Interactions involving electrons with other subatomic particles are of interest in fields such aschemistry andnuclear physics. TheCoulomb force interaction between the positiveprotons withinatomic nuclei and the negative electrons without allows the composition of the two known asatoms. Ionization or differences in the proportions of negative electrons versus positive nuclei changes thebinding energy of an atomic system. The exchange or sharing of the electrons between two or more atoms is the main cause ofchemical bonding.[17]
Theancient Greeks noticed thatamber attracted small objects when rubbed with fur. Along withlightning, this phenomenon is one of humanity's earliest recorded experiences withelectricity.[18] In his 1600 treatiseDe Magnete, the English scientistWilliam Gilbert coined theNeo-Latin termelectrica, to refer to those substances with property similar to that of amber which attract small objects after being rubbed.[19] Bothelectric andelectricity are derived from the Latinēlectrum (also the root of thealloy of the same name), which came from theGreek word for amber,ἤλεκτρον (ēlektron).
In the early 1700s, French chemistCharles 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 twoelectrical fluids,vitreous fluid from glass rubbed with silk andresinous fluid from amber rubbed with wool. These two fluids can neutralize each other when combined.[19][20] American scientistEbenezer Kinnersley later also independently reached the same conclusion.[21]: 118 A decade laterBenjamin Franklin proposed that electricity was not from different types of electrical fluid, but a single electrical fluid showing an excess (+) or deficit (−). He gave them the moderncharge nomenclature of positive and negative respectively.[22] Franklin thought of the charge carrier as being positive, but he did not correctly identify which situation was a surplus of the charge carrier, and which situation was a deficit.[23]
Between 1838 and 1851, British natural philosopherRichard Laming developed the idea that an atom is composed of a core of matter surrounded by subatomic particles that had unitelectric charges.[2] Beginning in 1846, German physicistWilhelm Eduard Weber theorized that electricity was composed of positively and negatively charged fluids, and their interaction was governed by theinverse square law. After studying the phenomenon ofelectrolysis in 1874, Irish physicistGeorge Johnstone Stoney suggested that there existed a "single definite quantity of electricity", the charge of amonovalention. He was able to estimate the value of this elementary chargee by means ofFaraday's laws of electrolysis.[24] However, Stoney believed these charges were permanently attached to atoms and could not be removed. In 1881, German physicistHermann von Helmholtz argued that both positive and negative charges were divided into elementary parts, each of which "behaves like atoms of electricity".[3]
Stoney initially coined the termelectrolion in 1881. Ten years later, he switched toelectron 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 nameelectron". A 1906 proposal to change toelectrion failed becauseHendrik Lorentz preferred to keepelectron.[25][26] The wordelectron is a combination of the wordselectric andion.[27] The suffix-on which is now used to designate other subatomic particles, such as a proton or neutron, is in turn derived from electron.[28][29]
A beam of electrons deflected by a magnetic field into a circle[30]
While studying electrical conductivity inrarefied gases in 1859, the German physicistJulius 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.[31] In 1869, Plücker's studentJohann 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.[32]
In 1876, the German physicistEugen 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 rayscathode rays.[33][34]: 393 Decades of experimental and theoretical research involving cathode rays were important inJ. J. Thomson's eventual discovery of electrons.[3] Goldstein also experimented with double cathodes and hypothesized that one ray may repulse another, although he didn't believe that any particles might be involved.[35]
During the 1870s, the English chemist and physicist SirWilliam Crookes developed the first cathode-ray tube to have ahigh vacuum inside.[36] He then showed in 1874 that the cathode rays can turn a small paddle wheel when placed in their path. Therefore, he concluded that the rays carried momentum. Furthermore, by applying a magnetic field, he was able to deflect the rays, thereby demonstrating that the beam behaved as though it were negatively charged.[33] In 1879, he proposed that these properties could be explained by regarding cathode rays as composed of negatively charged gaseousmolecules in a fourthstate of matter, in which the mean free path of the particles is so long that collisions may be ignored.[34]: 394–395
In 1883, not yet well-known German physicistHeinrich 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, asJ. 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.[35]
The German-born British physicistArthur Schuster expanded upon Crookes's experiments by placing metal plates parallel to the cathode rays and applying anelectric potential between the plates.[37] 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 givenelectric andmagnetic field, in 1890 Schuster was able to estimate thecharge-to-mass ratio[c] 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.[33] This is because it was assumed that the charge carriers were much heavierhydrogen ornitrogen atoms.[37] Schuster's estimates would subsequently turn out to be largely correct.
