Rydberg constant

The Rydberg constant, symbol R_∞ for heavy atoms or R_H for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to atomic spectra, in the science of spectroscopy. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants, explaining the relationship via his "Bohr model". As of 2012, R_∞ and electron spin g-factor are the most accurately measured fundamental physical constants.

The Rydberg constant represents the limiting value of the highest wavenumber (the inverse wavelength) of any photon that can be emitted from the hydrogen atom, or, alternatively, the wavenumber of the lowest-energy photon capable of ionizing the hydrogen atom from its ground state. The spectrum of hydrogen can be expressed simply in terms of the Rydberg constant, using the Rydberg formula.

The Rydberg unit of energy, symbol Ry, is closely related to the Rydberg constant. It corresponds to the energy of the photon whose wavenumber is the Rydberg constant, i.e. the ionization energy of the hydrogen atom.

According to the 2014 CODATA, the constant is:

where ${\displaystyle m_{\text{e}}}$ is the rest mass of the electron, ${\displaystyle e}$ is the elementary charge, ${\displaystyle \varepsilon _{0}}$ is the permittivity of free space, ${\displaystyle h}$ is the Planck constant, and ${\displaystyle c}$ is the speed of light in a vacuum.

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