Definitions

# electron spin resonance (ESR)

or electron paramagnetic resonance (EPR)

Technique of spectroscopic analysis (see spectroscopy) used to identify paramagnetic substances (see paramagnetism) and investigate the nature of the bonding within molecules by identifying unpaired electrons and their interaction with their immediate surroundings. Unpaired electrons, because of their spin, behave like tiny magnets and can be lined up in an applied magnetic field; energy applied by alternating microwave radiation is absorbed when its frequency coincides with that of precession of the electron magnets in the sample. The graph or spectrum of radiation absorbed as the field changes gives information valuable in chemistry, biology, and medicine.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

The electron is a fundamental subatomic particle that was identified and assigned the negative charge in 1897 by J.J. Thomson and his team of British physicists. These electrically-charged particles, together with the protons and neutrons that comprise atomic nuclei, make up atoms. Electron–electron interaction between atoms is the main cause of chemical bonding. Electrons also play an essential role in electricity and magnetism.

All electrons are identical particles that belong to the first generation of the lepton particle family. Each electron carries a negative elementary charge and participates in electromagnetic and weak interactions. It has a property of intrinsic angular momentum called spin, with a standardized value of . The mass of an electron is approximately of that of the proton, and it is believed to be a point particle with no apparent substructure. The properties of the electron are determined by its interaction with other particles.

## Etymology

The English name electron is a combination of the word and the suffix -on, with the latter now used to designate a subatomic particle. Both electric and electricity are derived from the Latin ēlectrum, which in turn came from the Greek word ēlektron (ήλεκτρον) for amber; a gemstone that is formed from the hardened sap of trees (the ancient Greeks noticed that amber, when rubbed with fur, attracted small objects). Apart from lightning this phenomenon was man's earliest experience of electricity.

## History

As early as 1838–51, the 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. 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, the Anglo-Irish physicist G. Johnstone Stoney suggested that there existed a "single definite quantity of electricity." He was able to estimate the value of the charge e of a monovalent ion by means of Faraday's laws of electrolysis. 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".

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

### Identification

Progress in the study of electrons began to occur once a cathode ray tube was developed that had a high vacuum within its interior. Once he had accomplished this during the 1870s, English chemist and physicist Sir William Crookes was able to show that the luminescence rays appearing within the tube carried energy and moved from the cathode to the anode. Further, by applying a magnetic field, he was able to deflect the rays, thereby demonstrating that the beam behaved as though it were negatively charged. 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.

The German-born British physicist Arthur Schuster expanded upon Crookes's experiments by placing metal plates in parallel to the cathode rays and applying an electrical potential between the plates. The resulting 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.

In 1896, British physicist J.J. Thomson, with his colleagues John S. Townsend and H. A. Wilson, performed experiments indicating that cathode rays really were unique particles, rather than waves, atoms or molecules as was believed earlier. 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 also 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. The name electron was again proposed for these particles by the Irish physicist George F. Fitzgerald, and it has since gained universal acceptance.

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. 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. This evidence strengthened the view that electrons existed as components of atoms.

The electron's charge was more carefully measured by American physicist Robert Millikan in his oil-drop experiment of 1909. 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. 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.

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.

### 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. 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.

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

In 1924, Austrian physicist Wolfgang Pauli observed that the shell-like structure of the atom could be explained if each quantum energy state was described by a set of four parameters, 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.) 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. 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.

### Modern particle physics

During his 1924 dissertation Recherches sur la théorie des quanta, French physicist Louis de Broglie hypothesized that all matter possesses a wave–particle duality similar to photons. That is, under the appropriate conditions, electrons and other matter would show properties of either particles or waves. The wave-like nature of light occurs, for example, when light is passed through parallel slits, resulting in interference patterns. In 1937, a similar effect was demonstrated from 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.

