for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom.
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 according to his model of the atom.
and the electron spin g-factor were the most accurately measured physical constants.
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 a hydrogen atom, or, alternatively, the wavenumber of the lowest-energy photon capable of ionizing a hydrogen atom from its ground state.
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 in a simplified Bohr model.
[citation needed] The CODATA value is where The symbol
means that the nucleus is assumed to be infinitely heavy, an improvement of the value can be made using the reduced mass of the atom: with
For example, deuterium, an isotope of hydrogen with a nucleus formed by a proton and a neutron (
[3] The Rydberg unit of energy is The corresponding angular wavelength is The Bohr model explains the atomic spectrum of hydrogen (see Hydrogen spectral series) as well as various other atoms and ions.
It is not perfectly accurate, but is a remarkably good approximation in many cases, and historically played an important role in the development of quantum mechanics.
The Bohr model then predicts that the wavelengths of hydrogen atomic transitions are (see Rydberg formula): where n1 and n2 are any two different positive integers (1, 2, 3, ...), and
is the wavelength (in vacuum) of the emitted or absorbed light, giving where
This formula comes from substituting the reduced mass of the electron.
[2] This precision constrains the values of the other physical constants that define it.
[8] Since the Bohr model is not perfectly accurate, due to fine structure, hyperfine splitting, and other such effects, the Rydberg constant
cannot be directly measured at very high accuracy from the atomic transition frequencies of hydrogen alone.
Detailed theoretical calculations in the framework of quantum electrodynamics are used to account for the effects of finite nuclear mass, fine structure, hyperfine splitting, and so on.
and in energy units where The last expression in the first equation shows that the wavelength of light needed to ionize a hydrogen atom is 4π/α times the Bohr radius of the atom.