Electron

Characterization

Electrons belong to the first generation of the lepton particle family, | access-date = 2020-08-25 | url-status = live | archive-url = https://web.archive.org/web/20200316220442/https://books.google.com/books?id=KmwCsuvxClAC&pg=PA74 | archive-date = 2020-03-16 elementary particles that do not feel the strong nuclear force, and only interact through the weak and electromagnetic forces. Electrons are generally thought to be elementary particles because they have no known components or substructure. An electron's mass is approximately that of a proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of half the reduced Planck constant, i.e. . Being fermions, no two electrons can occupy the same quantum state, according to the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves. For example, electrons can collide like particles with other particles and can also be diffracted like light waves. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

The concept of electrons is essential to explain physical phenomena, such as electricity, magnetism, chemistry, and thermal conductivity; they are subject to the forces of gravity, electromagnetism, and the weak interaction. Since an electron has charge, it has a surrounding electric field; if that electron is moving relative to an observer, the observer will observe it to generate a magnetic field. Electromagnetic fields produced from other sources will affect the motion of an electron according to the Lorentz force law. Electrons radiate or absorb energy in the form of photons when they are accelerated.

Laboratory instruments are capable of trapping individual electrons as well as electron plasma by the use of electromagnetic fields. Special telescopes can detect electron plasma in outer space. Electrons are involved in many applications, such as tribology or frictional charging, electrolysis, electrochemistry, battery technologies, electronics, welding, cathode-ray tubes, photoelectricity, photovoltaic solar panels, electron microscopes, radiation therapy, lasers, gaseous ionization detectors, and particle accelerators.

Interactions involving electrons with other subatomic particles are of interest in fields such as chemistry and nuclear physics. Atoms are composed of positive protons within atomic nuclei and the negative electrons without, held together by Coulomb force interaction. Ionization state (differences in the proportions of negative electrons versus positive nuclei) or sharing of the electrons between two or more atoms are the main causes of chemical bonding.

Electrons participate in nuclear reactions, such as nucleosynthesis in stars, where they are known as beta particles. Electrons can be created through beta decay of radioactive isotopes and in high-energy collisions, for instance, when cosmic rays enter the atmosphere. The antiparticle of the electron is called the positron; it is identical to the electron, except that it carries electrical charge of the opposite sign. When an electron collides with a positron, both particles can be annihilated, producing gamma ray photons.

History

Discovery of effect of electric force

The ancient Greeks noticed that amber attracted small objects when rubbed with fur. Along with lightning, this phenomenon is one of humanity's earliest recorded experiences with electricity. In his 1600 treatise De Magnete, the English scientist William Gilbert coined the Neo-Latin term electrica, to refer to those substances with property similar to that of amber which attract small objects after being rubbed.

Discovery of two kinds of charges

In the early 1700s, French chemist Charles François du Fay found that if a charged gold leaf is repulsed by glass rubbed with silk, then the same charged gold leaf is attracted by amber rubbed with wool. From this and other results of similar types of experiments, du Fay concluded that electricity consists of two electrical fluids, vitreous fluid from glass rubbed with silk and resinous fluid from amber rubbed with wool. These two fluids can neutralize each other when combined. | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204082420/https://books.google.com/books?id=uwgNAtqSHuQC&pg=PR7 | url-status = live | access-date = 2010-12-16 | archive-date = 2013-08-27 | archive-url = https://web.archive.org/web/20130827114343/http://scienceworld.wolfram.com/biography/FranklinBenjamin.html | url-status = live | url-access=registration

Between 1838 and 1851, British natural philosopher Richard Laming developed the idea that an atom is composed of a core of matter surrounded by subatomic particles that had unit electric charges. | access-date = 2020-08-25 | archive-date = 2021-01-07 | archive-url = https://web.archive.org/web/20210107160308/https://books.google.com/books?id=rZHT-chpLmAC&pg=PA70 | url-status = live

Stoney initially coined the term electrolion in 1881. Ten years later, he switched to electron to describe these elementary charges, writing in 1894: "... an estimate was made of the actual amount of this most remarkable fundamental unit of electricity, for which I have since ventured to suggest the name electron". A 1906 proposal to change to electrion failed because Hendrik Lorentz preferred to keep electron. | access-date=29 May 2015 | archive-date=11 May 2016 | archive-url=https://web.archive.org/web/20160511214552/https://books.google.com/books?id=VHFyngmO95YC&pg=PR11 | url-status=live | access-date = 2019-08-25 | archive-date = 2020-10-31 | archive-url = https://web.archive.org/web/20201031080323/https://zenodo.org/record/1431209 | url-status = live | editor-last = Soukhanov | editor-first = A.H. | editor-last = Guralnik | editor-first = D.B.

Discovery of free electrons outside matter

| access-date = 2020-08-25 | archive-date = 2021-01-26 | archive-url = https://web.archive.org/web/20210126003322/https://books.google.com/books?id=NmM-KujxMtoC&pg=PA26 | url-status = live

While studying electrical conductivity in rarefied gases in 1859, the German physicist Julius Plücker observed the radiation emitted from the cathode caused phosphorescent light to appear on the tube wall near the cathode; and the region of the phosphorescent light could be moved by application of a magnetic field. In 1869, Plücker's student Johann Wilhelm Hittorf found that a solid body placed in between the cathode and the phosphorescence would cast a shadow upon the phosphorescent region of the tube. Hittorf inferred that there are straight rays emitted from the cathode and that the phosphorescence was caused by the rays striking the tube walls. Furthermore, he also discovered that these rays are deflected by magnets just like lines of current.

In 1876, the German physicist Eugen Goldstein showed that the rays were emitted perpendicular to the cathode surface, which distinguished between the rays that were emitted from the cathode and the incandescent light. Goldstein dubbed the rays cathode rays.

