Balmer and Rydberg Equations for Hydrogen Spectra Revisited

TL;DR

This paper revisits the Balmer and Rydberg equations for hydrogen spectra, challenging traditional explanations and proposing a wave-based interpretation of quantum numbers and energy levels.

Contribution

It demonstrates that Rydberg's equation relates to de Broglie waves and electromagnetic energy levels, offering a new perspective beyond Bohr's angular momentum quantization.

Findings

Rydberg's quantum numbers correspond to integral de Broglie waves

Hydrogen's ground state energy is electromagnetic in nature

Frequency of spectral lines equals the difference in electromagnetic energy levels

Abstract

Balmer equation for the atomic spectral lines was generalized by Rydberg. Here it is shown that 1) while Bohr's theory explains the Rydberg constant in terms of the ground state energy of the hydrogen atom, quantizing the angular momentum does not explain the Rydberg equation, 2) on reformulating Rydberg's equation, the principal quantum numbers are found to correspond to integral numbers of de Broglie waves and 3) the ground state energy of hydrogen is electromagnetic like that of photons and the frequency of the emitted or absorbed light is the difference in the frequencies of the electromagnetic energy levels.