Authors: Brian Beverly
This started as a [trial] derivation for force coupling constants but it is the simplest derivation of alpha, the fine structure constant, using Coulomb's law and the Planck-Einstein relations. The derivation shows that coupling constants are wavenumbers. Another derivation using Newton's law of gravity also provides the coupling constant for the gravitational force. I argue that alpha and the coupling constants represents the minimum uncertainty between wavenumber and radial distance. This is like the uncertainty between momentum (wavelength) and position. Wavenumber is defined as the inverse of the wavelength per unit distance. This is equivalent to saying that alpha is about 137 wavelengths per unit distance of radius. I go on to show this provides the correct ionization wavelengths of light for the hydrogen atom. Using whole integers, n number of energy levels, allowed me to derive the Rydberg formula. Alpha is nearly an integer number because we are using a wavenumber. This derivation is equivalent to that of the Bohr model but without needing to use classical ideas of electrons in orbit around the nucleus like planets in orbit around the sun.
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