The success of de Broglie's prediction led to the publication, by Erwin Schrödinger in 1926, of the wave equation that successfully describes how electron waves propagated. Rather than yielding a solution that determines the location of an electron over time, this wave equation gives the probability of finding an electron near a position. This approach became the theory of quantum mechanics, which provided an exact derivation to the energy states of an electron in a hydrogen atom. Once the electron spin and the interaction between multiple electrons is taken into consideration, the Schroedinger wave equation successfully predicted the configuration of electrons in atoms with higher atomic numbers than hydrogen. However, for atoms with multiple electrons, the exact solution to the wave equation is much more complicated, so approximations were often necessary.

In 1948, Richard Feynman proposed an alternative view of the electron's quantum mechanical behavior, known as the path integral formulation. He suggested that a particle simultaneously traversed every possible path to reach its destination. Thus, in the double-slit experiment, an electron passed through both of the slits, rather than choosing one or the other. Each of the possible paths could be assigned a value in such a manner that the averaged behavior matched the probabilities computed from the wave function. When an electron is detected following a particular path, the numerical contributions all of the other paths cancel themselves out. This formulation has proved crucial to the subsequent development of theoretical physics.

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. The first successful attempt to accelerate electrons using magnetic induction was made in 1942 by Donald Kerst. His first betatron reached energies of 2.3 MeV, while subsequent betatrons achieved 300 MeV. In 1947, synchrotron radiation was discovered with a 70 MeV electron synchrotron at GE. This radiation was caused by the acceleration of electrons, moving near the speed of light, through a magnetic field. With a beam energy of 1.5 GeV, the first high-energy particle collider was ADONE, which began operations in 1968. 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). The Large Electron-Positron Collider at CERN, which was operational from 1989–2000, achieved energies of 209 GeV and made important measurements for the Standard Model of particle physics.

## Characteristics

### Classification

The electron belongs to the group of subatomic particles called leptons, which are believed to be fundamental particles. Electrons have lepton number 1, and have the lowest mass of any electrically charged lepton. In the Standard Model of particle physics, the electron is the first-generation charged lepton. It forms a weak isospin doublet with the electron neutrino; an uncharged, first generation lepton with little or no mass.

The electron is very similar to the two more massive particles of higher generations, the muon and the tau lepton, which are identical in charge, spin, and interaction, but differ in mass. 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.

The antiparticle of an electron is the positron, which has the same mass and spin as the electron but a positive rather than negative charge. The discoverer of the positron, Carl D. Anderson, 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 also be shortened to "negaton".

### Fundamental properties

When an electron is stationary, its rest mass is 9.11 kg. On the atomic scale, this is equal to 5.489 u, where 1 u is one-twelfth the mass of a neutral 12C atom. Based on Einstein's principle of mass–energy equivalence, this mass corresponds to a rest energy of 0.511 MeV, where an eV, or electron volt, is defined as the energy acquired by an electron being accelerated through an electrical potential of one volt. The relative mass of the electron (when compared to the remainder of a hydrogen atom) is given by the proton-to-electron mass ratio, which is about 1836. 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. However, the rest energy of the electron has been shown to vary by 10−6–10−9 eV because of local fluctuations of temperature and magnetic field.

Electrons have an electric charge of −1.602 × 10−19 C, 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. As the symbol e is used for the constant of electrical charge, the electron is commonly symbolized by e−, where the minus sign indicates the negative charge.

The electron is described as a fundamental or elementary particle. It has no known substructure. Hence, for convenience, it is usually defined or assumed to be a point charge with no spatial extent; a point particle. Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10−22 m. The classical electron radius is 2.8179 m. This is the radius that is inferred from the electron's electric charge, by using the classical theory of electrodynamics alone, ignoring quantum mechanics.

Several elementary particles are known to spontaneously decay into different particles. An example is the muon, which decays into an electron and two neutrinos with a half life of 2.2 seconds. However, the electron is thought to be stable on theoretical grounds; an electron decaying into a neutrino and photon would mean that electrical charge is not conserved. The experimental lower bound for the electron's mean lifetime is 4.6 years, with a 90% confidence interval.

### Quantum mechanics

As with all particles, electrons can also 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 the wavefunction, which is represented by the Greek letter Psi (Ψ). When this function is squared, it gives the probabilility that an electron will be observed near a location—the electron density.

