Electron Explained

Electron
Composition:Elementary particle
Family:Fermion
Group:Lepton
Generation:First
Interaction:Gravity, Electromagnetic, Weak
Antiparticle:Positron (also called antielectron)
Theorized:Richard Laming (1838–51),
G. Johnstone Stoney (1874) and others.
Discovered:J. J. Thomson (1897)[1]
Symbol:,
Mass:
 u
[1822.888<span style="margin-left:0.25em">502</span><span style="margin-left:0.25em">04</span>(77)]-1 u[2]
0.510998910(13) MeV/c2
Electric Charge:−1 e[3]
Magnetic Moment:−1.00115965218111 μB

The electron is a subatomic particle that carries a negative electric charge. It has no known substructure and is believed to be a point particle. Electrons participate in gravitational, electromagnetic and weak interactions. Like its rest mass and elementary charge, the intrinsic angular momentum (or spin) of an electron has a constant value. In the collision of an electron and a positron, the electron's antiparticle, both are annihilated. An electron–positron pair can be produced from gamma ray photons with sufficient energy.[4]

The concept of an indivisible amount of electrical charge was theorized to explain the chemical properties of atoms, beginning in 1838 by British natural philosopher Richard Laming; the name electron was introduced for this charge in 1894 by Irish physicist George Johnstone Stoney. The electron was identified as a particle in 1897 by J. J. Thomson and his team of British physicists.[1] [5] Electrons are identical particles that belong to the first generation of the lepton particle family. Electrons have quantum mechanical properties of both a particle and a wave, so they can collide with other particles and be diffracted like light. Each electron occupies a quantum state that describes its random behavior upon measuring a physical parameter, such as its energy or spin orientation. Because they are a type of fermion, no two electrons can occupy the same quantum state; a property known as the Pauli exclusion principle.

In many physical phenomena, such as electricity, magnetism, and thermal conductivity, electrons play an essential role. An electron generates a magnetic field while moving, and it is deflected by external magnetic fields. When an electron is accelerated, it can absorb or radiate energy in the form of photons. Electrons, together with atomic nuclei made of protons and neutrons, make up atoms. However, electrons contribute less than 0.06% to an atom's total mass. The attractive Coulomb force between an electron and a proton causes electrons to be bound into atoms. The exchange, sharing or interaction of the electrons in two or more atoms is the main cause of chemical bonding.[6]

Electrons were created by the big bang, and they can be annihilated during stellar nucleosynthesis. Electrons are produced by Hawking radiation at the event horizon of a black hole and by cosmic rays entering the atmosphere. Radioactive isotopes can release an electron from an atomic nucleus as a result of negative beta decay. Laboratory instruments are capable of containing and observing individual electrons, while telescopes can detect electron plasma by its energy emission. Electron plasma has multiple applications, including welding, cathode ray tubes, electron microscopes, radiation therapy, lasers and particle accelerators.

Etymology

The ancient Greeks noticed that amber, a gemstone that is formed from the hardened sap of trees, attracted small objects when rubbed with fur; apart from lightning, this phenomenon was man's earliest experience of electricity.[7] In his 1600 treatise De Magnete, the English physician William Gilbert coined the New Latin term electricus, to refer to this property of attracting small objects after being rubbed.[8] Both electric and electricity are derived from the Latin ēlectrum, which came from the Greek word ēlektron (ήλεκτρον) for amber. The English name electron is a combination of the word electric and the suffix -on, with the latter now used to designate a subatomic particle, such as a proton or neutron.[9] [10]

History

See main article: History of electromagnetism.

During the period 1838–51, British natural philosopher Richard Laming conceived the idea that an atom is composed of a core of matter surrounded by subatomic particles that had unit electrical charges.[11] Beginning in 1846, German physicist William Weber theorized that electricity was composed of positively and negatively charged fluids, and their interaction was governed by the inverse square law. After studying the phenomenon of electrolysis in 1874, Irish physicist George Johnstone Stoney suggested that there existed a "single definite quantity of electricity", the charge of a monovalent ion. He was able to estimate the value of this elementary charge e by means of Faraday's laws of electrolysis.[12] However, Stoney believed these charges were permanently attached to atoms and could not be removed. In 1881, German physicist Hermann von Helmholtz argued that both positive and negative charges were divided into elementary parts, each of which "behaves like atoms of electricity".[13]

In 1894, Stoney coined the term electron to represent these elementary charges.

However, it was only at the end of the nineteenth century that these various concepts came together to form a unified theory based upon an electron as a fundamental component of matter.[14]

Discovery

During the 1870s, English chemist and physicist Sir William Crookes developed the first cathode ray tube to have a high vacuum inside.[15] He then showed that the luminescence rays appearing within the tube carried energy and moved from the cathode to the anode. 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.[16] [17] In 1879, he proposed that these properties could be explained by what he termed 'radiant matter'. He suggested that this was a fourth state of matter, consisting of negatively charged molecules that were being projected with high velocity from the cathode.[18]

The German-born British physicist Arthur Schuster expanded upon Crookes' experiments by placing metal plates in parallel to the cathode rays and applying an electrical potential between the plates. The field deflected the rays toward the positive plate, providing further evidence that the rays carried negative charge. By measuring the amount of deflection for a given level of current, in 1890 Schuster was able to estimate the charge-to-mass ratio of the ray components. However, this produced such an unexpectedly large value that little credence was given to his calculations at the time.[16]

In 1896, British physicist J. J. Thomson, with his colleagues John S. Townsend and H. A. Wilson,[1] performed experiments indicating that cathode rays really were unique particles, rather than waves, atoms or molecules as was believed earlier. Thomson made good estimates of both the charge e and the mass m, finding that cathode ray particles, which he called "corpuscles," had perhaps one thousandth of the mass of the least massive ion known: hydrogen. 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.[19] The name electron was again proposed for these particles by the Irish physicist George F. Fitzgerald, and it has since gained universal acceptance.[16]

While studying naturally fluorescing minerals in 1896, 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 New Zealand physicist Ernest Rutherford who discovered they emitted particles. He designated these particles alpha and beta, based on their ability to penetrate matter.[20] In 1900, Becquerel showed that the beta rays emitted by radium could be deflected by an electrical field, and that their mass-to-charge ratio was the same as for cathode rays.[21] This evidence strengthened the view that electrons existed as components of atoms.[22] [23]

The electron's charge was more carefully measured by American physicist Robert Millikan in his oil-drop experiment of 1909 (published in 1911). This experiment used an electrical field to prevent a charged droplet of oil from falling as a result of gravity. This device could measure the electrical 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 a clouds of charged water droplets generated by electrolysis,[1] and in 1911 by Abram Ioffe, who independently obtained the same result as Millikan using charged microparticles of metals (published in 1913).[24] [25] However, oil drops were more stable than water drops due to their slower evaporation rate, and thus more suited to precise experimentation over longer periods of time.[26]

Around the beginning of the twentieth century, it was found that under certain conditions a charged particle caused a condensation of water vapor. In 1911, Charles Wilson used this principle to devise his cloud chamber, allowing the tracks of charged particles, such as fast-moving electrons, to be photographed. This and subsequent particle detectors allowed electrons to be studied individually, rather than in bulk as had been the case before.[27]

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 the energy determined by the angular momentum of the electron's orbits about the nucleus. The electrons could move between these states, or orbits, by the emission or absorption of photons at specific frequencies. By means of these quantized orbits, he accurately explained the spectral lines of hydrogen that were formed when the gas is energized by heat or electricity.[28] However, Bohr's model failed to account for the relative intensities of the spectral lines and it was unsuccessful in explaining the spectrum of more complex atoms.[29]

Chemical bonds between atoms were explained in 1916 by Gilbert Newton Lewis, as the interactions between their constituent electrons.[30] As the chemical properties of the elements were known to largely repeat themselves according to the periodic law,[31] in 1919 the American chemist Irving Langmuir suggested that this could be explained if the electrons in an atom were connected or clustered. Groups of electrons were thought to occupy a set of electron shells about the nucleus, providing the necessary clustering.[32]

