Review on de Broglie Stationary Wave Hypothesis from Classical Mechanics

Abstract

This study examines the relationship between wavelengths and properties of orbiting leptons in atomic systems, with a focus on comparing the Bohr and de Broglie hypotheses. The analysis reveals that the orbitals are not equally spaced, contradicting initial assumptions. The de Broglie equations support this finding by demonstrating a non-linear relationship between wavelength and the principal quantum number, n. The number of wavelengths, denoted as η, is shown to be proportional to n, indicating that each orbital has a consistent number of wavelengths. The study argues that inner leptons moving at higher speeds exhibit shorter wavelengths, while outer leptons moving at slower speeds have longer wavelengths. Furthermore, it is observed that energy is higher in s state orbitals or perfectly circling orbits, which could offer insights into unresolved nuclear structure effects like the Lamb shift. The analysis points out limitations in both Bohr's consideration of lepton speed and the de Broglie hypothesis's failure to compare wavelength and lepton speed. By deepening our understanding of wavelength relationships, lepton speed, and orbital properties, this research paves the way for advancing atomic system theories and addressing unresolved phenomena. It underscores the importance of developing a comprehensive framework that reconciles the differing perspectives of the Bohr and de Broglie hypotheses to fully comprehend the behavior of orbiting leptons