The electron is a subatomic particle, symbol
e− or β−, whose electric charge is negative
one elementary charge. Electrons belong to
the first generation of the lepton particle
family, and are generally thought to be elementary
particles because they have no known components
or substructure. The electron has a mass that
is approximately 1/1836 that of the proton.
Quantum mechanical properties of the electron
include an intrinsic angular momentum (spin)
of a half-integer value, expressed in units
of the reduced Planck constant, ħ. As it
is a fermion, no two electrons can occupy
the same quantum state, in accordance with
the Pauli exclusion principle. Like all elementary
particles, electrons exhibit properties of
both particles and waves: they can collide
with other particles and can be diffracted
like light. The wave properties of electrons
are easier to observe with experiments than
those of other particles like neutrons and
protons because electrons have a lower mass
and hence a longer de Broglie wavelength for
a given energy.
Electrons play an essential role in numerous
physical phenomena, such as electricity, magnetism,
chemistry and thermal conductivity, and they
also participate in gravitational, electromagnetic
and weak interactions. Since an electron has
charge, it has a surrounding electric field,
and if that electron is moving relative to
an observer, it will generate a magnetic field.
Electromagnetic fields produced from other
sources will affect the motion of an electron
according to the Lorentz force law. Electrons
radiate or absorb energy in the form of photons
when they are accelerated. Laboratory instruments
are capable of trapping individual electrons
as well as electron plasma by the use of electromagnetic
fields. Special telescopes can detect electron
plasma in outer space. Electrons are involved
in many applications such as electronics,
welding, cathode ray tubes, electron microscopes,
radiation therapy, lasers, gaseous ionization
detectors and particle accelerators.
Interactions involving electrons with other
subatomic particles are of interest in fields
such as chemistry and nuclear physics. The
Coulomb force interaction between the positive
protons within atomic nuclei and the negative
electrons without, allows the composition
of the two known as atoms. Ionization or differences
in the proportions of negative electrons versus
positive nuclei changes the binding energy
of an atomic system. The exchange or sharing
of the electrons between two or more atoms
is the main cause of chemical bonding. In
1838, British natural philosopher Richard
Laming first hypothesized the concept of an
indivisible quantity of electric charge to
explain the chemical properties of atoms.
Irish physicist George Johnstone Stoney named
this charge 'electron' in 1891, and J. J.
Thomson and his team of British physicists
identified it as a particle in 1897. Electrons
can also participate in nuclear reactions,
such as nucleosynthesis in stars, where they
are known as beta particles. Electrons can
be created through beta decay of radioactive
isotopes and in high-energy collisions, for
instance when cosmic rays enter the atmosphere.
The antiparticle of the electron is called
the positron; it is identical to the electron
except that it carries electrical and other
charges of the opposite sign. When an electron
collides with a positron, both particles can
be annihilated, producing gamma ray photons.
== History ==
=== 
Discovery of effect of electric force ===
The ancient Greeks noticed that amber attracted
small objects when rubbed with fur. Along
with lightning, this phenomenon is one of
humanity's earliest recorded experiences with
electricity. In his 1600 treatise De Magnete,
the English scientist William Gilbert coined
the New Latin term electricus, to refer to
this property of attracting small objects
after being rubbed. Both electric and electricity
are derived from the Latin ēlectrum (also
the root of the alloy of the same name), which
came from the Greek word for amber, ἤλεκτρον
(ēlektron).
=== Discovery of two kinds of charges ===
In the early 1700s, Francis Hauksbee and French
chemist Charles François du Fay independently
discovered what they believed were two kinds
of frictional electricity—one generated
from rubbing glass, the other from rubbing
resin. From this, du Fay theorized that electricity
consists of two electrical fluids, vitreous
and resinous, that are separated by friction,
and that neutralize each other when combined.
American scientist Ebenezer Kinnersley later
also independently reached the same conclusion.
A decade later Benjamin Franklin proposed
that electricity was not from different types
of electrical fluid, but a single electrical
fluid showing an excess (+) or deficit (-). He
gave them the modern charge nomenclature of
positive and negative respectively. Franklin
thought of the charge carrier as being positive,
but he did not correctly identify which situation
was a surplus of the charge carrier, and which
situation was a deficit.Between 1838 and 1851,
British natural philosopher Richard Laming
developed the idea that an atom is composed
of a core of matter surrounded by subatomic
particles that had unit electric charges.
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.
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".Stoney initially coined the term
electrolion in 1881. Ten years later, he switched
to electron to describe these elementary charges,
writing in 1894: "... an estimate was made
of the actual amount of this most remarkable
fundamental unit of electricity, for which
I have since ventured to suggest the name
electron". A 1906 proposal to change to electrion
failed because Hendrik Lorentz preferred to
keep electron. The word electron is a combination
of the words electric and ion. The suffix
-on which is now used to designate other subatomic
particles, such as a proton or neutron, is
in turn derived from electron.
