# Elementary charge

The elementary charge, usually denoted by e or sometimes qe, is the electric charge carried by a single proton or, equivalently, the magnitude of the electric charge carried by a single electron, which has charge −1 e.[2] 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 1.602176634×10−19 C[1] (coulombs). When the 2019 redefinition of SI base units takes effect on 20 May 2019, its value will be exactly 1.602176634×10−19 C by definition of the coulomb. In the centimetre–gram–second system of units (CGS), it is 4.80320425(10)×10−10 statcoulombs.[3]

Robert A. Millikan's oil drop experiment first measured the magnitude of the elementary charge in 1909.[4]

Elementary electric charge
Definition:Charge of a proton
Symbol:e or sometimes qe
Value in coulombs:1.602176634×10−19 C[1]

## As a unit

Elementary charge (as a unit of charge)
Unit systemAtomic units
Unit ofelectric charge
Symbole or q
Conversions
1 e or q in ...... is equal to ...
coulomb   1.602176634×10−19[1]
statcoulomb   4.80320425(10)×10−10
HEP: ħc   0.30282212088
1.4399764

In some natural unit systems, such as the system of atomic units, e functions as the 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.[5] 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.

The maximum capacity of each pixel in a charge-coupled device image sensor, known as the well depth, is typically given in units of electrons,[6] commonly around 105
e
per pixel.

In high-energy physics (HEP), Lorentz–Heaviside units are used, and the charge unit is a dependent one, ${\displaystyle {\sqrt {\hbar c}}}$, so that e = 0.30282212088 ħc.

## 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, say, 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.

### Charges less than an 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 1/3e. 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 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 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.

### What is the quantum of charge?

All known elementary particles, including quarks, have charges that are integer multiples of 1/3 e. Therefore, one can say that 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 only exist in collective states 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".

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.

## Experimental measurements of the elementary charge

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

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

(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 NA 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.[8] Today the value of NA 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: NA = M/m.[9]

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.[10] 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.[9]

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.[9][11]

### 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.[12] However, it was used in the first direct observation of Laughlin quasiparticles, implicated in the fractional quantum Hall effect.[13]

### 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

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

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

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

It can be measured directly using the quantum Hall effect.

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

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

### CODATA method

In the most recent CODATA adjustments,[9] the elementary charge is not an independently defined quantity.[14] Instead, a value is derived from the relation

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

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. The uncertainty in the value of e is currently determined almost entirely by the uncertainty in the Planck constant.

The most precise values of the Planck constant come from Kibble balance experiments, which are used to measure the product K2
J
RK. 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.[9]

## References

1. ^ a b c "CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. US National Institute of Standards and Technology. 20 May 2019. Retrieved 2019-05-20. 2018 CODATA recommended values
2. ^ 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.
3. ^ This is derived from the National Institute of Standards and Technology value and uncertainty, using the fact that one coulomb is exactly 2997924580 statcoulombs. The conversion factor is ten times the numerical speed of light in metres per second.
4. ^ Robert Millikan: The Oil-Drop Experiment
5. ^ G. J. Stoney (1894). "Of the "Electron," or Atom of Electricity". Philosophical Magazine. 5. 38: 418–420. doi:10.1080/14786449408620653.
6. ^ Apogee CCD University – Pixel Binning
7. ^ Q is for Quantum, by John R. Gribbin, Mary Gribbin, Jonathan Gribbin, page 296, Web link
8. ^ 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.
9. 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..
10. ^ 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.
11. ^ 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..
12. ^ Beenakker, Carlo; Schönenberger, Christian. "Quantum Shot Noise. Fluctuations in the flow of electrons signal the transition from particle to wave behavior". arXiv:cond-mat/0605025..
13. ^ 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. Bibcode:1997Natur.389..162D. doi:10.1038/38241..
14. ^ Mohr, Peter J.; Newell, David B. (2010). "The physics of fundamental constants". American Journal of Physics. 78 (4): 338–358. Bibcode:2010AmJPh..78..338M. doi:10.1119/1.3279700. p. 356.

• Fundamentals of Physics, 7th Ed., Halliday, Robert Resnick, and Jearl Walker. Wiley, 2005
Ampere

The ampere (; symbol: A), often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

The International System of Units defines the ampere in terms of other base units by measuring the electromagnetic force between electrical conductors carrying electric current. The earlier CGS measurement system had two different definitions of current, one essentially the same as the SI's and the other using electric charge as the base unit, with the unit of charge defined by measuring the force between two charged metal plates. The ampere was then defined as one coulomb of charge per second. In SI, the unit of charge, the coulomb, is defined as the charge carried by one ampere during one second.

