The classical electron radius, also known as the Compton radius or the Thomson scattering length is based on a classical (i.e., non-quantum) relativistic model of the electron. Its value is calculated as Arthur H. Compton on the cover of Time Magazine, January 13, 1936 Arthur Holly Compton (September 10, 1892 – March 15, 1962) won the Nobel Prize in Physics (1927) for discovery of the effect named after him. ... Thomson scattering is the scattering of electromagnetic radiation by a charged particle. ... Fig. ... A simple introduction to this subject is provided in Special relativity for beginners Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. SR theory is based on the previous works of... Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ...

where e and m are the electric charge and the mass of the electron, c is the speed of light, and ε₀ is the permittivity of free space. Using classical electrostatics, the amount of energy required to assemble a sphere of constant charge density, of radius r_e and charge e is approximately Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... Mass is a property of physical objects that, roughly speaking, measures the amount of matter they contain. ... // Headline text Headline text Headline text Cherenkov effect in a swimming pool nuclear reactor. ... Permittivity is an intensive physical quantity that describes how an electric field affects and is affected by a medium. ... Electrostatics is the branch of physics that deals with the forces exerted by a static (i. ... Charge density is the amount of electric charge per unit volume. ...

.

If this is equated to the relativistic energy of the electron (E = mc²) and solved for r_e, the above result is obtained.

In simple terms, the classical electron radius is roughly the size the electron would need to have for its mass to be completely due to its electrostatic potential energy - not taking quantum mechanics into account. We now know that quantum mechanics, indeed quantum field theory, is needed to understand the behavior of electrons at such short distance scales, thus the classical electron radius is no longer regarded as the actual size of an electron. Still, the classical electron radius is used in modern classical-limit theories involving the electron, such as non-relativistic Thomson scattering. Also, the classical electron radius is roughly the length scale at which renormalization becomes important in quantum electrodynamics. Thomson scattering is the scattering of electromagnetic radiation by a charged particle. ... Figure 1. ... Quantum electrodynamics (QED) is a quantum field theory of electromagnetism. ...

The classical electron radius is one of a trio of related units of length, the other two being the Bohr radius and the Compton wavelength of the electron. The classical electron radius is built from the electron mass m_e, the speed of light c and the electron charge e. The Bohr radius is built from m_e, e and Planck's constant h. The Compton wavelength is built from m_e, h and c. In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. ... The Compton wavelength of a particle is given by , where is the Planck constant, is the particles mass and is the speed of light. ... Properties The electron is a fundamental subatomic particle which carries a negative electric charge. ... // Headline text Headline text Headline text Cherenkov effect in a swimming pool nuclear reactor. ... Properties The electron (also called negatron, commonly represented as e−) is a subatomic particle. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... The Compton wavelength of a particle is given by , where is the Planck constant, is the particles mass and is the speed of light. ...

Extrapolating from the initial equation, any mass m₀ can be imagined to have an 'electromagnetic radius' similar to the electron's classical radius.

where K is Coulomb's constant, α is the fine structure constant and is Planck's constant. Such a radius does not exist as a physical entity but it is sometimes useful in theoretical calculations. It has been suggested that this article or section be merged into Electrostatic force. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ...

References

• CODATA value for the classical electron radius at NIST.
• Arthur N. Cox, Ed. "Allen's Astrophysical Quantities", 4th Ed, Springer, 1999.

CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ... As a non-regulatory agency of the United States Department of Commerce’s Technology Administration, the National Institute of Standards (NIST) develops and promotes measurement, standards, and technology to enhance productivity, facilitate trade, and improve the quality of life. ...

External Links

• Length Scales in Physics: the Classical Electron Radius