The elementary charge, usually denoted by , is a fundamental

physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a ...

, defined as the

electric charge Electric charge (symbol ''q'', sometimes ''Q'') is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative''. Like charges repel each other and ...

carried by a single

proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...

(+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

, which has charge −1 . In

SI units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...

, the

coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is defined to be equal to the electric charge delivered by a 1 ampere current in 1 second, with the elementary charge ''e'' as a defining c ...

is defined such that the value of the elementary charge is exactly or 160.2176634 zeptocoulombs (zC). Since the

2019 revision of the SI In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artefacts such as the standard kilogram. Effective 20 May 2019, the 144th ...

, 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 al ...

s are defined in terms of 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 (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 mechanical units are unamb ...

(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 ...

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 that matter is composed of particles called atoms. The definition of the word "atom" has changed over the years in response to scientific discoveries. Initially, it referred to a hypothetical concept of ...

, 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 German Theoretical physics, theoretical physicist whose discovery of energy quantum, 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 (symbol , sometimes stylized as ℱ) is a physical constant defined as the quotient of the total electric charge () by the amount () of elementary charge carriers in any given sample of matter: it ...

) at order-of-magnitude accuracy by Johann Loschmidt's measurement of the

Avogadro constant The Avogadro constant, commonly denoted or , is an SI defining constant with an exact value of when expressed in reciprocal moles. It defines the ratio of the number of constituent particles to the amount of substance in a sample, where th ...

in 1865.

As a unit

In some natural unit systems, such as the system of

atomic units The atomic units are a system of natural units of measurement that is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They were originally suggested ...

, ''e'' functions as the unit of

. The use of elementary charge as a unit was promoted by

George Johnstone Stoney George Johnstone Stoney (15 February 1826 – 5 July 1911) was an Irish physicist known for introducing the term ''electron'' as the "fundamental unit quantity of electricity". He initially named it ''electrolion'' in 1881, and later named it ...

in 1874 for the first system of natural units, called

Stoney units In physics, the Stoney units form a system of units named after the Irish physicist George Johnstone Stoney, who first proposed them in 1874 (but published only in 1881). They are the earliest example of natural units, i.e., a coherent set of unit ...

. Later, he proposed the name ''electron'' for this unit. At the time, the particle we now call the

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 through an Voltage, electric potential difference of one volt in vacuum ...

(eV) is a remnant of the fact that the elementary charge was once called ''electron''. In other natural unit systems, the unit of charge is defined as

\sqrt,

with the result that

e = \sqrt\sqrt \approx 0.30282212088 \sqrt,

where is the

fine-structure constant In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Alpha, Greek letter ''alpha''), is a Dimensionless physical constant, fundamental physical constant that quantifies the strength of the el ...

, is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

, is the electric constant, and is the

reduced Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

Quantization

''Charge quantization'' is the principle that the charge of any object is an

integer An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...

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 condensed matter physics, a quasiparticle is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Formally, quasiparticles and collective excitations are closely relate ...

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

, 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 (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...

of charge", depending on the context. This charge commensurability, "charge quantization", has partially motivated grand unified theories. *

Quasiparticle In condensed matter physics, a quasiparticle is a concept used to describe a collective behavior of a group of particles that can be treated as if they were a single particle. Formally, quasiparticles and collective excitations are closely relate ...

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 The fractional quantum Hall effect (fractional QHE or FQHE) is the observation of precisely quantized plateaus in the Hall conductance of 2-dimensional (2D) electrons at fractional values of e^2/h, where ''e'' is the electron charge and ''h'' i ...

by postulating the existence of fractionally charged

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. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a con ...

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. The Standard Model presently recognizes seventeen distinct particles—twelve fermions and five bosons. As a c ...

s, including quarks, have charges that are integer multiples of ''e''. Therefore, 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 mathematician and Theoretical physics, theoretical physicist who is considered to be one of the founders of quantum mechanics. Dirac laid the foundations for bot ...

argued in 1931 that if

magnetic monopole In particle physics, a magnetic monopole is a hypothetical 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 "magnetic charge". ...

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 In string theory, the string theory landscape (or landscape of vacua) is the collection of possible false vacua,The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See M. Douglas, "The stat ...

appears to admit fractional charges.

Experimental measurements of the elementary charge

The elementary charge is exactly defined since 20 May 2019 by the

International System of Units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...

. Prior to this change, the elementary charge was a measured quantity whose magnitude was determined experimentally. This section summarizes these historical experimental measurements.

In terms of the Avogadro constant and Faraday constant

If the

''N''_A and the

''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 Johann Josef Loschmidt (15 March 1821 – 8 July 1895), better known as Josef Loschmidt, was an Austrian scientist who performed ground-breaking work in chemistry, physics (thermodynamics, optics, electrodynamics), and crystal forms. Born in Karl ...

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; it has symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic lustre, and is a tetravalent metalloid (sometimes considered a non-metal) and semiconductor. It is a membe ...

), measuring how far apart the atoms are spaced using

X-ray diffraction X-ray diffraction is a generic term for phenomena associated with changes in the direction of X-ray beams due to interactions with the electrons around atoms. It occurs due to elastic scattering, when there is no change in the energy of the waves. ...

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 () (sometimes called molecular weight or formula weight, but see related quantities for usage) of a chemical substance ( element or compound) is defined as the ratio between the mass () and the amount of substance ...

(''M'') is known, the number of atoms in a mole can be calculated: . 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 chemist and physicist who contributed to the study of electrochemistry and electromagnetism. His main discoveries include the principles underlying electromagnetic inducti ...

in 1834. In an

electrolysis In chemistry and manufacturing, electrolysis is a technique that uses Direct current, direct electric current (DC) to drive an otherwise non-spontaneous chemical reaction. Electrolysis is commercially important as a stage in the separation of c ...

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 flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...

), 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 (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...

viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...

(of traveling through the air), and

electric force Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that calculates the amount of force between two electrically charged particles at rest. This electric force is conventionally called the ''electrostatic f ...

. 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

will be associated with

noise Noise is sound, chiefly unwanted, unintentional, or harmful sound considered unpleasant, loud, or disruptive to mental or hearing faculties. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrat ...

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 electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in photon counting in optical devices, where s ...

. 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, 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

s, implicated in the

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 the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

: 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. The effect is named after the British physicist Brian Josephson, who predicted in 1962 ...

, voltage oscillations that arise in certain

superconducting Superconductivity is a set of physical properties observed in superconductors: materials where electrical resistance vanishes and magnetic fields are expelled from the material. Unlike an ordinary metallic conductor, whose resistance decreases g ...

structures; and the

quantum Hall effect The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exhi ...

, 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, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

. It can be measured directly using the

. The von Klitzing constant is

R_\text = \frac.

It can be measured directly using 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

, ''α'' is the

, ''μ''₀ is the

magnetic constant The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum'', ''magnetic constant'') is the magnetic permeability in a classical vacuum. It is a physical constant, conventionall ...

, ''ε''₀ is the electric constant, and ''c'' is the

. 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.

As a unit

Quantization

Fractional elementary charge

Quantum of charge

Lack of fractional charges

Experimental measurements of the elementary charge

In terms of the Avogadro constant and Faraday constant

Oil-drop experiment

Shot noise

From the Josephson and von Klitzing constants

CODATA method

Tests of the universality of elementary charge

See also

Notes

References

Further reading