Classical electron radius

The classical electron radius is based on a classical relativistic model of the electron. Its value is calculated as

$r_{e}={\frac {e^{2}}{mc^{2}}}=2.81794092\times 10^{-15}m$

where e is the electron charge (esu), m is the mass of the electron and c is the speed of light. Using classical electrostatics, the amount of energy required to assemble a sphere of constant charge density, of radius r_e is just e²/r_e. If we equate this to the relativistic energy of the electron mc² and solve for r_e we arrive at the above answer. As a physical concept, this has been outdated by the advent of the quantum mechanical description of the electron, however the above expression appears even in the quantum description, but without the classical interpretation.

References

• Arthur N. Cox, Ed. "Allen's Astrophysical Quantities", 4th Ed, Springer, 1999.