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. That is, the probability distribution for an identical pair must remain unchanged after they switch positions. The wavefunction describing such an interaction can either remain the same following a particle swap or it change sign; mathematically, the square of −Ψ will have the same probability density as the function with a positive sign. The sign-changing case is called an antisymmetrical wavefunction and it is characteristic of all identical fermions, including electrons. Bosons, such as the photon, have symmetric wave functions.

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.

### 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. 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, $begin\left\{smallmatrix\right\}Delta E Delta t ge hbarend\left\{smallmatrix\right\}$. 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 Dirac constant, . Thus, for a virtual electron, Δt is at most .

While a 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. This polarization was confirmed experimentally in 1997 using the Japanese TRISTAN particle accelerator.

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. The resulting total mass is referred to as the renormalized mass, because a technique called renormalization is used by physicists to relate the observed and bare mass of the electron.

The electron has an intrinsic angular momentum of spin as measured in units of ħ, and an intrinsic magnetic moment along its spin axis. The concept of a dimensionless particle possessing properties that, in classical electromagnetism, normally require a physical size is unclear. A possible explanation lies in the formation of virtual photons in the electric field generated by the electron. The continual creation and absorption of these photons causes the electron to move about in a jittery fashion (known as zitterbewegung). As photons possess angular momentum, this jittering of the electron causes a net precession, which, on average, results in a circulatory motion of the mass and charge. In atoms, this creation of virtual photons is also responsible for the Lamb shift that causes a small difference in electron energy for quantum states that, otherwise, ought to be identical.

The gyromagnetic ratio of an electron is the ratio of its magnetic moment to its angular momentum. Virtual particles and antiparticles provide a correction of just over 0.1% to the electron's gyromagnetic ratio, compared to the value of exactly 2 predicted by Paul Dirac's single-particle model. The extraordinarily precise agreement of this prediction with the experimentally determined value is viewed as one of the great achievements of modern physics.

### Interaction

Electrons are a key element in electromagnetism, a theory that is accurate for macroscopic systems, and for classical modeling of microscopic systems. 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.

The Coulomb force between charged particles is mediated by photons, which are quanta of electromagnetic energy. However, 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 Coulomb force. 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 of Bremsstrahlung radiation.

The outcome of an elastic collision between a photon and a solitary elecron 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. The maximum magnitude of this wavelength shift is h/mc, which is known as the Compton wavelength. For a electron, it has a value of 2.43 m.

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 repulsion at a separation of one Compton wavelength, and the rest energy of the charge. It is given by α = (7.29720±0.00003), which is approximately equal to 1/137. This constant appears frequently in the physics of atoms and in the theory of quantum electrodynamics.

When an electron is in motion, it generates a magnetic field. 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. As an example, it is this property of induction which supplies the magnetic field that drives an electric motor. The full electromagnetic effect from a moving charge can be derived mathematically using the Liénard-Wiechert potential, which includes special corrections for when the velocity is close to the speed of light; known as 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 the resulting acceleration causes the electron to radiate energy. At relatively low velocities the energy emission in a magnetic field is called cyclotron radiation, while for electrons moving at relativistic velocities it is termed synchrotron radiation. 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.

In the theory of electroweak interaction, 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 also undergo a neutral current interaction via a Z0 boson exchange, and this is responsible for neutrino-electron elastic scattering.

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 had negligible momentum, each gamma ray will have an energy of 0.511 MeV. 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.

### Atoms

An electron can be bound to an atom by the attractive coulomb force generated by the nucleus. 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. In order to escape the atom, the energy of the electron must be increased above its binding energy. This occurs with the photoelectric effect, where an incident photon exceeding the atom's ionization energy is absorbed by the electron.

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. Because of the Pauli exclusion principle, pairs of electrons in an atom align their spins in opposite directions, resulting in different spin quantum numbers. Thus the magnetic moments of an atom's electrons cancel each other out, with the exception of the outermost electron. The nucleus also contributes a magnetic moment, but this is negligible compared to the effect from the electrons.

