• Tags: spectral-series, lyman, balmer, paschen
• Difficulty: Moderate

Lyman series ($n_f$ = 1): All transitions to n=1. Located in the UV region. First line (Lyman-α): 2→1 at 121.6 nm. Series limit: ∞→1 at 91.2 nm. Balmer series ($n_f$ = 2): All transitions to n=2. Partly visible. Hα (3→2) = 656.3 nm (red), Hβ (4→2) = 486.1 nm (blue-green), Hγ (5→2) = 434.0 nm (violet), Hδ (6→2) = 410.2 nm. Series limit: 364.6 nm. Paschen series ($n_f$ = 3): IR region. First line 4→3 at 1875 nm. Brackett ($n_f$ = 4) and Pfund ($n_f$ = 5) are in the far IR.

Key relations: 1/λ_Lyman(first) = R(1 - 1/4) = 3R/4. 1/λ_Balmer(first) = R(1/4 - 1/9) = 5R/36. The Balmer first line is about 5× longer than the Lyman first line.