Elementary charge

Elementary charge
Elementary charge
Unit system	Atomic units
Unit of	electric charge
Symbol	e
Conversions
1 ein ...	... is equal to ...
coulombs	1.602176634×10−19
; (natural units)	0.30282212088
; (megaelectronvolt-femtometers)
statC	≘ 4.80320425(10)×10−10

Elementary charge
Elementary charge
Definition:	charge of a proton
Symbol:	e
SI value:	1.602176634×10−19 C

Last updated March 13, 2023

The elementary charge, usually denoted by e, is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 e.^[2] This elementary charge is a fundamental physical constant.

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
References
Further reading

In the SI system of units, the value of the elementary charge is exactly defined as $e$ = 1.602176634×10⁻¹⁹ coulombs, or 160.2176634 zeptocoulombs (zC).^[1] 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 4.8032047...×10⁻¹⁰ statcoulombs .^[3]

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, the elementary charge had also been indirectly inferred to ~3% accuracy from blackbody spectra by Max Planck in 1901^[4] and (through the Faraday constant) at order-of-magnitude accuracy by Johann Loschmidt's measurement of the Avogadro number 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.^[6] 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 some other natural unit systems the unit of charge is defined as ${\sqrt {\varepsilon _{0}\hbar c}},$ with the result that

e={\sqrt {4\pi \alpha }}{\sqrt {\varepsilon _{0}\hbar c}}\approx 0.30282212088{\sqrt {\varepsilon _{0}\hbar c}},

where $α$ is the fine-structure constant, $c$ is the speed of light, $ε 0$ 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 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 1/2 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 1/3 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 e or 1/3e can be justifiably considered to be "the quantum 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 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 particles, including quarks, have charges that are integer multiples of 1/3 e. Therefore, the "quantum of charge" is 1/3 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.^[7] 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 monopoles exist, then electric charge must be quantized; however, it is unknown whether magnetic monopoles actually exist.^[8]^[9] It is currently unknown why isolatable particles are restricted to integer charges; much of the string theory landscape appears to admit fractional charges.^[10]^[11]

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.

In terms of the Avogadro constant and Faraday constant

If the Avogadro constant N_A and the Faraday constant F are independently known, the value of the elementary charge can be deduced using the formula

e={\frac {F}{N_{\text{A}}}}.

(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.^[12] Today the value of N_A 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: N_A = M/m.^[13]

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.^[14] 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.^[13]

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.^[13]^[15]

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

Any electric current will be associated with 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.^[16] However, it was used in the first direct observation of Laughlin quasiparticles, implicated in the fractional quantum Hall effect.^[17]

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

K_{\text{J}}={\frac {2e}{h}},

where h is the Planck constant. It can be measured directly using the Josephson effect.

The von Klitzing constant is

R_{\text{K}}={\frac {h}{e^{2}}}.

It can be measured directly using the quantum Hall effect.

From these two constants, the elementary charge can be deduced:

e={\frac {2}{R_{\text{K}}K_{\text{J}}}}.

CODATA method

The relation used by CODATA to determine elementary charge was:

e^{2}={\frac {2h\alpha }{\mu _{0}c}}=2h\alpha \varepsilon _{0}c,

where h is the Planck constant, α is the fine-structure constant, μ₀ is the magnetic constant, ε₀ is the electric constant, and c is the speed of light. Presently this equation reflects a relation between ε₀ 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


Particle	Expected charge	Experimental constraint	Notes
electron	$q_{\text{e}}=-e$	exact	by definition
proton	$q_{\text{p}}=e$	$\left\|{q_{\text{p}}-e}\right\|<10^{-21}e$	by finding no measurable sound when an alternating electric field is applied to SF₆ gas in a spherical resonator^[18]
positron	$q_{{\text{e}}^{+}}=e$	$\left\|{q_{{\text{e}}^{+}}-e}\right\|<10^{-9}e$	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.^[19]
antiproton	$q_{\bar {\text{p}}}=-e$	$\left\|{q_{\bar {\text{p}}}+q_{\text{p}}}\right\|<10^{-9}e$	Hori et al.^[20] as cited in antiproton/proton charge difference listing of the Particle Data Group ^[21] The Particle Data Group Wikipedia article has a link to the current online version of the particle data.