In 1892Hendrik Lorentz suggested that the mass of these particles (electrons) could be a consequence of their electric charge.[38]
While studying naturallyfluorescing minerals in 1896, the French physicistHenri Becquerel discovered that they emitted radiation without any exposure to an external energy source. Theseradioactive materials became the subject of much interest by scientists, including the New Zealand physicistErnest Rutherford who discovered they emitted particles. He designated these particlesalpha andbeta, on the basis of their ability to penetrate matter.[39] In 1900, Becquerel showed that the beta rays emitted byradium could be deflected by an electric field, and that their mass-to-charge ratio was the same as for cathode rays.[40] This evidence strengthened the view that electrons existed as components of atoms.[41][42]
In 1897, the British physicistJ. J. Thomson, with his colleaguesJohn S. Townsend andH. A. Wilson, performed experiments indicating that cathode rays really were unique particles, rather than waves, atoms or molecules as was believed earlier.[5] 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.[5][43] Thomson measuredm/e for cathode ray "corpuscles", and made good estimates of the chargee, leading to value for the massm, finding a value 1400 times less massive than the least massive ion known: hydrogen.[34]: 364 [5] In the same yearEmil Wiechert andWalter Kaufmann also calculated thee/m ratio but did not take the step of interpreting their results as showing a new particle, while J. J. Thomson would subsequently in 1899 give estimates for the electron charge and mass as well:e ~ 6.8×10−10esu andm ~ 3×10−26 g[44][45]
The name "electron" was adopted for these particles by the scientific community, mainly due to the advocation byG. F. FitzGerald,J. Larmor, andH. A. Lorentz.[46]: 273 The term was originally coined byGeorge Johnstone Stoney in 1891 as a tentative name for the basic unit of electrical charge (which had then yet to be discovered).[47][26]
The electron's charge was more carefully measured by the American physicistsRobert Millikan andHarvey Fletcher in theiroil-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,[5] using clouds of charged water droplets generated by electrolysis, and in 1911 byAbram Ioffe, who independently obtained the same result as Millikan using charged microparticles of metals, then published his results in 1913.[48] However, oil drops were more stable than water drops because of their slower evaporation rate, and thus more suited to precise experimentation over longer periods of time.[49]
Around the beginning of the twentieth century, it was found that under certain conditions a fast-moving charged particle caused a condensation ofsupersaturated water vapor along its path. In 1911,Charles Wilson used this principle to devise hiscloud chamber so he could photograph the tracks of charged particles, such as fast-moving electrons.[50]
TheBohr model of the atom, showing states of an electron with energyquantized by the numbern. An electron dropping to a lower orbit emits a photon equal to the energy difference between the orbits
By 1914, experiments by physicistsErnest Rutherford,Henry Moseley,James Franck andGustav Hertz had largely established the structure of an atom as a densenucleus of positive charge surrounded by lower-mass electrons.[51] In 1913, Danish physicistNiels 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 thespectral lines of the hydrogen atom.[52] However, Bohr's model failed to account for the relative intensities of the spectral lines and it was unsuccessful in explaining the spectra of more complex atoms.[51]
Chemical bonds between atoms were explained byGilbert Newton Lewis, who in 1916 proposed that acovalent bond between two atoms is maintained by a pair of electrons shared between them.[53] Later, in 1927,Walter Heitler andFritz London gave the full explanation of the electron-pair formation and chemical bonding in terms ofquantum mechanics.[54] In 1919, the American chemistIrving Langmuir elaborated on the Lewis's static model of the atom and suggested that all electrons were distributed in successive "concentric (nearly) spherical shells, all of equal thickness".[55] In turn, he divided the shells into a number of cells each of which contained one pair of electrons. With this model Langmuir was able to qualitatively explain thechemical properties of all elements in the periodic table,[54] which were known to largely repeat themselves according to theperiodic law.[56]
In 1924, Austrian physicistWolfgang 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 thePauli exclusion principle.[57] The physical mechanism to explain the fourth parameter, which had two distinct possible values, was provided by the Dutch physicistsSamuel Goudsmit andGeorge Uhlenbeck. In 1925, they suggested that an electron, in addition to the angular momentum of its orbit, possesses an intrinsic angular momentum andmagnetic dipole moment.[51][58] This is analogous to the rotation of the Earth on its axis as it orbits the Sun. The intrinsic angular momentum became known asspin, and explained the previously mysterious splitting of spectral lines observed with a high-resolutionspectrograph; this phenomenon is known asfine structure splitting.[59]
In his 1924 dissertationRecherches sur la théorie des quanta (Research on Quantum Theory), French physicistLouis de Broglie hypothesized that all matter can be represented as ade Broglie wave in the manner oflight.[60] That is, under the appropriate conditions, electrons and other matter would show properties of either particles or waves. Thecorpuscular properties of a particle are demonstrated when it is shown to have a localized position in space along its trajectory at any given moment.[61] The wave-like nature of light is displayed, for example, when a beam of light is passed through parallel slits thereby creatinginterference patterns. In 1927,George Paget Thomson and Alexander Reid discovered the interference effect was produced when a beam of electrons was passed through thin celluloid foils and later metal films, and by American physicistsClinton Davisson andLester Germer by the reflection of electrons from a crystal ofnickel.[62] Alexander Reid, who was Thomson's graduate student, performed the first experiments but he died soon after in a motorcycle accident[63] and is rarely mentioned.
