Energy Levels

Atomic energy levels are the discrete energies an electron can have in an atom: E_n = −13.6 Z²/n² eV for hydrogen-like.

Levels are NEGATIVE for bound states (relative to a free electron at rest, E = 0).

Larger n: shallower (less negative) — closer to ionisation. Smaller n: deeper (more negative).

Ground state: n = 1 (lowest energy, most stable). Excited states: n = 2, 3, …

Differences between levels give photon energies in transitions: hf = E_i − E_f.

Energy-level diagram: horizontal lines labelled with n; arrows showing transitions.

Hydrogen's first excited state (n=2) is −3.4 eV; spacing E₁ − E₂ = 10.2 eV (Lyman-α).

Multi-electron atoms have more complex level structure (different sub-shells s, p, d, f within same n).