Lyman-alpha line
In physics, the Lyman-alpha line, sometimes written as Ly-α 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, corresponding to a frequency of, places the Lyman-alpha line in the vacuum ultraviolet part of the electromagnetic spectrum, which is absorbed by air. Lyman-alpha astronomy must therefore ordinarily be carried out by satellite-borne instruments, except for extremely distant sources whose redshifts 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, not just the orbital angular momentum l. In the n = 2 orbital, there are two possible states, j = and j = , resulting in a spectral doublet. The j = state is of higher energy and so is energetically farther from the n = 1 orbital to which it is transitioning. Thus, the j = state is associated with the more energetic spectral line in the doublet.
The less energetic spectral line has been measured at, or. The line has also been measured in antihydrogen.
A K-alpha line, or Kα, analogous to the Lyman-alpha line for hydrogen, occurs in the high-energy induced emission spectra of all chemical elements, since it results from the same electron transition as in hydrogen. The equation for the frequency of this line uses the same base-frequency as Lyman-alpha, but multiplied by a 2 factor to account for the differing atomic numbers of heavier elements, as approximated by Moseley's law.
The Lyman-alpha line is most simply described by the = solutions to the empirical Rydberg formula for hydrogen's Lyman spectral series., by a factor of 2 − 2 = .) Empirically, the Rydberg equation is in turn modeled by the semi-classical Bohr model of the atom.
