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Concept
Rydberg constant
Summary
In spectroscopy, the Rydberg constant, symbol for
heavy atoms or 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.
Before the 2019 redefinition of the SI base units, and the electron spin g-factor were the most accurately measured physical constants.
The constant is expressed for either hydrogen as , or at the limit of infinite nuclear mass as . 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. The hydrogen spectral series can be expressed simply in terms of the Rydberg constant for hydrogen 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 in a simplified Bohr model.
The CODATA value is
or,
where
is the rest mass of the electron (i.e. the Electron mass),
is the elementary charge,
is the permittivity of free space,
is the Planck constant, and
is the speed of light in vacuum.
The Rydberg constant for hydrogen may be calculated from the reduced mass of the electron:
where
is the mass of the electron,
is the mass of the nucleus (a proton).
The Rydberg unit of energy is equivalent to joules and electronvolts in the following manner:
The angular wavelength is
Bohr model
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.
Official source
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