The chemical bond between atoms occurs as a result of electromagnetic interactions, as described by the laws of quantum electrodynamics. The strongest bonds are formed by the sharing or transfer of electrons between atoms. Within a molecule, these electrons move under the influence of the nuclei, and occupy molecular orbitals.

### Conductivity

A body has an electric charge when that object has more or fewer electrons than are required to balance the positive charge of the nuclei. (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.

Electrons moving freely in vacuum, space or certain media are free electrons. When free electrons move, there is 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.

At a given temperature, each material has a level of electrical conductivity that measures the electric current when an electric potential is applied. Examples of good conductors include metals such as copper and gold. 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 through the material. However, unlike an atmospheric gas (which follows the Maxwell–Boltzmann distribution of energies), the states of this cloud of electrons obeys Fermi–Dirac statistics; hence the reason for the electron's family name, fermions.

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. This occurs because electrical signals propagate as a wave, with the velocity dependent on the dielectric constant of the material. 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.

In some superconductors, pairs of electrons move as Cooper pairs in which their motion is coupled to nearby matter via lattice vibrations called phonons. The distance of separation between Cooper pairs is roughly 100 nm.

### Motion and energy

The speed of an electron can approach, but never reach the speed of light in a vacuum, c. This limitation is attributed to Einstein's theory of special relativity which defines the speed of light as a constant regardless of the relative velocity of observers—their inertial frames. However, when relativistic electrons 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 bluish light called Cherenkov radiation.

The effects of special relativity are based on a quantity known as the Lorentz factor γ, which is a function of the velocity v of the particle compared to c. The kinetic energy Ke of an electron moving with velocity v is:

$begin\left\{smallmatrix\right\}K_e = left\left(gamma - 1right\right)m_e c^2.end\left\{smallmatrix\right\}$

where me is the electron mass. For example, the Stanford linear accelerator can accelerate an electron to roughly 51 GeV. 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 classical momentum of an electron at the same speed.

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. At energies of just a few electron volts this wavelength determines the size of atoms, while at thousands of electron volts this results in the Bragg angles for electron diffraction. (J. J. Thomson's son G. P. Thomson discovered this angle to be much smaller than one degree.) For the 51 GeV electron above, proper-velocity is approximately γc, making the wavelength of those electrons small enough to explore structures well below the size of an atomic nucleus.

## Production

The big bang theory is the accepted scientific theory to explain the early stages in the evolution of the Universe. For the first millisecond of the big bang, the temperatures were over 10 billion K 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,

$begin\left\{smallmatrix\right\}gamma + gamma leftrightharpoons e^\left\{+\right\} + e^\left\{-\right\}end\left\{smallmatrix\right\}$

where γ is a photon, e+ is a positron and e- is an electron. Likewise, positron-electron pairs annihilated each other, emitting photons of gamma rays with energies of 511 keV. 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.

For reasons that remain uncertain, there was a slight excess in the number of electrons over positrons; a problem known as baryon asymmetry. Hence a few electrons survived the annihilation process. This excess also matched the excess of protons over anti-protons, resulting in a net charge of zero for the universe. The surviving protons and neutrons begin to undergo nucleosynthesis, forming isotopes of hydrogen and helium, with trace amounts of lithium. This process peaked after a few hundred seconds, and any leftover neutrons thereafter underwent negative beta decay with a half-life of about a thousand seconds, releasing a proton and electron in the process,

$begin\left\{smallmatrix\right\}n Rightarrow p + e^\left\{-\right\} + bar\left\{nu\right\}_eend\left\{smallmatrix\right\}$

where n is a neutron, p is a proton, e- is an electron and $begin\left\{smallmatrix\right\}bar\left\{nu\right\}_eend\left\{smallmatrix\right\}$ is an electron antineutrino. For the next million years, the excess electrons remained too energetic to bind with atomic nuclei. Once atoms were formed, the universe became transparent to radiation and it continued to cool and expand.