During the 1870s, the English chemist and physicist Sir William Crookes developed the first cathode-ray tube to have a high vacuum inside. | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204082418/https://books.google.com/books?id=aJZVQnqcwv4C&pg=PA221 | url-status = live

In 1883, not yet well-known German physicist Heinrich Hertz tried to prove that cathode rays are electrically neutral and got what he interpreted as a confident absence of deflection in electrostatic, as opposed to magnetic, field. However, as J. J. Thomson explained in 1897, Hertz placed the deflecting electrodes in a highly conductive area of the tube, resulting in a strong screening effect close to their surface.

The German-born British physicist Arthur Schuster expanded upon Crookes's experiments by placing metal plates parallel to the cathode rays and applying an electric potential between the plates. The field deflected the rays toward the positively charged plate, providing further evidence that the rays carried negative charge. By measuring the amount of deflection for a given electric and magnetic field, in 1890 Schuster was able to estimate the charge-to-mass ratio of the ray components. However, this produced a value that was more than a thousand times greater than what was expected, so little credence was given to his calculations at the time. This is because it was assumed that the charge carriers were much heavier hydrogen or nitrogen atoms. Schuster's estimates would subsequently turn out to be largely correct.

In 1892 Hendrik Lorentz suggested that the mass of these particles (electrons) could be a consequence of their electric charge.

While studying naturally fluorescing minerals in 1896, the French physicist Henri Becquerel discovered that they emitted radiation without any exposure to an external energy source. These radioactive materials became the subject of much interest by scientists, including the New Zealand physicist Ernest Rutherford who discovered they emitted particles. He designated these particles alpha and beta, on the basis of their ability to penetrate matter. | access-date = 2022-02-24 | archive-date = 2008-12-22 | archive-url = https://web.archive.org/web/20081222023947/http://jnm.snmjournals.org/cgi/content/abstract/17/7/579 | url-status = live

In 1897, the British physicist J. J. Thomson, with his colleagues John S. Townsend and H. A. Wilson, performed experiments indicating that cathode rays really were unique particles, rather than waves, atoms or molecules as was believed earlier. By 1899 he showed that their charge-to-mass ratio, e/m, was independent of cathode material. He further showed that the negatively charged particles produced by radioactive materials, by heated materials and by illuminated materials were universal. |access-date = 2008-08-25 |df=dmy-all |archive-url = https://web.archive.org/web/20081010100408/https://nobelprize.org/nobel_prizes/physics/laureates/1906/thomson-lecture.pdf |archive-date = 2008-10-10

The name "electron" was adopted for these particles by the scientific community, mainly due to the advocation by G. F. FitzGerald, J. Larmor, and H. A. Lorentz.

The electron's charge was more carefully measured by the American physicists Robert Millikan and Harvey Fletcher in their oil-drop experiment of 1909, the results of which were published in 1911. This experiment used an electric field to prevent a charged droplet of oil from falling as a result of gravity. This device could measure the electric charge from as few as 1–150 ions with an error margin of less than 0.3%. Comparable experiments had been done earlier by Thomson's team, using clouds of charged water droplets generated by electrolysis, and in 1911 by Abram Ioffe, who independently obtained the same result as Millikan using charged microparticles of metals, then published his results in 1913. | doi-access = free | access-date = 2019-06-21 | archive-date = 2020-03-17 | archive-url = https://web.archive.org/web/20200317204458/https://authors.library.caltech.edu/6437/1/MILpr11b.pdf | url-status = live

Around the beginning of the twentieth century, it was found that under certain conditions a fast-moving charged particle caused a condensation of supersaturated water vapor along its path. In 1911, Charles Wilson used this principle to devise his cloud chamber so he could photograph the tracks of charged particles, such as fast-moving electrons.

Atomic theory

By 1914, experiments by physicists Ernest Rutherford, Henry Moseley, James Franck and Gustav Hertz had largely established the structure of an atom as a dense nucleus of positive charge surrounded by lower-mass electrons. In 1913, Danish physicist Niels Bohr postulated that electrons resided in quantized energy states, with their energies determined by the angular momentum of the electron's orbit about the nucleus. The electrons could move between those states, or orbits, by the emission or absorption of photons of specific frequencies. By means of these quantized orbits, he accurately explained the spectral lines of the hydrogen atom. | access-date = 2008-12-03 | archive-date = 2008-12-03 | archive-url = https://web.archive.org/web/20081203124237/http://nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-lecture.pdf | url-status = live | access-date = 2020-08-25 | archive-date = 2020-05-09 | archive-url = https://web.archive.org/web/20200509044538/https://books.google.com/books?id=I1O8WYOcUscC&pg=PA14 | url-status = live

Chemical bonds between atoms were explained by Gilbert Newton Lewis, who in 1916 proposed that a covalent bond between two atoms is maintained by a pair of electrons shared between them. | access-date = 2019-08-25 | archive-date = 2019-08-25 | archive-url = https://web.archive.org/web/20190825132554/https://zenodo.org/record/1429068/files/article.pdf | url-status = live | archive-url = https://web.archive.org/web/20200605041731/https://pdfs.semanticscholar.org/3804/783ac9fc011aeae884a3d370a474cbfdd46f.pdf | archive-date = 2020-06-05 | access-date = 2019-06-21 | archive-date = 2021-01-26 | archive-url = https://web.archive.org/web/20210126003324/https://zenodo.org/record/1429026 | url-status = live | url-access = registration | pages=205–226

In 1924, Austrian physicist Wolfgang Pauli observed that the shell-like structure of the atom could be explained by a set of four parameters that defined every quantum energy state, as long as each state was occupied by no more than a single electron. This prohibition against more than one electron occupying the same quantum energy state became known as the Pauli exclusion principle. | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204071142/https://books.google.com/books?id=YS91Gsbd13cC&pg=PA7 | url-status = live