In quantum mechanics, the behavior of an electron in an atom is described by anorbital, which is a probability distribution rather than an orbit. In the figure, the shading indicates the relative probability to "find" the electron, having the energy corresponding to the givenquantum numbers, at that point.
De Broglie's prediction of a wave nature for electrons ledErwin Schrödinger to postulate a wave equation for electrons moving under the influence of the nucleus in the atom. In 1926, this equation, theSchrödinger equation, successfully described how electron waves propagated.[64] Rather than yielding a solution that determined the location of an electron over time, this wave equation also could be used to predict the probability of finding an electron near a position, especially a position near where the electron was bound in space, for which the electron wave equations did not change in time. This approach led to a second formulation ofquantum mechanics (the first by Heisenberg in 1925), and solutions of Schrödinger's equation, like Heisenberg's, provided derivations of the energy states of an electron in a hydrogen atom that were equivalent to those that had been derived first by Bohr in 1913, and that were known to reproduce the hydrogen spectrum.[65] Once spin and the interaction between multiple electrons were describable, quantum mechanics made it possible to predict the configuration of electrons in atoms with atomic numbers greater than hydrogen.[66]
In 1928, building on Wolfgang Pauli's work,Paul Dirac produced a model of the electron – theDirac equation, consistent withrelativity theory, by applying relativistic and symmetry considerations to thehamiltonian formulation of the quantum mechanics of the electro-magnetic field.[67] In order to resolve some problems within his relativistic equation, Dirac developed in 1930 a model of the vacuum as an infinite sea of particles with negative energy, later dubbed theDirac sea. This led him to predict the existence of a positron, theantimatter counterpart of the electron.[68] This particle was discovered in 1932 byCarl Anderson, who proposed calling standard electronsnegatrons and usingelectron as a generic term to describe both the positively and negatively charged variants.[69]
With the development of theparticle accelerator during the first half of the twentieth century, physicists began to delve deeper into the properties ofsubatomic particles.[71] The first successful attempt to accelerate electrons usingelectromagnetic induction was made in 1942 byDonald Kerst. His initialbetatron reached energies of 2.3 MeV, while subsequent betatrons achieved 300 MeV. In 1947,synchrotron radiation was discovered with a 70 MeV electron synchrotron atGeneral Electric. This radiation was caused by the acceleration of electrons through a magnetic field as they moved near the speed of light.[72]
With a beam energy of 1.5 GeV, the first high-energyparticlecollider wasADONE, which began operations in 1968.[73] This device accelerated electrons and positrons in opposite directions, effectively doubling the energy of their collision when compared to striking a static target with an electron.[74] TheLarge Electron–Positron Collider (LEP) atCERN, which was operational from 1989 to 2000, achieved collision energies of 209 GeV and made important measurements for theStandard Model of particle physics.[75][76]
Individual electrons can now be easily confined in ultra small (L = 20 nm,W = 20 nm) CMOS transistors operated at cryogenic temperature over a range of −269 °C (4 K) to about −258 °C (15 K).[77] The electron wavefunction spreads in a semiconductor lattice and negligibly interacts with the valence band electrons, so it can be treated in the single particle formalism, by replacing its mass with theeffective-mass tensor.
Standard Model of elementary particles. The electron (symbol e) is on the left.
