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 lies at the barycenter of the nucleus. This infinite mass approximation is what is alluded to with the subscript. 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.
A refinement of the Bohr model takes into account the fact that the mass of the atomic nucleus is not actually infinite compared to the mass of the electron. Then the formula is:
where and M is the mass of the atomic nucleus. This formula comes from substituting the reduced mass for the mass of the electron.
A generalization of the Bohr model discusses a hydrogen-like ions; that is, an atom with atomic number Z that has only one electron, such as C5+. In this case, the wavenumbers and photon energies are scaled up by a factor of Z2 in the model.
Read more about this topic: Rydberg Constant
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