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 inhabited 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.)[33] However, what physicists lacked was a physical mechanism to explain the fourth parameter, which had two possible values. This was provided by the Dutch physicists Abraham Goudsmith and George Uhlenbeck when they suggested that an electron, in addition to the angular momentum of its orbit, could possess an intrinsic angular momentum.[29] [34] This property became known as spin, and it explained the previously mysterious splitting of spectral lines observed with a high resolution spectrograph; a phenomenon known as fine structure splitting.[35]

Quantum mechanics

See also: History of quantum mechanics. During his 1924 dissertation French: Recherches sur la théorie des quanta, French physicist Louis de Broglie hypothesized that all matter possesses a wave–particle duality similar to light: the de Broglie hypothesis.[36] That is, under the appropriate conditions, electrons and other matter would show properties of either particles or waves. The classical properties of a particle are demonstrated when it is shown to have a localized position in space at each moment in time and a trajectory that is subject to modification by external forces.[37] The wave-like nature is observed, for example, when a beam of light is passed through parallel slits and creates interference patterns. In 1927, the interference effect was demonstrated with a beam of electrons; by English physicist George Paget Thomson with a thin metal film and by American physicists Clinton Davisson and Lester Germer using a crystal of nickel.[38]

The success of de Broglie's prediction led to the publication, by Erwin Schrödinger in 1926, of the equation named after him that successfully describes how electron waves propagated.[39] Rather than yielding a solution that determines the location of an electron over time, this wave equation can be used to predict the probability of finding an electron near a position. This approach became the theory of quantum mechanics, which provided an almost exact derivation to the energy states of an electron in a hydrogen atom.[40]

In 1928, building on Wolfgang Pauli's work, Paul Dirac formulated the Dirac equation. This provided the wavefunction of an electron moving at velocities close to the speed of light.[41] Once spin and the interaction between multiple electrons was also considered, this work allowed the configuration of electrons in atoms with higher atomic numbers than hydrogen to be successfully predicted. However, for atoms with multiple electrons, the exact solution to the wave equation is much more complicated, so approximations are necessary.[42]

In 1930 Paul Dirac developed a model of the vacuum as an infinite sea of particles having negative energy, which was dubbed the Dirac sea. This led him to predict the existence of a positron, the antimatter counterpart of the electron.[43] This particle was discovered in 1932 by Carl D. Anderson. He proposed calling standard electrons negatrons, and using electron as a generic term to describe both the positively and negatively charged variants. This usage of the term 'negatron' is still occasionally encountered today, and it may be shortened to 'negaton'.[44] [45]

The first experimental discrepancy in this theory was discovered in 1947 by Willis Lamb, working in collaboration with graduate student Robert Retherford. They found that certain energy levels of hydrogen that should have the same value, were shifted relative to each other - the Lamb shift. About the same time, Polykarp Kusch, working with Henry M. Foley,discovered the anomalous magnetic dipole moment of the electron, which produced a larger than expected value for the magnetic moment. To resolve these issues, a refined version of the quantum electrodynamics theory was developed by Sin-Itiro Tomonaga, Julian Schwinger andRichard P. Feynman.[46]

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.[47] The first successful attempt to accelerate electrons using magnetic induction was made in 1942 by Donald Kerst. His initial betatron reached energies of 2.3 MeV (million electron volts), while subsequent betatrons achieved 300 MeV. In 1947, synchrotron radiation was discovered with a 70 MeV electron synchrotron at General Electric. This radiation was caused by the acceleration of electrons, moving near the speed of light, through a magnetic field.[48]

With a beam energy of 1.5 GeV, the first high-energyparticle collider was ADONE, which began operations in 1968.[49] This device accelerated electrons and positrons - the antiparticle of the electron - in opposite directions, effectively doubling the energy of their collision when compared to striking a static target with an electron.[50] TheLarge Electron-Positron Collider (LEP) at CERN, which was operational from 1989 to 2000, achieved collision energies of 209 GeV and made important measurements for the Standard Model of particle physics.[51] [52]

Characteristics

Classification

The electron belongs to the group of subatomic particles called leptons, which are believed to be fundamental particles. Electrons have the lowest mass of any electrically charged lepton. In the Standard Model of particle physics, the electron is the first-generation charged lepton.[53]

If the spin of the electron is oriented in the same direction as its momentum, it is called a right-handed spin; otherwise it is left-handed. Thus the same electron can have left or right-handed spin, depending on its velocity with respect to an observer. The left-handed spin component of the electron forms a weak isospin doublet with the electron neutrino, which is an uncharged, first generation lepton with little or no mass.[54] The right-handed component of the electron spin is an isospin singlet.[55]

The electron is very similar to the two charged leptons of higher generations, the muon and the tauon, which are identical in charge, spin, and interaction, but are more massive. All members of the lepton group belong to the family of fermions. This family includes all elementary particles with half-odd integer spin; the electron has spin . Leptons differ from the other basic constituent of matter, the quarks, by their lack of strong interaction.[56]

Fundamental properties

The mass of a stationary electron is approximately, or . Based on Einstein's principle of mass–energy equivalence, this mass corresponds to an energy of 0.511 MeV. The ratio between the mass of a proton and that of an electron is about 1836.[57] This ratio is one of the fundamental constants of physics, and the Standard Model of particle physics assumes this and other constants are unchanging. Astronomical measurements show that the ratio has held the same value for at least half the age of the universe.[58]

Electrons have an electric charge of,[59] which is used as a standard unit of elementary charge for subatomic particles. Within the limits of experimental accuracy, the electron charge is identical to the charge of a proton, but with the opposite sign.[60] As the symbol e is used for the constant of electrical charge, the electron is commonly symbolized by, where the minus sign indicates the negative charge. The positron is symbolized by because it has the same properties as the electron but with a positive rather than negative charge.[59] [56]

The electron is described as a fundamental or elementary particle. It has no known substructure.[61] [62] Hence, it is defined or assumed to be a point charge with no spatial extent; a point particle.[63] Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10-22 meters.[64] The classical electron radius is . This is the radius that is inferred from the electron's electric charge, by assuming that its mass energy has exclusively electrostatic origin and using the classical theory of electrodynamics alone ignoring quantum mechanics.[65]

There are elementary particles that spontaneously decay into different particles. An example is the muon, which decays into an electron, a neutrino and an antineutrino, with a half life of . However, the electron is thought to be stable on theoretical grounds; an electron decaying into a neutrino and photon would mean that electric charge is not conserved.[66] The experimental lower bound for the electron's mean lifetime is, with a 90% confidence interval.[67]

Quantum mechanics

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 an electron is described mathematically by a complex-valued function of the position, the wavefunction, commonly denoted by the Greek letter psi (ψ). When the absolute value of this function is squared, it gives the probability that an electron will be observed near a location - the electron density.[68]

Electrons are identical particles because they can not 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 their condition. 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 variables r1 and r2 correspond to the first and second electrons, respectively. Since the absolute square is not changed by a sign swap, this corresponds to equal probabilities. Bosons, such as the photon, have symmetric wave functions instead.[68]

In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a zero probability that each pair will occupy the exact same location or state. This is responsible for the Pauli exclusion principle, which precludes any two electrons from occupying the same energy state. This principle explains many of the properties of electrons. For example, this causes groups of bound electrons to occupy different orbitals in an atom, rather than all overlapping each other in the same orbit.[68]

Virtual particles

Physicists believe that empty space may be continually creating pairs of virtual particles, such as a positron and electron, which rapidly annihilate each other shortly thereafter.[69] The net energy from this reaction is zero. 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 the Heisenberg uncertainty relation, ΔE

