# Lyman-alpha line

In physics, the Lyman-alpha line, sometimes written as Ly-$\alpha$ line, is a spectral line of hydrogen, or more generally of one-electron ions, in the Lyman series, emitted when the electron falls from the $n = 2$ orbital to the $n = 1$ orbital, where n is the principal quantum number. In hydrogen, its wavelength of 1215.67 angstroms (121.567 nm or 1.21567 × 10−7 m), corresponding to a frequency of 2.47 × 1015 hertz, places the Lyman-alpha line in the vacuum ultraviolet part of the electromagnetic spectrum. Lyman-alpha astronomy must therefore ordinarily be carried out by satellite-borne instruments, except for extremely distant sources whose red-shifts allow the hydrogen line to penetrate the atmosphere.
Because of fine structure perturbations, the Lyman-alpha line splits into a doublet with wavelengths 1215.668 and 1215.674 angstroms. Specifically, because of the electron's spin-orbit interaction, the stationary eigenstates of the perturbed Hamiltonian must be labeled by the total angular momentum j of the electron (spin plus orbital), not just the orbital angular momentum $l$. In the $n = 2$ orbital, there are two possible states, $j = 1/2$ and $j = 3/2$, resulting in a spectral doublet. The $j = 3/2$ state is of higher energy (less negative) and so is energetically farther from the $n = 1$ orbital to which it is transitioning. Thus, the $j = 3/2$ state is associated with the more energetic (shorter wavelength) spectral line in the doublet.[1]