# Rydberg constant

The Rydberg constant, symbol R for hivy atoms or RH for hydrogen, named after the Swedish physicist Johannes Rydberg, is a pheesical constant relating to atomic spectra, in the science of spectroscopy. The constant wae first an empiricel fittin' parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later pruived that its vailyie coud be calculatit frae mair fundamental constants, explainin the relationship via his "Bohr model". As o 2018, R and electron spin g-factor are the most accurately measured fundamental physical constants.[1]

The Rydberg constant represents the leemitin vailyie o the heichest wavenumber (the inverse wavelength) o ony photon thae can be emittit frae the hydrogen atom, or, in ither wirds, the wavenumber o the lawest-energy photon thae can ionise the hydrogen atom frae its grund state. The spectrum o hydrogen can be expressed semply in terms o the Rydberg constant, uisin the Rydberg formula.

The Rydberg unit o energy, symbol Ry, is closely relatit tae the Rydberg constant. It corresponds tae the energy o a photon whose wavenumber is the Rydberg constant, i.e. the ionisation energy o the hydrogen atom.

## Vailyie o the Rydberg constant an Rydberg unit o energy

Accordin to the 2014 CODATA, the constant is:

${\displaystyle R_{\infty }={\frac {m_{\text{e}}e^{4}}{8\varepsilon _{0}^{2}h^{3}c}}=10\;973\;731.568\;508\;(65)\,{\text{m}}^{-1},}$[2]

whaur ${\displaystyle m_{\text{e}}}$ is the rest mass o the electron, ${\displaystyle e}$ is the elementary chairge, ${\displaystyle \varepsilon _{0}}$ is the permittivity o free space, ${\displaystyle h}$ is the Planck constant, an ${\displaystyle c}$ is the speed of licht in a vacuum.

This constant is aft uised in atomic pheesics in the form o the Rydberg unit o energy:

${\displaystyle 1\ {\text{Ry}}\equiv hcR_{\infty }={\frac {m_{\text{e}}e^{4}}{8\varepsilon _{0}^{2}h^{2}}}=13.605\;693\;009(84)\,{\text{eV}}\approx 2.179\times 10^{-18}{\text{J}}.}$[2]

## See anaw

• Rydberg formula, whilk discusses Rydberg's original discovery
1. Empty citation (help)
2. P.J. Mohr, B.N. Taylor, and D.B. Newell (2015), "The 2014 CODATA Recommended Values of the Fundamental Physical Constants" (Web Version 7.0). This database was developed by J. Baker, M. Douma, and S. Kotochigova. Available: http://physics.nist.gov/constants. National Institute of Standards and Technology, Gaithersburg, MD 20899. Link to R, Link to hcR. Published in Empty citation (help) and Empty citation (help). Cite error: Invalid <ref> tag; name "codata" defined multiple times wi different content