Balmer formula

Between two frequencies and , characterising the lines in the spectrum of the hydrogen atom, on subtracting them there is the Balmer formula (from the name of its discoverer) :

where n and m are non-zero integers, the Rydberg constant, and c is the speed of light.

This is the frequency of the photon emitted or absorbed during the atomic transition of one electron between two principle energy levels with quantum numbers n and m.

Johann Jacob Balmer (1825-1898).

Johann Balmer had in fact studied the series of spectral lines of the atom hydrogen atom such as m=2. There are other series of transitions such as the famous Lyman series which is important in cosmology.

Spectral series of the hydrogen atom; N.B. here n corresponds to m in the previous formula.
Credit: Olivier Thizy