Quantum mechanics

In his 1924 dissertation Recherches sur la théorie des quanta (Research on Quantum Theory), French physicist Louis de Broglie hypothesized that all matter can be represented as a de Broglie wave in the manner of light. | access-date = 2008-08-30 | archive-date = 2008-10-04 | archive-url = https://web.archive.org/web/20081004022001/http://nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf | url-status = live | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204082417/https://books.google.com/books?id=EbOz5I9RNrYC&pg=PA85 | url-status = live | access-date = 2008-08-30 | archive-date = 2008-07-09 | archive-url = https://web.archive.org/web/20080709090839/http://nobelprize.org/nobel_prizes/physics/laureates/1937/davisson-lecture.pdf | url-status = live

De Broglie's prediction of a wave nature for electrons led Erwin Schrödinger to postulate a wave equation for electrons moving under the influence of the nucleus in the atom. In 1926, this equation, the Schrödinger equation, successfully described how electron waves propagated. | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204082407/https://books.google.com/books?id=FhFxn_lUvz0C&pg=PT66 | url-status = live | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204082419/https://books.google.com/books?id=4sluccbpwjsC&pg=PA275 | url-status = live

In 1928, building on Wolfgang Pauli's work, Paul Dirac produced a model of the electron – the Dirac equation, consistent with relativity theory, by applying relativistic and symmetry considerations to the hamiltonian formulation of the quantum mechanics of the electromagnetic field. |doi-access = free |access-date = 2022-02-24 |archive-date = 2018-11-25 |archive-url = https://web.archive.org/web/20181125224103/http://rspa.royalsocietypublishing.org/content/royprsa/117/778/610.full.pdf |url-status = live | access-date = 2008-11-01 | archive-date = 2008-07-23 | archive-url = https://web.archive.org/web/20080723220816/http://nobelprize.org/nobel_prizes/physics/laureates/1933/dirac-lecture.pdf | url-status = live

In 1947, Willis Lamb, working in collaboration with graduate student Robert Retherford, found that certain quantum states of the hydrogen atom, which should have the same energy, were shifted in relation to each other; the difference came to be called the Lamb shift. About the same time, Polykarp Kusch, working with Henry M. Foley, discovered the magnetic moment of the electron is slightly larger than predicted by Dirac's theory. This small difference was later called anomalous magnetic dipole moment of the electron. This difference was later explained by the theory of quantum electrodynamics, developed by Sin-Itiro Tomonaga, Julian Schwinger and Richard Feynman in the late 1940s. | access-date = 2008-11-04 | archive-date = 2008-10-24 | archive-url = https://web.archive.org/web/20081024052537/http://nobelprize.org/nobel_prizes/physics/laureates/1965/ | url-status = live

Particle accelerators

With the development of the particle accelerator during the first half of the twentieth century, physicists began to delve deeper into the properties of subatomic particles. | access-date = 2008-09-15 | archive-date = 2008-09-09 | archive-url = https://web.archive.org/web/20080909234139/http://www.slac.stanford.edu/pubs/beamline/27/1/27-1-panofsky.pdf | url-status = live | display-authors=etal

With a beam energy of 1.5 GeV, the first high-energy particle collider was ADONE, which began operations in 1968. | display-authors = etal | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204082414/https://books.google.com/books?id=klLUs2XUmOkC&pg=PA25 | url-status = live | access-date = 2008-09-15 | archive-date = 2008-09-14 | archive-url = https://web.archive.org/web/20080914164129/http://public.web.cern.ch/public/en/Research/LEPExp-en.html | url-status = live | access-date = 2022-02-24 | archive-date = 2017-09-30 | archive-url = https://web.archive.org/web/20170930222305/http://cerncourier.com/cws/article/cern/28335 | url-status = live

Confinement of individual electrons

Individual electrons can now be easily confined in ultra small (, ) CMOS transistors operated at cryogenic temperature over a range of about 4 K (−269 °C) to 15 K (−258 °C).

Classification

In the Standard Model of particle physics, electrons belong to the group of subatomic particles called leptons, which are believed to be fundamental or elementary particles. Electrons have the lowest mass of any charged lepton (or electrically charged particle of any type) and belong to the first generation of fundamental particles.

Fundamental properties

Mass

The invariant mass of an electron is approximately or Due to mass–energy equivalence, this corresponds to a rest energy of (). The ratio between the mass of a proton and that of an electron is about 1836. | access-date = 2009-07-18 | archive-date = 2019-03-28 | archive-url = https://web.archive.org/web/20190328001314/https://physics.nist.gov/cgi-bin/cuu/Value?mpsme | url-status = live | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204082414/https://books.google.com/books?id=tp_G85jm6IAC&pg=PA14 | url-status = live |display-authors=etal

Charge

Electrons have an electric charge of ,The original source for CODATA is : Individual physical constants from the CODATA are available at: | access-date = 2009-01-15 | archive-date = 2009-01-16 | archive-url = https://web.archive.org/web/20090116162522/http://physics.nist.gov/cuu/ | url-status = live

The electron is commonly symbolized by to indicate its negative charge (an electron's anti-particle, the positron, is symbolized by to indicate its identical but positive charge).

Angular momentum

The electron has an intrinsic angular momentum or spin of . This property is usually stated by referring to the electron as a spin-1/2 particle. For such particles the spin magnitude is , while the result of the measurement of a projection of the spin on any axis can only be ±. In addition to spin, the electron has an intrinsic magnetic moment along its spin axis. It is approximately equal to one Bohr magneton,{{efn|Bohr magneton: : \textstyle\mu_{\mathrm{B}}=\frac{e\hbar}{2m_{\mathrm{e}}}}} which is a physical constant that is equal to The orientation of the spin with respect to the momentum of the electron defines the property of elementary particles known as helicity. | access-date = 2020-08-25 | archive-date = 2021-01-07 | archive-url = https://web.archive.org/web/20210107160318/https://books.google.com/books?id=rDEvQZhpltEC&pg=PA261 | url-status = live

Structure

The electron has no known substructure. |display-authors=etal | article-number = 030802

Size

Electron–electron scattering shows no deviation from Coulomb's law: experimentally the electron is structureless and point-like. Observation of a single electron in a Penning trap suggests the upper limit of the particle's radius to be . The upper bound of the electron radius of can be derived using the uncertainty relation in energy.