Δt. In effect, the energy needed to create these virtual particles, ΔE, can be "borrowed" from the vacuum for a period of time, Δt, such that their product is no more than the reduced Planck constant, . Thus, for a virtual electron, Δt is at most .[70]

While an electron-positron virtual pair is in existence, the coulomb force from the ambient electrical field surrounding an electron causes a created positron to be attracted to the original electron, while a created electron experiences a repulsion. This causes the two charged virtual particles to physically separate for a brief period before merging back together, and during this period they behave like an electric dipole. The combined effect of many such pair creations is to partially shield the charge of the electron, a process called vacuum polarization. Thus the effective charge of an electron is actually smaller than its true value, and the charge increases with decreasing distance from the electron.[71] [72] This polarization was confirmed experimentally in 1997 using the Japanese TRISTAN particle accelerator.[73]

A comparable shielding effect is seen for the mass of the electron. The equivalent rest energy consists of the mass-energy of the "bare" particle plus the energy of the surrounding electric field. In classical physics, the energy of the electric field is dependent upon the size of the charged object, which, for a dimensionless particle, results in an infinite energy. Instead, because of vacuum fluctuations, allowance must be made for an electron–positron pair appearing in the electric field and the positron annihilating the original electron; causing the virtual electron to become a real electron via the emitted photon. This interaction creates a negative energy imbalance that counteracts the radius-dependency of the electric field.[74] The total mass is referred to as the renormalized mass, because a mathematical technique called renormalization is used by physicists to relate the observed and bare mass of the electron. This method replaces the terms used to compute the mass with the actual mass found experimentally, thereby avoiding problems with divergences in the formulas.[75]

The electron has an intrinsic angular momentum of spin as measured in units of ħ, and an intrinsic magnetic moment along its spin axis.[59] The magnitude of the spin is ħ.[76] A measurement of its component along any axis can only be ±; this property is usually stated by referring to the electron as a spin- particle.

In classical physics, the angular momentum and magnetic moment of an object depends upon its physical dimensions. Hence, the concept of a dimensionless electron possessing these properties is unclear. A possible explanation lies in the formation of virtual photons in the electric field generated by the electron. These photons cause the electron to shift about in a jittery fashion (known as zitterbewegung),[77] which results in a net circular motion with precession. This motion produces both the spin and the magnetic moment of the electron.[63] [78] In atoms, this creation of virtual photons explains the Lamb shift observed in spectral lines.[71]

The magnetic moment associated with the orbital motion of an electron in an atom is expressed in terms of the Bohr magneton, which is a physical constant equal to .[59] The intrinsic angular momentum of an electron is almost equal to one Bohr magneton, with the 0.1% difference being explained by interaction with virtual particles and antiparticles.[79] [80] The extraordinarily precise agreement of this predicted difference with the experimentally determined value is viewed as one of the great achievements of modern physics.[81]

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 is determined by Coulomb's law.[82] The Coulomb force between charged particles is mediated by photons, which are quanta of the electromagnetic field.

An isolated electron that is not undergoing acceleration is unable to emit or absorb energy via a photon; doing so would violate conservation of energy and momentum. Instead, virtual photons can transfer momentum (but no net energy) between two charged particles. It is this exchange of virtual photons that generates the Coulombforce.[83] Energy emission can occur when a moving electron is deflected by a charged particle, such as a proton. The acceleration of the electron results in the emission of Bremsstrahlung radiation.[84]

The outcome of an elastic collision between a photon and a solitary electron is called Compton scattering. This collision results in a transfer of momentum between the particles, which modifies the wavelength of the photon by an amount called the Compton shift.[85] The maximum magnitude of this wavelength shift is h/mc, which is known as the Compton wavelength.[86] For an electron, it has a value of .[59]

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  7.297

353 , which is approximately equal to .[59]

When an electron is in motion, it generates a magnetic field.[87] This magnetic field is related to the motion of one or more electrons (the current) with respect to an observer by the Ampère-Maxwell law. It is this property of induction which supplies the magnetic field that drives an electric motor.[88] The electromagnetic field of an arbitrary moving charged particle is expressed by the Liénard-Wiechert Potentials, which are valid even when the particle's speed is close to that of light (or relativistic velocities).

When an electron is moving through a magnetic field, it is subject to the Lorentz force that exerts an influence in a direction perpendicular to the plane defined by the magnetic field and the electron velocity. This causes the electron to follow a helical trajectory through the field at a radius equal to the Gyroradius. The curving motion creates a centripetal force on the particle, and this acceleration causes the electron to radiate energy called synchrotron radiation.[89] [90] [91] The energy emission in turn causes a recoil of the electron, known as the Abraham-Lorentz-Dirac force, which creates a friction that slows the electron. This force is caused by a back-reaction of the electron's own field upon itself.[92]

In the theory of electroweak interaction, the left-handed spin component of the electron 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 W boson and be converted into the other member. Charge is conserved during this reaction because the W boson also carries a charge, cancelling 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 Z0 boson exchange, and this is responsible for neutrino-electron elastic scattering.[54]

When electrons and positrons collide, they annihilate each other, giving rise to two gamma ray photons emitted at roughly 180° to each other. If the electron and positron have negligible momentum, a positronium atom can form before annihilation results in two 0.511 MeV gamma ray photons.[93] [94] On the other hand, high-energy photons may transform into an electron and a positron by a process called pair production, but only in the presence of a nearby charged particle, such as a nucleus.[95] [96]

Atoms

See main article: article and Atom. An electron can be bound to the nucleus of an atom by the attractive coulomb force. The wave-like behavior of a bound electron is described by a function called an atomic orbital. An orbital consists of a set of quantum states that have a particular energy, and only a discrete set of these orbitals exist around the nucleus. Electrons can transfer between different orbitals by the emission or absorption of photons with an energy that matches the difference in potential.[97] Other methods of orbital transfer include collisions with particles, such as electrons, and the Auger effect.[98] In order to escape the atom, the energy of the electron must be increased above the atom's binding energy. This occurs, for example, with the photoelectric effect, where an incident photon exceeding the atom's ionization energy is absorbed by the electron.[99]

A bound electron gains a quantized angular momentum from its orbital state; this is analogous to the angular momentum of an orbit in classical mechanics. Because the electron is charged, this produces a magnetic moment that is proportional to the angular momentum. The net magnetic moment of an atom is equal to the vector sum of all its component orbital and spin magnetic moments. Pairs of electrons in an atom align their spins in opposite directions, giving them different spin quantum numbers that satisfy the Pauli exclusion principle. Thus the magnetic moments of an atom's paired electrons cancel each other out. The nucleus contributes a magnetic moment, but this is negligible compared to the effect from the electrons.[100]

The chemical bond between atoms occurs as a result of electromagnetic interactions, as described by the laws of quantum electrodynamics.[101] The strongest bonds are formed by the sharing or transfer of electrons between atoms, allowing the formation of molecules.[102] Within a molecule, electrons move under the influence of the collective nuclei, and occupy molecular orbitals; much as they can occupy atomic orbitals in isolated atoms.[103] A fundamental factor in these molecular structures is the existence of electron pairs. These are electrons with opposed spins, allowing them to occupy the same orbital without violating the Pauli exclusion principle. With high probability, a molecular system will contain pairs of electrons in localized regions of space.[104]

Conductivity

If a body has more or fewer electrons than are required to balance the positive charge of the nuclei, then that object has an electric charge. (For a single atom or molecule, the object is termed an ion.) When there is an excess of electrons, the object is said to be negatively charged. When there are fewer electrons than protons, 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 phenomenon of triboelectricity.[105]

Independent electrons moving in vacuum or certain media are termed free electrons. When free electrons move, they produce a net flow of charge called an electric current. A current of electrons acquires the cumulative electromagnetic properties of the individual particles, so it generates a magnetic field. Likewise a current can be created by a moving magnetic field. These interactions are described mathematically by Maxwell's equations.[106]

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. A material with metallic bonds has an electronic band structure that allows for delocalized electrons. These electrons are not associated with specific atoms, so when an electric field is applied, they are free to move like a gas (called Fermi gas)[107] through the material.