=== Discovery of free electrons outside matter
===
The German physicist Johann Wilhelm Hittorf
studied electrical conductivity in rarefied
gases: in 1869, he discovered a glow emitted
from the cathode that increased in size with
decrease in gas pressure. In 1876, the German
physicist Eugen Goldstein showed that the
rays from this glow cast a shadow, and he
dubbed the rays cathode rays. During the 1870s,
the English chemist and physicist Sir William
Crookes developed the first cathode ray tube
to have a high vacuum inside. 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.
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' experiments by placing metal
plates parallel to the cathode rays and applying
an electric potential between the plates.
The field deflected the rays toward the positively
charged plate, providing further evidence
that the rays carried negative charge. By
measuring the amount of deflection for a given
level of current, in 1890 Schuster was able
to estimate the charge-to-mass ratio of the
ray components. However, this produced a value
that was more than a thousand times greater
than what was expected, so little credence
was given to his calculations at the time.In
1892 Hendrik Lorentz suggested that the mass
of these particles (electrons) could be a
consequence of their electric charge.
While studying naturally fluorescing minerals
in 1896, the French physicist Henri Becquerel
discovered that they emitted radiation without
any exposure to an external energy source.
These radioactive materials became the subject
of much interest by scientists, including
the New Zealand physicist Ernest Rutherford
who discovered they emitted particles. He
designated these particles alpha and beta,
on the basis of their ability to penetrate
matter. In 1900, Becquerel showed that the
beta rays emitted by radium could be deflected
by an electric 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.In 1897, the
British physicist J. J. Thomson, with his
colleagues John S. Townsend and H. A. Wilson,
performed experiments indicating that cathode
rays really were unique particles, rather
than waves, atoms or molecules as was believed
earlier. 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. The name electron was again proposed
for these particles by the Irish physicist
George Johnstone Stoney, and the name has
since gained universal acceptance.
The electron's charge was more carefully measured
by the American physicists Robert Millikan
and Harvey Fletcher in their oil-drop experiment
of 1909, the results of which were published
in 1911. This experiment used an electric
field to prevent a charged droplet of oil
from falling as a result of gravity. This
device could measure the electric charge from
as few as 1–150 ions with an error margin
of less than 0.3%. Comparable experiments
had been done earlier by Thomson's team, using
clouds of charged water droplets generated
by electrolysis, and in 1911 by Abram Ioffe,
who independently obtained the same result
as Millikan using charged microparticles of
metals, then published his results in 1913.
However, oil drops were more stable than water
drops because of their slower evaporation
rate, and thus more suited to precise experimentation
over longer periods of time.Around the beginning
of the twentieth century, it was found that
under certain conditions a fast-moving charged
particle caused a condensation of supersaturated
water vapor along its path. In 1911, Charles
Wilson used this principle to devise his cloud
chamber so he could photograph the tracks
of charged particles, such as fast-moving
electrons.
=== Atomic theory ===
By 1914, experiments by physicists Ernest
Rutherford, Henry Moseley, James Franck and
Gustav Hertz had largely established the structure
of an atom as a dense nucleus of positive
charge surrounded by lower-mass electrons.
In 1913, Danish physicist Niels Bohr postulated
that electrons resided in quantized energy
states, with their energies determined by
the angular momentum of the electron's orbit
about the nucleus. The electrons could move
between those states, or orbits, by the emission
or absorption of photons of specific frequencies.
By means of these quantized orbits, he accurately
explained the spectral lines of the hydrogen
atom. However, Bohr's model failed to account
for the relative intensities of the spectral
lines and it was unsuccessful in explaining
the spectra of more complex atoms.Chemical
bonds between atoms were explained by Gilbert
Newton Lewis, who in 1916 proposed that a
covalent bond between two atoms is maintained
by a pair of electrons shared between them.
Later, in 1927, Walter Heitler and Fritz London
gave the full explanation of the electron-pair
formation and chemical bonding in terms of
quantum mechanics. In 1919, the American chemist
Irving Langmuir elaborated on the Lewis' static
model of the atom and suggested that all electrons
were distributed in successive "concentric
(nearly) spherical shells, all of equal thickness".
In turn, he divided the shells into a number
of cells each of which contained one pair
of electrons. With this model Langmuir was
able to qualitatively explain the chemical
properties of all elements in the periodic
table, which were known to largely repeat
themselves according to the periodic law.In
1924, Austrian physicist Wolfgang Pauli observed
that the shell-like structure of the atom
could be explained by a set of four parameters
that defined every quantum energy state, as
long as each state was occupied by no more
than a single electron. This prohibition against
more than one electron occupying the same
quantum energy state became known as the Pauli
exclusion principle. The physical mechanism
to explain the fourth parameter, which had
two distinct possible values, was provided
by the Dutch physicists Samuel Goudsmit and
George Uhlenbeck. In 1925, they suggested
that an electron, in addition to the angular
momentum of its orbit, possesses an intrinsic
angular momentum and magnetic dipole moment.