In theStandard Model of particle physics, electrons belong to the group of subatomic particles calledleptons, which are believed to be fundamental orelementary particles. Electrons have the lowest mass of any charged lepton (or electrically charged particle of any type) and belong to the firstgeneration of fundamental particles.[78] The second and third generation contain charged leptons, themuon and thetau, which are identical to the electron in charge,spin andinteractions, but are more massive. Leptons differ from the other basic constituent of matter, thequarks, by their lack ofstrong interaction. All members of the lepton group are fermions because they all have half-odd integer spin; the electron has spin1/2.[79]
Electrons have anelectric charge of−1.602176634×10−19coulombs,[80] which is used as a standard unit of charge for subatomic particles, and is also called theelementary charge. Within the limits of experimental accuracy, the electron charge is identical to the charge of a proton, but with the opposite sign.[83] The electron is commonly symbolized by e− , and the positron is symbolized by e+ .[79][80]
The electron has an intrinsicangular momentum or spin ofħ/2.[80] This property is usually stated by referring to the electron as aspin-1/2 particle.[79] For such particles the spin magnitude isħ/2,[84] while the result of the measurement of aprojection of the spin on any axis can only be ±ħ/2. In addition to spin, the electron has an intrinsicmagnetic moment along its spin axis.[80] It is approximately equal to oneBohr magneton,[85][d] which is a physical constant that is equal to9.2740100657(29)×10−24 J⋅T−1.[86] The orientation of the spin with respect to the momentum of the electron defines the property of elementary particles known ashelicity.[87]
The electron has no knownsubstructure.[1][88] Nevertheless, incondensed matter physics,spin–charge separation can occur in some materials. In such cases, electrons 'split' into three independent particles, thespinon, theorbiton and theholon (or chargon). The electron can always be theoretically considered as a bound state of the three, with the spinon carrying the spin of the electron, the orbiton carrying the orbital degree of freedom and the chargon carrying the charge, but in certain conditions they can behave as independentquasiparticles.[89][90][91]
The issue of the radius of the electron is a challenging problem of modern theoretical physics. The admission of the hypothesis of a finite radius of the electron is incompatible to the premises of the theory of relativity. On the other hand, a point-like electron (zero radius) generates serious mathematical difficulties due to theself-energy of the electron tending to infinity.[92] Observation of a single electron in aPenning trap suggests the upper limit of the particle's radius to be 10−22 meters.[93]The upper bound of the electron radius of 10−18 meters[94] can be derived using theuncertainty relation in energy. Thereis also a physical constant called the "classical electron radius", with the much larger value of2.8179×10−15 m, greater than the radius of the proton. However, the terminology comes from a simplistic calculation that ignores the effects ofquantum mechanics; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron.[95][96][e]
There areelementary particles that spontaneouslydecay into less massive particles. An example is themuon, with amean lifetime of2.2×10−6 seconds, which decays into an electron, a muonneutrino and an electronantineutrino. The electron, on the other hand, is thought to be stable on theoretical grounds: the electron is the least massive particle with non-zero electric charge, so its decay would violatecharge conservation.[97] The experimental lower bound for the electron's mean lifetime is6.6×1028 years, at a 90%confidence level.[9][98][99]
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 acomplex-valued function, thewave function, commonly denoted by theGreek letterpsi (ψ). When theabsolute value of this function issquared, it gives the probability that a particle will be observed near a location—aprobability density.[100]: 162–218
Example of an antisymmetric wave function for a quantum state oftwo identical fermions in a one-dimensional box, with each horizontal axis corresponding to the position of one particle. If the particles swap position, the wave function inverts its sign.
Electrons areidentical 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,ψ(r1,r2) = −ψ(r2,r1), where the variablesr1 andr2 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.[100]: 162–218
In the case of antisymmetry, solutions of the wave equation for interacting electrons result in azero probability that each pair will occupy the same location or state. This is responsible for thePauli 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 differentorbitals in an atom, rather than all overlapping each other in the same orbit.[100]: 162–218
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 rapidlyannihilate each other shortly thereafter.[101] The combination of the energy variation needed to create these particles, and the time during which they exist, fall under the threshold of detectability expressed by theHeisenberg uncertainty relation, ΔE · Δt ≥ ħ. In effect, the energy needed to create these virtual particles, ΔE, can be "borrowed" from thevacuum for a period of time, Δt, so that their product is no more than thereduced Planck constant,ħ ≈6.6×10−16 eV·s. Thus, for a virtual electron, Δt is at most1.3×10−21 s.[102]
A schematic depiction of virtual electron–positron pairs appearing at random near an electron (at lower left)
While an electron–positron virtual pair is in existence, theCoulomb force from the ambientelectric 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 calledvacuum polarization. In effect, the vacuum behaves like a medium having adielectric permittivity more thanunity. Thus the effective charge of an electron is actually smaller than its true value, and the charge decreases with increasing distance from the electron.[103][104] This polarization was confirmed experimentally in 1997 using the JapaneseTRISTAN particle accelerator.[105] Virtual particles cause a comparableshielding effect for the mass of the electron.[106]
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 (theanomalous magnetic moment).[85][107] The extraordinarily precise agreement of this predicted difference with the experimentally determined value is viewed as one of the great achievements ofquantum electrodynamics.[108]
The apparent paradox inclassical physics of a point particle electron having intrinsic angular momentum and magnetic moment can be explained by the formation ofvirtual 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 aszitterbewegung), which results in a net circular motion withprecession.[109] This motion produces both the spin and the magnetic moment of the electron.[14] In atoms, this creation of virtual photons explains theLamb shift observed inspectral lines.[103] The Compton Wavelength shows that near elementary particles such as the electron, the uncertainty of the energy allows for the creation of virtual particles near the electron. This wavelength explains the "static" of virtual particles around elementary particles at a close distance.
