Rydberg formula

The Rydberg formula ( Rydberg - Ritz formula also ) is used in atomic physics to determine the complete spectrum of light emitted by hydrogen light. It shows that the energy of the electron in the hydrogen atom is proportional to the principal quantum number.

The formula was presented on 5 November 1888 by the Swedish physicist Johannes Rydberg; Walter Ritz worked on it. Later it was extended to determine the spectrum of other elements. Corrections due to angular momentum or relativistic effects are not considered.

Rydberg formula for hydrogen

Here are

  • The wavelength of light in vacuum
  • The Rydberg constant for the respective element: with   the mass of the electron
  • The core mass (depending on the isotope present )
  • The Rydberg constant for hydrogen

Energy and spectral series

For the energy of the emitted photon, and thus for the corresponding energy level in the atom (see also Rydberg energy):


  • Speed ​​of light in vacuum
  • Planck constant shear.

With ( ground state) and one obtains a series of spectral lines, which is also called the Lyman series. The first transition series has a wavelength of 121 nm, the series limit is 91 nm Analogously, the other series:

Rydberg formula for hydrogen-like atoms

For hydrogen-like ions, that is, Ions, which have only one electron, such as He , Li2 , Be3 or K10 , can extend the above formula to:

With the atomic number, that is, the number of protons in the nucleus.

A generalization to the light emission of atoms having a single electron in a non- closed shell, leading to Moseley law.

  • Atomic physics
  • Spectroscopy