Related Research Articles

The electron 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 no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, $ħ$ . Being fermions, no two electrons can occupy the same quantum state, per the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

In physics, an electronvolt 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 vacuum. When used as a unit of energy, the numerical value of 1 eV in joules is equivalent to the numerical value of the charge of an electron in coulombs. Under the 2019 redefinition of the SI base units, this sets 1 eV equal to the exact value 1.602176634×10⁻¹⁹ J.

An electromagnetic field is a classical field produced by moving electric charges. It is the field described by classical electrodynamics and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics. The electromagnetic field propagates at the speed of light and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature.

Electric charge is the physical property of matter that causes matter to experience a force when placed in an electromagnetic field. Electric charge can be positive or negative. Like charges repel each other and unlike charges attract each other. An object with an absence of net charge is referred to as neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

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, as well as the fundamental bosons, which generally are force particles that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle.

A proton is a stable subatomic particle, symbol p, 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 ratio). Protons and neutrons, each with masses of approximately one atomic mass unit, are jointly referred to as "nucleons" (particles present in atomic nuclei).

In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by $α$ , is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.

The 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 $R xy$ exhibits steps that take on the quantized values

The Bohr radius (a₀) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.29177210903(80)×10⁻¹¹ m.

The Hartree atomic units are a system of natural units of measurement which is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They are named after the physicist Douglas Hartree. Atomic units are often abbreviated "a.u." or "au", not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in other contexts.

In spectroscopy, the Rydberg constant, symbol $for heavy atoms or for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants according to his model of the atom.$

The magnetic flux, represented by the symbol $Φ$ , threading some contour or loop is defined as the magnetic field $B$ multiplied by the loop area $S$ , i.e. $Φ = B \cdot S$ . Both $B$ and $S$ can be arbitrary, meaning $Φ$ can be as well. However, if one deals with the superconducting loop or a hole in a bulk superconductor, the magnetic flux threading such a hole/loop is quantized. The (superconducting) magnetic flux quantum $Φ 0 = h /(2 e)$ ≈ 2.067833848...×10⁻¹⁵ Wb is a combination of fundamental physical constants: the Planck constant $h$ and the electron charge $e$ . Its value is, therefore, the same for any superconductor. The phenomenon of flux quantization was discovered experimentally by B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Näbauer, in 1961. The quantization of magnetic flux is closely related to the Little–Parks effect, but was predicted earlier by Fritz London in 1948 using a phenomenological model.

In physics, a coupling constant or gauge coupling parameter, is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies divided by the distance squared, $, between the bodies; thus: in for Newtonian gravity and in for electrostatic. This description remains valid in modern physics for linear theories with static bodies and massless force carriers.$

Charge number (z) refers to a quantized value of electric charge, with the quantum of electric charge being the elementary charge, so that the charge number equals the electric charge (q) in coulombs divided by the elementary-charge constant (e), or z = q/e. The charge numbers for ions (and also subatomic particles) are written in superscript, e.g. Na⁺ is a sodium ion with charge number positive one (an electric charge of one elementary charge). Atomic numbers (Z) are a special case of charge numbers, referring to the charge number of an atomic nucleus, as opposed to the net charge of an atom or ion. All particles of ordinary matter have integer-value charge numbers, with the exception of quarks, which cannot exist in isolation under ordinary circumstances (the strong force keeps them bound into hadrons of integer charge numbers).

The conductance quantum, denoted by the symbol $G 0$ , is the quantized unit of electrical conductance. It is defined by the elementary charge e and Planck constant h as:

The mass-to-charge ratio (m/Q) is a physical quantity relating the mass (quantity of matter) and the electric charge of a given particle, expressed in units of kilograms per coulomb (kg/C). It is most widely used in the electrodynamics of charged particles, e.g. in electron optics and ion optics.

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 equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by $. The reduced Planck constant, or Dirac constant, equal to the constant divided by, is denoted by .$

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 coherent unit of a quantity. For example, the elementary charge $e$ may be used as a natural unit of electric charge, and the speed of light $c$ may be used as a natural unit of speed. A purely natural system of units has all of its units defined such that each of these can be expressed as a product of powers of defining physical constants.