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 byCoulomb's inverse square law.[110]: 58–61 When an electron is in motion, it generates amagnetic field.[100]: 140 TheAmpère–Maxwell law relates the magnetic field to the mass motion of electrons (thecurrent) with respect to an observer. This property of induction supplies the magnetic field that drives anelectric motor.[111] The electromagnetic field of an arbitrary moving charged particle is expressed by theLiénard–Wiechert potentials, which are valid even when the particle's speed is close to that of light (relativistic).[110]: 429–434
A particle with chargeq (at left) is moving with velocityv through a magnetic fieldB that is oriented toward the viewer. For an electron,q is negative, so it follows a curved trajectory toward the top.
When an electron is moving through a magnetic field, it is subject to theLorentz force that acts perpendicularly to the plane defined by the magnetic field and the electron velocity. Thiscentripetal force causes the electron to follow ahelical trajectory through the field at a radius called thegyroradius. The acceleration from this curving motion induces the electron to radiate energy in the form of synchrotron radiation.[112][f][100]: 160 The energy emission in turn causes a recoil of the electron, known as theAbraham–Lorentz–Dirac Force, which creates a friction that slows the electron. This force is caused by aback-reaction of the electron's own field upon itself.[113]
Here,Bremsstrahlung is produced by an electrone deflected by the electric field of an atomic nucleus. The energy changeE2 − E1 determines the frequencyf of the emitted photon.
Photons mediate electromagnetic interactions between particles inquantum electrodynamics. An isolated electron at a constant velocity cannot emit or absorb a real photon; doing so would violateconservation of energy andmomentum. Instead, virtual photons can transfer momentum between two charged particles. This exchange of virtual photons, for example, generates the Coulomb force.[114] Energy emission can occur when a moving electron is deflected by a charged particle, such as a proton. The deceleration of the electron results in the emission ofBremsstrahlung radiation.[115]
An inelastic collision between a photon (light) and a solitary (free) electron is calledCompton 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 theCompton shift.[g] The maximum magnitude of this wavelength shift ish/mec, which is known as theCompton wavelength.[116] For an electron, it has a value of2.43×10−12 m.[80] When the wavelength of the light is long (for instance, the wavelength of thevisible light is 0.4–0.7 μm) the wavelength shift becomes negligible. Such interaction between the light and free electrons is calledThomson scattering or linear Thomson scattering.[117]
The relative strength of the electromagnetic interaction between two charged particles, such as an electron and a proton, is given by thefine-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 byα ≈ 0.007297353,[118] which is approximately equal to1/137.
When electrons and positrons collide, theyannihilate each other, giving rise to two or more gamma ray photons. If the electron and positron have negligible momentum, apositronium atom can form before annihilation results in two or three gamma ray photons totalling 1.022 MeV.[119][120] On the other hand, a high-energy photon can transform into an electron and a positron by a process calledpair production, but only in the presence of a nearby charged particle, such as a nucleus.[121][122]
In the theory ofelectroweak interaction, theleft-handed component of electron's wavefunction forms aweak isospin doublet with theelectron neutrino. This means that duringweak interactions, electron neutrinos behave like electrons. Either member of this doublet can undergo acharged current interaction by emitting or absorbing a W 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 ofbeta decay in aradioactive atom. Both the electron and electron neutrino can undergo aneutral current interaction via a Z0 exchange, and this is responsible for neutrino–electronelastic scattering.[123]
Probability densities for the first few hydrogen atom orbitals, seen in cross-section. The energy level of a bound electron determines the orbital it occupies, and the color reflects the probability of finding the electron at a given position.
An electron can bebound 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 anion. The wave-like behavior of a bound electron is described by a function called anatomic orbital. Each orbital has its own set of quantum numbers such as energy, angular momentum and projection of angular momentum, and 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 theirspin quantum number.