This is analogous to the rotation of the Earth
on its axis as it orbits the Sun. The intrinsic
angular momentum became known as spin, and
explained the previously mysterious splitting
of spectral lines observed with a high-resolution
spectrograph; this phenomenon is known as
fine structure splitting.
=== Quantum mechanics ===
In his 1924 dissertation Recherches sur la
théorie des quanta (Research on Quantum Theory),
French physicist Louis de Broglie hypothesized
that all matter can be represented as a de
Broglie wave in the manner of light. That
is, under the appropriate conditions, electrons
and other matter would show properties of
either particles or waves. The corpuscular
properties of a particle are demonstrated
when it is shown to have a localized position
in space along its trajectory at any given
moment. The wave-like nature of light is displayed,
for example, when a beam of light is passed
through parallel slits thereby creating interference
patterns. In 1927 George Paget Thomson, discovered
the interference effect was produced when
a beam of electrons was passed through thin
metal foils and by American physicists Clinton
Davisson and Lester Germer by the reflection
of electrons from a crystal of nickel.
De Broglie's prediction of a wave nature for
electrons led Erwin Schrödinger to postulate
a wave equation for electrons moving under
the influence of the nucleus in the atom.
In 1926, this equation, the Schrödinger equation,
successfully described how electron waves
propagated. Rather than yielding a solution
that determined the location of an electron
over time, this wave equation also could be
used to predict the probability of finding
an electron near a position, especially a
position near where the electron was bound
in space, for which the electron wave equations
did not change in time. This approach led
to a second formulation of quantum mechanics
(the first by Heisenberg in 1925), and solutions
of Schrödinger's equation, like Heisenberg's,
provided derivations of the energy states
of an electron in a hydrogen atom that were
equivalent to those that had been derived
first by Bohr in 1913, and that were known
to reproduce the hydrogen spectrum. Once spin
and the interaction between multiple electrons
were describable, quantum mechanics made it
possible to predict the configuration of electrons
in atoms with atomic numbers greater than
hydrogen.In 1928, building on Wolfgang Pauli's
work, Paul Dirac produced a model of the electron
– the Dirac equation, consistent with relativity
theory, by applying relativistic and symmetry
considerations to the hamiltonian formulation
of the quantum mechanics of the electro-magnetic
field. In order to resolve some problems within
his relativistic equation, Dirac developed
in 1930 a model of the vacuum as an infinite
sea of particles with negative energy, later
dubbed the Dirac sea. This led him to predict
the existence of a positron, the antimatter
counterpart of the electron. This particle
was discovered in 1932 by Carl Anderson, who
proposed calling standard electrons negatons
and using electron as a generic term to describe
both the positively and negatively charged
variants.
In 1947 Willis Lamb, working in collaboration
with graduate student Robert Retherford, found
that certain quantum states of the hydrogen
atom, which should have the same energy, were
shifted in relation to each other; the difference
came to be called the Lamb shift. About the
same time, Polykarp Kusch, working with Henry
M. Foley, discovered the magnetic moment of
the electron is slightly larger than predicted
by Dirac's theory. This small difference was
later called anomalous magnetic dipole moment
of the electron. This difference was later
explained by the theory of quantum electrodynamics,
developed by Sin-Itiro Tomonaga, Julian Schwinger
and
Richard Feynman in the late 1940s.
=== 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. The first
successful attempt to accelerate electrons
using electromagnetic induction was made in
1942 by Donald Kerst. His initial 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 General Electric. This radiation
was caused by the acceleration of electrons
through a magnetic field as they moved near
the speed of light.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 in opposite directions, effectively
doubling the energy of their collision when
compared to striking a static target with
an electron. The Large 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.
=== Confinement of individual electrons ===
Individual electrons can now be easily confined
in ultra small (L = 20 nm, W = 20 nm) CMOS
transistors operated at cryogenic temperature
over a range of −269 °C (4 K) to about
−258 °C (15 K). The electron wavefunction
spreads in a semiconductor lattice and negligibly
interacts with the valence band electrons,
so it can be treated in the single particle
formalism, by replacing its mass with the
effective mass tensor.
== Characteristics ==
=== Classification ===
In the Standard Model of particle physics,
electrons belong to the group of subatomic
particles called leptons, which are believed
to be fundamental or elementary particles.
Electrons have the lowest mass of any charged
lepton (or electrically charged particle of
any type) and belong to the first-generation
of fundamental particles. The second and third
generation contain charged leptons, the muon
and the tau, which are identical to the electron
in charge, spin and interactions, but are
more massive. Leptons differ from the other
basic constituent of matter, the quarks, by
their lack of strong interaction. All members
of the lepton group are fermions, because
they all have half-odd integer spin; the electron
has spin 1/2.
