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| {{infobox
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| | above = Elementary electric charge
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| | label1 = Definition:
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| | data1 = [[Electric charge|Charge]] of a [[proton]]
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| | label2 = Symbol
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| | data2 = ''e''
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| | label3 = Value in [[Coulomb]]s:
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| | data3 = {{physconst|e}}
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| }}
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| The '''elementary charge''', usually denoted as ''e'', is the [[electric charge]] carried by a single [[proton]], or equivalently, the [[Negation (algebra)|negation]] (opposite) of the electric charge carried by a single [[electron]].<ref>Note that the symbol ''e'' has many other meanings. Somewhat confusingly, in [[atomic physics]], ''e'' sometimes denotes the electron charge, i.e. the ''negative'' of the elementary charge.</ref> This elementary charge is a fundamental [[physical constant]]. To avoid confusion over its sign, ''e'' is sometimes called the '''elementary positive charge'''. This charge has a measured value of approximately {{physconst|e|unit=no|after= [[coulomb]]s.}} In the [[centimeter gram second system of units|cgs]] system, ''e'' is {{val|4.80320425|(10)|e=-10|u=[[statcoulomb]]s}}.<ref>This is derived from the NIST value and uncertainty, using the fact that one coulomb is ''exactly'' {{val|2997924580}} statcoulombs. (The conversion is ten times the numerical [[speed of light]] in meters/second.)</ref>
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| == Elementary charge as a unit ==
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| {{see also|New SI definitions}}
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| {{Infobox unit
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| | bgcolour =
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| | name = Elementary charge <small>(as a [[Units of measurement|unit]] of [[electric charge|charge]])</small>
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| | image =
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| | caption =
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| | standard = [[Atomic units]]
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| | quantity = [[electric charge]]
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| | symbol = e
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| | namedafter =
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| | units1 = [[coulomb]]
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| | inunits1 = {{physconst|e|unit=no}}
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| | units2 =[[statcoulomb]]
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| | inunits2 ={{val|4.80320425|(10)|e=-10}}
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| | units3 = √([[MeV]]*[[Femtometre|fm]])
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| | inunits3 = √1.4399764
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| | units4 =
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| | inunits4 =
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| | units5 =
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| | inunits5 =
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| }}
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| In some [[natural unit]] systems, such as the system of [[atomic units]], ''e'' functions as the [[units of measurement|unit]] of electric charge, that is ''e'' is equal to 1 e in those unit systems. 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>
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| {{cite journal
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| |author=G. J. Stoney
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| |year=1894
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| |title=Of the "Electron," or Atom of Electricity
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| |url=http://www.chemteam.info/Chem-History/Stoney-1894.html
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| |journal=[[Philosophical Magazine]]
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| |series=5 |volume=38 |pages=418–420
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| |doi=10.1080/14786449408620653
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| }}</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]] reminds us that the elementary charge was once called ''electron''.
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| The magnitude of the elementary charge was first measured in [[Robert Andrews Millikan|Robert A. Millikan]]'s noted [[oil drop experiment]] in 1909.<ref>[http://www.juliantrubin.com/bigten/millikanoildrop.html Robert Millikan: The Oil-Drop Experiment]</ref>
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| == Quantization ==
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| ''Charge quantization'' is the principle that the charge of any object is an [[integer]] multiple of the elementary charge. Thus, e.g., an object's charge can be exactly 0 ''e'', or exactly 1 ''e'', −1 ''e'', 2 ''e'', etc., but not, say, {{frac|1|2}} ''e'', or −3.8 ''e'', etc. (There may be exceptions to this statement, depending on how "object" is defined; see below.)
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| This is the reason for the terminology "elementary charge": it is meant to imply that it is an indivisible unit of charge.
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| === Charges less than an elementary charge ===
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| There are two known sorts of exceptions to the indivisibility of the elementary charge: [[quark]]s and [[quasiparticle]]s.
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| *[[Quark]]s, first posited in the 1960s, have quantized charge, but the charge is quantized into multiples of {{frac|1|3}} ''e''. However, quarks cannot be seen as isolated particles; 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 {{frac|1|3}} ''e'' can be justifiably considered to be "the [[quantum]] of charge", depending on the context.
