Classical Electron Radius

The classical electron radius is the hypothetical distance between two quantum charges with an electrical potential energy of mec2, or 511,000 electron-volts.

One of the most fascinating things about the classical electron radius is that it is the smallest of three important fundamental distances; all separated by the same factor, 137.  (Actually, it's the reciprocal of the fine structure constant, but so close to 137, I'll use that.)

Next, the reduced Compton wavelength, (The radius of a circle with a circumference of one Compton wavelength.), is 137 classical electron radii.  The Compton wavelength, by the way, is the wavelength of a photon with an energy of mec2.

Finally, the Bohr radius is equal to 137 reduced Compton wavelengths.  Since potential energy decreases inversely proportional to distance, the potential energy between two quantum charges separated by one Bohr radius can be calculated by dividing 511,000 eV by 137 twice, i.e. 27.2eV.