## The Hydrogen Spectrum

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

whereandand 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 isand is called the Rydberg formula.

Ifthe wavelengths are in the ultraviolet and are called the Lyman series.

Ifthe wavelengths are in the infrared and are called the Paschen series.

Other series are called the Brackett series (), and the Pfund series ().