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| *[[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]].
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| ===What is the quantum of charge?===
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| All known [[elementary particle]]s, including quarks, have charges that are integer multiples of {{frac|1|3}} ''e''. Therefore, one can say that the "[[quantum]] of charge" is {{frac|1|3}} ''e''. In this case, one says that the "elementary charge" is three times as large as the "quantum of charge".
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| On the other hand, all ''isolatable'' particles have charges that are integer multiples of ''e''. (Quarks cannot be isolated, except in combinations like protons that have total charges that are integer multiples of ''e''.) Therefore, one can say that 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".
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| In fact, both terminologies are used.<ref>''Q is for Quantum'', by John R. Gribbin, Mary Gribbin, Jonathan Gribbin, page 296, [http://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 universally refers to the charge of a proton.
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| == Experimental measurements of the elementary charge ==
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| === In terms of the Avogadro constant and Faraday constant ===
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| 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
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| ::<math>e = \frac{F}{N_{\mathrm{A}}} </math>
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| (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.)
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| In practice, 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:
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| 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 | authorlink = 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].</ref> Today the value of ''N''<sub>A</sub> can be measured at very high accuracy by taking an extremely pure crystal (in practice, 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: ''N''<sub>A</sub> = ''M''/''m''.<ref name=CODATA />
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| 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 | coauthors = Ihde, Aaron | 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''.<ref name=CODATA>{{CODATA2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?e}}.</ref>
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| 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.<ref name=CODATA /><ref>{{CODATA1998}}.</ref>
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| === Oil-drop experiment ===
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| {{main|Oil-drop experiment}}
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| 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''.
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| 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.
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| === Shot noise ===
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| {{main|Shot noise}}
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| 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 give only a value of ''e'' accurate to a few percent.<ref>{{Cite arxiv | first1 = Carlo | last1 = Beenakker | first2 = Christian | last2 = Schönenberger | title = Quantum Shot Noise. Fluctuations in the flow of electrons signal the transition from particle to wave behavior | eprint = cond-mat/0605025 | postscript = <!--None-->}}.</ref> However, it was used in the first direct observation of [[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 | postscript = <!--None-->|bibcode = 1997Natur.389..162D }}.</ref>
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| ===From the Josephson and von Klitzing constants===
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| 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
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| :<math>K_\mathrm{J} = \frac{2e}{h}</math>
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| (where ''h'' is the [[Planck constant]]). It can be measured directly using the [[Josephson effect]].
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| The [[von Klitzing constant]] is
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| :<math>R_\mathrm{K} = \frac{h}{e^2}.</math>
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| It can be measured directly using the [[quantum Hall effect]].
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| From these two constants, the elementary charge can be deduced:
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| :<math>e = \frac{2}{R_\mathrm{K} K_\mathrm{J}}.</math>
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| ===CODATA method===
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| In the most recent [[CODATA]] adjustments,<ref name=CODATA /> the elementary charge is not an independently defined quantity. Instead, a value is derived from the relation
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| :<math>e^2 = \frac{2h \alpha}{\mu_0 c} = 2h \alpha \epsilon_0 c</math>
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| 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]]. The [[Measurement uncertainty|uncertainty]] in the value of ''e'' is currently determined entirely by the uncertainty in the Planck constant.
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| The most precise values of the Planck constant come from [[watt balance]] experiments, which are currently used to measure the product ''K''{{su|p=2|b=J}}''R''<sub>K</sub>. The most precise values of the fine structure constant come from comparisons of the measured and calculated value of the [[gyromagnetic ratio]] of the electron.<ref name=CODATA />
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| ==References==
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| *'''Fundamentals of Physics''', 7th Ed., Halliday, Robert Resnick, and Jearl Walker. Wiley, 2005
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| {{reflist}}
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| [[Category:Physical constants]]
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| [[Category:Units of electrical charge]]
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| [[es:Carga eléctrica#Carga eléctrica elemental]]
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