The Compton Radius, the de Broglie Radius, the Planck Constant, and the Bohr Orbits

The Bohr orbits of the hydrogen atom and the Planck constant can be derived classically from the Maxwell equations and the assumption that there is a variation in the electron’s velocity about its average value [1]. The resonant nature of the circulating electron and its induced magnetic and Faraday fields prevents a radiative collapse of the electron into the nuclear proton. The derived Planck constant is h = 2πe2/αc, where e, α, and c are the electronic charge, the fine structure constant, and the speed of light. The fact that the Planck vacuum (PV) theory [2] derives the same Planck constant independently of the above implies that the two derivations are related. The following highlights that connection.