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 electrons res ...

carried by a single proton 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 electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

, which has charge −1 . This elementary charge is a fundamental physical constant. In the SI system of units, the value of the elementary charge is exactly defined as

e

= coulombs, or 160.2176634 zeptocoulombs (zC). Since the 2019 redefinition of SI base units, the seven SI base units are defined by seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment 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. Atomic theory traces its origins to an ancient philosophical tradition known as atomism. According to this idea, if one were to take a lump of matter ...

, the elementary charge had also been indirectly inferred to ~3% accuracy from blackbody spectra by Max Planck 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 of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of ...

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

Avagadro's number The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining co ...

in 1865.

As a unit

In some natural unit systems, such as the system of atomic units, ''e'' functions as the unit of electric charge. The use of elementary charge as a unit was promoted by George Johnstone Stoney in 1874 for the first system of natural units, called Stoney units. 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 from rest through an electric potential difference of one volt in vacu ...

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, ''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 theory of relativity, is the upper limit fo ...

, ''ε''₀ is the electric constant, and ''ħ'' is the reduced Planck constant.

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 languag ...

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: quarks and quasiparticles. * Quarks, 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, 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 interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizat ...

of charge", depending on the context. This charge commensurability, "charge quantization", has partially motivated Grand unified Theories. * Quasiparticles 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 (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of e^2/h. It is a property of a collective state in which elec ...

by postulating the existence of fractionally charged quasiparticles. 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.

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, ...

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 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 monopoles 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 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 pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...

In terms of the Avogadro constant and Faraday constant

If the

Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining ...

''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 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 Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic ...

), measuring how far apart the atoms are spaced using X-ray diffraction 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 (''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 inducti ...

in 1834. In an electrolysis 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), 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 stro ...

viscosity The viscosity of a fluid is a measure of its 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 quantifies the int ...

(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 quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventio ...

. 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 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 aris ...

from a variety of sources, one of which is shot noise. 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 vacuum tube in 1915 while working at Siemen ...

, 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 quasiparticles, 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 a fundamental 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 quantum chemistry, ...

: The Josephson effect, voltage oscillations that arise in certain superconducting structures; and the quantum Hall effect, 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 equivale ...

. It can be measured directly using the Josephson effect. The von Klitzing constant is :

R_\text = \frac.

It can be measured directly using the quantum Hall effect. From these two constants, the elementary charge can be deduced: :

e = \frac.

CODATA method

The relation used by CODATA to determine elementary charge was: :

e^2 = \frac = 2h \alpha \varepsilon_0 c,

where ''h'' is the

, ''α'' is the fine-structure constant, ''μ''₀ is the magnetic constant, ''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.