To use all functions of this page, please activate cookies in your browser.

my.chemeurope.com

With an accout for my.chemeurope.com you can always see everything at a glance – and you can configure your own website and individual newsletter.

- My watch list
- My saved searches
- My saved topics
- My newsletter

## Rydberg formulaThe ## Additional recommended knowledge
## HistoryIn the 1880's, 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 a set unit of length, equal to First he tried the formula: , where Rydberg was just trying: when he saw Balmer's formula for the hydrogen spectrum λ= Rydberg rewrote this in terms of wavenumbers as This shows that hydrogen is a special case with Expressing results in terms of wavenumber, not wavelength, was the key to Rydberg's discovery. The fundamental role of wavenumbers was also emphasized by the Rydberg-Ritz combination principle of 1908. The fundamental reason for this lies in quantum mechanics. Light wavenumber is proportional to frequency (1/λ = frequency/c), and therefore also proportional to light quantum energy In Bohr's conception of the atom, the integer Rydberg (and Balmer) n therefore represents the photon energy emitted or absorbed when an electron makes a jump from orbital _{2}1 to orbital 2.
## Rydberg formula for hydrogenWhere - λ
_{vac}is the wavelength of the light emitted in vacuum, *R*_{H}is the Rydberg constant for hydrogen,*n*_{1}and*n*_{2}are integers such that*n*_{1}<*n*_{2},
By setting
The Lyman series is in the ultraviolet while the Balmer series is in the visible and the Paschen, Brackett, Pfund, and Humphreys series are in the infrared. ## Rydberg formula for any hydrogen-like elementThe formula above can be extended for use with any hydrogen-like chemical elements. where - is the wavelength of the light emitted in vacuum;
- is the Rydberg constant for this element;
- is the atomic number, i.e. the number of protons in the atomic nucleus of this element;
- and are integers such that .
It's important to notice that this formula can be applied only to hydrogen-like, also called The Rydberg formula provides correct wavelengths for extremely distant electrons, where the effective nuclear charge can be estimated as the same as that for hydrogen, since all but one of the nuclear charges have been screened by other electrons, and the core of the atom has an effective positive charge of +1. Finally, with certain modifications (replacement of For other spectral transitions in multi-electron atoms, the Rydberg formula generally provides ## References- Mike Sutton, “Getting the numbers right – the lonely struggle of Rydberg” Chemistry World, Vol. 1, No. 7, July 2004.
- Martinson, Indrek; L.J. Curtis (2005). "Janne Rydberg – his life and work".
*NIM B***235**: 17-22.
## See alsoCategories: Atomic physics | Foundational quantum physics | Hydrogen physics |
|||||||||||||||||||||||||||||

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Rydberg_formula". A list of authors is available in Wikipedia. |