Why atoms give line spectra, how electrons are arranged in energy levels and orbitals, and how to write any configuration.
This is the Higher Level lesson. The core S1.3.1–S1.3.5 (spectra, levels, orbitals, configurations) is shared with SL; the HL-only statements S1.3.6–S1.3.7 — ionisation energy carry a purple HL badge.
When electrons are excited to higher energy levels and then fall back down, they emit photons of specific energies — giving a line spectrum, not a continuous rainbow. The fixed lines are direct evidence that electrons occupy discrete energy levels. The lines converge (get closer) at higher energy. Click a jump down to level n=2 (the visible Balmer lines):
Each main energy level n holds up to 2n² electrons (n=1 → 2; n=2 → 8; n=3 → 18). Each level is divided into sub-levels — s, p, d, f — of rising energy, made of orbitals. Each orbital holds 2 electrons of opposite spin. An s sub-level has 1 orbital (2 e⁻), p has 3 (6 e⁻), d has 5 (10 e⁻).
Electrons fill from lowest energy up (Aufbau), one per orbital before pairing (Hund), with opposite spins (Pauli). Drag the slider to change the atomic number and watch the orbitals fill:
Two exceptions you must know: chromium (Cr, Z=24) is [Ar]3d⁵4s¹ and copper (Cu, Z=29) is [Ar]3d¹⁰4s¹ — a half-full or full d sub-level is extra stable, so one 4s electron shifts into 3d.
The first ionisation energy is the energy to remove one mole of electrons from one mole of gaseous atoms. Two pieces of evidence at HL:
The emission lines get closer together (converge) at higher frequency. At the convergence limit the electron has been removed entirely — so this limit corresponds to the ionisation energy. Measuring the frequency at convergence lets you calculate it (E = hf).
Keep removing electrons one at a time and the energy needed rises — but with big jumps whenever you break into a new, closer main energy level. The pattern of jumps reveals the electron arrangement. Pick an element and click the bars:
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