=== Fundamental properties ===
The invariant mass of an electron is approximately
9.109×10−31 kilograms, or 5.489×10−4
atomic mass units. On the basis of Einstein's
principle of mass–energy equivalence, this
mass corresponds to a rest energy of 0.511
MeV. The ratio between the mass of a proton
and that of an electron is about 1836. Astronomical
measurements show that the proton-to-electron
mass ratio has held the same value, as is
predicted by the Standard Model, for at least
half the age of the universe.Electrons have
an electric charge of −1.602×10−19 coulombs,
which is used as a standard unit of charge
for subatomic particles, and is also called
the elementary charge. This elementary charge
has a relative standard uncertainty of 2.2×10−8.
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 elementary charge,
the electron is commonly symbolized by e−,
where the minus sign indicates the negative
charge. The positron is symbolized by e+ because
it has the same properties as the electron
but with a positive rather than negative charge.The
electron has an intrinsic angular momentum
or spin of 1/2. This property is usually stated
by referring to the electron as a spin-1/2
particle. For such particles the spin magnitude
is √3/2 ħ. while the result of the measurement
of a projection of the spin on any axis can
only be ±ħ/2. In addition to spin, the electron
has an intrinsic magnetic moment along its
spin axis. It is approximately equal to one
Bohr magneton, which is a physical constant
equal to 9.27400915(23)×10−24 joules per
tesla. The orientation of the spin with respect
to the momentum of the electron defines the
property of elementary particles known as
helicity.The electron has no known substructure
and it is assumed to be a point particle with
a point charge and no spatial extent.The issue
of the radius of the electron is a challenging
problem of the modern theoretical physics.
The admission of the hypothesis of a finite
radius of the electron is incompatible to
the premises of the theory of relativity.
On the other hand, a point-like electron (zero
radius) generates serious mathematical difficulties
due to the self-energy of the electron tending
to infinity. Observation of a single electron
in a Penning trap suggests the upper limit
of the particle's radius to be 10−22 meters.
The upper bound of the electron radius of
10−18 meters can be derived using the uncertainty
relation in energy. There is also a physical
constant called the "classical electron radius",
with the much larger value of 2.8179×10−15
m, greater than the radius of the proton.
However, the terminology comes from a simplistic
calculation that ignores the effects of quantum
mechanics; in reality, the so-called classical
electron radius has little to do with the
true fundamental structure of the electron.There
are elementary particles that spontaneously
decay into less massive particles. An example
is the muon, with a mean lifetime of 2.2×10−6
seconds, which decays into an electron, a
muon neutrino and an electron antineutrino.
The electron, on the other hand, is thought
to be stable on theoretical grounds: the electron
is the least massive particle with non-zero
electric charge, so its decay would violate
charge conservation. The experimental lower
bound for the electron's mean lifetime is
6.6×1028 years, at a 90% confidence level.
=== Quantum properties ===
As with all particles, electrons can act as
waves. This is called the wave–particle
duality and can be demonstrated using the
double-slit experiment.
The wave-like nature of the electron allows
it to pass through two parallel slits simultaneously,
rather than just one slit as would be the
case for a classical particle. In quantum
mechanics, the wave-like property of one particle
can be described mathematically as a complex-valued
function, the wave function, commonly denoted
by the Greek letter psi (ψ). When the absolute
value of this function is squared, it gives
the probability that a particle will be observed
near a location—a probability density.
Electrons are identical particles because
they cannot be distinguished from each other
by their intrinsic physical properties. In
quantum mechanics, this means that a pair
of interacting electrons must be able to swap
positions without an observable change to
the state of the system. The wave function
of fermions, including electrons, is antisymmetric,
meaning that it changes sign when two electrons
are swapped; that is, ψ(r1, r2) = −ψ(r2,
r1), where the variables r1 and r2 correspond
to the first and second electrons, respectively.
Since the absolute value is not changed by
a sign swap, this corresponds to equal probabilities.
Bosons, such as the photon, have symmetric
wave functions instead.In the case of antisymmetry,
solutions of the wave equation for interacting
electrons result in a zero probability that
each pair will occupy the same location or
state. This is responsible for the Pauli exclusion
principle, which precludes any two electrons
from occupying the same quantum state. This
principle explains many of the properties
of electrons. For example, it causes groups
of bound electrons to occupy different orbitals
in an atom, rather than all overlapping each
other in the same orbit.
=== Virtual particles ===
In a simplified picture, every photon spends
some time as a combination of a virtual electron
plus its antiparticle, the virtual positron,
which rapidly annihilate each other shortly
thereafter. 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 ≥ ħ. In effect, the energy needed
to create these virtual particles, ΔE, can
be "borrowed" from the vacuum for a period
of time, Δt, so that their product is no
more than the reduced Planck constant, ħ
≈ 6.6×10−16 eV·s. Thus, for a virtual
electron, Δt is at most 1.3×10−21 s.