New definitions, in terms of invariant constants of nature, specifically the elementary charge, took effect on 20 May 2019.

Atomic units

Atomic units (au or a.u.) form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of atomic units, Hartree atomic units and Rydberg atomic units, which differ in the choice of the unit of mass and charge. This article deals with Hartree atomic units, where the numerical values of the following four fundamental physical constants are all unity by definition:

In Hartree units, the speed of light is approximately ${\displaystyle 137}$. 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 different contexts.

Bohr magneton

In atomic physics, the Bohr magneton (symbol μB) is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum.

The Bohr magneton is defined in SI units by

${\displaystyle \mu _{\mathrm {B} }={\frac {e\hbar }{2m_{\mathrm {e} }}}}$

and in Gaussian CGS units by

${\displaystyle \mu _{\mathrm {B} }={\frac {e\hbar }{2m_{\mathrm {e} }c}}}$

where

e is the elementary charge,
ħ is the reduced Planck constant,
me is the electron rest mass and
c is the speed of light.

The electron magnetic moment, which is the electron's intrinsic spin magnetic moment, is approximately one Bohr magneton.

Charge density

In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C•m−3), at any point in a volume. Surface charge density (σ) is the quantity of charge per unit area, measured in coulombs per square meter (C•m−2), at any point on a surface charge distribution on a two dimensional surface. Linear charge density (λ) is the quantity of charge per unit length, measured in coulombs per meter (C•m−1), at any point on a line charge distribution. Charge density can be either positive or negative, since electric charge can be either positive or negative.

Like mass density, charge density can vary with position. In classical electromagnetic theory charge density is idealized as a continuous scalar function of position ${\displaystyle {\boldsymbol {x}}}$, like a fluid, and ${\displaystyle \rho ({\boldsymbol {x}})}$, ${\displaystyle \sigma ({\boldsymbol {x}})}$, and ${\displaystyle \lambda ({\boldsymbol {x}})}$ are usually regarded as continuous charge distributions, even though all real charge distributions are made up of discrete charged particles. Due to the conservation of electric charge, the charge density in any volume can only change if an electric current of charge flows into or out of the volume. This is expressed by a continuity equation which links the rate of change of charge density ${\displaystyle \rho ({\boldsymbol {x}})}$ and the current density ${\displaystyle {\boldsymbol {J}}({\boldsymbol {x}})}$.

Since all charge is carried by subatomic particles, which can be idealized as points, the concept of a continuous charge distribution is an approximation, which becomes inaccurate at small length scales. A charge distribution is ultimately composed of individual charged particles separated by regions containing no charge. For example the charge in an electrically charged metal object is made up of conduction electrons moving randomly in the metal's crystal lattice. Static electricity is caused by surface charges consisting of ions on the surface of objects, and the space charge in a vacuum tube is composed of a cloud of free electrons moving randomly in space. The charge carrier density in a conductor is equal to the number of mobile charge carriers (electrons, ions, etc.) per unit volume. The charge density at any point is equal to the charge carrier density multiplied by the elementary charge on the particles. However because the elementary charge on an electron is so small (1.6•10−19 C) and there are so many of them in a macroscopic volume (there are about 1022 conduction electrons in a cubic centimeter of copper) the continuous approximation is very accurate when applied to macroscopic volumes, and even microscopic volumes above the nanometer level.

At atomic scales, due to the uncertainty principle of quantum mechanics, a charged particle does not have a precise position but is represented by a probability distribution, so the charge of an individual particle is not concentrated at a point but is 'smeared out' in space and acts like a true continuous charge distribution. This is the meaning of 'charge distribution' and 'charge density' used in chemistry and chemical bonding. An electron is represented by a wavefunction ${\displaystyle \psi ({\boldsymbol {x}})}$ whose square is proportional to the probability of finding the electron at any point ${\displaystyle {\boldsymbol {x}}}$ in space, so ${\displaystyle |\psi ({\boldsymbol {x}})|^{2}}$ is proportional to the charge density of the electron at any point. In atoms and molecules the charge of the electrons is distributed in clouds called orbitals which surround the atom or molecule, and are responsible for chemical bonds.

