Editing Elementary charge

{{short description|Charge carried by one proton or electron}}
{{Infobox physical quantity
| name = Elementary charge
| unit = coulomb
| otherunits = 
| symbols = <math>e</math>
| dimension = <math>\mathsf{T I}</math>
| derivations = 
| value = {{physical constants|e}}
}}

The '''elementary charge''', usually denoted by {{Var|e}}, is a fundamental [[physical constant]], defined as the [[electric charge]] [[Charge carrier|carried]] by a single [[proton]]  (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single [[electron]], which has charge −1&nbsp;{{Var|e}}.<ref name="SIBrochure9thEd">{{citation |title=The International System of Units (SI) |author=International Bureau of Weights and Measures |author-link=New SI |date=20 May 2019  |edition=9th |isbn=978-92-822-2272-0 |url=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf| archive-url = https://web.archive.org/web/20211018184555/https://www.bipm.org/documents/20126/41483022/SI-Brochure-9.pdf/fcf090b2-04e6-88cc-1149-c3e029ad8232 |archive-date=18 October 2021 |url-status=live}}</ref>{{efn|The symbol ''e'' has another useful mathematical meaning due to which its use as label for elementary charge is avoided in [[theoretical physics]]. For example, in [[quantum mechanics]] one wants to be able to write compactly [[plane waves]] <math> e^{i \mathbf k \cdot \mathbf r}</math> with the use of [[E (mathematical constant)|Euler's number]] <math> e = e^{1} = \exp(1)</math>. In the US, [[E (mathematical constant)|Euler's number]] is often denoted ''e'' (italicized), while it is usually denoted e (roman type) in the UK and Continental Europe. Somewhat confusingly, in [[atomic physics]], ''e'' sometimes denotes the electron charge, i.e. the ''negative'' of the elementary charge. The symbol ''q''<sub>e</sub> is also used for the charge of an electron.}}

In [[International System of Units|SI units]], the value of the elementary charge is exactly defined as {{nowrap|<math>e</math> {{=}} {{val|1.602176634|e=−19|u=}} [[coulomb]]s,}} or 160.2176634 [[Orders of magnitude (numbers)#10−21|zepto]]<nowiki/>coulombs (zC).<ref name="SI2019">
{{cite book
 | last1 = Newell
 | first1 = David B.
 | last2 = Tiesinga
 | first2 = Eite
 | year = 2019
 | title = The International System of Units (SI)
 | series = NIST Special Publication 330
 | publisher = National Institute of Standards and Technology
 | location = Gaithersburg, Maryland
 | url = https://www.nist.gov/si-redefinition/meet-constants
 | doi = 10.6028/nist.sp.330-2019
 | s2cid = 242934226
}}</ref>  Since the [[2019 revision of the SI]], the seven [[SI base unit]]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]] (CGS), the corresponding quantity is {{val|4.8032047|end=...|e=-10|u=[[statcoulomb]]s}}.{{efn|This is derived from the [[CODATA]] 2018 value, since one coulomb corresponds to exactly {{val|2997924580}} statcoulombs. The conversion factor is ten times the numerical value of [[speed of light]] in [[metres per second]].}}

[[Robert Andrews Millikan|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%.<ref name="Millikan1910">
{{cite journal
 | author = Millikan, R. A.
 | title = The isolation of an ion, a precision measurement of its charge, and the correction of Stokes's law
 | journal = Science
 | volume = 32
 | number = 822
 | pages = 436-448
 | doi = 10.1126/science.32.822.436
 | year = 1910
}}</ref><ref name="Fletcher1982">
{{cite journal
 | author = Fletcher, Harvey
 | title = My work with Millikan on the oil-drop experiment
 | journal = Physics Today
 | volume = 35
 | number = 6
 | pages = 43-47
 | doi = 10.1063/1.2915126
 | year = 1982
}}</ref>  Under assumptions of the then-disputed [[atomic theory]], the elementary charge had also been indirectly inferred to ~3% accuracy from [[Planck%27s_law_of_black-body_radiation|blackbody spectra]] by [[Max Planck]] in 1901<ref name="Klein">{{cite journal|first1=Martin J.|last1=Klein|title=Max Planck and the beginnings of the quantum theory|url=https://doi.org/10.1007/BF00327765|journal=Archive for History of Exact Sciences|date=1 October 1961|issn=1432-0657|volume=1|issue=5|pages=459–479 |doi=10.1007/BF00327765|s2cid=121189755 |url-access=subscription}}</ref> and (through the [[Faraday constant]]) at order-of-magnitude accuracy by [[Johann_Josef_Loschmidt| Johann Loschmidt]]'s measurement of the [[Avogadro constant]] in 1865.

