Rydberg constant

The Rydberg constant, symbol R_∞ for hivy atoms or R_H for hydrogen, named efter the Swedish physicist Johannes Rydberg, is a pheesical constant relating to atomic spectra, in the science of spectroscopy. The constant wis first an empiricel fittin' parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later pruived that its value 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.

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.

Value o the Rydberg constant an Rydberg unit o energy

Accordin to the 2014 CODATA, the constant is:

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

whaur $m_{\text{e}}$ is the rest mass o the electron, $e$ is the elementary chairge, $\varepsilon _{0}$ is the permittivity o free space, $h$ is the Planck constant, an $c$ 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:

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

See anaw

• The Bohr model

• Rydberg formula, whilk discusses Rydberg's original discovery