While an electron–positron virtual pair
is in existence, the coulomb force from the
ambient electric field surrounding an electron
causes a created positron to be attracted
to the original electron, while a created
electron experiences a repulsion. This causes
what is called vacuum polarization. In effect,
the vacuum behaves like a medium having a
dielectric permittivity more than unity. Thus
the effective charge of an electron is actually
smaller than its true value, and the charge
decreases with increasing distance from the
electron. This polarization was confirmed
experimentally in 1997 using the Japanese
TRISTAN particle accelerator. Virtual particles
cause a comparable shielding effect for the
mass of the electron.The interaction with
virtual particles also explains the small
(about 0.1%) deviation of the intrinsic magnetic
moment of the electron from the Bohr magneton
(the anomalous magnetic moment). The extraordinarily
precise agreement of this predicted difference
with the experimentally determined value is
viewed as one of the great achievements of
quantum electrodynamics.The apparent paradox
in classical physics of a point particle electron
having intrinsic angular momentum and magnetic
moment can be explained by the formation of
virtual photons in the electric field generated
by the electron. These photons cause the electron
to shift about in a jittery fashion (known
as zitterbewegung), which results in a net
circular motion with precession. This motion
produces both the spin and the magnetic moment
of the electron. In atoms, this creation of
virtual photons explains the Lamb shift observed
in spectral lines.
=== Interaction ===
An electron generates an electric field that
exerts an attractive force on a particle with
a positive charge, such as the proton, and
a repulsive force on a particle with a negative
charge. The strength of this force in nonrelativistic
approximation is determined by Coulomb's inverse
square law. When an electron is in motion,
it generates a magnetic field. The Ampère-Maxwell
law relates the magnetic field to the mass
motion of electrons (the current) with respect
to an observer. This property of induction
supplies the magnetic field that drives an
electric motor. 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 (relativistic).
When an electron is moving through a magnetic
field, it is subject to the Lorentz force
that acts perpendicularly to the plane defined
by the magnetic field and the electron velocity.
This centripetal force causes the electron
to follow a helical trajectory through the
field at a radius called the gyroradius. The
acceleration from this curving motion induces
the electron to radiate energy in the form
of synchrotron radiation. 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.
Photons mediate electromagnetic interactions
between particles in quantum electrodynamics.
An isolated electron at a constant velocity
cannot emit or absorb a real photon; doing
so would violate conservation of energy and
momentum. Instead, virtual photons can transfer
momentum between two charged particles. This
exchange of virtual photons, for example,
generates the Coulomb force. 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.An inelastic
collision between a photon (light) and a solitary
(free) electron is called Compton scattering.
This collision results in a transfer of momentum
and energy between the particles, which modifies
the wavelength of the photon by an amount
called the Compton shift. The maximum magnitude
of this wavelength shift is h/mec, which is
known as the Compton wavelength. For an electron,
it has a value of 2.43×10−12 m. When the
wavelength of the light is long (for instance,
the wavelength of the visible light is 0.4–0.7
μm) the wavelength shift becomes negligible.
Such interaction between the light and free
electrons is called Thomson scattering or
linear Thomson scattering.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 α ≈ 7.297353×10−3,
which is approximately equal to 1/137.When
electrons and positrons collide, they annihilate
each other, giving rise to two or more gamma
ray photons. If the electron and positron
have negligible momentum, a positronium atom
can form before annihilation results in two
or three gamma ray photons totalling 1.022
MeV. On the other hand, a high-energy photon
can 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.In the theory of electroweak
interaction, the left-handed component of
electron's wavefunction forms a weak isospin
doublet with the electron neutrino. This means
that during weak interactions, electron neutrinos
behave like electrons. Either member of this
doublet can undergo a charged current interaction
by emitting or absorbing a W and be converted
into the other member. Charge is conserved
during this reaction because the W boson also
carries a charge, canceling out any net change
during the transmutation. Charged current
interactions are responsible for the phenomenon
of beta decay in a radioactive atom. Both
the electron and electron neutrino can undergo
a neutral current interaction via a Z0 exchange,
and this is responsible for neutrino-electron
elastic scattering.
=== Atoms and molecules ===
An electron can be bound to the nucleus of
an atom by the attractive Coulomb force. A
system of one or more electrons bound to a
nucleus is called an atom. If the number of
electrons is different from the nucleus' electrical
charge, such an atom is called an ion. The
wave-like behavior of a bound electron is
described by a function called an atomic orbital.
Each orbital has its own set of quantum numbers
such as energy, angular momentum and projection
of angular momentum, and only a discrete set
of these orbitals exist around the nucleus.
According to the Pauli exclusion principle
each orbital can be occupied by up to two
electrons, which must differ in their spin
quantum number.
Electrons can transfer between different orbitals
by the emission or absorption of photons with
an energy that matches the difference in potential.