Charge number

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).

Coulomb

The coulomb (symbol: C) is the International System of Units (SI) unit of electric charge. It is the charge (symbol: Q or q) transported by a constant current of one ampere in one second:

${\displaystyle 1~{\text{C}}=1~{\text{A}}\times 1~{\text{s}}}$

Thus, it is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt:

${\displaystyle 1~{\text{C}}=1~{\text{F}}\times 1~{\text{V}}}$

The coulomb is equivalent to the charge of approximately 6.242×1018 (1.036×10−5 mol) protons, and −1 C is equivalent to the charge of approximately 6.242×1018 electrons.

A new definition, in terms of the elementary charge, took effect on 20 May 2019. The new definition defines the elementary charge (the charge of the proton) as exactly 1.602176634×10−19 coulombs.

DLVO theory

The DLVO theory (named after Boris Derjaguin and Lev Landau, Evert Verwey and Theodoor Overbeek) explains the aggregation of aqueous dispersions quantitatively and describes the force between charged surfaces interacting through a liquid medium. It combines the effects of the van der Waals attraction and the electrostatic repulsion due to the so-called double layer of counterions. The electrostatic part of the DLVO interaction is computed in the mean field approximation in the limit of low surface potentials - that is when the potential energy of an elementary charge on the surface is much smaller than the thermal energy scale, ${\displaystyle k_{B}T}$. For two spheres of radius ${\displaystyle a}$ each having a charge ${\displaystyle Z}$ (expressed in units of the elementary charge) separated by a center-to-center distance ${\displaystyle r}$ in a fluid of dielectric constant ${\displaystyle \epsilon _{r}}$ containing a concentration ${\displaystyle n}$ of monovalent ions, the electrostatic potential takes the form of a screened-Coulomb or Yukawa potential,

${\displaystyle \beta U(r)=Z^{2}\lambda _{B}\,\left({\frac {e^{\kappa a}}{1+\kappa a}}\right)^{2}\,{\frac {e^{-\kappa r}}{r}},}$

where ${\displaystyle \lambda _{B}}$ is the Bjerrum length, ${\displaystyle \kappa ^{-1}}$ is the Debye–Hückel screening length, which is given by ${\displaystyle \kappa ^{2}=4\pi \lambda _{B}n}$, and ${\displaystyle \beta ^{-1}=k_{B}T}$ is the thermal energy scale at absolute temperature ${\displaystyle T}$.

Electric charge

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two-types of electric charges; positive and negative (commonly carried by protons and electrons respectively). Like charges repel and unlike attract. 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.

Electric charge is a conserved property; the net charge of an isolated system, the amount of positive charge minus the amount of negative charge, cannot change. Electric charge is carried by subatomic particles. In ordinary matter, negative charge is carried by electrons, and positive charge is carried by the protons in the nuclei of atoms. If there are more electrons than protons in a piece of matter, it will have a negative charge, if there are fewer it will have a positive charge, and if there are equal numbers it will have none. Charge is quantized; it comes in integer multiples of individual small units called the elementary charge, e, about 1.602×10−19 coulombs, which is the smallest charge which can exist freely (particles called quarks have smaller charges, multiples of 1/3e, but they are only found in combination, and always combine to form particles with integer charge). The proton has a charge of +e, and the electron has a charge of −e.

An electric charge has an electric field, and if the charge is moving it also generates a magnetic field. The combination of the electric and magnetic field is called the electromagnetic field, and its interaction with charges is the source of the electromagnetic force, which is one of the four fundamental forces in physics. The study of photon-mediated interactions among charged particles is called quantum electrodynamics.

The SI derived unit of electric charge is the coulomb (C) named after French physicist Charles-Augustin de Coulomb. In electrical engineering, it is also common to use the ampere-hour (Ah); in physics and chemistry, it is common to use the elementary charge (e as a unit). Chemistry also uses the Faraday constant as the charge on a mole of electrons. The symbol Q often denotes charge.

Electronvolt

In physics, the electronvolt (symbol eV, also written electron-volt and electron volt) is a unit of energy equal to approximately 1.6×10−19 joules (symbol J) in SI units.

Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric charge q has an energy E = qV after passing through the potential V; if q is quoted in integer units of the elementary charge and the potential in volts, one gets an energy in eV.

Like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C √2hα / μ0c0. It is a common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics. It is commonly used with the metric prefixes milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). In some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion (109) electronvolts; it is equivalent to the GeV.