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,[107] 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 electrical current.[108]

Because of collisions between electrons and atoms, the drift velocity of electrons in a conductor is on the order of millimetres per second. However, the speed at which a current at one point in the material causes a current in other parts of the material, the velocity of propagation, is typically about 75% of light speed.[109] This occurs because electrical signals propagate as a wave, with the velocity dependent on the dielectric constant of the material.[110] In dielectric materials, the electrons remain bound to their respective atoms and the material behaves as an insulator. Semiconductors have a variable level of conductivity that lies between the extremes of conduction and insulation.[111]

When cooled below a point called the critical temperature, materials can undergo a phase transition in which they lose all resistivity to electrical current; a process known as superconductivity. In BCS theory, this behavior is modeled by pairs of electrons entering a quantum state known as a Bose–Einstein condensate. These Cooper pairs have their motion coupled to nearby matter via lattice vibrations called phonons, thereby avoiding the collisions with atoms that normally creates electrical resistance.[112] (Cooper pairs are separated by roughly 100 nm, so they can overlap each other.)[113] However, the mechanism by which higher temperature superconductors operate remains uncertain.

Motion and energy

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 from within the observer's frame of reference. The speed of an electron can approach, but never reach the speed of light in a 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.[114]

The effects of special relativity are based on a quantity known as the Lorentz factor, defined as γ = 1/ where v is the speed of the particle. The kinetic energy Ke of an electron moving with velocity v is:

\displaystyleKe=(\gamma-1)mec2

where me is the electron rest mass. For example, the Stanford linear accelerator can accelerate an electron to roughly 51 GeV.[115] This gives a value of 100,000 for γ, since the mass of an electron is 0.51 MeV/c2. The relativistic momentum of this electron is 100,000 times the momentum that classical mechanics would predict for an electron at the same speed.[116]

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 Planck's constant and p is the momentum.[36] For the 51 GeV electron above, the wavelength is about, small enough to explore structures well below the size of an atomic nucleus.[117]

Formation

The big bang theory is the most widely accepted scientific theory to explain the early stages in the evolution of the Universe.[118] For the first millisecond of the big bang, the temperatures were over 10 billion kelvins and photons had mean energies over a million electron volts. These photons were sufficiently energetic that they could react with each other to form pairs of electrons and positrons,

\gamma+\gamma\leftrightharpoonse++e-

where is a photon, is a positron and is an electron. Likewise, positron-electron pairs annihilated each other emitting energetic photons. An equilibrium between electrons, positrons and protons was maintained during this creation and destruction cycle. 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.[119]

For reasons that remain uncertain, during the process of leptogenesis there was an excess in the number of electrons over positrons.[120] Hence, about one electron in every billion survived the annihilation process. This excess matched the excess of protons over anti-protons, a condition known as baryon asymmetry, resulting in a net charge of zero for the universe.[121] [122] The surviving protons and neutrons begin to undergo nucleosynthesis, forming isotopes of hydrogen and helium, with trace amounts of lithium. This process peaked after about five minutes.[123] Any leftover neutrons underwent negative beta decay with a half-life of about a thousand seconds, releasing a proton and electron in the process,

n ⇒ p+e-+\bar{\nu}e

where is a neutron, is a proton and is an electron antineutrino. For about the next 300,000 - 400,000 years, the excess electrons remained too energetic to bind with atomic nuclei.[124] What followed is a period known as recombination, when atoms were formed and the expanding universe became transparent to radiation.[125]

Roughly one million years after the big bang, the first generation of stars began to form.[125] 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.[126] An example is the cobalt-60 (60Co) isotope, which decays to form nickel-60 (60Ni).[127]

At the end of their lifetime, stars with more than about 20 solar masses can undergo gravitational collapse to form a black hole.[128] According to classical physics, these massive stellar objects exert a gravitational attraction that is strong enough to prevent anything, including radiation, from escaping past the Schwarzschild radius. However, it is believed that quantum mechanical effects may allow Hawking radiation to be emitted at this distance. Electrons (and positrons) are thought to be created at the event horizon of these stellar remnants.

When pairs of virtual particles (such as an electron and positron) are created just inside the event horizon, the random spacial distribution of these particles may permit one of them to appear on the exterior; a process called quantum tunneling. 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.[129] 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.[130]

Cosmic rays are particles travelling through space with high energies. Energy events as high as have been recorded.[131] When these particles collide with nucleons in the Earth's atmosphere, a shower of particles is generated, including pions.[132] More than half of the cosmic radiation observed from the Earth's surface consists of muons. This particle is a lepton which is produced in the upper atmosphere by the decay of pions. Muons in turn can decay to form an electron or positron by means of the weak force. Thus, for the negatively charged pion,[133]

\displaystyle\pi- ⇒ \mu-+\nu\mu

\displaystyle\mu- ⇒ e-+\bar{\nu}e+\nu\mu

where is a muon and is a muon neutrino.

Observation

Remote observation of electrons requires the 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. Electron gas can undergo plasma oscillation, which are waves caused by synchronized variations in electron density, and these produce energy emissions that can be detected using radio telescopes.[134]

The frequency of a photon is proportional to its energy. As a bound electron transitions between different energy levels of an atom it will absorb or emit photons of characteristic frequencies. When atoms are radiated by a continuum of electromagnetic energy, this transition of electrons between quantum states will cause distinct absorption or emission bands to appear in the spectrum. Each element or molecule displays a characteristic set of spectral lines, such as the Hydrogen spectral series. Spectroscopic measurements of the strength and width of these lines allow the composition and physical properties of a substance to be determined.[135] [136]

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.[99] The development of the Paul trap and Penning trap allows charged particles to be contained within a small region for long durations. This allows for very precise measurements to be made of the particle properties. For example, in one instance the Penning trap was used to contain a single electron for a period of 10 months.[137] Measurements allowed the magnetic moment of the electron to be measured to a precision of eleven digits, which, in 1980, was a greater accuracy than for any other physical constant.[138]

The first video images of an electron's energy distribution were captured by a team at Lund University in Sweden, February 2008. To capture this phenomena, the scientists used extremely short flashes of light. To produce this light, newly developed technology for generating short pulses from intense laser light, called attosecond pulses, allowed the team at the university’s Faculty of Engineering to capture the electron's motion for the first time.[139] [140]

The distribution of the electrons in solid materials can be visualized by angle resolved photoemission spectroscopy (ARPES). This technique uses the photoelectric effect to measure the reciprocal space, a mathematical representation of periodic structures that can be used to infer the original structure. ARPES can be used to determine the direction, speed and scattering of electrons within the material.[141]

Plasma applications

Industry

There are specialized industrial applications that utilize free electrons. Electron beams are used in welding[142] and lithography.[143] Electron beam processing is used to irradiate products in order to change their material properties or sterilize medical and food products.[144] LEED and RHEED are surface-imaging techniques that use electron diffraction.[145]

Electrons are at the heart of cathode ray tubes, which are used extensively as display devices in laboratory instruments, computer monitors and television sets.[146] In a photomultiplier tube, one photon strikes the photocathode, initiating an avalanche of electrons that produces a detectable current.[147] Vacuum tubes used the flow of electron in a near vacuum to manipulate electrical signals, and they played a critical role in the development of electronics technology. However, vacuum tubes have been largely supplanted by solid-state devices such as the transistor.[148]

Laboratory

In blue light, conventional optical microscopes have a diffraction-limited resolution of about 100 nm. By comparison, electron microscopes are limited by the de Broglie wavelength of the electron. This is equal to 0.0037 nm for electrons accelerated across a 100,000 volt potential.[149] For example, the TEAM electron microscope is capable of 0.05 nm resolution: small enough to resolve individual atoms.[150] This makes the electron microscope a useful laboratory instrument for high resolution imaging. However, electron microscopes are expensive instruments that are costly to maintain. The high vacuum required to operate an electron microscope also prevents them from being used to observe living organisms.[151]

