Hydrogen Spectrum

Hydrogen's optical spectrum was the most-studied — its simplicity (one electron) makes it a textbook of quantum mechanics.

Five named series, each ending on a specific lower level n_f:

Lyman (n_f = 1): UV, lines at 121.6, 102.6, 97.3, … nm. Series limit at 91.2 nm.

Balmer (n_f = 2): visible, Hα 656.3, Hβ 486.1, Hγ 434.0, Hδ 410.2 nm. Limit at 364.6 nm.

Paschen (n_f = 3): near-IR, longest 1875 nm. Limit at 820 nm.

Brackett (n_f = 4): IR, around 4 μm. Limit at 1458 nm.

Pfund (n_f = 5): far-IR, around 7.5 μm. Limit at 2280 nm.

Universal pattern: 1/λ = R · (1/n_f² − 1/n_i²) — works for ALL series.