The Faraday constant, denoted by the symbol F and sometimes stylized as ℱ, is named after Michael Faraday. In physics and chemistry, this constant represents the magnitude of electric charge per mole of electrons. It has the currently accepted value

96485.33212... C mol−1.

This constant has a simple relation to two other physical constants:

${\displaystyle F\,=\,eN_{A}}$

where

e ≈ 1.602176634×10−19 C;
NA ≈ 6.02214076×1023 mol−1.

NA is the Avogadro constant (the ratio of the number of particles, N, which is unitless, to the amount of substance, n, in units of moles), and e is the elementary charge or the magnitude of the charge of an electron. This relation holds because the amount of charge of a mole of electrons is equal to the amount of charge in one electron multiplied by the number of electrons in a mole.

One common use of the Faraday constant is electrolysis. One can divide the amount of charge in coulombs by the Faraday constant in order to find the amount (in moles) of the element that has been oxidized.

The value of F was first determined by weighing the amount of silver deposited in an electrochemical reaction in which a measured current was passed for a measured time, and using Faraday's law of electrolysis. Research is continuing into more accurate ways of determining the interrelated constants F, NA, and e.

Fine-structure constant

In physics, the fine-structure constant, also known as Sommerfeld's constant, commonly denoted by α (the Greek letter alpha), is a dimensionless physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles. It is related to the elementary charge e, which characterizes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula 4πε0ħcα = e2. As a dimensionless quantity, it has the same numerical value in all systems of units, which is approximately 1/137 . The inverse of α is 137.035999084(21).While there are multiple physical interpretations for α, it received its name from Arnold Sommerfeld introducing it (1916) in extending the Bohr model of the atom: α quantifies the gap in the fine structure of the spectral lines of the hydrogen atom, which had been precisely measured by Michelson and Morley.

Lambda baryon

The Lambda baryons are a family of subatomic hadron particles containing one up quark, one down quark, and a third quark from a higher flavour generation, in a combination where the quantum wave function changes sign upon the flavour of any two quarks being swapped (thus differing from a Sigma baryon). They are thus baryons, with total isospin of 0, and have either neutral electric charge or the elementary charge +1.

Lambda baryons are usually represented by the symbols Λ0, Λ+c, Λ0b, and Λ+t. In this notation, the superscript character indicates whether the particle is electrically neutral (0) or carries a positive charge (+). The subscript character, or its absence, indicates whether the third quark is a strange quark (Λ0) (no subscript), a charm quark (Λ+c), a bottom quark (Λ0b), or a top quark (Λ+t). Physicists do not expect to observe a Lambda baryon with a top quark because the Standard Model of particle physics predicts that the mean lifetime of top quarks is roughly 5×10−25 seconds; that is about 1/20 of the mean timescale for strong interactions, which indicates that the top quark would decay before a Lambda baryon could form a hadron.

Natural units

In physics, natural units are physical units of measurement based only on universal physical constants. For example, the elementary charge e is a natural unit of electric charge, and the speed of light c is a natural unit of speed. A purely natural system of units has all of its units defined in this way, and usually such that the numerical values of the selected physical constants in terms of these units are exactly 1. These constants are then typically omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of fundamental physical constants, such as e and c, unless it is known which units (in dimensionful units) the expression is supposed to have. In this case, the reinsertion of the correct powers of e, c, etc., can be uniquely determined.

Nuclear magneton

The nuclear magneton (symbol μN), is a physical constant of magnetic moment, defined in SI units by:

${\displaystyle \mu _{\mathrm {N} }={{e\hbar } \over {2m_{\mathrm {p} }}}}$

and in Gaussian CGS units by:

${\displaystyle \mu _{\mathrm {N} }={{e\hbar } \over {2m_{\mathrm {p} }c}}}$

where:

e is the elementary charge,
ħ is the reduced Planck constant,
mp is the proton rest mass, and
c is the speed of light

In SI units, its value is approximately:

μN = 5.050783699(31)×10−27 J/T

In Gaussian CGS units, its value can be given in convenient units as

μN = 0.10515446 e⋅fm

The nuclear magneton is the natural unit for expressing magnetic dipole moments of heavy particles such as nucleons and atomic nuclei.

