Spectral Lines

Atoms emit and absorb light only at DISCRETE wavelengths (spectral lines) — direct evidence of quantised energy levels.

Each line corresponds to a transition between two specific levels: hf = E_i − E_f.

Hydrogen line series (named by final state n_f): Lyman (n_f=1, UV), Balmer (n_f=2, visible), Paschen (n_f=3, IR), Brackett (n_f=4, IR), Pfund (n_f=5, IR).

Lyman-α (n=2 → 1): 121.6 nm (UV). Balmer-α (n=3 → 2): 656.3 nm (red, Hα).

Series limit: shortest wavelength in a series — corresponds to n_i = ∞. λ_lim(Lyman) = 91.2 nm. λ_lim(Balmer) = 364.6 nm.

Emission spectrum (hot atoms emit lines) vs absorption spectrum (cool atoms in front of bright continuum — dark lines).

Fraunhofer lines in the solar spectrum are absorption lines from cooler gas in the Sun's atmosphere.