Other methods of orbital transfer include
collisions with particles, such as electrons,
and the Auger effect. To escape the atom,
the energy of the electron must be increased
above its binding energy to the atom. This
occurs, for example, with the photoelectric
effect, where an incident photon exceeding
the atom's ionization energy is absorbed by
the electron.The orbital angular momentum
of electrons is quantized. Because the electron
is charged, it produces an orbital magnetic
moment that is proportional to the angular
momentum. The net magnetic moment of an atom
is equal to the vector sum of orbital and
spin magnetic moments of all electrons and
the nucleus. The magnetic moment of the nucleus
is negligible compared with that of the electrons.
The magnetic moments of the electrons that
occupy the same orbital (so called, paired
electrons) cancel each other out.The chemical
bond between atoms occurs as a result of electromagnetic
interactions, as described by the laws of
quantum mechanics. The strongest bonds are
formed by the sharing or transfer of electrons
between atoms, allowing the formation of molecules.
Within a molecule, electrons move under the
influence of several nuclei, and occupy molecular
orbitals; much as they can occupy atomic orbitals
in isolated atoms. 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 molecular orbital without violating the
Pauli exclusion principle (much like in atoms).
Different molecular orbitals have different
spatial distribution of the electron density.
For instance, in bonded pairs (i.e. in the
pairs that actually bind atoms together) electrons
can be found with the maximal probability
in a relatively small volume between the nuclei.
By contrast, in non-bonded pairs electrons
are distributed in a large volume around nuclei.
=== Conductivity ===
If a body has more or fewer electrons than
are required to balance the positive charge
of the nuclei, then that object has a net
electric charge. When there is an excess of
electrons, the object is said to be negatively
charged. When there are fewer electrons than
the number of protons in nuclei, the object
is said to be positively charged. When the
number of electrons and the number of protons
are equal, their charges cancel each other
and the object is said to be electrically
neutral. A macroscopic body can develop an
electric charge through rubbing, by the triboelectric
effect.Independent electrons moving in vacuum
are termed free electrons. Electrons in metals
also behave as if they were free. In reality
the particles that are commonly termed electrons
in metals and other solids are quasi-electrons—quasiparticles,
which have the same electrical charge, spin,
and magnetic moment as real electrons but
might have a different mass. When free electrons—both
in vacuum and metals—move, they produce
a net flow of charge called an electric current,
which generates a magnetic field. Likewise
a current can be created by a changing magnetic
field. These interactions are described mathematically
by Maxwell's equations.At a given temperature,
each material has an electrical conductivity
that determines the value of electric current
when an electric potential is applied. Examples
of good conductors include metals such as
copper and gold, whereas glass and Teflon
are poor conductors. In any dielectric material,
the electrons remain bound to their respective
atoms and the material behaves as an insulator.
Most semiconductors have a variable level
of conductivity that lies between the extremes
of conduction and insulation. On the other
hand, metals have an electronic band structure
containing partially filled electronic bands.
The presence of such bands allows electrons
in metals to behave as if they were free or
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) through
the material much like free electrons.
Because of collisions between electrons and
atoms, the drift velocity of electrons in
a conductor is on the order of millimeters
per second. However, the speed at which a
change of current at one point in the material
causes changes in currents in other parts
of the material, the velocity of propagation,
is typically about 75% of light speed. This
occurs because electrical signals propagate
as a wave, with the velocity dependent on
the dielectric constant of 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,
which states that the ratio of thermal conductivity
to the electrical conductivity is proportional
to the temperature. The thermal disorder in
the metallic lattice increases the electrical
resistivity of the material, producing a temperature
dependence for electric current.When cooled
below a point called the critical temperature,
materials can undergo a phase transition in
which they lose all resistivity to electric
current, in a process known as superconductivity.
In BCS theory, 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 create electrical resistance.
(Cooper pairs have a radius of roughly 100
nm, so they can overlap each other.) However,
the mechanism by which higher temperature
superconductors operate remains uncertain.
Electrons inside conducting solids, which
are quasi-particles themselves, when tightly
confined at temperatures close to absolute
zero, behave as though they had split into
three other quasiparticles: spinons, orbitons
and holons. The former carries spin and magnetic
moment, the next carries its orbital location
while the latter electrical charge.
=== 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.
The effects of special relativity are based
on a quantity known as the Lorentz factor,
defined 
as
γ
=
1
/
1
−
v
2
/
c
2
{\displaystyle \scriptstyle \gamma =1/{\sqrt
{1-{v^{2}}/{c^{2}}}}}
where v is the speed of the particle. The
kinetic energy Ke of an electron moving with
velocity v is:
K
e
=
(
γ
−
1
)
m
e
c
2
,
{\displaystyle \displaystyle K_{\mathrm {e}
}=(\gamma -1)m_{\mathrm {e} }c^{2},}
where me is the mass of electron. For example,
the Stanford linear accelerator can accelerate
an electron to roughly 51 GeV.