Due to the fact that neutrons and protons consist of quarks and thus are no real Dirac particles, their magnetic moment differ from ${\displaystyle \mu _{\mathrm {N} }}$:

${\displaystyle \mu _{\mathrm {p} }=2{.}79\mu _{\mathrm {N} }}$
${\displaystyle \mu _{\mathrm {n} }=-1{.}91\mu _{\mathrm {N} }}$

The magnetic dipole moment of the electron, which is much larger as a consequence of much larger charge-to-mass ratio, is usually expressed in units of the Bohr magneton. The Bohr magneton, which is calculated in the same fashion as the nuclear magneton, is larger than μN by a factor equal to the ratio of the proton to electron mass, or about a factor of 1836.

Physical constant

A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.

There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed for any object and its dimension is length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless.

The term fundamental physical constant is sometimes used to refer to universal but dimensioned physical constants such as those mentioned above. Increasingly, however, physicists reserve the use of the term fundamental physical constant for dimensionless physical constants, such as the fine-structure constant α.

Physical constant in the sense under discussion in this article should not be confused with other quantities called "constants" that are assumed to be constant in a given context without the implication that they are fundamental, such as the "time constant" characteristic of a given system, or material constants, such as the Madelung constant, electrical resistivity, and heat capacity.

The International Bureau of Weights and Measures decided to redefine several SI base units as from 20 May 2019 by fixing the SI value of several physical constants, including the Planck constant, h, the elementary charge, e, the Boltzmann constant, kB, and the Avogadro constant, NA. The new fixed values are based on the best measurements of the constants based on the earlier definitions, including the kilogram, to ensure minimal impact. As a consequence, the uncertainty in the value of many physical constants when expressed in SI units are substantially reduced.

Planck constant

The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.

At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories. In 1900, Max Planck empirically derived a formula for the observed spectrum. He assumed that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, h, from the experimental measurements, and that constant is named in his honor. In 1905, the value E was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called a photon. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".

Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to the project of replacing the International Prototype of the Kilogram, a metal cylinder that had defined the kilogram since 1889. The new definition was unanimously approved at the General Conference on Weights and Measures (CGPM) on 16 November 2018 as part of the 2019 redefinition of SI base units. For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.62607015×10−34 J⋅s exactly. The kilogram was the last SI base unit to be re-defined by a fundamental physical property to replace a physical artifact.

Quantum Hall effect

The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ undergoes quantum Hall transitions to take on the quantized values

${\displaystyle \sigma ={\frac {I_{\text{channel}}}{V_{\text{Hall}}}}=\nu {\frac {e^{2}}{h}},}$

where Ichannel is the channel current, VHall is the Hall voltage, e is the elementary charge and h is Planck's constant. The prefactor ν is known as the filling factor, and can take on either integer (ν = 1, 2, 3,…) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5,…) values. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction, respectively.

The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density is varied. Since the electron density remains constant when the Fermi level is in a clean spectral gap, this situation corresponds to one where the Fermi level is an energy with a finite density of states, though these states are localized (see Anderson localization).

The fractional quantum Hall effect is more complicated, as its existence relies fundamentally on electron–electron interactions. The fractional quantum Hall effect is also understood as an integer quantum Hall effect, although not of electrons but of charge-flux composites known as composite fermions. In 1988, it was proposed that there was quantum Hall effect without Landau levels. This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents.

Sigma baryon

The Sigma baryons are a family of subatomic hadron particles which have two quarks from the first flavour generation (up and/or down quarks), and a third quark from higher flavour generations, in a combination where the wavefunction does not swap sign when any two quark flavours are swapped. They are thus baryons, with total Isospin of 1, and can either be neutral or have an elementary charge of +2, +1, 0, or −1. They are closely related to the Lambda baryons, which differ only in the wavefunction's behaviour upon flavour exchange.

The third quark can hence be either a strange (symbols Σ+, Σ0, Σ−), a charm (symbols Σ++c, Σ+c, Σ0c), a bottom (symbols Σ+b, Σ0b, Σ−b) or a top (symbols Σ++t, Σ+t, Σ0t) quark. However, the top Sigmas are not expected to be observed as the Standard Model predicts the mean lifetime of top quarks to be roughly 5×10−25 s. This is about 20 times shorter than the timescale for strong interactions, and therefore it does not form hadrons.

Volt

The volt (symbol: V) is the derived unit for electric potential, electric potential difference (voltage), and electromotive force. It is named after the Italian physicist Alessandro Volta (1745–1827).

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