Theoretical concepts of the electron size are ambiguous. In relativisitic quantum mechanics, the Dirac equation treats the electron as a point charge, but the equivalent Newton–Wigner form does not. In quantum field theory mathematical treatments of self-energy involve a minimal distance cutoff or equivalent energy. Shorter distances (high energies) involve adding more terms.

Attempts to create non-quantum mechanical, non-point models lead to contradictions. For example, a mechanically spinning electron with the classical electron radius and the observed gyromagnetic ratio of the electron would have a tangential velocity exceeding the speed of light. The classical electron radius, with the much larger value of (greater than the radius of the proton), is used as a physical constant but is not a measure of the fundamental structure of the electron.

Lifetime

Within the Standard Model of particle physics, the electron is considered stable.{{cite journal | display-authors=etal The electron is the least massive known particle with non-zero electric charge: assuming conservation of energy, its decay would violate charge conservation. | display-authors=etal | display-authors=etal |display-authors = etal |article-number = 010001 |doi-access = free |access-date = 2022-02-24 |archive-date = 2022-01-15 |archive-url = https://web.archive.org/web/20220115063155/https://pdg.lbl.gov/2012/listings/rpp2012-list-electron.pdf |url-status = live

Quantum properties

As with all particles, electrons can act as waves. This is called the wave–particle duality and can be demonstrated using the double-slit experiment.

The wave-like nature of the electron allows it to pass through two parallel slits simultaneously, rather than just one slit as would be the case for a classical particle. In quantum mechanics, the wave-like property of one particle can be described mathematically as a complex-valued function, the wave function, commonly denoted by the Greek letter psi (ψ). When the absolute value of this function is squared, it gives the probability that a particle will be observed near a location—a probability density. | url-access = registration | page = 162 | publisher = Oxford University Press

Electrons are identical particles because they cannot be distinguished from each other by their intrinsic physical properties. In quantum mechanics, this means that a pair of interacting electrons must be able to swap positions without an observable change to the state of the system. The wave function of fermions, including electrons, is antisymmetric, meaning that it changes sign when two electrons are swapped; that is, , where the variables r1 and r2 correspond to the first and second electrons, respectively. Since the absolute value is not changed by a sign swap, this corresponds to equal probabilities. Bosons, such as the photon, have symmetric wave functions instead.

In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a zero probability that each pair will occupy the same location or state. This is responsible for the Pauli exclusion principle, which precludes any two electrons from occupying the same quantum state. This principle explains many of the properties of electrons. For example, it causes groups of bound electrons to occupy different orbitals in an atom, rather than all overlapping each other in the same orbit.

Virtual particles

Main article: Virtual particle

In a simplified picture, which often tends to give the wrong idea but may serve to illustrate some aspects, every photon spends some time as a combination of a virtual electron plus its antiparticle, the virtual positron, which rapidly annihilate each other shortly thereafter. | access-date = 2008-09-19 |df=dmy-all | chapter-url = https://books.google.com/books?id=akb2FpZSGnMC&pg=PA464 | access-date = 2020-08-25 | archive-date = 2014-09-21 | archive-url = https://web.archive.org/web/20140921171834/http://books.google.com/books?id=akb2FpZSGnMC&pg=PA464 | url-status = live

While an electron–positron virtual pair is in existence, the Coulomb force from the ambient electric field surrounding an electron causes a created positron to be attracted to the original electron, while a created electron experiences a repulsion. This causes what is called vacuum polarization. In effect, the vacuum behaves like a medium having a dielectric permittivity more than unity. Thus the effective charge of an electron is actually smaller than its true value, and the charge decreases with increasing distance from the electron. | access-date = 2008-09-17 | archive-date = 2015-02-11 | archive-url = https://web.archive.org/web/20150211085433/http://www.newscientist.com/article/mg15320662.300-science--more-to-electrons-than-meets-the-eye.html | url-status = live

The interaction with virtual particles also explains the small (about 0.1%) deviation of the intrinsic magnetic moment of the electron from the Bohr magneton (the anomalous magnetic moment). | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204071144/https://books.google.com/books?id=q-CIFHpHxfEC&pg=PA123 | url-status = live

The apparent paradox in classical physics of a point particle electron having intrinsic angular momentum and magnetic moment can be explained by the formation of virtual photons in the electric field generated by the electron. These photons can heuristically be thought of as causing the electron to shift about in a jittery fashion (known as zitterbewegung), which results in a net circular motion with precession.

Interaction

An electron generates an electric field that exerts an attractive force on a particle with a positive charge, such as the proton, and a repulsive force on a particle with a negative charge. The strength of this force in nonrelativistic approximation is determined by Coulomb's inverse square law. |access-date=2020-08-25 |archive-date=2022-02-04 |archive-url=https://web.archive.org/web/20220204083733/https://books.google.com/books?id=s9QWZNfnz1oC&pg=PT129 |url-status=live

When an electron is moving through a magnetic field, it is subject to the Lorentz force that acts perpendicularly to the plane defined by the magnetic field and the electron velocity. This centripetal force causes the electron to follow a helical trajectory through the field at a radius called the gyroradius. The acceleration from this curving motion induces the electron to radiate energy in the form of synchrotron radiation.