The concentrations of mass in the universe allow stars to form. Within a star, stellar nucleosynthesis results in the production of positrons from the fusion of atomic nuclei. These antimatter particles immediately annihilate with electrons, releasing gamma rays. The net result is a steady reduction in the number of electrons, and a matching increase in the number of neutrons. However, the process of stellar evolution can also result in the synthesis of radioactive isotopes. Some of these isotopes can subsequently undergo negative beta decay, emitting an electron and antineutrino from the nucleus. An example is the cobalt-60 (60Co) isotope, which decays to form nickel-60 (60Ni).

Electrons (and positrons) are also thought to be created at the event horizon of a black hole. 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.

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. 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.

Cosmic rays are particles travelling through space with high energies. Energy events as high as 3.0 eV have been recorded. When these particles collide with nucleons in the Earth's atmosphere, a shower of particles is generated, including pions. 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 $pi^\left\{-\right\}$,

$begin\left\{smallmatrix\right\}$
pi^{-} Rightarrow mu^{-} + nu_{mu}end{smallmatrix}
$begin\left\{smallmatrix\right\}mu^\left\{-\right\} Rightarrow e^\left\{-\right\} + bar\left\{nu\right\}_e + nu_\left\{mu\right\}end\left\{smallmatrix\right\}$

where $mu^\left\{-\right\}$ is a muon, $nu_\left\{mu\right\}$ is a muon neutrino and $begin\left\{smallmatrix\right\}bar\left\{nu\right\}_eend\left\{smallmatrix\right\}$ is an electron antineutrino.

## Observation

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. More distant 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 also 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.

The development of the Paul trap and Penning trap allows charged particles to be contained within a small region for long durations. This allows 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. Measurements allowed the dimensionless g-factor 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.

The first video images of an electron were captured by a team at Lund University in Sweden, February 2008. To capture this event, 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.

"It takes about 150 attoseconds for an electron to circle the nucleus of an atom. An attosecond is related to a second as a second is related to the age of the universe," explained Johan Mauritsson, an assistant professor in atomic physics at the Faculty of Engineering, Lund University.

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.

## Applications

At some level, virtually every developed technology depends upon electrons. The chemical industry is based upon the chemical properties of atoms, which in turn depend on the interaction of bound electrons. Thus the thermodynamic properties for the solid, liquid and gaseous phases of matter are all decided by the interactions of electrons in atoms. In the electronics industry, electrical devices rely on the flow of electrons. Even technology that generates electromagnetic radiation, such as lasers, depend upon the electron. There are also certain specialized applications that primarily use free electrons.

### Industry

Electron beams are used in welding, lithography, scanning electron microscopes and transmission electron microscopes. LEED and RHEED are surface-imaging techniques that use electrons.

Electrons are also at the heart of cathode ray tubes, which are used extensively as display devices in laboratory instruments, computer monitors and television sets. In a photomultiplier tube, one photon strikes the photocathode, initiating an avalanche of electrons that produces a detectable current.

### Laboratory

The uniquely high charge-to-mass ratio of electrons means that they interact strongly with atoms, and are easy to accelerate and focus with electric and magnetic fields. Hence some of today's aberration-corrected transmission electron microscopes use 300keV electrons with velocities greater than the speed light travels in water (approximagely 1/2 to 2/3 of c), wavelengths below 2 picometers, transverse coherence-widths over a nanometer, and longitudinal coherence-widths 100 times that. This allows such microscopes to image scattering from individual atomic-nuclei (HAADF) as well as interference-contrast from solid-specimen exit-surface deBroglie-phase (HRTEM) with lateral point-resolutions down to 60 picometers. Magnifications approaching 100 million are needed to make the resulting image detail comfortably visible to the naked eye.

Quantum effects of electrons are also used in the scanning tunneling microscope to study features on solid surfaces with lateral-resolution at the atomic scale (around 200 picometers) and vertical-resolutions much better than that. In such microscopes, the quantum tunneling is strongly dependent on tip-specimen separation, and, precise control of the separation (vertical sensitivity) is made possible with a piezoelectric scanner.

### Medicine

In radiation therapy, electron beams are used for treatment of superficial tumours.

## External links

• The Discovery of the Electron from the American Institute of Physics History Center
• Particle Data Group
• Eric Weisstein's World of Physics: Electron
• Researchers Catch Motion of a Single Electron on Video
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