== As a unit ==
{{see also|2019 revision of the SI}}
{{Infobox unit
| bgcolour      = 
| name          = Elementary charge
| image         = 
| caption       = 
| standard      = [[Atomic units]]
| quantity      = [[electric charge]]
| symbol        = ''e''
| namedafter    = 
| units1        = [[coulomb]]s
| inunits1      = {{physconst|e|unit=no}}
| units2        = <math>\sqrt{\varepsilon_0\hbar c}</math>{{br}}([[natural units]])
| inunits2      = 0.30282212088
| units3        = [[statC]]
| inunits3      = ≘&nbsp;{{val|4.80320425|(10)|e=-10}}
}}

In some [[natural unit]] systems, such as the system of [[atomic units]], ''e'' functions as the [[units of measurement|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]].<ref>
{{cite journal
 |author=G. J. Stoney
 |year=1894
 |title=Of the "Electron," or Atom of Electricity
 |url=http://www.chemteam.info/Chem-History/Stoney-1894.html
 |journal=[[Philosophical Magazine]]
 |series=5 |volume=38 |pages=418–420
 |doi=10.1080/14786449408620653
|url-access=subscription
 }}</ref> Later, he proposed the name ''electron'' for this unit. At the time, the particle we now call the [[electron]] 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]] (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 <math>\sqrt{\varepsilon_0\hbar c},</math> with the result that 
<math display=block>e = \sqrt{4\pi\alpha}\sqrt{\varepsilon_0 \hbar c} \approx 0.30282212088 \sqrt{\varepsilon_0 \hbar c},</math>
where {{mvar|α}} is the [[fine-structure constant]], {{mvar|c}} is the [[speed of light]], {{math|''ε''<sub>0</sub>}} is the [[electric constant]], and {{mvar|ħ}} is the [[reduced Planck constant]].

== Quantization ==
{{See also|Partial charge}}
''Charge quantization'' is the principle that the charge of any object is an [[integer]] multiple of the elementary charge. Thus, an object's charge can be exactly 0&nbsp;''e'', or exactly 1&nbsp;''e'', −1&nbsp;''e'', 2&nbsp;''e'', etc., but not  {{sfrac|1|2}}&nbsp;''e'', or −3.8&nbsp;''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]]s and [[quasiparticle]]s.
* [[Quark]]s, first posited in the 1960s, have quantized charge, but the charge is quantized into multiples of {{nowrap|{{sfrac|1|3}}&thinsp;''e''}}. 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&nbsp;''e'' or {{nowrap|{{sfrac|1|3}} ''e''}} can be justifiably considered to be "the [[quantum]] of charge", depending on the context. This charge commensurability, "charge quantization", has partially motivated [[Grand Unified Theory#Motivation|grand unified theories]].
* [[Quasiparticle]]s are not particles as such, but rather an [[emergence|emergent]] entity in a complex material system that behaves like a particle. In 1982 [[Robert B. Laughlin|Robert Laughlin]] explained the [[fractional quantum Hall effect]] by postulating the existence of fractionally charged [[quasiparticle]]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]].

=== Quantum of charge ===
All known [[elementary particle]]s, including quarks, have charges that are integer multiples of {{sfrac|1|3}}&nbsp;''e''. Therefore, the "[[quantum]] of charge" is {{sfrac|1|3}}&nbsp;''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.<ref>''Q is for Quantum'', by John R. Gribbin, Mary Gribbin, Jonathan Gribbin, page 296, [https://books.google.com/books?id=zBsDkgI1uQsC&pg=RA1-PA296 Web link]</ref> 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]] argued in 1931 that if [[magnetic monopole]]s exist, then electric charge must be quantized; however, it is unknown whether magnetic monopoles actually exist.<ref>{{cite journal|doi=10.1146/annurev.ns.34.120184.002333|doi-access=free|title=Magnetic Monopoles|year=1984|last1=Preskill|first1=J.|journal=[[Annual Review of Nuclear and Particle Science]]|volume=34|issue=1|pages=461–530|bibcode=1984ARNPS..34..461P}}</ref><ref>{{cite news |title=Three Surprising Facts About the Physics of Magnets |url=https://www.space.com/42685-physics-of-magnets-surprising-facts.html |access-date=17 July 2019 |work=Space.com |date=2018 |language=en}}</ref> It is currently unknown why isolatable particles are restricted to integer charges; much of the [[string theory landscape]] appears to admit fractional charges.<ref>{{cite journal |last1=Schellekens |first1=A. N. |title=Life at the interface of particle physics and string theory |journal=Reviews of Modern Physics |date=2 October 2013 |volume=85 |issue=4 |pages=1491–1540 |doi=10.1103/RevModPhys.85.1491|arxiv=1306.5083 |bibcode=2013RvMP...85.1491S |s2cid=118418446 }}</ref><ref>{{cite journal |last1=Perl |first1=Martin L. |last2=Lee |first2=Eric R. |last3=Loomba |first3=Dinesh |title=Searches for Fractionally Charged Particles |journal=[[Annual Review of Nuclear and Particle Science]] |date=November 2009 |volume=59 |issue=1 |pages=47–65 |doi=10.1146/annurev-nucl-121908-122035| doi-access=free|bibcode=2009ARNPS..59...47P }}</ref>