Photons mediate electromagnetic interactions between particles in quantum electrodynamics. An isolated electron at a constant velocity cannot emit or absorb a real photon; doing so would violate conservation of energy and momentum. Instead, virtual photons can transfer momentum between two charged particles. This exchange of virtual photons, for example, generates the Coulomb force. |chapter-url=https://books.google.com/books?id=akb2FpZSGnMC&pg=PA427 |access-date=2020-08-25 |archive-date=2014-09-21 |archive-url=https://web.archive.org/web/20140921171123/http://books.google.com/books?id=akb2FpZSGnMC&pg=PA427 |url-status=live

An inelastic collision between a photon (light) and a solitary (free) electron is called Compton scattering. This collision results in a transfer of momentum and energy between the particles, which modifies the wavelength of the photon by an amount called the Compton shift.{{efn|The change in wavelength, Δλ, depends on the angle of the recoil, θ, as follows, : \textstyle \Delta \lambda = \frac{h}{m_{\mathrm{e}}c} (1 - \cos \theta), where c is the speed of light in vacuum and me is the electron mass. See Zombeck (2007). }} The maximum magnitude of this wavelength shift is h/mec, which is known as the Compton wavelength. |access-date=2008-09-28 |archive-date=2008-10-24 |archive-url=https://web.archive.org/web/20081024124054/http://nobelprize.org/nobel_prizes/physics/laureates/1927/ |url-status=live

The relative strength of the electromagnetic interaction between two charged particles, such as an electron and a proton, is given by the fine-structure constant. This value is a dimensionless quantity formed by the ratio of two energies: the electrostatic energy of attraction (or repulsion) at a separation of one Compton wavelength, and the rest energy of the charge. It is given by which is approximately equal to .

When electrons and positrons collide, they annihilate each other, giving rise to two or more gamma ray photons. If the electron and positron have negligible momentum, a positronium atom can form before annihilation results in two or three gamma ray photons whose energies total 1.022 MeV. | access-date = 2019-06-21 | archive-date = 2019-06-21 | archive-url = https://web.archive.org/web/20190621192329/https://zenodo.org/record/1259327 | url-status = live

In the theory of electroweak interaction, the left-handed component of electron's wavefunction forms a weak isospin doublet with the electron neutrino. This means that during weak interactions, electron neutrinos behave like electrons. Either member of this doublet can undergo a charged current interaction by emitting or absorbing a and be converted into the other member. Charge is conserved during this reaction because the W boson also carries a charge, canceling out any net change during the transmutation. Charged current interactions are responsible for the phenomenon of beta decay in a radioactive atom. Both the electron and electron neutrino can undergo a neutral current interaction via a exchange, and this is responsible for neutrino–electron elastic scattering.

In atoms and molecules

Main article: Atom

An electron can be bound to the nucleus of an atom by the attractive Coulomb force. A system of one or more electrons bound to a nucleus is called an atom. If the number of electrons is different from the nucleus's electrical charge, such an atom is called an ion. The wave-like behavior of a bound electron is described by a function called an atomic orbital. Each orbital has its own set of quantum numbers such as energy, angular momentum, and projection of angular momentum. Only a discrete set of these orbitals exist around the nucleus. According to the Pauli exclusion principle, each orbital can be occupied by up to two electrons, which must differ in their spin quantum number.

Electrons can transfer between different orbitals by the emission or absorption of photons with an energy that matches the difference in potential between the orbitals. Other methods of orbital transfer include collisions with particles, such as electrons, and the Auger effect. | author-link = Eric Burhop | orig-date= 1952

The orbital angular momentum of electrons is quantized. Because the electron is charged, it produces an orbital magnetic moment that is proportional to the angular momentum. The net magnetic moment of an atom is equal to the vector sum of orbital and spin magnetic moments of all electrons and the nucleus. The magnetic moment of the nucleus is negligible compared with that of the electrons. The magnetic moments of the electrons that occupy the same orbital, called paired electrons, cancel each other out. | access-date = 2020-08-25 | archive-date = 2021-01-26 | archive-url = https://web.archive.org/web/20210126003325/https://books.google.com/books?id=axyWXjsdorMC&pg=PA280 | url-status = live

The chemical bond between atoms occurs as a result of electromagnetic interactions, as described by the laws of quantum mechanics. |access-date = 2020-08-25 |archive-date = 2022-02-04 |archive-url = https://web.archive.org/web/20220204071147/https://books.google.com/books?id=8QiR8lCX_qcC&pg=PA393 |url-status = live | url-access = registration | pages =4–10 | access-date = 2020-08-25 | archive-date = 2021-01-07 | archive-url = https://web.archive.org/web/20210107160307/https://books.google.com/books?id=f-bje0-DEYUC&pg=PA325 | url-status = live |display-authors=etal |doi-access=free

Conductivity

| access-date = 2020-08-25 | archive-date = 2021-01-26 | archive-url = https://web.archive.org/web/20210126003319/https://books.google.com/books?id=TuMa5lAa3RAC&pg=PA4 | url-status = live An object has a net electric charge if the total negative charge provided by electrons does not equal the positive charge from the nuclei. When there is an excess of electrons, the object is said to be negatively charged. When there is a lack of electrons, the object is said to be positively charged. When the number of electrons and the number of protons are equal, their charges cancel each other and the object is said to be electrically neutral. A macroscopic body can develop an electric charge through rubbing, by the triboelectric effect. | url-access = registration | pages =15–16

Independent electrons moving in vacuum are termed free electrons. Electrons in metals also behave as if they were free. In reality the particles that are commonly termed electrons in metals and other solids are quasi-electrons – quasiparticles, which have the same electrical charge, spin, and magnetic moment as real electrons but might have a different mass. | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204071149/https://books.google.com/books?id=XMv-vfsoRF8C&pg=PA162 | url-status = live | url-access=registration

At a given temperature, each material has an electrical conductivity that determines the value of electric current when an electric potential is applied. Examples of good conductors include metals such as copper and gold, whereas glass and Teflon are poor conductors. In any dielectric material, the electrons remain bound to their respective atoms and the material behaves as an insulator. Most semiconductors have a variable level of conductivity that lies between the extremes of conduction and insulation. | access-date = 2020-08-25 | archive-date = 2021-01-07 | archive-url = https://web.archive.org/web/20210107160319/https://books.google.com/books?id=REQkwBF4cVoC&pg=PA49 | url-status = live | access-date = 2020-08-25 | archive-date = 2022-02-24 | archive-url = https://web.archive.org/web/20220224105543/https://books.google.com/books?id=UtEy63pjngsC&pg=PA260 | url-status = live

