From the home page, the velocitytolight speed ratio for the ground state is:
Making the relativistic Lorentz factor, gamma:
Another property of the singleelectron ion's ground state is that its shell circumference must be equal to the electron's de Broglie wavelength. The ground state shell circumferences are, therefore:
So that the ratio of the Compton wavelength to shell circumference is:
From the definitions of alpha and the classical electron radius, the potential energy at a shell circumference of one Compton wavelength is:
Since potential energy is inversely proportional to shell radius, (and circumference), the potential at any allowed circumference is the product of the two previous equations.
Since,
,