{{see also|Anomaly (physics)#Anomaly cancellation}}

== Experimental measurements of the elementary charge ==
The elementary charge is exactly defined since 20 May 2019 by the [[International System of Units]]. 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 [[Avogadro constant]] ''N''<sub>A</sub> and the [[Faraday constant]] ''F'' are independently known, the value of the elementary charge can be deduced using the formula
<math display="block">e = \frac{F}{N_\text{A}}.</math>
(In other words, the charge of one [[Mole (unit)|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''<sub>A</sub> 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.<ref>{{cite journal | first = J. | last = Loschmidt | author-link = Johann Josef Loschmidt | title = Zur Grösse der Luftmoleküle | journal = Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien | volume = 52 | issue = 2 | pages = 395–413 | year =1865}} [http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html English translation] {{webarchive |url=https://web.archive.org/web/20060207130125/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html |date=February 7, 2006 }}.</ref> Today the value of ''N''<sub>A</sub> can be measured at very high accuracy by taking an extremely pure crystal (often [[silicon]]), 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: {{nowrap|1=''N''<sub>A</sub> = ''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]] in 1834.<ref>{{cite journal | author = Ehl, Rosemary Gene |author2=Ihde, Aaron |author-link2=Aaron J. Ihde |title = Faraday's Electrochemical Laws and the Determination of Equivalent Weights | journal = Journal of Chemical Education | year = 1954 | volume = 31 | issue = May | pages = 226–232 | doi = 10.1021/ed031p226 |bibcode = 1954JChEd..31..226E }}</ref> 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''.{{physconst|e|ref=only}}

The limit to the precision of the method is the measurement of ''F'': the best experimental value has a relative uncertainty of 1.6&nbsp;ppm, about thirty times higher than other modern methods of measuring or calculating the elementary charge.<ref>{{cite journal |author-first1=Peter J. |author-last1=Mohr |author-first2=Barry N. |author-last2=Taylor |title=CODATA recommended values of the fundamental physical constants: 1998 |journal=[[Journal of Physical and Chemical Reference Data]] |volume=28 |issue=6 |pages=1713–1852 |bibcode=1999JPCRD..28.1713M |doi=10.1063/1.556049 |year=1999 |url=https://www.nist.gov/pml/div684/fcdc/upload/rmp1998-2.pdf |archive-url=https://web.archive.org/web/20171001122752/https://www.nist.gov/sites/default/files/documents/pml/div684/fcdc/rmp1998-2.pdf|archive-date=2017-10-01}}</ref>

=== Oil-drop experiment ===
{{main|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]], [[viscosity]] (of traveling through the air), and [[electric force]]. 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 ===
{{main|Shot noise}}

Any [[electric current]] will be associated with [[electronic noise|noise]] 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]], can determine a value of ''e'' of which the accuracy is limited to a few percent.<ref>{{Cite journal |last1=Beenakker |first1=Carlo |last2=Schönenberger |first2=Christian |author-link2=Christian Schönenberger |year=2006 |title=Quantum Shot Noise |journal=Physics Today |volume=56 |issue=5 |pages=37–42 |arxiv=cond-mat/0605025 |doi=10.1063/1.1583532 |s2cid=119339791}}</ref> However, it was used in the first direct observation of [[Laughlin wavefunction|Laughlin]] [[quasiparticle]]s, implicated in the [[fractional quantum Hall effect]].<ref>{{Cite journal | journal = Nature | volume = 389 | issue = 162–164 | year = 1997 | doi = 10.1038/38241 | title = Direct observation of a fractional charge | first1 = R. | last1 = de-Picciotto | first2 = M. | last2 = Reznikov | first3 = M. | last3 = Heiblum | first4 = V. | last4 = Umansky | first5 = G. | last5 = Bunin | first6 = D. | last6 = Mahalu | pages = 162 |bibcode = 1997Natur.389..162D | arxiv = cond-mat/9707289 | s2cid = 4310360 }}</ref>

=== 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]]: 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
<math display="block">K_\text{J} = \frac{2e}{h},</math>
where ''h'' is the [[Planck constant]]. It can be measured directly using the [[Josephson effect]].

