elementary charge

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The elementary charge, usually denoted by is the
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electron ...
carried by a single
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
or, equivalently, the magnitude of the negative electric charge carried by a single
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
, which has charge −1 . This elementary charge is a fundamental
physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant (mathematics), constant value in time. It is contrasted with a ...
. In the SI system of units, the value of the elementary charge is exactly defined as $e$ =
coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In 2019 redefinition of the SI base units, the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant curre ...
s, or 160.2176634
zepto A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple (mathematics), multiple or submultiple of the unit. All metric prefixes used today are decimal, decadic. Each prefix has a unique symbol that is prepen ...
coulombs (zC). Since the 2019 redefinition of SI base units, the seven
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which a ...
s are defined by seven fundamental physical constants, of which the elementary charge is one. In the
centimetre–gram–second system of units The centimetre–gram–second system of units (abbreviated CGS or cgs) is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanics, mechani ...
(CGS), the corresponding quantity is . Robert A. Millikan and
Harvey Fletcher Harvey Fletcher (September 11, 1884 – July 23, 1981) was an American physicist. Known as the "father of stereophonic sound", he is credited with the invention of the 2-A audiometer and an early electronic hearing aid. He was an investigator in ...
's
oil drop experiment The oil drop experiment was performed by Robert Andrews Millikan, Robert A. Millikan and Harvey Fletcher in 1909 to measure the Elementary charge, elementary electric charge (the charge of the electron). The experiment took place in the Ryerson ...
first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed
atomic theory Atomic theory is the scientific theory A scientific theory is an explanation of an aspect of the natural science, natural world and universe that has been reproducibility, repeatedly tested and corroborated in accordance with the scientifi ...
, the elementary charge had also been indirectly inferred to ~3% accuracy from blackbody spectra by
Max Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a Germans, German theoretical physicist whose discovery of quantum mechanics, energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...
in 1901 and (through the
Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole (unit), mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefi ...
) at order-of-magnitude accuracy by Johann Loschmidt's measurement of Avagadro's number in 1865.

# As a unit

In some
natural unit In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a Coherence (units of measurement), coherent unit of a quantity. For e ...
systems, such as the system of atomic units, ''e'' functions as the
unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * Unit (album), ...
of electric charge. The use of elementary charge as a unit was promoted by
George Johnstone Stoney George Johnstone Stoney FRS (15 February 1826 – 5 July 1911) was an Irish people, Irish physicist. He is most famous for introducing the term ''electron'' as the "fundamental unit quantity of electricity". He had introduced the concept, thoug ...
in 1874 for the first system of
natural units In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a Coherence (units of measurement), coherent unit of a quantity. For e ...
, called Stoney units. Later, he proposed the name ''electron'' for this unit. At the time, the particle we now call the
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
was not yet discovered and the difference between the particle ''electron'' and the unit of charge ''electron'' was still blurred. Later, the name ''electron'' was assigned to the particle and the unit of charge ''e'' lost its name. However, the unit of energy
electronvolt In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an Voltage, electric potential difference of one volt i ...
is a remnant of the fact that the elementary charge was once called ''electron''. In some other natural unit systems the unit of charge is defined as , with the result that , where ''α'' is the
fine-structure constant In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scien ...
, ''c'' is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
, ''ε''0 is the
electric constant Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the Permittivity, absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the el ...
, and ''ħ'' is the
reduced Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
.

# Quantization

''Charge quantization'' is the principle that the charge of any object is an
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of ...
multiple of the elementary charge. Thus, an object's charge can be exactly 0 ''e'', or exactly 1 ''e'', −1 ''e'', 2 ''e'', etc., but not  ''e'', or −3.8 ''e'', etc. (There may be exceptions to this statement, depending on how "object" is defined; see below.) This is the reason for the terminology "elementary charge": it is meant to imply that it is an indivisible unit of charge.

