Hydrogen Spectrum
All 5 series on a log-wavelength axis with visible-band zoom toggle.
Key Notes
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.
Formulas
Rydberg formula
R = 1.097 × 10⁷ m⁻¹.
Balmer-α (Hα)
λ ≈ 656.3 nm — distinctive red.
Lyman-α
λ ≈ 121.6 nm — UV; dominant in interstellar HI gas.
Hydrogen-21cm line
Forbidden hyperfine transition; radio astronomy probe of HI.
Important Points
Balmer's formula (1885) preceded Bohr by 30 years — but only Bohr derived it from theory.
Balmer series (visible) is the most prominent in stellar spectra — astrophysicists tag stars by Hα.
Lyman-α is used to map cosmological neutral hydrogen — galaxies at high redshift glow in Lyα.
21-cm hydrogen line: hyperfine splitting of the ground state — different mechanism (electron-proton spin coupling) but immensely useful in astronomy.
All lines have very small widths (a few Å) — used to identify hydrogen unambiguously.
Isotope shift: deuterium spectral lines are slightly shifted (reduced-mass effect) — observable in high-resolution spectroscopy.
Hydrogen Spectrum notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.