It was known by the nineteenth century that the atoms of each element emitted photons with wavelengths characteristic of the element. No formula existed for the wavelengths or frequencies present in any spectrum and no explanation existed for the wavelengths or frequencies present.
Johann Balmer discovered a formula for the visible wavelengths present. The wavelengths are now known as the Balmer series and are given by the formula
where
and
and is called the Rydberg constant.
The formula was later discovered to be one of a series of formulae, each formula giving rise to a particular series of wavelengths.
and so on.
The general formula is
and is called the Rydberg formula.
If
the wavelengths are in the ultraviolet and are called the Lyman series.
If
the wavelengths are in the infrared and are called the Paschen series.
Other series are called the Brackett series (
), and the Pfund series (
).