The [[von Klitzing constant]] is
<math display="block">R_\text{K} = \frac{h}{e^2}.</math>
It can be measured directly using the [[quantum Hall effect]].

From these two constants, the elementary charge can be deduced:
<math display="block">e = \frac{2}{R_\text{K} K_\text{J}}.</math>

=== CODATA method ===
The relation used by [[CODATA]] to determine elementary charge was:
<math display="block">e^2 = \frac{2h \alpha}{\mu_0 c} = 2h \alpha \varepsilon_0 c,</math>
where ''h'' is the [[Planck constant]], ''α'' is the [[fine-structure constant]], ''μ''<sub>0</sub> is the [[magnetic constant]], ''ε''<sub>0</sub> is the [[electric constant]], and ''c'' is the [[speed of light]]. Presently this equation reflects a relation between ''ε''<sub>0</sub> and  ''α'', while all others are fixed values. Thus the relative standard uncertainties of both will be same.

=== Tests  of the universality of elementary charge ===
{| class="wikitable"
|+ 
|-
! Particle !! Expected charge !! Experimental constraint !! Notes
|-
| electron || <math>q_{\text{e}^-}=-e</math> || exact || by definition
|-
| proton || <math>q_\text{p}=e</math> || <math>\left|{q_\text{p} - e}\right| < 10^{-21}e</math> || by finding no measurable sound when an alternating electric field is applied to [[sulfur hexafluoride|SF<sub>6</sub>]] gas in a spherical resonator<ref>
{{cite journal
 | last1      = Bressi | first1     = G.
 | last2      = Carugno | first2     = G.
 | last3      = Della Valle | first3     = F.
 | last4      = Galeazzi | first4     = G.
 | last5      = Sartori | first5      = G.
 | date       = 2011
 | title      = Testing the neutrality of matter by acoustic means in a spherical resonator
 | journal    = Physical Review A
 | volume     = 83
 | number     = 5
 | pages      = 052101
 | doi        = 10.1103/PhysRevA.83.052101
 | arxiv = 1102.2766
 | s2cid = 118579475
}}</ref>
|-
| [[positron]] || <math>q_{\text{e}^+}=e</math> || <math>\left|{q_{\text{e}^+} - e}\right| < 10^{-9}e</math> || by combining the best measured value of the antiproton charge (below) with the low limit placed on antihydrogen's net charge by the [[ALPHA Collaboration]] at [[CERN]].<ref>
{{cite journal
 | display-authors = etal
 | last1 = Ahmadi | first1 = M.
 | date       = 2016
 | title      = An improved limit on the charge of antihydrogen from stochastic acceleration
 | url        = https://www.nature.com/articles/nature16491.pdf
 | journal    = Nature
 | volume     = 529
 | issue      = 7586
 | pages      = 373–376
 | doi        = 10.1038/nature16491
 | pmid = 26791725
 | s2cid = 205247209
 | access-date = May 1, 2022
}}</ref>
|-
| [[antiproton]] || <math>q_{\bar{\text{p}}}=-e</math> || <math>\left|{q_{\bar{\text{p}}} + q_\text{p}}\right| < 10^{-9}e</math> || Hori et al.<ref>
{{cite journal
 | display-authors = etal
 | last1 = Hori | first = M.
 | date       = 2011
 | title      = Two-photon laser spectroscopy of antiprotonic helium and the antiproton-to-electron mass ratio.
 | journal    = Nature
 | volume     = 475
 | issue = 7357
 | pages      = 484–488
 | doi        = 10.1038/nature10260
 | pmid = 21796208
 | arxiv = 1304.4330
 | s2cid = 4376768
}}</ref> as cited in antiproton/proton charge difference listing of the [[Particle Data Group]]<ref>
{{cite journal
 | display-authors = etal
 | last1 = Olive | first1 = K. A.
 | date       = 2014
 | title      = Review of particle physics
 | journal    = Chinese Physics C
 | volume     = 38
 | number     = 9
 | pages      = 090001
 | doi        = 10.1088/1674-1137/38/9/090001
 | s2cid = 118395784
 | url = http://bib-pubdb1.desy.de/record/172097/files/PUBDB-2014-03548.pdf
}}</ref> The Particle Data Group article has a link to the current online version of the particle data.
|}

== See also ==
* [[Committee on Data of the International Science Council]]

== Notes ==
{{notelist}}

== References ==
{{reflist}}

== Further reading ==
* ''Fundamentals of Physics'', 7th Ed., Halliday, Robert Resnick, and Jearl Walker. Wiley, 2005
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[[Category:Physical constants]]
[[Category:Units of electrical charge]]

[[es:Carga eléctrica#Carga eléctrica elemental]]