Since an electron behaves as a wave, at a
given velocity it has a characteristic de
Broglie wavelength. This is given by λe = h/p
where h is the Planck constant and p is the
momentum. For the 51 GeV electron above, the
wavelength is about 2.4×10−17 m, small
enough to explore structures well below the
size of an atomic nucleus.
== Formation ==
The Big Bang theory is the most widely 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 kelvins and photons had
mean energies over a million electronvolts.
These photons were sufficiently energetic
that they could react with each other to form
pairs of electrons and positrons. Likewise,
positron-electron pairs annihilated each other
and emitted energetic photons:
γ + γ ↔ e+ + e−An equilibrium between
electrons, positrons and photons was maintained
during this phase of the evolution of the
Universe. After 15 seconds had passed, however,
the temperature of the universe dropped below
the threshold where electron-positron formation
could occur. Most of the surviving electrons
and positrons annihilated each other, releasing
gamma radiation that briefly reheated the
universe.For reasons that remain uncertain,
during the annihilation process there was
an excess in the number of particles over
antiparticles. Hence, about one electron for
every billion electron-positron pairs survived.
This excess matched the excess of protons
over antiprotons, in a condition known as
baryon asymmetry, resulting in a net charge
of zero for the universe. The surviving protons
and neutrons began to participate in reactions
with each other—in the process known as
nucleosynthesis, forming isotopes of hydrogen
and helium, with trace amounts of lithium.
This process peaked after about five minutes.
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− + νeFor about the next 300000–400000
years, the excess electrons remained too energetic
to bind with atomic nuclei. What followed
is a period known as recombination, when neutral
atoms were formed and the expanding universe
became transparent to radiation.Roughly one
million years after the big bang, the first
generation of stars began to form. Within
a star, stellar nucleosynthesis results in
the production of positrons from the fusion
of atomic nuclei. These antimatter particles
immediately annihilate with electrons, releasing
gamma rays. The net result is a steady reduction
in the number of electrons, and a matching
increase in the number of neutrons. However,
the process of stellar evolution can result
in the synthesis of radioactive isotopes.
Selected isotopes can subsequently undergo
negative beta decay, emitting an electron
and antineutrino from the nucleus. An example
is the cobalt-60 (60Co) isotope, which decays
to form nickel-60 (60Ni).
At the end of its lifetime, a star with more
than about 20 solar masses can undergo gravitational
collapse to form a black hole. According to
classical physics, these massive stellar objects
exert a gravitational attraction that is strong
enough to prevent anything, even electromagnetic
radiation, from escaping past the Schwarzschild
radius. However, quantum mechanical effects
are believed to potentially allow the emission
of Hawking radiation at this distance. Electrons
(and positrons) are thought to be created
at the event horizon of these stellar remnants.
When a pair of virtual particles (such as
an electron and positron) is created in the
vicinity of the event horizon, random spatial
positioning might result in one of them to
appear on the exterior; this process is called
quantum tunnelling. The gravitational potential
of the black hole can then supply the energy
that transforms this virtual particle into
a real particle, allowing it to radiate away
into space. 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
traveling through space with high energies.
Energy events as high as 3.0×1020 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. The particle called a muon is a
lepton produced in the upper atmosphere by
the decay of a pion.
π− → μ− + νμA muon, in turn, can
decay to form an electron or positron.
μ− → e− + νe + νμ
== Observation ==
Remote observation of electrons requires detection
of their radiated energy. For example, in
high-energy environments such as the corona
of a star, free electrons form a plasma that
radiates energy due to Bremsstrahlung radiation.
Electron gas can undergo plasma oscillation,
which is waves caused by synchronized variations
in electron density, and these produce energy
emissions that can be detected by using radio
telescopes.The frequency of a photon is proportional
to its energy. As a bound electron transitions
between different energy levels of an atom,
it absorbs or emits photons at characteristic
frequencies. For instance, when atoms are
irradiated by a source with a broad spectrum,
distinct absorption lines appear in the spectrum
of transmitted radiation. 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.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. The development
of the Paul trap and Penning trap allows charged
particles to be contained within a small region
for long durations. This enables precise measurements
of the particle properties. For example, in
one instance a Penning trap was used to contain
a single electron for a period of 10 months.
The magnetic moment of the electron was measured
to a precision of eleven digits, which, in
1980, was a greater accuracy than for any
other physical constant.The first video images
of an electron's energy distribution were
captured by a team at Lund University in Sweden,
February 2008. The scientists used extremely
short flashes of light, called attosecond
pulses, which allowed an electron's motion
to be observed for the first time.The distribution
of the electrons in solid materials can be
visualized by angle-resolved photoemission
spectroscopy (ARPES). This technique employs
the photoelectric effect to measure the reciprocal
space—a mathematical representation of periodic
structures that is used to infer the original
structure. ARPES can be used to determine
the direction, speed and scattering of electrons
within the material.