Transmission electron microscopes function in a manner similar to optical microscopes, with a beam of electrons passing through a material. The magnifications range from 1,000× to 1,000,000× or better. Quantum effects of electrons are used in the scanning tunneling microscope to study features on solid surfaces with lateral-resolution at the atomic scale of around 0.2 nm.[151] [152]

Particle accelerators use electrical fields to propel electrons and their antiparticles to high energies. As these particles pass through magnetic fields, they can emit synchrotron radiation by changing their spin orientation, a process known as the Sokolov-Ternov effect. This causes the particles to self-polarize, which can be useful for various experiments. Synchrotron radiation can be used for radiation damping, which reduces the spread of the particles. Magnets are then used to increase the momentum of the particles in the desired direction. Once the particles have accelerated to the required energies, separate electron and positron beams are brought into collision. The resulting energy emissions are observed with particle detectors and used to study particle physics.[153]

Other

In radiation therapy, electron beams are generated by linear accelerators for treatment of superficial tumors. Because an electron beam only penetrates to a limited depth before being absorbed, typically up to 5 cm for beams in the range 5–20 MeV, electron therapy is useful for treating skin lesions such as basal cell carcinomas. It is also used to supplement the treatment of areas that have been irradiated by X-rays.[154] [155]

In the free electron laser (FEL), a relativistic electron beam is passed through a laser cavity containing an array of magnetic fields that are oriented in alternating directions. The resulting synchrotron radiation from the electrons is emitted in a coherent form, creating a laser. FEL can emit a wide range of frequencies, from microwaves to soft X-rays. These devices are used for manufacturing, communication and various medical applications, such as soft tissue surgery.[156]

See also

Notes

  1. Book: Dahl, Per F.. Flash of the Cathode Rays: A History of J.J. Thomson's Electron. 1997. CRC Press. 0750304535. 122 - 185.
  2. The fractional version’s denominator is the inverse of the decimal value (along with its relative standard uncertainty of).
  3. The electron’s charge is the negative of elementary charge, which is a positive value for the proton.
  4. Book: Anastopoulos, Charis. 2008. Particle Or Wave: The Evolution of the Concept of Matter in Modern Physics. Princeton University Press. 236 - 237. 0691135126.
  5. Book: Wilson, Robert. 1997. Astronomy Through the Ages: The Story of the Human Attempt to Understand the Universe. 138. CRC Press. 0748407480.
  6. Web site: Freudenrich. Craig. 2000. How Atoms Work. How Stuff Works. 2008-09-17. See also the related categories on that web site.
  7. Book: Shipley, Joseph T.. 1945. Dictionary of Word Origins. 133. New York, N. Y.: The Philosophical Library.
  8. Book: Baigrie, Brian. 2006. Electricity and Magnetism: A Historical Perspective. Greenwood Press. 7 - 8. 0-3133-3358-0.
  9. Book: Soukhanov, Anne H. ed.. Word Mysteries & Histories. 1986. Houghton Mifflin Company. 73. Boston, MA. 0-395-40265-4.
  10. Book: Guralnik, David B. ed.. Webster's New World Dictionary. 1970. Prentice-Hall, Incorporated. 450. Englewood Cliffs, N. J..
  11. Farrar. W. V.. Richard Laming and the Coal-Gas Industry, with His Views on the Structure of Matter. Annals of Science. 1969. 25. 243–254. 10.1080/00033796900200141.
  12. Barrow. J. D.. Natural Units Before Planck. Royal Astronomical Society Quarterly Journal. 1983. 24. 24–26. 2008-08-30.
  13. Book: Arabatzis, Theodore. 2006. Representing Electrons: A Biographical Approach to Theoretical Entities. 70 - 74. University of Chicago Press. 0226024210.
  14. Book: Buchwald, Jed Z.. Warwick, Andrew. Histories of the Electron: The Birth of Microphysics. 2001. MIT Press. 0262524244. 195 - 203.
  15. DeKosky. Robert. William Crookes and the quest for absolute vacuum in the 1870s. Annals of Science. 1983. 40. 1. 1–18. 10.1080/00033798300200101.
  16. Book: Leicester, Henry M.. 1971. The Historical Background of Chemistry. Courier Dover Publications. 0486610535. 221 - 222.
  17. Book: Dahl, Per F.. 1997. Flash of the Cathode Rays: A History of J. J. Thomson's Electron. CRC Press. 64–78. 0750304537.
  18. Zekman, P.. Sir William Crookes, F.R.S.. Nature. 1907. 77. 1984. 1–3. 2008-08-25. 10.1038/077001a0.
  19. Web site: Thomson. J. J.. 1906-12-11. Lecture, The Nobel Prize in Physics 1906. The Nobel Foundation. 2008-08-25.
  20. Trenn. Thaddeus J.. Rutherford on the Alpha-Beta-Gamma Classification of Radioactive Rays. Isis. March. 1976. 67. 1. 61–75. 2008-09-04. 10.1086/351545.
  21. Becquerel. Henri. Déviation du Rayonnement du Radium dans un Champ Électrique. Comptes Rendus de l'Académie des Sciences. 1900. 130. 809–815. French.
  22. [#refBaW2001|Buchwald and Warwick (2001:90-91).]
  23. Myers. William G.. Becquerel's Discovery of Radioactivity in 1896. Journal of Nuclear Medicine. 1976-07-01. 17. 7. 579–582. 2008-09-04. 775027.
  24. Kikoin. I. K.. Sominskiĭ, M. S.. Abram Fedorovich Ioffe (on his eightieth birthday). Soviet Physics Uspekhi. 1961. 3. 798-809. 10.1070/PU1961v003n05ABEH005812.
  25. Web site: Kizilova. Anna. Abram Ioffe (biography. Russia-InfoCentre. 2006-09-22.
  26. Millikan. R. A.. The Isolation of an Ion, a Precision Measurement of its Charge, and the Correction of Stokes's Law. Physical Review. 1911. 32. 2. 349–397. 10.1103/PhysRevSeriesI.32.349.
  27. Das Gupta. N. N.. Ghosh, S. K.. A Report on the Wilson Cloud Chamber and Its Applications in Physics. Reviews of Modern Physics. 1999. 18. 225–290. 10.1103/RevModPhys.18.225.
  28. Web site: Bohr. Niels. 1922-12-11. Nobel Lecture: The Structure of the Atom. The Nobel Foundation. 2008-12-03.
  29. Book: Smirnov, Boris M.. 2003. Physics of Atoms and Ions. 14 - 21. Springer. 038795550X.
  30. Lewis. Gilbert N.. The Atom and the Molecule. Journal of the American Chemical Society. April. 1916. 38. 4. 762–786. 10.1021/ja02261a002.
  31. Book: Scerri, Eric R.. 2007. The Periodic Table. Oxford University Press US. 0195305736. 205–226.
  32. Langmuir. Irving. The Arrangement of Electrons in Atoms and Molecules. Journal of the American Chemical Society. 1919. 41. 6. 868–934. 2008-09-01. 10.1021/ja02227a002.
  33. Book: Massimi, Michela. 2005. Pauli's Exclusion Principle, The Origin and Validation of a Scientific Principle. Cambridge University Press. 7 - 8. 0521839114.
  34. Uhlenbeck. G. E.. Goudsmith, S.. Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons. Die Naturwissenschaften. 1925. 13. 47. German. 2008-09-02.
  35. W.. Pauli. Über die Gesetzmäßigkeiten des anomalen Zeemaneffektes. Zeitschrift für Physik. 1923. 16. 1. 155–164. German. 2008-09-02. 10.1007/BF01327386.
  36. Web site: de Broglie. Louis. 1929-12-12. Lecture, The Nobel Prize in Physics 1929. Nobel Foundation. 2008-08-30.
  37. Book: Falkenburg, Brigitte. 2007. Particle Metaphysics: A Critical Account of Subatomic Reality. Springer. 85. 3540337318.
  38. Web site: Davisson. Clinton. 1937-12-13. Lecture, The Nobel Prize in Physics 1937. Nobel Foundation. 2008-08-30.
  39. Schrödinger. Erwin. Quantisierung als Eigenwertproblem. Annalen der Physik. 1926. 385. 13. 437–490. German. 2008-08-31. 10.1002/andp.19263851302.
  40. Book: Rigden, John S.. 2003. Hydrogen. Harvard University Press. 59–86. 0674012526.
  41. Dirac. P. A. M.. The Quantum Theory of the Electron. Proceedings of the Royal Society of London. Series A. 1928-02-01. 117. 778. 610–624. 10.1098/rspa.1928.0023.
  42. Book: Reed, Bruce Cameron. 2007. 275–350. Quantum Mechanics. 0763744514. Jones & Bartlett Publishers.
  43. Web site: Dirac. Paul A. M.. 1933-12-12. Theory of Electrons and Positrons. The Nobel Foundation. 2008-11-01.
  44. Book: Kragh, Helge. 132. 2002. Princeton University Press. Quantum Generations: A History of Physics in the Twentieth Century. 0691095523.
  45. Book: Gaynor, Frank. 1950. Concise Encyclopedia of Atomic Energy. Philosophical Library. 117. New York.
  46. Web site: The Nobel Prize in Physics 1965. The Nobel Foundation. 2008-11-04.
  47. Web site: Panofsky. Wolfgang K. H.. 1997. The Evolution of Particle Accelerators & Colliders. PDF. Stanford University. 2008-09-15.
  48. Elder. F. R.. Gurewitsch, A. M.; Langmuir, R. V.; Pollock, H. C.. Radiation from Electrons in a Synchrotron. Physical Review. 1947. 71. 11. 829–830. 10.1103/PhysRev.71.829.5.
  49. Book: Hoddeson, Lillian. Brown, Laurie; Riordan, Michael; Dresden, Max. The Rise of the Standard Model: Particle Physics in the 1960s and 1970s. Cambridge University Press. 1997. 25 - 26. 0521578167.
  50. Bernardini. Carlo. AdA:The First Electron-Positron Collider. Physics in Perspective. 2004. 6. 2. 156–183. 2008-09-15. 10.1007/s00016-003-0202-y.
  51. Web site: Staff. 2008. Testing the Standard Model: The LEP experiments. CERN. 2008-09-15.
  52. News: Staff. 2000-12-01. LEP reaps a final harvest. CERN Courier. 2008-11-01.
  53. Frampton. Paul H.. Hung, P. Q.; Sher, Marc. Quarks and Leptons Beyond the Third Generation. Physics Reports. June. 2000. 330. 263–3485. 10.1016/S0370-1573(99)00095-2.
  54. Quigg. Chris. The Electroweak Theory. TASI 2000: Flavor Physics for the Millennium. 80. arXiv. June 4–30, 2000. Boulder, Colorado. 2008-09-21.
  55. Rosen. S. P.. Universality and the weak isospin of leptons, nucleons, and quarks. Physical Review D. 1978. 17. 2471–2474. 10.1103/PhysRevD.17.2471.
  56. Book: Raith, Wilhelm. Mulvey, Thomas. 2001. Constituents of Matter: Atoms, Molecules, Nuclei and Particles. CRC Press. 0849312027. 777–781.
  57. Book: Zombeck, Martin V.. 2007. Handbook of Space Astronomy and Astrophysics. Cambridge University Press. 14. Third edition. 0521782422.
  58. Murphy. Michael T.. Flambaum, Victor V.; Muller, Sébastien; Henkel, Christian. Strong Limit on a Variable Proton-to-Electron Mass Ratio from Molecules in the Distant Universe. Science. 2008-06-20. 320. 5883. 1611–1613. 2008-09-03. 10.1126/science.1156352. 18566280.
  59. The original source for CODATA is:

