Lyman series

The Lyman series is the set of emission lines (Lyman lines) from atomic hydrogen gas, due to electrons descending from an electron shell of number n greater than 1 down to that of n = 1, or the analogous absorption lines when absorbed electromagnetic radiation (EMR) makes electrons do the opposite. It is one of the hydrogen line series, such as the Balmer series, and is named after Theodore Lyman. The lines fall within extreme ultraviolet (EUV) and those produced by astronomical sources cannot be observed from the ground unless considerably redshifted. Lines:

• 2 -> 1: 121.6 nm (aka Lyman alpha, Ly-α)
• 3 -> 1: 102.6 nm (aka Lyman beta, Ly-β)
• 4 -> 1: 97.3 nm (etc.)
• 5 -> 1: 95.0 nm
• 6 -> 1: 93.8 nm
• 7 -> 1: 93.1 nm
• 8 -> 1: 92.6 nm
• 9 -> 1: 92.3 nm
• 10 -> 1: 92.1 nm
• 11 -> 1: 91.9 nm
• ...
• infinity -> 1: 91.18 nm (the Lyman limit)

Formula for the wavelengths:

1/wavelength = RH ( 1 - 1/n² )

• wavelength is that of a Lyman series line.
• R_H is the Rydberg constant for hydrogen, 1.0973731568160 × 10⁷m^-1 ≈ 13.6 eV / (hc)
• n is the higher electron shell number.
• h - Planck constant.
• c - speed of light in a vacuum.

Photons with wavelength at or shorter than the Lyman limit can ionize any neutral atomic hydrogen atom, and are termed Lyman continuum photons (LyC photons), thus they are likely to ionize any such hydrogen in clouds they pass through, regardless of whether the hydrogen is excited. Cases where photons, e.g., from a galaxy, avoid such absorption (Lyman continuum escape, LyC escape) are of research interest. The galaxies from which this occurred are termed Lyman continuum leakers (LyC leakers).

Hydrogen with neutrons (its other isotopes) have analogous series (i.e., a Lyman series, a Balmer series, etc.) that have slightly different wavelengths, as do other elements when ionized to the point that they have just one electron. Their series wavelengths can be calculated by the same formula, but each with its own specific Rydberg constant, for example:

deuterium Rydberg constant, RD = 1.09707417 × 107
helium-4 Rydberg constant, R4He = 1.09722267 × 107

The series names are sometimes used for these as well, e.g., deuterium Lyman series, HE-II Lyman series, deuterium Balmer series, HE-II Balmer series, etc.