Electrons can transfer between different orbitals by the emission or absorption of photons with an energy that matches the difference in potential.[124]: 159–160 Other methods of orbital transfer include collisions with particles, such as electrons, and theAuger effect.[125] To escape the atom, the energy of the electron must be increased above itsbinding energy to the atom. This occurs, for example, with thephotoelectric effect, where an incident photon exceeding the atom'sionization energy is absorbed by the electron.[124]: 127–132
The orbital angular momentum of electrons isquantized. 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.[126]
Thechemical bond between atoms occurs as a result of electromagnetic interactions, as described by the laws of quantum mechanics.[127] The strongest bonds are formed by thesharing ortransfer of electrons between atoms, allowing the formation ofmolecules.[17] Within a molecule, electrons move under the influence of several nuclei, and occupymolecular orbitals; much as they can occupy atomic orbitals in isolated atoms.[128] A fundamental factor in these molecular structures is the existence ofelectron pairs. These are electrons with opposed spins, allowing them to occupy the same molecular orbital without violating the Pauli exclusion principle (much like in atoms). Different molecular orbitals have different spatial distribution of the electron density. For instance, in bonded pairs (i.e. in the pairs that actually bind atoms together) electrons can be found with the maximal probability in a relatively small volume between the nuclei. By contrast, in non-bonded pairs electrons are distributed in a large volume around nuclei.[129]
Alightning discharge consists primarily of a flow of electrons.[130] The electric potential needed for lightning can be generated by a triboelectric effect.[131][132]
If a body has more or fewer electrons than are required to balance the positive charge of the nuclei, then that object has a net electric charge. When there is an excess of electrons, the object is said to be negatively charged. When there are fewer electrons than the number of protons in nuclei, 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 thetriboelectric effect.[133]
Independent electrons moving in vacuum are termedfree 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.[134] When free electrons—both in vacuum and metals—move, they produce anet flow of charge called anelectric current, which generates a magnetic field. Likewise a current can be created by a changing magnetic field. These interactions are described mathematically byMaxwell's equations.[135]
At a given temperature, each material has anelectrical conductivity that determines the value of electric current when anelectric potential is applied. Examples of good conductors include metals such as copper and gold, whereas glass andTeflon are poor conductors. In anydielectric material, the electrons remain bound to their respective atoms and the material behaves as aninsulator. Mostsemiconductors have a variable level of conductivity that lies between the extremes of conduction and insulation.[136] On the other hand,metals have anelectronic band structure containing partially filled electronic bands. The presence of such bands allows electrons in metals to behave as if they were free ordelocalized electrons. These electrons are not associated with specific atoms, so when an electric field is applied, they are free to move like a gas (calledFermi gas)[137] through the material much like free electrons.
Because of collisions between electrons and atoms, thedrift 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, thevelocity of propagation, is typically about 75% of light speed.[138] This occurs because electrical signals propagate as a wave, with the velocity dependent on thedielectric constant of the material.[139]
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 theWiedemann–Franz law,[137] which states that the ratio ofthermal conductivity to the electrical conductivity is proportional to the temperature. The thermal disorder in the metallic lattice increases the electricalresistivity of the material, producing a temperature dependence for electric current.[140]
When cooled below a point called thecritical temperature, materials can undergo a phase transition in which they lose all resistivity to electric current, in a process known assuperconductivity. InBCS theory, pairs of electrons calledCooper pairs have their motion coupled to nearby matter via lattice vibrations calledphonons, thereby avoiding the collisions with atoms that normally create electrical resistance.[141] (Cooper pairs have a radius of roughly 100 nm, so they can overlap each other.)[142] However, the mechanism by whichhigher temperature superconductors operate remains uncertain.
Electrons inside conducting solids, which are quasi-particles themselves, when tightly confined at temperatures close toabsolute zero, behave as though they had split into three otherquasiparticles:spinons,orbitons andholons.[143][144] The former carries spin and magnetic moment, the next carries its orbital location while the latter electrical charge.
According toEinstein's theory ofspecial relativity, as an electron's speed approaches thespeed of light, from an observer's point of view itsrelativistic mass increases, thereby making it more and more difficult to accelerate it from within 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 toc—are injected into a dielectric medium such as water, where the local speed of light is significantly less thanc, the electrons temporarily travel faster than light in the medium. As they interact with the medium, they generate a faint light calledCherenkov radiation.[145]
Lorentz factor as a function of velocity. It starts at value 1 and goes to infinity asv approachesc.
The effects of special relativity are based on a quantity known as theLorentz factor, defined as wherev is the speed of the particle. The kinetic energyKe of an electron moving with velocityv is:
whereme is the mass of electron. For example, theStanford linear accelerator canaccelerate an electron to roughly 51 GeV.[146]Since an electron behaves as a wave, at a given velocity it has a characteristicde Broglie wavelength. This is given byλe = h/p whereh is thePlanck constant andp is the momentum.[60] For the 51 GeV electron above, the wavelength is about2.4×10−17 m, small enough to explore structures well below the size of an atomic nucleus.[147]
Pair production of an electron and positron, caused by the close approach of a photon with an atomic nucleus. The lightning symbol represents an exchange of a virtual photon, thus an electric force acts. The angle between the particles is very small.[148]
TheBig Bang theory is the most widely accepted scientific theory to explain the early stages in the evolution of the Universe.[149] For the first millisecond of the Big Bang, the temperatures were over 10 billion kelvins and photons had mean energies over a millionelectronvolts. These photons were sufficiently energetic that they could react with each other to form pairs of electrons and positrons. Likewise, positron–electron pairs annihilated each other and emitted energetic photons:
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.[150]
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 asbaryon asymmetry, resulting in a net charge of zero for the universe.[151][152] The surviving protons and neutrons began to participate in reactions with each other—in the process known asnucleosynthesis, forming isotopes of hydrogen andhelium, with trace amounts oflithium. This process peaked after about five minutes.[153] Any leftover neutrons underwent negativebeta decay with a half-life of about a thousand seconds, releasing a proton and electron in the process,
For about the next300000–400000 years, the excess electrons remained too energetic to bind withatomic nuclei.[154] What followed is a period known asrecombination, when neutral atoms were formed and the expanding universe became transparent to radiation.[155]
Roughly one million years after the big bang, the first generation ofstars began to form.[155] 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 ofstellar 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.[156] An example is thecobalt-60 (60Co) isotope, which decays to formnickel-60 (60 Ni ).[157]
An extended air shower generated by an energetic cosmic ray striking the Earth's atmosphere
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 calledquantum tunnelling. Thegravitational 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.[159] In exchange, the other member of the pair is given negative energy, which results in a net loss of mass–energy by the black hole. The rate of Hawking radiation increases with decreasing mass, eventually causing the black hole to evaporate away until, finally, it explodes.[160]
Cosmic rays are particles traveling through space with high energies. Energy events as high as3.0×1020 eV have been recorded.[161] When these particles collide with nucleons in theEarth's atmosphere, a shower of particles is generated, includingpions.[162] More than half of the cosmic radiation observed from the Earth's surface consists ofmuons. The particle called a muon is a lepton produced in the upper atmosphere by the decay of a pion.