The nucleon magnetic moments are the intrinsic magnetic dipole moments of the proton and neutron, symbols μ_p and μ_n. The nucleus of atoms comprises protons and neutrons, both nucleons that behave as small magnets. Their magnetic strengths are measured by their magnetic moments. The nucleons interact with normal matter through either the nuclear force or their magnetic moments, with the charged proton also interacting by the Coulomb force.

References

1 2 Newell, David B.; Tiesinga, Eite (2019). The International System of Units (SI). NIST Special Publication 330. Gaithersburg, Maryland: National Institute of Standards and Technology. doi:10.6028/nist.sp.330-2019. S2CID 242934226.
↑ 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. In the US, the base of the natural logarithm is often denoted e (italicized), while it is usually denoted e (roman type) in the UK and Continental Europe.
↑ This is derived from the CODATA 2018 value, since one coulomb corresponds to exactly 2997924580 statcoulombs. The conversion factor is ten times the numerical value of speed of light in metres per second.
↑ Klein, Martin J. (1 October 1961). "Max Planck and the beginnings of the quantum theory". Archive for History of Exact Sciences. 1 (5): 459–479. doi:10.1007/BF00327765. ISSN 1432-0657. S2CID 121189755.
↑ "2018 CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
↑ G. J. Stoney (1894). "Of the "Electron," or Atom of Electricity". Philosophical Magazine . 5. 38: 418–420. doi:10.1080/14786449408620653.
↑ Q is for Quantum, by John R. Gribbin, Mary Gribbin, Jonathan Gribbin, page 296, Web link
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↑ Loschmidt, J. (1865). "Zur Grösse der Luftmoleküle". Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien. 52 (2): 395–413. English translation Archived February 7, 2006, at the Wayback Machine .
1 2 3 Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006" (PDF). Reviews of Modern Physics . 80 (2): 633–730. arXiv: 0801.0028 . Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633. Archived from the original (PDF) on 2017-10-01. Direct link to value .
↑ Ehl, Rosemary Gene; Ihde, Aaron (1954). "Faraday's Electrochemical Laws and the Determination of Equivalent Weights". Journal of Chemical Education. 31 (May): 226–232. Bibcode:1954JChEd..31..226E. doi:10.1021/ed031p226.
↑ Mohr, Peter J.; Taylor, Barry N. (1999). "CODATA recommended values of the fundamental physical constants: 1998" (PDF). Journal of Physical and Chemical Reference Data . 28 (6): 1713–1852. Bibcode:1999JPCRD..28.1713M. doi:10.1063/1.556049. Archived from the original (PDF) on 2017-10-01.
↑ Beenakker, Carlo; Schönenberger, Christian (2006). "Quantum Shot Noise". Physics Today. 56 (5): 37–42. arXiv: cond-mat/0605025 . doi:10.1063/1.1583532. S2CID 119339791.
↑ de-Picciotto, R.; Reznikov, M.; Heiblum, M.; Umansky, V.; Bunin, G.; Mahalu, D. (1997). "Direct observation of a fractional charge". Nature. 389 (162–164): 162. arXiv: cond-mat/9707289 . Bibcode:1997Natur.389..162D. doi:10.1038/38241. S2CID 4310360.
↑ Bressi, G.; Carugno, G.; Della Valle, F.; Galeazzi, G.; Sartori, G. (2011). "Testing the neutrality of matter by acoustic means in a spherical resonator". Physical Review A. 83 (5): 052101. arXiv: 1102.2766 . doi:10.1103/PhysRevA.83.052101. S2CID 118579475.
↑ Ahmadi, M.; et al. (2016). "An improved limit on the charge of antihydrogen from stochastic acceleration" (PDF). Nature. 529 (7586): 373–376. doi:10.1038/nature16491. PMID 26791725. S2CID 205247209 . Retrieved May 1, 2022.
↑ Hori, M.; et al. (2011). "Two-photon laser spectroscopy of antiprotonic helium and the antiproton-to-electron mass ratio". Nature. 475 (7357): 484–488. arXiv: 1304.4330 . doi:10.1038/nature10260. PMID 21796208. S2CID 4376768.
↑ Olive, K. A.; et al. (2014). "Review of particle physics" (PDF). Chinese Physics C. 38 (9): 090001. doi:10.1088/1674-1137/38/9/090001. S2CID 118395784.