# Lyman-alpha line

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Lyman-alpha line

In physics, the Lyman-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 121.6 nanometres, corresponding to a frequency of 2.47 &times; 1015 hertz, places the Lyman-alpha line in the far ultraviolet part of the electromagnetic spectrum.

Because of fine structure perturbations, the Lyman-alpha line splits into a doublet. 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.

A K-alpha or Kα line analogous to the Lyman-alpha line for hydrogen, occur 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 prediction of the frequency of this line (usually in the X-ray range for heavier elements), uses the same base-frequency as Lyman-alpha, but modified by a (Z-1)² factor to account for differing atomic numbers (Z) between elements, and is expressed as Moseley's law. The Lyman-alpha line and the rest of the hydrogen Lyman spectral series are most simply described by the empiric Rydberg equation and semi-classic Bohr model of the atom.

ee also

*Lyman-alpha blob
*Moseley's law
*Lyman series
*Bohr model

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