Cornell Note: Hydrogen Spectrum & Rydberg Formula

Cue Column	Note Column
Rydberg formula?	$\frac{1}{\lambda} = R_H\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$ R_H = $1.097 \times 10^{7}$ $m^{-1}$
Lyman series region?	n_{1}=1; ultraviolet; first line λ = 121.6 nm
Balmer series region?	n_{1}=2; visible; first line λ = 656.3 nm (red H_α)
Paschen series region?	n_{1}=3; infrared; first line λ = 1875 nm
Brackett series region?	n_{1}=4; infrared; first line λ = 4051 nm
Pfund series region?	n_{1}=5; far infrared; first line λ = 7460 nm
Which series only visible?	ONLY Balmer. Mnemonic: "B for Balmer, B for Bright"
Lines from level n?	n(n−1)/2. From n=5: 10 lines. TRAP: not $n^{2}$ (orbitals), not n.
Max wavelength in a series?	First line (smallest n_{2}, smallest $\Delta E$ ).
Min wavelength (series limit)?	n_{2} → ∞. For Lyman: λ_min = 91.2 nm. Balmer: 364.7 nm.

Summary: The Rydberg formula predicts all hydrogen spectral lines. The five series are identified by n_{1} (lower level). Only Balmer is visible. The number of lines from level n = n(n−1)/2. Series limit corresponds to ionization from that level.