classical electron radius , also called the Compton radius, is defined in cgs by equating the electrostatic potential energy of a sphere of charge e and radius with the rest energy of the electron.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.)
classical electron radius is classified under Electron Constant
Another characteristic length scale is the length scale at which renormalization becomes really important. Renormalization is an aspect of field theory which deals with such issues as the fact that the electromagnetic field produced by an electron has energy and thus should be counted as part of the mass of the electron! The length scale at which these effects become really important is called the classical electron radius.It's important to note that it is really classical, not quantum mechanical, because it only depends on classical electromagneticsm, which doesn't involve ?, and the formula for the rest energy of an electron, which involves c but not ?. Indeed, renormalization was an issue in classical field theory before quantum field theory came along.
Value: 2.817 940 3267 x 10-15 m
Standard uncertainty: 0.000 000 0027 x 10-15 m
Relative standard uncertainty : 9.7 x 10-10
Concise form: 2.817 940 3267(27) x 10-15 m