Classical electron radius

The classical electron radius is the length scale obtained by equating an electron’s electromagnetic self-energy with its rest energy. It is about 2.82 femtometres, but is not the electron’s measured physical size.

Elementary charge: The magnitude of the electric charge carried by a proton and by an electron. The radius grows with the square of this charge.
Electrostatic potential energy: Energy associated with the configuration of stationary electric charges. A charge distribution’s electrostatic energy is compared with the electron’s rest energy.
Compton wavelength: The wavelength associated with a particle’s mass through Planck’s constant and the speed of light. It is a quantum length scale for the electron, much larger than its classical radius.
Thomson cross section: The classical cross section for low-energy electromagnetic scattering by a free electron. Its standard expression is proportional to the square of the classical electron radius.
Electron mass: The rest mass of an electron, approximately 9.109 × 10⁻³¹ kilograms. The radius is inversely proportional to this mass.
Charged sphere: An idealized spherical distribution of electric charge. Treating the electron as a charged sphere gives a model-dependent self-energy.
Bohr radius: The characteristic size of the ground-state orbital in the hydrogen atom. It describes an atomic state, not the electron’s electromagnetic self-energy.
Classical radius of a charged particle: A characteristic length defined by comparing a charged particle’s electromagnetic energy with its rest energy. The electron’s radius is one instance of this broader construction.
Speed of light: The speed at which light travels in vacuum, denoted by c. Converting the electron’s rest energy to mass introduces this constant.
Lorentz invariance: The principle that physical laws are unchanged under Lorentz transformations between inertial frames. A classical sphere model must confront relativistic stresses and frame dependence.

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