Abstract
The relationship E = −K holds between the energy E and kinetic energy K of the electron constituting a hydrogen atom. If the kinetic energy of the electron is determined based on that relationship, then the energy levels of the hydrogen atom are also determined. In classical quantum theory, there is a formula called the Rydberg formula for calculating the wavelength of a photon emitted by an electron. In this paper, in contrast, the formula for the wavelength of a photon is derived from the relativistic energy levels of a hydrogen atom derived by the author. The results show that, although the Rydberg constant is classically a physical constant, it cannot be regarded as a fundamental physical constant if the theory of relativity is taken into account.
Highlights
In the classical quantum theory of Bohr, the energy levels of the hydrogen atom are given by the following formula [1] [2]
The relationship E = −K holds between the energy E and kinetic energy K of the electron constituting a hydrogen atom
If the kinetic energy of the electron is determined based on that relationship, the energy levels of the hydrogen atom are determined
Summary
In the classical quantum theory of Bohr, the energy levels of the hydrogen atom are given by the following formula [1] [2]. Bohr thought the following quantum condition was necessary to find the energy levels of the hydrogen atom. The energy of the hydrogen atom is given by the following formula. If E in Equation (1b) is substituted into Equation (4), the following formula can be derived as the orbital radius of the electron. The photonic energy emitted during a transition between energy levels ( ) EBO,n − EBO,m and wavelength λ for principal quantum numbers m and n can be expressed as follows. R∞ is the Rydberg constant, which is defined by the following equation. The Rydberg formula can be derived from Equation (6) as indicated below
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