# Rydberg constant

In spectroscopy, the Rydberg constant is a physical constant relating to the electromagnetic spectra of an atom. Its symbol is ${\displaystyle R_{\infty }}$ for heavy atoms or ${\displaystyle R_{\text{H}}}$ for hydrogen. The constant is named after the Swedish physicist Johannes Rydberg. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series. Niels Bohr later showed that its value could be calculated from more fundamental constants via his Bohr model. As of 2018, ${\displaystyle R_{\infty }}$ and electron spin g-factor are the most accurately measured physical constants.[1]

The constant is expressed for either hydrogen as ${\displaystyle R_{\text{H}}}$, or at the limit of infinite nuclear mass as ${\displaystyle R_{\infty }}$. In either case, the constant is used to express the limiting value of the highest wavenumber (inverse wavelength) of any photon that can be emitted from an atom, or, alternatively, the wavenumber of the lowest-energy photon capable of ionizing an atom from its ground state. The hydrogen spectral series can be expressed simply in terms of the Rydberg constant for hydrogen ${\displaystyle R_{\text{H}}}$ and the Rydberg formula.

In atomic physics, Rydberg unit of energy, symbol Ry, corresponds to the energy of the photon whose wavenumber is the Rydberg constant, i.e. the ionization energy of the hydrogen atom.[source?]

## References

1. Pohl, Randolf; Antognini, Aldo; Nez, François; Amaro, Fernando D.; Biraben, François; Cardoso, João M. R.; Covita, Daniel S.; Dax, Andreas; Dhawan, Satish; Fernandes, Luis M. P.; Giesen, Adolf; Graf, Thomas; Hänsch, Theodor W.; Indelicato, Paul; Julien, Lucile; Kao, Cheng-Yang; Knowles, Paul; Le Bigot, Eric-Olivier; Liu, Yi-Wei; Lopes, José A. M.; Ludhova, Livia; Monteiro, Cristina M. B.; Mulhauser, Françoise; Nebel, Tobias; Rabinowitz, Paul; Dos Santos, Joaquim M. F.; Schaller, Lukas A.; Schuhmann, Karsten; Schwob, Catherine; Taqqu, David (2010). "The size of the proton". Nature. 466 (7303): 213–216. Bibcode:2010Natur.466..213P. doi:10.1038/nature09250. PMID 20613837. S2CID 4424731.