Transitions Between Levels

An atomic transition is the jump of an electron between two energy levels, with absorption or emission of a photon.

Energy conservation: hf = |E_i − E_f|. Frequency uniquely set by the level pair.

Emission (downward): electron drops from higher to lower level, EMITS a photon.

Absorption (upward): electron jumps from lower to higher level after ABSORBING a photon of matching energy.

Selection rules (full QM): Δl = ±1, Δm = 0, ±1. Not all transitions are allowed.

Lifetime of typical excited states: ~10⁻⁸ s (allowed) to ~10⁻³ s or longer (forbidden metastable).

Spontaneous emission: an isolated excited atom decays randomly; lifetime obeys exponential decay.

Stimulated emission: a photon of matching energy stimulates an excited atom to emit a coherent photon — basis of LASERS.