## Fractional elementary charge

There are two known sorts of exceptions to the indivisibility of the elementary charge:
quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
s and
quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exam ...
s. *
Quark A quark () is a type of elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nucleus, atomic nuclei ...
s, first posited in the 1960s, have quantized charge, but the charge is quantized into multiples of . However, quarks cannot be isolated; they exist only in groupings, and stable groupings of quarks (such as a
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
, which consists of three quarks) all have charges that are integer multiples of ''e''. For this reason, either 1 ''e'' or can be justifiably considered to be "the
quantum In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an fundamental interaction, interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the ...
of charge", depending on the context. This charge commensurability, "charge quantization", has partially motivated Grand unified Theories. *
Quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exam ...
s are not particles as such, but rather an emergent entity in a complex material system that behaves like a particle. In 1982 Robert Laughlin explained the fractional quantum Hall effect by postulating the existence of fractionally charged
quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exam ...
s. This theory is now widely accepted, but this is not considered to be a violation of the principle of charge quantization, since quasiparticles are not
elementary particles In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, antiqu ...
.

## Quantum of charge

All known
elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, antiqu ...
s, including quarks, have charges that are integer multiples of  ''e''. Therefore, the "
quantum In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an fundamental interaction, interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the ...
of charge" is  ''e''. In this case, one says that the "elementary charge" is three times as large as the "quantum of charge". On the other hand, all ''isolatable'' particles have charges that are integer multiples of ''e''. (Quarks cannot be isolated: they exist only in collective states like protons that have total charges that are integer multiples of ''e''.) Therefore, the "quantum of charge" is ''e'', with the proviso that quarks are not to be included. In this case, "elementary charge" would be synonymous with the "quantum of charge". In fact, both terminologies are used. For this reason, phrases like "the quantum of charge" or "the indivisible unit of charge" can be ambiguous unless further specification is given. On the other hand, the term "elementary charge" is unambiguous: it refers to a quantity of charge equal to that of a proton.

## Lack of fractional charges

Paul Dirac Paul Adrien Maurice Dirac (; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century. He was the Lucasian Professor of Mathematics at the Univer ...
argued in 1931 that if
magnetic monopole In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magneti ...
s exist, then electric charge must be quantized; however, it is unknown whether magnetic monopoles actually exist. It is currently unknown why isolatable particles are restricted to integer charges; much of the
string theory landscape The string theory landscape or landscape of vacua refers to the collection of possible false vacuum, false vacua in string theory,The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See Micha ...
appears to admit fractional charges.

# Experimental measurements of the elementary charge

Before reading, it must be remembered that the elementary charge is exactly defined since 20 May 2019 by the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
.

## In terms of the Avogadro constant and Faraday constant

If the Avogadro constant ''N''A and the
Faraday constant In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole (unit), mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefi ...
''F'' are independently known, the value of the elementary charge can be deduced using the formula : $e = \frac.$ (In other words, the charge of one mole of electrons, divided by the number of electrons in a mole, equals the charge of a single electron.) This method is ''not'' how the ''most accurate'' values are measured today. Nevertheless, it is a legitimate and still quite accurate method, and experimental methodologies are described below. The value of the Avogadro constant ''N''A was first approximated by Johann Josef Loschmidt who, in 1865, estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas. Today the value of ''N''A can be measured at very high accuracy by taking an extremely pure crystal (often
silicon Silicon is a chemical element with the Symbol (chemistry), symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a Tetravalence, tetravalent metalloid and semiconductor. It is a member ...
), measuring how far apart the atoms are spaced using
X-ray diffraction X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to Diffraction, diffract into many specific directions. By measurin ...
or another method, and accurately measuring the density of the crystal. From this information, one can deduce the mass (''m'') of a single atom; and since the
molar mass In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance which is the number of moles in that sample, measured in mole (unit), moles. The molar mass is a bulk, not ...
(''M'') is known, the number of atoms in a mole can be calculated: ''N''A = ''M''/''m''. The value of ''F'' can be measured directly using Faraday's laws of electrolysis. Faraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published by
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, ...
in 1834. In an
electrolysis In chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, str ...
experiment, there is a one-to-one correspondence between the electrons passing through the anode-to-cathode wire and the ions that plate onto or off of the anode or cathode. Measuring the mass change of the anode or cathode, and the total charge passing through the wire (which can be measured as the time-integral of
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving par ...
), and also taking into account the molar mass of the ions, one can deduce ''F''. The limit to the precision of the method is the measurement of ''F'': the best experimental value has a relative uncertainty of 1.6 ppm, about thirty times higher than other modern methods of measuring or calculating the elementary charge.