Because of collisions between electrons and atoms, the drift velocity of electrons in a conductor is on the order of millimeters per second. However, the speed at which a change of current at one point in the material causes changes in currents in other parts of the material, the velocity of propagation, is typically about 75% of light speed. | access-date = 2008-10-09 | archive-date = 2015-02-11 | archive-url = https://web.archive.org/web/20150211085229/http://www.newscientist.com/article/mg13818774.500-when-electrons-go-with-the-flow-remove-the-obstacles-thatcreate-electrical-resistance-and-you-get-ballistic-electrons-and-a-quantumsurprise.html | url-status = live | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204083743/https://books.google.com/books?id=D0PBG53PQlUC&pg=SA6-PA39 | url-status = live

Metals make relatively good conductors of heat, primarily because the delocalized electrons are free to transport thermal energy between atoms. However, unlike electrical conductivity, the thermal conductivity of a metal is nearly independent of temperature. This is expressed mathematically by the Wiedemann–Franz law, which states that the ratio of thermal conductivity to the electrical conductivity is proportional to the temperature. The thermal disorder in the metallic lattice increases the electrical resistivity of the material, producing a temperature dependence for electric current. | access-date = 2015-10-16 | archive-date = 2016-05-27 | archive-url = https://web.archive.org/web/20160527150628/https://books.google.com/books?id=F0JmHRkJHiUC&pg=PA43 | url-status = live

When cooled below a point called the critical temperature, materials can undergo a phase transition in which they lose all resistivity to electric current, in a process known as superconductivity. In BCS theory, pairs of electrons called Cooper pairs have their motion coupled to nearby matter via lattice vibrations called phonons, thereby avoiding the collisions with atoms that normally create electrical resistance. | access-date = 2008-10-13 | archive-date = 2008-10-11 | archive-url = https://web.archive.org/web/20081011050516/http://nobelprize.org/nobel_prizes/physics/laureates/1972/ | url-status = live

Electrons inside conducting solids, which are quasi-particles themselves, when tightly confined at temperatures close to absolute zero, behave as though they had split into three other quasiparticles: spinons, orbitons and holons. | access-date = 2009-08-01 | archive-date = 2019-04-04 | archive-url = https://web.archive.org/web/20190404130054/https://www.sciencedaily.com/releases/2009/07/090730141607.htm | url-status = live

Relativistic effects

According to Einstein's theory of special relativity, as an electron's speed approaches the speed of light, from an observer's point of view its relativistic mass increases, thereby making it more and more difficult to accelerate it with respect to the observer's frame of reference. The speed of an electron can approach, but never reach, the speed of light in vacuum, c. However, when relativistic electrons—that is, electrons moving at a speed close to c—are injected into a dielectric medium such as water, where the local speed of light is significantly less than c, the electrons temporarily travel faster than light in the medium. As they interact with the medium, they generate a faint light called Cherenkov radiation. | access-date = 2008-09-25 | archive-date = 2008-10-18 | archive-url = https://web.archive.org/web/20081018162638/http://nobelprize.org/nobel_prizes/physics/laureates/1958/ | url-status = live

The effects of special relativity are based on a quantity known as the Lorentz factor, defined as \textstyle \gamma=1/ \sqrt{ 1-{v^2}/{c^2} }, where v is the speed of the particle. The kinetic energy Ke of an electron moving with velocity v is: : \displaystyle K_{\mathrm{e}} = (\gamma - 1)m_{\mathrm{e}} c^2, where me is the mass of electron. For example, the Stanford linear accelerator can accelerate an electron to roughly 51 GeV. | access-date = 2008-09-25 | archive-date = 2008-08-28 | archive-url = https://web.archive.org/web/20080828113927/http://www2.slac.stanford.edu/VVC/theory/relativity.html | url-status = live Since an electron behaves as a wave, at a given velocity it has a characteristic de Broglie wavelength. This is given by λe = h/p where h is the Planck constant and p is the momentum. For the 51 GeV electron above, the wavelength is about , small enough to explore structures well below the size of an atomic nucleus. | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204071142/https://books.google.com/books?id=yIsMaQblCisC&pg=PA215 | url-status = live

Formation

|access-date=2018-04-20 |archive-date=2020-01-02 |archive-url=https://web.archive.org/web/20200102022221/https://books.google.com/books?id=lktADwAAQBAJ&pg=PA79 |url-status=live

The Big Bang theory is the most widely accepted scientific theory to explain the early stages in the evolution of the Universe. : + ↔ + An equilibrium between electrons, positrons and photons was maintained during this phase of the evolution of the Universe. After 15 seconds had passed, however, the temperature of the universe dropped below the threshold where electron–positron formation could occur. Most of the surviving electrons and positrons annihilated each other, releasing gamma radiation that briefly reheated the universe.

For reasons that remain uncertain, during the annihilation process there was an excess in the number of particles over antiparticles. Hence, about one electron for every billion electron–positron pairs survived. This excess matched the excess of protons over antiprotons, in a condition known as baryon asymmetry, resulting in a net charge of zero for the universe. | access-date = 2020-08-25 | archive-date = 2020-10-30 | archive-url = https://web.archive.org/web/20201030105942/https://authors.library.caltech.edu/99675/2/Development%20of%20Baryon%20Asymmetry%20in%20the%20Early%20Universe.pdf | url-status = live | access-date = 2008-11-01 | archive-date = 2008-10-12 | archive-url = https://web.archive.org/web/20081012012543/http://www.slac.stanford.edu/pubs/beamline/26/1/26-1-sather.pdf | url-status = live : → + + For about the next –, the excess electrons remained too energetic to bind with atomic nuclei.