    Mohr. Peter J.. Taylor, Barry N.; Newell, David B.. CODATA recommended values of the fundamental physical constants. Reviews of Modern Physics. 2006-06-06. 80. 633–730. 10.1103/RevModPhys.80.633. Individual physical constants from the CODATA are available at:

    Web site: The NIST Reference on Constants, Units and Uncertainty. National Institute of Standards and Technology. 2009-01-15.

  60. Zorn. Jens C.. Chamberlain, George E.; Hughes, Vernon W.. Experimental Limits for the Electron-Proton Charge Difference and for the Charge of the Neutron. Physical Review. 1963. 129. 6. 2566–2576. 10.1103/PhysRev.129.2566.
  61. Eichten. Estia J.. Lane, Kenneth D.; Peskin, Michael E.. New Tests for Quark and Lepton Substructure. Physical Review Letters. 1983. 50. 030802(1 - 4). 10.1103/PhysRevLett.97.030802.
  62. Gabrielse. G.. Hanneke, D.; Kinoshita, T.; Nio, M.; Odom, B.. New Determination of the Fine Structure Constant from the Electron g Value and QED. Physical Review Letters. 2006. 97. 811 - 814. 10.1103/PhysRevLett.50.811.
  63. Book: Curtis, Lorenzo J.. 74. 2003. Atomic Structure and Lifetimes: A Conceptual Approach. Cambridge University Press. 0521536359.
  64. Dehmelt. Hans. A Single Atomic Particle Forever Floating at Rest in Free Space: New Value for Electron Radius. Physica Scripta. 1988. T22. 102–110. 10.1088/0031-8949/1988/T22/016.
  65. From electrostatics theory, the potential energy of a sphere with radius r and charge e is given by:

    styleEp=

    e2
    8\pi\varepsilon0r
    where ε0 is the vacuum permittivity. For an electron with rest mass m0, the rest energy is equal to:

    styleEp=m0c2

    where c is the speed of light in a vacuum. Setting them equal and solving for r gives the classical electron radius.
    See: Book: Haken, Hermann. 2005. Wolf, Hans Christoph; Brewer, W. D.. The Physics of Atoms and Quanta: Introduction to Experiments and Theory. Springer. 70. 3540208070.
  66. Steinberg. R. I.. Kwiatkowski, K.; Maenhaut, W.; Wall, N. S.. Experimental test of charge conservation and the stability of the electron. Physical Review D. 1999. 61. 2. 2582–2586. 10.1103/PhysRevD.12.2582.
  67. Yao. W.-M.. Particle Data Group. Review of Particle Physics. Journal of Physics G: Nuclear and Particle Physics. July. 2006. 33. 1. 77–115. 10.1088/0954-3899/33/1/001.
  68. Book: Munowitz, Michael. 2005. Knowing, The Nature of Physical Law. Oxford University Press. 0195167376. 162 - 218.
  69. Web site: Kane. Gordon. 2006-10-09. Are virtual particles really constantly popping in and out of existence? Or are they merely a mathematical bookkeeping device for quantum mechanics?. Scientific American. 2008-09-19.
  70. Book: Taylor, John. 1989. Davies, Paul. The New Physics. Gauge Theories in Particle Physics. Cambridge University Press. 0521438314. 464.
  71. Book: Genz, Henning. 2001. Nothingness: The Science of Empty Space. Da Capo Press. 0738206105. 241 - 243, 245 - 247.
  72. News: Gribbin. John. 1997-01-25. More to electrons than meets the eye. New Scientist. 2008-09-17.
  73. Levine. I.. TOPAZ Collaboration. Measurement of the Electromagnetic Coupling at Large Momentum Transfer. Physical Review Letters. 1997. 78. 424–427. 10.1103/PhysRevLett.78.424.
  74. Hitoshi. Murayama. Supersymmetry Breaking Made Easy, Viable and Generic. Proceedings of the XLIInd Rencontres de Moriond on Electroweak Interactions and Unified Theories. March 10–17, 2006. La Thuile, Italy. 2008-09-30. - lists a 9% mass difference for an electron that is the size of the Planck distance.
  75. Modanese. Giovanni. Inertial Mass and Vacuum Fluctuations in Quantum Field Theory. Foundations of Physics Letters. 2003. 16. 135–141. 2008-09-30. 10.1023/A:1024118627357.
  76. This magnitude is given by the spin angular momentum,