Remote observation of electrons requires detection of their radiated energy. For example, in high-energy environments such as thecorona of a star, free electrons form aplasma that radiates energy due toBremsstrahlung radiation. Electron gas can undergoplasma oscillation, which is waves caused by synchronized variations in electron density, and these produce energy emissions that can be detected by usingradio telescopes.[165]
Thefrequency of aphoton 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, distinctdark 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 thehydrogen 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.[166][167]
In laboratory conditions, the interactions of individual electrons can be observed by means ofparticle detectors, which allow measurement of specific properties such as energy, spin and charge.[168] The development of thePaul trap andPenning trap allows charged particles to be contained within a small region for long durations. This enables precise measurements of the particle properties. For example, in one instance a Penning trap was used to contain a single electron for a period of 10 months.[169] The magnetic moment of the electron was measured to a precision of eleven digits, which, in 1980, was a greater accuracy than for any other physical constant.[170]
The first video images of an electron's energy distribution were captured by a team atLund University in Sweden, February 2008. The scientists used extremely short flashes of light, calledattosecond pulses, which allowed an electron's motion to be observed for the first time.[171][172]
The distribution of the electrons in solid materials can be visualized byangle-resolved photoemission spectroscopy (ARPES). This technique employs the photoelectric effect to measure thereciprocal 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.[173]
Electron beams are used inwelding.[175] They allow energy densities up to107 W·cm−2 across a narrow focus diameter of0.1–1.3 mm and usually require no filler material. This welding technique must be performed in a vacuum to prevent the electrons from interacting with the gas before reaching their target, and it can be used to join conductive materials that would otherwise be considered unsuitable for welding.[176][177]
Electron-beam lithography (EBL) is a method of etching semiconductors at resolutions smaller than amicrometer.[178] This technique is limited by high costs, slow performance, the need to operate the beam in the vacuum and the tendency of the electrons to scatter in solids. The last problem limits the resolution to about 10 nm. For this reason, EBL is primarily used for the production of small numbers of specializedintegrated circuits.[179]
Electron beam processing is used to irradiate materials in order to change their physical properties orsterilize medical and food products.[180] Electron beams fluidise or quasi-melt glasses without significant increase of temperature on intensive irradiation: e.g. intensive electron radiation causes a many orders of magnitude decrease of viscosity and stepwise decrease of its activation energy.[181]
Linear particle accelerators generate electron beams for treatment of superficial tumors inradiation therapy.Electron therapy can treat such skin lesions asbasal-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 byX-rays.[182][183]
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 theSokolov–Ternov effect.[h] Polarized electron beams can be useful for various experiments.Synchrotron radiation can alsocool 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, whichparticle physics studies.[184]
Low-energy electron diffraction (LEED) is a method of bombarding a crystalline material with acollimated 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 20–200 eV.[185] Thereflection high-energy electron diffraction (RHEED) technique uses the reflection of a beam of electrons fired at various low angles to characterize the surface of crystalline materials. The beam energy is typically in the range 8–20 keV and the angle of incidence is 1–4°.[186][187]
Theelectron 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.[188] In blue light, conventionaloptical microscopes have a diffraction-limited resolution of about 200 nm.[189] By comparison, electron microscopes are limited by thede Broglie wavelength of the electron. This wavelength, for example, is equal to 0.0037 nm for electrons accelerated across a 100,000-volt potential.[190] TheTransmission Electron Aberration-Corrected Microscope is capable of sub-0.05 nm resolution, which is more than enough to resolve individual atoms.[191] This capability makes the electron microscope a useful laboratory instrument for high resolution imaging. However, electron microscopes are expensive instruments that are costly to maintain.
