Part of JPC-07 — Atomic Structure: Quantum Numbers & Electronic Config

Hydrogen Spectrum and Spectral Lines

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Rydberg formula: 1/lambda = RZ2RZ^2(1/n12n1^2 - 1/n22n2^2), R = 1.097 x 10^7 m1m^{-1}. Five series: Lyman (n1=1, UV, 91.2-121.6 nm), Balmer (n1=2, visible, 364.7-656 nm), Paschen (n1=3, IR), Brackett (n1=4, IR), Pfund (n1=5, far IR). Total lines from level n: nn12\frac{n-1}{2}. Lines in specific series from n: n - n1. First line = longest wavelength = smallest energy gap (n2 = n1+1). Series limit = shortest wavelength = largest energy gap (n2 = infinity). For each series: lambdalimitlambda_{limit} = n12n1^2/R. Energy shortcut: E(eV) = 1240/lambda(nm). H-alpha (656 nm, red), H-beta (486 nm, blue-green), H-gamma (434 nm, violet), H-delta (410 nm, violet). An excited atom can emit multiple photons if it cascades through intermediate levels. Maximum photons from n = n-1 (one step at a time). Absorption spectrum at room temperature shows only ground-state transitions (fewer lines than emission spectrum).

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