# Rydberg formula - For hydrogen-like element

## Description

The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg, and presented on 5 November 1888.

In 1880, Rydberg worked on a formula describing the relation between the wavelengths in spectral lines of alkali metals. He noticed that lines came in series and he found that he could simplify his calculations by using the wavenumber (the number of waves occupying the unit length, equal to 1/λ, the inverse of the wavelength) as his unit of measurement. He plotted the wavenumbers (n) of successive lines in each series against consecutive integers which represented the order of the lines in that particular series. Finding that the resulting curves were similarly shaped, he sought a single function which could generate all of them, when appropriate constants were inserted.

For any hydrogen-like element the formula is expressed as shown

Related formulas## Variables

λ_{vac} | wavelength of electromagnetic radiation emitted in vacuum (m) |

R | Rydberg constant |

Z | atomic number (dimensionless) |

n_{1} | integer greater than or equal to 1 corresponding to the principal quantum numbers of the orbitals occupied before and after the 'quantum leap' (dimensionless) |

n_{2} | integer greater than or equal to 1 and larger than n1 corresponding to the principal quantum numbers of the orbitals occupied before and after the 'quantum leap'. (dimensionless) |