Radius of a classical electronThe classical electron radius is a length scale that emerges from treating the electron as a classical, point-like charge with a certain electromagnetic self-energy. It is defined as the radius at which the electrostatic potential energy of a sphere of charge equals the rest mass energy of the electron. Its value is approximately 2.818 × 10^-15 meters, about three femtometers.
The concept was introduced in the late 19th century by physicists such as Hendrik Lorentz and Max Abraham, who were exploring the idea that the electron's mass might be purely electromagnetic. It was later refined by others, but the classical electron radius remains a useful scale in classical electrodynamics.
The derivation assumes the electron's mass is entirely electromagnetic in origin. By equating the energy stored in the electric field of a uniformly charged sphere (given by Coulomb's law) to the electron's rest energy (E = mc²), one solves for the radius. This is a classical calculation that predates quantum mechanics and does not reflect the actual size of an electron, which experiments show to be point-like down to very small scales.
The classical electron radius appears in formulas for Thomson scattering (scattering of light by free electrons), in the calculation of the cross-section for electron-photon interactions, and as a natural unit in particle physics for comparing sizes of atomic and subatomic structures.
Despite its name, the classical electron radius is about 100,000 times smaller than the radius of a hydrogen atom, and modern experiments show the electron has no measurable size down to at least 10^-18 meters.
| E | variable | Kinetic energy of the charged particle — energy joule |
| x | variable | Path length in the material — length metre |
| \rho | variable | Density of the absorbing material — density kilogram per cubic metre |
| z | variable | Charge number of the incident particle — charge number |
| A | variable | Atomic mass number of the absorber — atomic mass number |
| \beta | variable | Speed of the particle relative to the speed of light — velocity ratio |
| \gamma | variable | Lorentz factor of the particle — lorentz factor |
| v | variable | Speed of the particle — velocity metre per second |
| W_{\text{max}} | variable | Maximum energy transfer in a single collision — energy joule |
| I | variable | Mean excitation potential of the absorber — energy joule |
| \delta | variable | Density correction factor — density correction |
| C | variable | Shell correction factor — shell correction |
| Z | variable | Atomic number of the absorber — atomic number |
| N_A | constant | Number of constituent particles per mole — avogadro constant = 6.02214076e23 per mole |
| r_e | constant | Radius of a classical electron — classical electron radius = 2.8179403262e-15 metre |
| m_e | constant | Rest mass of the electron — electron mass = 9.1093837015e-31 kilogram |
| c | constant | Speed of light in vacuum — speed of light = 299792458 metre per second |
| -\frac{d}{dx} | operator | Negative derivative with respect to path length — negative derivative |
| \ln | operator | Natural logarithm — natural logarithm |