Roughly one million years after the big bang, the first generation of stars began to form. Within a star, stellar nucleosynthesis results in the production of positrons from the fusion of atomic nuclei. These antimatter particles immediately annihilate with electrons, releasing gamma rays. The net result is a steady reduction in the number of electrons, and a matching increase in the number of neutrons. However, the process of stellar evolution can result in the synthesis of radioactive isotopes. Selected isotopes can subsequently undergo negative beta decay, emitting an electron and antineutrino from the nucleus. An example is the cobalt-60 (60Co) isotope, which decays to form nickel-60 ().

At the end of its lifetime, a star with more than about 20 solar masses can undergo gravitational collapse to form a black hole.

When a pair of virtual particles (such as an electron and positron) is created in the vicinity of the event horizon, random spatial positioning might result in one of them to appear on the exterior; this process is called quantum tunnelling. The gravitational potential of the black hole can then supply the energy that transforms this virtual particle into a real particle, allowing it to radiate away into space.

Cosmic rays are particles traveling through space with high energies. Energy events as high as have been recorded. : → + A muon, in turn, can decay to form an electron or positron. | access-date = 2008-08-28 | archive-date = 2015-02-11 | archive-url = https://web.archive.org/web/20150211085842/http://www.newscientist.com/article/mg12717284.700-muons-pions-and-other-strange-particles-.html | url-status = live : → + +

Observation

|access-date=2008-10-11 |df=dmy-all |archive-url=https://web.archive.org/web/20080817094058/https://www.universityofcalifornia.edu/news/article/18277 |archive-date=August 17, 2008 Remote observation of electrons requires detection of their radiated energy. For example, in high-energy environments such as the corona of a star, free electrons form a plasma that radiates energy due to Bremsstrahlung radiation. Electron gas can undergo plasma oscillation, which is waves caused by synchronized variations in electron density, and these produce energy emissions that can be detected by using radio telescopes.

The frequency of a photon is proportional to its energy. As a bound electron transitions between different energy levels of an atom, it absorbs or emits photons at characteristic frequencies. For instance, when atoms are irradiated by a source with a broad spectrum, distinct dark lines appear in the spectrum of transmitted radiation in places where the corresponding frequency is absorbed by the atom's electrons. Each element or molecule displays a characteristic set of spectral lines, such as the hydrogen spectral series. When detected, spectroscopic measurements of the strength and width of these lines allow the composition and physical properties of a substance to be determined. | access-date = 2007-01-08 | archive-date = 2007-02-08 | archive-url = https://web.archive.org/web/20070208113156/http://physics.nist.gov/Pubs/AtSpec/ | url-status = live | access-date = 2020-08-25 | archive-date = 2021-01-07 | archive-url = https://web.archive.org/web/20210107160307/https://books.google.com/books?id=SL1n9TuJ5YMC&pg=PA227 | url-status = live

In laboratory conditions, the interactions of individual electrons can be observed by means of particle detectors, which allow measurement of specific properties such as energy, spin and charge. | access-date = 2008-09-24 | archive-date = 2008-09-28 | archive-url = https://web.archive.org/web/20080928042325/http://nobelprize.org/nobel_prizes/physics/laureates/1989/illpres/ | url-status = live | access-date = 2008-09-24 | archive-date = 2019-09-16 | archive-url = https://web.archive.org/web/20190916211444/https://tf.nist.gov/general/pdf/166.pdf | url-status = live

The first video images of an electron's energy distribution were captured by a team at Lund University in Sweden, February 2008. The scientists used extremely short flashes of light, called attosecond pulses, which allowed an electron's motion to be observed for the first time. | access-date = 2008-09-17 |df=dmy-all | archive-url = https://web.archive.org/web/20090325194101/https://www.atto.fysik.lth.se/video/pressrelen.pdf | archive-date = March 25, 2009

The distribution of the electrons in solid materials can be visualized by angle-resolved photoemission spectroscopy (ARPES). This technique employs the photoelectric effect to measure the reciprocal space—a mathematical representation of periodic structures that is used to infer the original structure. ARPES can be used to determine the direction, speed and scattering of electrons within the material.

Plasma applications

Particle beams

|access-date=2008-09-20 |df=dmy-all |archive-url=https://web.archive.org/web/20081207041522/https://grin.hq.nasa.gov/ABSTRACTS/GPN-2000-003012.html |archive-date=December 7, 2008

Electron beams are used in welding. | access-date = 2008-10-16 |df=dmy-all | archive-url=https://web.archive.org/web/20080920142328/https://www.llnl.gov/str/MarApr08/elmer.html | archive-date=2008-09-20 | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204084011/https://books.google.com/books?id=I0xMo28DwcIC&pg=PA2 | url-status = live | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204084012/https://books.google.com/books?id=xdmNVSio8jUC&pg=PA273 | url-status = live

Electron-beam lithography (EBL) is a method of etching semiconductors at resolutions smaller than a micrometer. | access-date = 2008-10-16 |df=dmy-all | access-date = 2020-08-25 | archive-date = 2021-01-07 | archive-url = https://web.archive.org/web/20210107160805/https://books.google.com/books?id=9bk3gJeQKBYC&pg=PA53 | url-status = live

Electron beam processing is used to irradiate materials in order to change their physical properties or sterilize medical and food products.

