Rydberg constant
In spectroscopy, the Rydberg constant, symbol formula_1 for heavy atoms or formula_2 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 via his Bohr model. , formula_1 and electron spin "g"-factor are the most accurately measured physical constants. The constant is expressed for either hydrogen as formula_2, or at the limit of infinite nuclear  mass as formula_1. 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 an atom, or, alternatively, the wavenumber of the lowest-energy photon capable of ionizing an atom from its ground state. The hydrogen spectral series can be expressed simply in terms of the Rydberg constant for hydrogen formula_2 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. Value. Rydberg constant. The CODATA value is where The Rydberg constant for hydrogen may be calculated from the reduced mass of the electron: where Rydberg unit of energy. The Rydberg unit of energy is equivalent to joules and electronvolts in the following manner: Rydberg wavelength. The angular wavelength is Occurrence in 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. The Bohr model posits that electrons revolve around the atomic nucleus in a manner analogous to planets revolving around the sun. In the simplest version of the Bohr model, the mass of the atomic nucleus is considered to be infinite compared to the mass of the electron, so that the center of mass of the system, the barycenter, lies at the center of the nucleus. This infinite mass approximation is what is alluded to with the formula_20 subscript. The Bohr model then predicts that the wavelengths of hydrogen atomic transitions are (see Rydberg formula): where  n and "n" are any two different positive integers (1, 2, 3, ...), and formula_22 is the wavelength (in vacuum) of the emitted or absorbed light. where formula_24 and "M" is the total mass of the nucleus. This formula comes from substituting the reduced mass of the electron. Precision measurement. The Rydberg constant is one of the most precisely determined physical constants, with a relative standard uncertainty of under 2 parts in 10. This precision constrains the values of the other physical constants that define it. Since the Bohr model is not perfectly accurate, due to fine structure, hyperfine splitting, and  other such effects, the Rydberg constant formula_25 cannot be "directly" measured at very high accuracy from the atomic transition frequencies of hydrogen alone. Instead, the Rydberg constant is inferred from measurements of atomic transition frequencies in three different atoms (hydrogen, deuterium, and antiprotonic helium). 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. Finally, the value of formula_25 is determined from the best fit of the measurements to the theory. Alternative expressions. The Rydberg constant can also be expressed as in  the following equations. 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 4"π"/"α" times the Bohr radius of the atom. The second equation is relevant because its value is the coefficient for the energy of the atomic orbitals of a hydrogen atom: formula_41.