## Oil-drop experiment

A famous method for measuring ''e'' is Millikan's oil-drop experiment. A small drop of oil in an electric field would move at a rate that balanced the forces of
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
,
viscosity The viscosity of a fluid is a measure of its drag (physics), resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quant ...
(of traveling through the air), and
electric force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental scientific law, law of physics that quantifies the amount of force between two stationary, electric charge, electrically charged particles. The electric force between char ...
. The forces due to gravity and viscosity could be calculated based on the size and velocity of the oil drop, so electric force could be deduced. Since electric force, in turn, is the product of the electric charge and the known electric field, the electric charge of the oil drop could be accurately computed. By measuring the charges of many different oil drops, it can be seen that the charges are all integer multiples of a single small charge, namely ''e''. The necessity of measuring the size of the oil droplets can be eliminated by using tiny plastic spheres of a uniform size. The force due to viscosity can be eliminated by adjusting the strength of the electric field so that the sphere hovers motionless.

## Shot noise

Any
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving par ...
will be associated with
noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
from a variety of sources, one of which is
shot noise Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of Point (geometry), points ra ...
. Shot noise exists because a current is not a smooth continual flow; instead, a current is made up of discrete electrons that pass by one at a time. By carefully analyzing the noise of a current, the charge of an electron can be calculated. This method, first proposed by
Walter H. Schottky Walter Hans Schottky (23 July 1886 – 4 March 1976) was a German physicist who played a major early role in developing the theory of electron and ion emission phenomena, invented the Screen-grid#Screen grid, screen-grid vacuum tube in 1915 ...
, can determine a value of ''e'' of which the accuracy is limited to a few percent. However, it was used in the first direct observation of Laughlin
quasiparticle In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For exam ...
s, implicated in the fractional quantum Hall effect.

## From the Josephson and von Klitzing constants

Another accurate method for measuring the elementary charge is by inferring it from measurements of two effects in
quantum mechanics Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including qua ...
: The
Josephson effect In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mech ...
, voltage oscillations that arise in certain
superconducting Superconductivity is a set of physical properties observed in certain materials where Electrical resistance and conductance, electrical resistance vanishes and magnetic field, magnetic flux fields are expelled from the material. Any material e ...
structures; and the
quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantum mechanics, quantized version of the Hall effect which is observed in 2DEG, two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the ...
, a quantum effect of electrons at low temperatures, strong magnetic fields, and confinement into two dimensions. The Josephson constant is : $K_\text = \frac,$ where ''h'' is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
. It can be measured directly using the
Josephson effect In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mech ...
. The von Klitzing constant is : $R_\text = \frac.$ It can be measured directly using the
quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantum mechanics, quantized version of the Hall effect which is observed in 2DEG, two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the ...
. From these two constants, the elementary charge can be deduced: : $e = \frac.$

## CODATA method

The relation used by
CODATA The Committee on Data of the International Science Council (CODATA) was established in 1966 as the Committee on Data for Science and Technology, originally part of the International Council of Scientific Unions, now part of the International ...
to determine elementary charge was: : $e^2 = \frac = 2h \alpha \varepsilon_0 c,$ where ''h'' is the
Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalenc ...
, ''α'' is the
fine-structure constant In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scien ...
, ''μ''0 is the
magnetic constant The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant ...
, ''ε''0 is the
electric constant Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the Permittivity, absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the el ...
, and ''c'' is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
. Presently this equation reflects a relation between ''ε''0 and ''α'', while all others are fixed values. Thus the relative standard uncertainties of both will be same.

# See also

* Committee on Data of the International Science Council

# Further reading

*''Fundamentals of Physics'', 7th Ed., Halliday, Robert Resnick, and Jearl Walker. Wiley, 2005 {{Portal bar, Science Physical constants Units of electrical charge es:Carga eléctrica#Carga eléctrica elemental