Linear particle accelerators generate electron beams for treatment of superficial tumors in radiation therapy. Electron therapy can treat such skin lesions as basal-cell carcinomas because an electron beam only penetrates to a limited depth before being absorbed, typically up to 5 cm for electron energies in the range 5–20 MeV. An electron beam can be used to supplement the treatment of areas that have been irradiated by X-rays. | access-date = 2013-10-31 | archive-date = 2013-11-02 | archive-url = https://web.archive.org/web/20131102114151/http://www.thymic.org/uploads/reference_sub/02radtherapy.pdf | url-status = live

Particle accelerators use electric fields to propel electrons and their antiparticles to high energies. These particles emit synchrotron radiation as they pass through magnetic fields. The dependency of the intensity of this radiation upon spin polarizes the electron beam – a process known as the Sokolov–Ternov effect. Polarized electron beams can be useful for various experiments. Synchrotron radiation can also cool the electron beams to reduce the momentum spread of the particles. Electron and positron beams are collided upon the particles' accelerating to the required energies; particle detectors observe the resulting energy emissions, which particle physics studies. | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204071146/https://books.google.com/books?id=Z3J4SjftF1YC&pg=PA155 | url-status = live

Imaging

Low-energy electron diffraction (LEED) is a method of bombarding a crystalline material with a collimated beam of electrons and then observing the resulting diffraction patterns to determine the structure of the material. The required energy of the electrons is typically in the range . |display-authors=etal | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204084445/https://books.google.com/books?id=AUVbPerNxTcC&pg=PA1 | url-status = live

The electron microscope directs a focused beam of electrons at a specimen. Some electrons change their properties, such as movement direction, angle, and relative phase and energy as the beam interacts with the material. Microscopists can record these changes in the electron beam to produce atomically resolved images of the material. | access-date = 2009-03-23 | archive-date = 2009-03-16 | archive-url = https://web.archive.org/web/20090316071650/http://www-g.eng.cam.ac.uk/125/achievements/mcmullan/mcm.htm | url-status = live | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204084446/https://books.google.com/books?id=LlePVS9oq7MC&pg=PA1 | url-status = live | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204084443/https://books.google.com/books?id=obcmBZe9es4C&pg=PA42 | url-status = live |display-authors = etal |article-number = 096101 |access-date = 2018-08-17 |archive-date = 2020-01-02 |archive-url = https://web.archive.org/web/20200102164706/https://digital.library.unt.edu/ark:/67531/metadc927376/ |url-status = live

Two main types of electron microscopes exist: transmission and scanning. Transmission electron microscopes function like overhead projectors, with a beam of electrons passing through a slice of material then being projected by lenses on a photographic slide or a charge-coupled device. Scanning electron microscopes rasteri a finely focused electron beam, as in a TV set, across the studied sample to produce the image. Magnifications range from 100× to 1,000,000× or higher for both microscope types. The scanning tunneling microscope uses quantum tunneling of electrons from a sharp metal tip into the studied material and can produce atomically resolved images of its surface. | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204084447/https://books.google.com/books?id=RqSMzR-IXk0C&pg=PA12 | url-status = live | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204084444/https://books.google.com/books?id=RqSMzR-IXk0C&pg=PA9 | url-status = live

Other applications

In the free-electron laser (FEL), a relativistic electron beam passes through a pair of undulators that contain arrays of dipole magnets whose fields point in alternating directions. The electrons emit synchrotron radiation that coherently interacts with the same electrons to strongly amplify the radiation field at the resonance frequency. FEL can emit a coherent high-brilliance electromagnetic radiation with a wide range of frequencies, from microwaves to soft X-rays. These devices are used in manufacturing, communication, and in medical applications, such as soft tissue surgery. | access-date = 2020-08-25 | archive-date = 2022-02-04 | archive-url = https://web.archive.org/web/20220204084620/https://books.google.com/books?id=73w9tqTgbiIC&pg=PA1 | url-status = live

Electrons are important in cathode-ray tubes, which have been extensively used as display devices in laboratory instruments, computer monitors and television sets. | access-date = 2008-10-18 | archive-date = 2008-12-01 | archive-url = https://web.archive.org/web/20081201144536/http://nobelprize.org/educational_games/physics/integrated_circuit/history/ | url-status = live

Notes

References

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References

1. For discussion and sources see [[Electron#Lifetime]]
2. link. (2021-04-27)
3. Plücker, M.. (1858-12-01). "XLVI. Observations on the electrical discharge through rarefied gases". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science.
4. Darrigol, Olivier. (2003). "Electrodynamics from Ampère to Einstein". OUP Oxford.
5. Thomson, George. (1970). "An Unfortunate Experiment: Hertz and the Nature of Cathode Rays". Notes and Records of the Royal Society of London.
6. Schuster, Arthur. (1890). "The discharge of electricity through gases". Proceedings of the Royal Society of London.
7. Wilczek, Frank. (June 2012). "Happy birthday, electron".
8. [[#refBaW2001. Buchwald and Warwick (2001:90–91).]]
9. [[Abraham Pais]]. (1997). "The discovery of the electron – 100 years of elementary particles". Beam Line.
10. Kaufmann, W.. (1897). "Die magnetische Ablenkbarkeit der Kathodenstrahlen und ihre Abhängigkeit vom Entladungspotential". Annalen der Physik und Chemie.
11. Stoney, George Johnstone. (1891). "On the Cause of Double Lines and of Equidistant Satellites in the Spectra of Gases". The Scientific Transactions of the Royal Dublin Society.
12. Navarro, Jaume. (2010). "Electron diffraction chez Thomson: early responses to quantum physics in Britain". The British Journal for the History of Science.
13. Anderson, Carl D.. (1933-03-15). "The Positive Electron". Physical Review.
14. (2009-08-28). "UK {{pipe}} England {{pipe}} Physicists 'make electrons split'". BBC News.
15. [https://www.sciencedaily.com/releases/2009/07/090730141607.htm Discovery About Behavior Of Building Block Of Nature Could Lead To Computer Revolution] {{Webarchive. link. (2019-04-04 . ''Science Daily'' (July 31, 2009))
16. Yarris, Lynn. (2006-07-13). "First Direct Observations of Spinons and Holons". Lbl.gov.
17. Gabrielse, Gerald. "Electron Substructure". Harvard University.
18. (1995-12-01). "The Foldy–Wouthuysen transformation". American Journal of Physics.
19. (2013). "The Standard Model: a primer". Cambridge Univ. Press.
20. (2006-12-07). "The Standard Model: A Primer". Cambridge University Press.
21. (1957). "Synthesis of Elements in Stars". [[Reviews of Modern Physics]].