TITLE:
Relativistic Correction of the Rydberg Formula
AUTHORS:
Koshun Suto
KEYWORDS:
Rydberg Formula, Rydberg Constant, Classical Quantum Theory, Energy-Momentum Relationship in a Hydrogen Atom, Relativistic Kinetic Energy
JOURNAL NAME:
Journal of Modern Physics,
Vol.11 No.2,
February
21,
2020
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.