Balmer series

The Balmer series is the set of emission lines from atomic hydrogen gas, due to electrons descending from an electron shell of number n greater than 2 down to that of n = 2, 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 Lyman series, and is named after Johann Balmer. The lines are within the optical atmospheric window and given no redshift, those produced by astronomical sources can be observed by ground telescopes. Consequently the Balmer series was first series discovered and the lines are commonly seen in spectra of objects within the Milky Way, though the Lyman Series (down to n = 1) is in some sense more basic. Balmer series lines:

• 3 -> 2: H-alpha, H-α, 656.3 nm (red)
• 4 -> 2: H-beta, H-β, 486.1 nm (cyan)
• 5 -> 2: H-gamma, H-γ, 434.0 nm (blue)
• 6 -> 2: H-delta, H-δ, 410.2 nm (violet)
• 7 -> 2: H-epsilon, H-ε, 397.0 nm (ultraviolet)
• 8 -> 2: H-zeta, H-ζ, 388.9 nm (ultraviolet)
• 9 -> 2: H-eta, H-η, 383.5 nm (ultraviolet)
• ...
• infinity -> 2: the Balmer limit, 364.6 nm (ultraviolet)

Formula for the wavelengths:

wavelength = Balmer's constant × n² / ( n²-4 )

where

• wavelength is that of a Balmer series line.
• Balmer's constant = 3.6450682 × 10^-7 m or 364.50682 nm (same as 4/R_H where R_H is the Rydberg constant for hydrogen).
• n is the higher electron shell number.

The Balmer series, especially H-α, is often used to determine the redshift of quasars and distant galaxies because it is often prominent.