Two main types of electron microscopes exist:transmission andscanning. Transmission electron microscopes function likeoverhead projectors, with a beam of electrons passing through a slice of material then being projected by lenses on aphotographic slide or acharge-coupled device. Scanning electron microscopesrasteri 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. Thescanning 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.[192][193][194]
In thefree-electron laser (FEL), arelativistic electron beam passes through a pair ofundulators that contain arrays ofdipole magnets whose fields point in alternating directions. The electrons emit synchrotron radiation thatcoherently interacts with the same electrons to strongly amplify the radiation field at theresonance frequency. FEL can emit a coherent high-brilliance electromagnetic radiation with a wide range of frequencies, frommicrowaves to soft X-rays. These devices are used in manufacturing, communication, and in medical applications, such as soft tissue surgery.[195]
Electrons are important incathode-ray tubes, which have been extensively used as display devices in laboratory instruments,computer monitors andtelevision sets.[196] In aphotomultiplier tube, every photon striking thephotocathode initiates an avalanche of electrons that produces a detectable current pulse.[197]Vacuum tubes use the flow of electrons to manipulate electrical signals, and they played a critical role in the development of electronics technology. However, they have been largely supplanted bysolid-state devices such as thetransistor.[198]
^The classical electron radius is derived as follows. Assume that the electron's charge is spread uniformly throughout a spherical volume. Since one part of the sphere would repel the other parts, the sphere contains electrostatic potential energy. This energy is assumed to equal the electron'srest energy, defined byspecial relativity (E = mc2). Fromelectrostatics theory, thepotential energy of a sphere with radiusr and chargee is given by:
whereε0 is thevacuum permittivity. For an electron with rest massm0, the rest energy is equal to:
wherec is the speed of light in vacuum. Setting them equal and solving forr gives the classical electron radius. See: Haken, Wolf, & Brewer (2005).
^Radiation from non-relativistic electrons is sometimes termedcyclotron radiation.
^The change in wavelength, Δλ, depends on the angle of the recoil,θ, as follows,
wherec is the speed of light in vacuum andme is the electron mass. See Zombeck (2007).[81]: 393, 396
^The polarization of an electron beam means that the spins of all electrons point into one direction. In other words, the projections of the spins of all electrons onto their momentum vector have the same sign.
^Okamura, Sōgo (1994).History of Electron Tubes. IOS Press. p. 11.ISBN978-90-5199-145-1.Archived from the original on 11 May 2016. Retrieved29 May 2015.In 1881, Stoney named this electromagnetic 'electrolion'. It came to be called 'electron' from 1891. [...] In 1906, the suggestion to call cathode ray particles 'electrions' was brought up but through the opinion of Lorentz of Holland 'electrons' came to be widely used.
^O'Hara, J. G. (March 1975). "George Johnstone Stoney, F.R.S., and the Concept of the Electron".Notes and Records of the Royal Society of London.29 (2). Royal Society:265–276.doi:10.1098/rsnr.1975.0018.JSTOR531468.S2CID145353314.
^Murayama, H. (10–17 March 2006).Supersymmetry Breaking Made Easy, Viable and Generic. Proceedings of the XLIInd Rencontres de Moriond on Electroweak Interactions and Unified Theories. La Thuile, Italy.arXiv:0709.3041.Bibcode:2007arXiv0709.3041M. – lists a 9% mass difference for an electron that is the size of thePlanck distance.
^Sather, E. (Spring–Summer 1996)."The Mystery of Matter Asymmetry"(PDF).Beam Line. Stanford University.Archived(PDF) from the original on 12 October 2008. Retrieved1 November 2008.
^Burles, S.; Nollett, K.M.; Turner, M.S. (1999). "Big-Bang Nucleosynthesis: Linking Inner Space and Outer Space".arXiv:astro-ph/9903300.
^Ozdemir, F.S. (25–27 June 1979).Electron beam lithography. Proceedings of the 16th Conference on Design automation. San Diego, CA:IEEE Press. pp. 383–391. Retrieved16 October 2008.
^Beddar, A.S.; Domanovic, Mary Ann; Kubu, Mary Lou; Ellis, Rod J.; Sibata, Claudio H.; Kinsella, Timothy J. (2001). "Mobile linear accelerators for intraoperative radiation therapy".AORN Journal.74 (5):700–705.doi:10.1016/S0001-2092(06)61769-9.PMID11725448.
^Flegler, S.L.; Heckman, J.W. Jr.; Klomparens, K.L. (1995).Scanning and Transmission Electron Microscopy: An Introduction (Reprint ed.). Oxford University Press. pp. 43–45.ISBN978-0-19-510751-7.
^Kitzmiller, J.W. (1995).Television Picture Tubes and Other Cathode-Ray Tubes: Industry and Trade Summary. Diane Publishing. pp. 3–5.ISBN978-0-7881-2100-5.
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