Bohr hydrogen energy levels and emission spectrum

What you are seeing: the hydrogen energy ladder $E_n = -13.6\,\mathrm{eV}/n^2$ on the left, and the spectrum on the right. Each emission line $n_h \to n_\ell$ corresponds to a photon of wavelength $1/\lambda = R_H (1/n_\ell^2 - 1/n_h^2)$, where $R_H \approx 1.0968 \times 10^7 \, \mathrm{m}^{-1}$ is the hydrogen Rydberg constant (proton mass correction included).

The Lyman series ($n_\ell = 1$) lives in the UV and converges at 91.2 nm; the Balmer series ($n_\ell = 2$) is in the visible and converges at 365 nm; the Paschen series ($n_\ell = 3$) lies in the near IR. Select a series with the dropdown to highlight only its transitions and emphasise its series limit. The Bohr formula matches observed wavelengths to a few parts in $10^4$; the residual is the fine structure (Dirac equation plus QED corrections) that the classical Bohr model cannot capture.