}$ (the 3p electron is higher in energy and shielded by 3s) and $\ce{S}<\ce{P}$ (a paired 3p electron suffers extra repulsion).