    styleS=\sqrt{s(s+1)}

    h
    2\pi

    =

    \sqrt{3
    }
  77. Foldy. Leslie L.. Wouthuysen, Siegfried A.. On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit. Physical Review. 1950. 78. 29–36. 10.1103/PhysRev.78.29.
  78. Sidharth. Burra G.. Revisiting Zitterbewegung. International Journal of Theoretical Physics. August. 2008. 2008-11-10. 10.1007/s10773-008-9825-8.
  79. Schwinger. Julian. On Quantum-Electrodynamics and the Magnetic Moment of the Electron. Physical Review. 1948. 73. 4. 416–417. 10.1103/PhysRev.73.416.
  80. Odom. B.. Hanneke, D.; D'Urso, B.; Gabrielse, G.. New Measurement of the Electron Magnetic Moment Using a One-Electron Quantum Cyclotron. Physical Review Letters. 2006. 97. 030801(1–4). 10.1103/PhysRevLett.97.030801.
  81. Book: Huang, Kerson. 2007. 123 - 125. World Scientific. Fundamental Forces of Nature: The Story of Gauge Fields. 9812706453.
  82. Elliott. R. S.. The history of electromagnetics as Hertz would have known it. IEEE Transactions on Microwave Theory and Techniques. 1978. 36. 5. 806–823. 2008-09-22. 10.1109/22.3600. A subscription required for access.
  83. Book: Georgi, Howard. 1989. Davies, Paul. Grand Unified Theories. The New Physics. Cambridge University Press. 0521438314. 427.
  84. Blumenthal. George J.. Gould, Robert J.. Bremsstrahlung, Synchrotron Radiation, and Compton Scattering of High-Energy Electrons Traversing Dilute Gases. Reviews of Modern Physics. 1970. 42. 237–270. 10.1103/RevModPhys.42.237.
  85. The change in wavelength, Δ&lambda;, depends on the angle of the recoil, θ, as follows,

    style\Deltaλ=

    h
    mc

    (1-\cos\theta)

    where c is the speed of light in a vacuum and m is the electron mass. See Zombeck (2007:393,396).
  86. Web site: Staff. 2008. The Nobel Prize in Physics 1927. The Nobel Foundation. 2008-09-28.
  87. [#refMunowitz2005|Munowitz (2005:140).]
  88. Book: Crowell, Benjamin. 2000. Electricity and Magnetism. 129 - 152. Light and Matter. 0970467044.
  89. [#refMunowitz2005|Munowitz (2005:160).]
  90. Mahadevan. Rohan. Narayan, Ramesh; Yi, Insu. Harmony in Electrons: Cyclotron and Synchrotron Emission by Thermal Electrons in a Magnetic Field. Astrophysical Journal. 1996. 465. 327 - . 2008-09-28. 10.1086/177422.
  91. Radiation from non-relativistic electrons is sometimes termed cyclotron radiation.
  92. Rohrlich. F.. The self-force and radiation reaction. American Journal of Physics. 1999. December. 68. 12. 1109–1112. 10.1119/1.1286430.
  93. Beringer. Robert. Montgomery, C. G.. The Angular Distribution of Positron Annihilation Radiation. Physical Review. 1942. 61. 5 - 6. 222–224. 10.1103/PhysRev.61.222.
  94. Book: Wilson, Jerry. Buffa, Anthony. 2000. College Physics. 4th.. 888. Prentice Hall. 0130824445.
  95. Eichler. Jörg. Electron–positron pair production in relativistic ion–atom collisions. Physics Letters A. 2005-11-14. 347. 1 - 3. 67–72. 10.1016/j.physleta.2005.06.105.
  96. Hubbell. J. H.. Electron positron pair production by photons: A historical overview. Radiation Physics and Chemistry. 2006. June. 75. 6. 614–623. 10.1016/j.radphyschem.2005.10.008. 2006RaPC...75..614H.
  97. Mulliken. Robert S.. Spectroscopy, Molecular Orbitals, and Chemical Bonding. Science. 1967. 157. 3784. 13–24. 10.1126/science.157.3784.13. 5338306.
  98. Book: Burhop, Eric H. S.. 1952. The Auger Effect and Other Radiationless Transitions. Cambridge University Press. 2 - 3. New York.
  99. Grupen. C.. Physics of Particle Detection. AIP Conference Proceedings, Instrumentation in Elementary Particle Physics, VIII. 3 - 34. 536. Dordrecht, D. Reidel Publishing Company. June 28-July 10 1999. Istanbul. 10.1063/1.1361756.
  100. Book: Jiles, David. 1998. 280 - 287. Introduction to Magnetism and Magnetic Materials. CRC Press. 0412798603.
  101. Book: Löwdin, Per Olov; Erkki Brändas, Erkki; Kryachko, Eugene S.. Fundamental World of Quantum Chemistry: A Tribute to the Memory of Per-Olov Löwdin. 393 - 394. Springer. 2003. 140201290X.
  102. Book: Pauling, Linus. The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry. Cornell University Press. 1960. 5 - 10. 0801403332.
  103. Book: McQuarrie, Donald Allan; Simon, John Douglas. Physical Chemistry: A Molecular Approach. University Science Books. 1997. 325 - 361. 0935702997.
  104. Daudel. R.. 1973-10-11. Bader, R. F. W.; Stephens, M. E.; Borrett, D. S.. The Electron Pair in Chemistry. Canadian Journal of Chemistry. 52. 1310–1320. 2008-10-12. 10.1139/v74-201.
  105. Book: Weinberg, Steven. 2003. The Discovery of Subatomic Particles. Cambridge University Press. 15 - 16. 052182351X.
  106. Book: Guru, Bhag S.. Hızıroğlu, Hüseyin R.. 2004. Electromagnetic Field Theory. 138, 276. Cambridge University Press. 0521830168.
  107. Book: Ziman, J. M.. 2001. Electrons and Phonons: The Theory of Transport Phenomena in Solids. Oxford University Press. 260. 0198507798.
  108. Book: Durrant, Alan. 2000. 0750307218. Quantum Physics of Matter: The Physical World. 43, 71 - 78. CRC Press.
  109. Main. Peter. 1993-06-12. When electrons go with the flow: Remove the obstacles that create electrical resistance, and you get ballistic electrons and a quantum surprise. New Scientist. 1887. 30. 2008-10-09.
  110. Book: Blackwell, Glenn R.. 2000. The Electronic Packaging Handbook. 6.39–6.40. CRC Press. 0849385911.
  111. Book: Achuthan, M. K.. Bhat, K. N.. Fundamentals of Semiconductor Devices. 2007. Tata McGraw-Hill. 49 - 67. 007061220X.
  112. Web site: Staff. 2008. The Nobel Prize in Physics 1972. The Nobel Foundation. 2008-10-13.
  113. Kadin. Alan M.. Spatial Structure of the Cooper Pair. Journal of Superconductivity and Novel Magnetism. 2007. 20. 4. 285–292. 2008-10-13. 10.1007/s10948-006-0198-z.
  114. Web site: Staff. 2008. The Nobel Prize in Physics 1958, for the discovery and the interpretation of the Cherenkov effect. The Nobel Foundation. 2008-09-25.
  115. Web site: Staff. 2008-08-26. Special Relativity. Stanford Linear Accelerator Center. 2008-09-25.
  116. Solving for the velocity of the electron, and using an approximation for large γ, gives:

    stylev=c\sqrt{1 -

    1
    \gamma2
    } \approx \left(1 - \frac
  117. Book: Adams, Steve. 2000. Frontiers: Twentieth Century Physics. 215. CRC Press. 0748408401.
  118. Book: Lurquin, Paul F.. 2003. The Origins of Life and the Universe. 2. Columbia University Press. 0231126557.
  119. Book: Silk, Joseph. 2000. The Big Bang: The Creation and Evolution of the Universe. 3rd. 110 - 112, 134 - 137. Macmillan. 080507256X.
  120. Christianto. Vic. Smarandache, Florentin. Thirty Unsolved Problems in the Physics of Elementary Particles. Progress in Physics. October. 2007. 4. 112–114. PDF. 2008-09-04.
  121. Kolb. Edward W.. Wolfram, Stephen. The Development of Baryon Asymmetry in the Early Universe. Physics Letters B. 1980-04-07. 91. 2. 217–221. 10.1016/0370-2693(80)90435-9.
  122. Web site: Sather. Eric. Spring/Summer 1996. The Mystery of Matter Asymmetry. PDF. Beam Line. University of Stanford. 2008-11-01.
  123. Web site: Burles. Scott. Nollett, Kenneth M.; Turner, Michael S.. 1999-03-19. Big-Bang Nucleosynthesis: Linking Inner Space and Outer Space. arXiv, University of Chicago. 2008-10-15.
  124. Boesgaard. A. M.. Steigman, G.. Big bang nucleosynthesis - Theories and observations. Annual review of astronomy and astrophysics. 1985. 23. 2. 319–378. 2008-08-28. 10.1146/annurev.aa.23.090185.001535.
  125. Barkana. Rennan. The First Stars in the Universe and Cosmic Reionization. Science. 2006-08-18. 313. 5789. 931–934. 2008-11-01. 10.1126/science.1125644. 16917052.
  126. Burbidge. E. Margaret. Burbidge, G. R.; Fowler, William A.; Hoyle, F.. Synthesis of Elements in Stars. Reviews of Modern Physics. 1957. 29. 4. 548–647. 10.1103/RevModPhys.29.547.
  127. Rodberg. L. S.. Weisskopf, V. F.. Fall of Parity: Recent Discoveries Related to Symmetry of Laws of Nature. Science. 1957. 125. 3249. 627–633. 10.1126/science.125.3249.627. 17810563.
  128. Fryer, Chris L.. Mass Limits For Black Hole Formation. The Astrophysical Journal. 522. 1. 413 - 418. September. 1999. 10.1086/307647. 1999ApJ...522..413F.
  129. Parikh. Maulik K.. Wilczek, Frank. Hawking Radiation As Tunneling. Physical Review Letters. 2000. 85. 24. 5042–5045. 10.1103/PhysRevLett.85.5042.
  130. Hawking. S. W.. Black hole explosions?. Nature. 1974-03-01. 248. 30–31. 10.1038/248030a0.
  131. Halzen. F.. Hooper, D.. High-energy neutrino astronomy: the cosmic ray connection. Reports on Progress in Physics. 2002. 66. 1025–1078. 2008-08-28. 10.1088/0034-4885/65/7/201.
  132. J. F.. Ziegler. Terrestrial cosmic ray intensities. IBM Journal of Research and Development. 117 - 139. 42. 1. 10.1147/rd.421.0117.
  133. News: Sutton. Christine. 1990-08-04. Muons, pions and other strange particles. New Scientist. 2008-08-28.
  134. Gurnett. Donald A.. Anderson, Roger R.. Electron Plasma Oscillations Associated with Type III Radio Bursts. Science. 1976-12-10. 194. 4270. 1159–1162. 10.1126/science.194.4270.1159. 17790910.
  135. Web site: Martin. W. C.. Wiese, W. L.. May. 2007. Atomic Spectroscopy: A Compendium of Basic Ideas, Notation, Data, and Formulas. National Institute of Standards and Technology. 2007-01-08.
  136. Book: Fowles, Grant R.. 1989. Introduction to Modern Optics. Courier Dover Publications. 0486659577. 227 - 233.
  137. Web site: Staff. 2008. The Nobel Prize in Physics 1989. The Nobel Foundation. 2008-09-24.
  138. Ekstrom. Philip. Wineland, David. The isolated Electron. Scientific American. 1980. 243. 2. 91–101. PDF. 2008-09-24.
  139. Web site: Mauritsson. Johan. Electron filmed for the first time ever. PDF. Lunds Universitet. 2009-09-17.
  140. Web site: Staff. 2008-02-25. Research Highlight. Attosecond Physics & High-Order Harmonic Generation. Lund Institute of Technology. 2009-09-17.
  141. Damascelli. Andrea. Probing the Electronic Structure of Complex Systems by ARPES. Physica Scripta. 2004. T109. 61–74. 10.1238/Physica.Topical.109a00061.
  142. Web site: Elmer. John. 2008-03-03. [https://www.llnl.gov/str/MarApr08/elmer.html Standardizing the Art of Electron-Beam Welding]. Lawrence Livermore National Laboratory. 2008-10-16.
  143. Faik S.. Ozdemir. Electron beam lithography. Proceedings of the 16th Conference on Design automation. 383 - 391. IEEE Press. June 25 - 27, 1979. San Diego, CA, USA. 2008-10-16.
  144. Yves. Jongen. Herer, Arnold. Electron Beam Scanning in Industrial Applications. APS/AAPT Joint Meeting. May 2-5, 1996. American Physical Society. 2008-10-16.
  145. Heppell. T. A.. A combined low energy and reflection high energy electron diffraction apparatus. Journal of Scientific Instruments. 1967. 44. 686–688. 10.1088/0950-7671/44/9/311.
  146. Book: Kitzmiller, John W.. 1995. Television Picture Tubes and Other Cathode-Ray Tubes: Industry and Trade Summary. 3 - 5. DIANE Publishing. 0788121006.
  147. Book: Sclater, Neil. 1999. 227 - 228. Electronic Technology Handbook. 0070580480. McGraw-Hill Professional.
  148. Web site: Staff. 2008. The History of the Integrated Circuit. The Nobel Foundation. 2008-10-18.
  149. Book: Cember, Herman. 1996. Introduction to Health Physics. 42 - 43. McGraw-Hill Professional. 0071054618.
  150. News: Staff. 2008-01-22. PhysOrg. Debut of TEAM 0.5, the World's Best Microscope. 2008-10-21.
  151. Book: Bozzola, John J.. Russell, Lonnie D.. 1999. Electron Microscopy: Principles and Techniques for Biologists. Jones & Bartlett Publishers. 12, 197 - 199. 0763701920.
  152. Book: Flegler, Stanley L.. 1995-10-01. Heckman Jr., John W.; Klomparens, Karen L.. Scanning and Transmission Electron Microscopy: An Introduction. Oxford University Press. 43 - 45. Reprint edition. 0195107519.
  153. Book: Chao, Alexander W.. Tigner, Maury. Handbook of Accelerator Physics and Engineering. World Scientific Publishing Company. 1999. 155, 188. 9810235003.
  154. Beddar. A. S.. Domanovic, M. A.; Kubu, M. L.; Ellis, R. J.; Sibata, C. H.; Kinsella, T. J.. Mobile linear accelerators for intraoperative radiation therapy. AORN Journal. 2001. November. 2008-10-26. 10.1016/S0001-2092(06)61769-9. 74. 700.
  155. Web site: Gazda. Michael J.. Coia, Lawrence R.. 2007-06-01. Principles of Radiation Therapy. Cancer Network. 2008-10-26.
  156. Book: Freund, Henry P.; Antonsen, Thomas. 1996. Principles of Free-Electron Lasers. 1 - 30. Springer. 0412725401.

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