The classical electron radius, also known as the Lorentz radius or the Thomson scattering length, is based on a classical (i. Hendrik Antoon Lorentz ( July 18, 1853 &ndash February 4, 1928) was a Dutch Physicist who shared the 1902 Nobel In Physics, Thomson scattering is the scattering of Electromagnetic radiation by acharged particle e. , non-quantum) relativistic model of the electron. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J Its value is calculated as

$r_\mathrm{e}=\frac{1}{4\pi\epsilon_0}\frac{e^2}{mc^2} = 2.8179402894(58)\times 10^{-15} \mathrm{m}$

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. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object Permittivity is a Physical quantity that describes how an Electric field affects and is affected by a Dielectric medium and is determined by the ability

In cgs units, this becomes more simply

$r_\mathrm{e}= \frac{e^2}{mc^2} = 2.8179402894(58)\times 10^{-13} \mathrm{cm}$

with (to three significant digits)

$e = 4.80 \times 10^{-10}\mathrm{esu}, m = 9.11 \times 10^{-28} \mathrm{g}, c =3.00 \times 10^{10} \mathrm{cm/sec}$.

Using classical electrostatics, the energy required to assemble a sphere of constant charge density, of radius re and charge e is

$E=\frac{3}{5}\,\,\frac{1}{4\pi\epsilon_0}\frac{e^2}{r_\mathrm{e}}$. Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical The linear surface or volume charge density is the amount of Electric charge in a line, Surface, or Volume.

If the charge is on the surface the energy is

$E=\frac{1}{2}\,\,\frac{1}{4\pi\epsilon_0}\frac{e^2}{r_\mathrm{e}}$.

Ignoring the factors 3/5 or 1/2, if this is equated to the relativistic energy of the electron (E = mc2) and solved for re, 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. In fact, modern particle physics experiments indicate that the electron is a point particle, i. Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them A point particle (or point-like, often spelled pointlike) is an idealized object heavily used in Physics. e. it has no size and its radius is zero. Still, the classical electron radius is used in modern classical-limit theories involving the electron, such as non-relativistic Thomson scattering and the relativistic Klein-Nishina formula. In Physics, Thomson scattering is the scattering of Electromagnetic radiation by acharged particle The Klein-Nishina formula provides an accurate prediction of the angular distribution of X-rays and Gamma-rays which are incident upon a single Electron. Also, the classical electron radius is roughly the length scale at which renormalization becomes important in quantum electrodynamics. In Quantum field theory, the Statistical mechanics of fields and the theory of self-similar geometric structures renormalization refers to a collection Quantum electrodynamics ( QED) is a relativistic Quantum field theory of Electrodynamics.

The classical electron radius is one of a trio of related units of length, the other two being the Bohr radius a0 and the Compton wavelength of the electron λe. 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 \lambda \ of a particle is given by \lambda = \frac{h}{m c} = 2 \pi \frac{\hbar}{m c} \, where The classical electron radius is built from the electron mass me, the speed of light c and the electron charge e. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried The Bohr radius is built from me, e and Planck's constant h. The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. The Compton wavelength is built from me, h and c. The Compton wavelength \lambda \ of a particle is given by \lambda = \frac{h}{m c} = 2 \pi \frac{\hbar}{m c} \, where Any one of these three lengths can be written in terms of any other using the fine structure constant α:

$r_e = {\alpha \lambda_e \over 2\pi} = \alpha^2 a_0$

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

$r=\frac{k_{C}e^2}{m_0 c^2}=\frac{\alpha\hbar}{m_0 c}$

where kC is Coulomb's constant, α is the fine structure constant and $\hbar$ is Planck's constant. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. Such a radius does not exist as a physical entity but it is sometimes useful in theoretical calculations.

## References

• CODATA value for the classical electron radius at NIST. CODATA ( Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU formerly
• Arthur N. Cox, Ed. "Allen's Astrophysical Quantities", 4th Ed, Springer, 1999.