== Plasma applications ==
=== 
Particle beams ===
Electron beams are used in welding. They allow
energy densities up to 107 W·cm−2 across
a narrow focus diameter of 0.1–1.3 mm and
usually require no filler material. This welding
technique must be performed in a vacuum to
prevent the electrons from interacting with
the gas before reaching their target, and
it can be used to join conductive materials
that would otherwise be considered unsuitable
for welding.Electron-beam lithography (EBL)
is a method of etching semiconductors at resolutions
smaller than a micrometer. This technique
is limited by high costs, slow performance,
the need to operate the beam in the vacuum
and the tendency of the electrons to scatter
in solids. The last problem limits the resolution
to about 10 nm. For this reason, EBL is primarily
used for the production of small numbers of
specialized integrated circuits.Electron beam
processing is used to irradiate materials
in order to change their physical properties
or sterilize medical and food products. Electron
beams fluidise or quasi-melt glasses without
significant increase of temperature on intensive
irradiation: e.g. intensive electron radiation
causes a many orders of magnitude decrease
of viscosity and stepwise decrease of its
activation energy.Linear particle accelerators
generate electron beams for treatment of superficial
tumors in radiation therapy. Electron therapy
can treat such skin lesions as basal-cell
carcinomas because an electron beam only penetrates
to a limited depth before being absorbed,
typically up to 5 cm for electron energies
in the range 5–20 MeV. An electron beam
can be used to supplement the treatment of
areas that have been irradiated by X-rays.Particle
accelerators use electric fields to propel
electrons and their antiparticles to high
energies. These particles emit synchrotron
radiation as they pass through magnetic fields.
The dependency of the intensity of this radiation
upon spin polarizes the electron beam—a
process known as the Sokolov–Ternov effect.
Polarized electron beams can be useful for
various experiments. Synchrotron radiation
can also cool the electron beams to reduce
the momentum spread of the particles. Electron
and positron beams are collided upon the particles'
accelerating to the required energies; particle
detectors observe the resulting energy emissions,
which particle physics studies .
=== Imaging ===
Low-energy electron diffraction (LEED) is
a method of bombarding a crystalline material
with a collimated beam of electrons and then
observing the resulting diffraction patterns
to determine the structure of the material.
The required energy of the electrons is typically
in the range 20–200 eV. The reflection high-energy
electron diffraction (RHEED) technique uses
the reflection of a beam of electrons fired
at various low angles to characterize the
surface of crystalline materials. The beam
energy is typically in the range 8–20 keV
and the angle of incidence is 1–4°.The
electron microscope directs a focused beam
of electrons at a specimen. Some electrons
change their properties, such as movement
direction, angle, and relative phase and energy
as the beam interacts with the material. Microscopists
can record these changes in the electron beam
to produce atomically resolved images of the
material. In blue light, conventional optical
microscopes have a diffraction-limited resolution
of about 200 nm. By comparison, electron microscopes
are limited by the de Broglie wavelength of
the electron. This wavelength, for example,
is equal to 0.0037 nm for electrons accelerated
across a 100,000-volt potential. The Transmission
Electron Aberration-Corrected Microscope is
capable of sub-0.05 nm resolution, which is
more than enough to resolve individual atoms.
This capability makes the electron microscope
a useful laboratory instrument for high resolution
imaging. However, electron microscopes are
expensive instruments that are costly to maintain.
Two main types of electron microscopes exist:
transmission and scanning. Transmission electron
microscopes function like overhead projectors,
with a beam of electrons passing through a
slice of material then being projected by
lenses on a photographic slide or a charge-coupled
device. Scanning electron microscopes rasteri
a finely focused electron beam, as in a TV
set, across the studied sample to produce
the image. Magnifications range from 100×
to 1,000,000× or higher for both microscope
types. The scanning tunneling microscope uses
quantum tunneling of electrons from a sharp
metal tip into the studied material and can
produce atomically resolved images of its
surface.
=== Other applications ===
In the free-electron laser (FEL), a relativistic
electron beam passes through a pair of undulators
that contain arrays of dipole magnets whose
fields point in alternating directions. The
electrons emit synchrotron radiation that
coherently interacts with the same electrons
to strongly amplify the radiation field at
the resonance frequency. FEL can emit a coherent
high-brilliance electromagnetic radiation
with a wide range of frequencies, from microwaves
to soft X-rays. These devices are used in
manufacturing, communication, and in medical
applications, such as soft tissue surgery.Electrons
are important in cathode ray tubes, which
have been extensively used as display devices
in laboratory instruments, computer monitors
and television sets. In a photomultiplier
tube, every photon striking the photocathode
initiates an avalanche of electrons that produces
a detectable current pulse. Vacuum tubes use
the flow of electrons to manipulate electrical
signals, and they played a critical role in
the development of electronics technology.
However, they have been largely supplanted
by solid-state devices such as the transistor.
== See also ==
== Notes
