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46-417: The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by μ = g e 2 m S , {\displaystyle {\boldsymbol {\mu }}=g{e \over 2m}\mathbf {S} ,} where μ is the spin magnetic moment of the particle, g is the g -factor of the particle, e is the elementary charge , m

92-743: A result of the mass difference between the particles. However, not all of the difference between the g -factors for electrons and muons is exactly explained by the Standard Model . The muon g -factor can, in theory, be affected by physics beyond the Standard Model , so it has been measured very precisely, in particular at the Brookhaven National Laboratory . In the E821 collaboration final report in November 2006,

138-524: Is K J = 2 e h , {\displaystyle 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 K = h e 2 . {\displaystyle R_{\text{K}}={\frac {h}{e^{2}}}.} It can be measured directly using

184-402: 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. However, it

230-779: Is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by its orbital or spin angular momentum. In SI units , the Bohr magneton is defined as μ B = e ℏ 2 m e {\displaystyle \mu _{\mathrm {B} }={\frac {e\hbar }{2m_{\mathrm {e} }}}} and in the Gaussian CGS units as μ B = e ℏ 2 m e c , {\displaystyle \mu _{\mathrm {B} }={\frac {e\hbar }{2m_{\mathrm {e} }c}},} where The idea of elementary magnets

276-504: Is a fundamental physical constant , defined as the electric charge carried by a single proton (+ 1e) or, equivalently, the magnitude of the negative electric charge carried by a single electron , which has charge −1  e . In the SI system of units , the value of the elementary charge is exactly defined as e {\displaystyle e} = 1.602 176 634 × 10 coulombs , or 160.2176634 zepto coulombs (zC). Since

322-413: Is a one-to-one correspondence between the electrons passing through the anode-to-cathode wire and the ions that plate onto or off of the anode or cathode. Measuring the mass change of the anode or cathode, and the total charge passing through the wire (which can be measured as the time-integral of electric current ), and also taking into account the molar mass of the ions, one can deduce F . The limit to

368-416: 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. There are two known sorts of exceptions to the indivisibility of the elementary charge: quarks and quasiparticles . All known elementary particles , including quarks, have charges that are integer multiples of ⁠ 1 / 3 ⁠   e . Therefore,

414-520: Is due to Walther Ritz (1907) and Pierre Weiss . Already before the Rutherford model of atomic structure, several theorists commented that the magneton should involve the Planck constant h . By postulating that the ratio of electron kinetic energy to orbital frequency should be equal to h , Richard Gans computed a value that was twice as large as the Bohr magneton in September 1911. At

460-589: 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. If the Avogadro constant N A and the Faraday constant F are independently known, the value of the elementary charge can be deduced using

506-696: Is its spin angular momentum, and μ B = eħ /2 m e is the Bohr magneton . In atomic physics, the electron spin g -factor is often defined as the absolute value of g e : g s = | g e | = − g e . {\displaystyle g_{\text{s}}=|g_{\text{e}}|=-g_{\text{e}}.} The z -component of the magnetic moment then becomes μ z = − g s μ B m s {\displaystyle \mu _{\text{z}}=-g_{\text{s}}\mu _{\text{B}}m_{\text{s}}} The value g s

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552-594: Is its orbital angular momentum, and μ B is the Bohr magneton. For an infinite-mass nucleus, the value of g L is exactly equal to one, by a quantum-mechanical argument analogous to the derivation of the classical magnetogyric ratio . For an electron in an orbital with a magnetic quantum number m l , the z -component of the orbital magnetic moment is μ z = − g L μ B m l {\displaystyle \mu _{\text{z}}=-g_{L}\mu _{\text{B}}m_{\text{l}}} which, since g L = 1,

598-496: Is roughly equal to 2.002319 and is known to extraordinary precision – one part in 10. The reason it is not precisely two is explained by quantum electrodynamics calculation of the anomalous magnetic dipole moment . The spin g -factor is related to spin frequency for a free electron in a magnetic field of a cyclotron: ν s = g 2 ν c {\displaystyle \nu _{\text{s}}={\frac {g}{2}}\nu _{\text{c}}} Secondly,

644-425: Is the Planck constant , α is the fine-structure constant , μ 0 is the magnetic constant , ε 0 is the electric constant , and c is the speed of light . Presently this equation reflects a relation between ε 0 and α , while all others are fixed values. Thus the relative standard uncertainties of both will be same. Bohr magneton In atomic physics , the Bohr magneton (symbol μ B )

690-421: Is the electron spin g-factor (more often called simply the electron g-factor ), g e , defined by μ s = g e μ B ℏ S {\displaystyle {\boldsymbol {\mu }}_{\text{s}}=g_{\text{e}}{\mu _{\text{B}} \over \hbar }\mathbf {S} } where μ s is the magnetic moment resulting from the spin of an electron, S

736-473: Is the speed of light , ε 0 is the electric constant , and ħ is the reduced Planck constant . 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"

782-575: Is the magnetic moment of the nucleon or nucleus resulting from its spin, g is the effective g -factor, I is its spin angular momentum, μ N is the nuclear magneton, e is the elementary charge, and m p is the proton rest mass. There are three magnetic moments associated with an electron: one from its spin angular momentum , one from its orbital angular momentum , and one from its total angular momentum (the quantum-mechanical sum of those two components). Corresponding to these three moments are three different g -factors: The most known of these

828-441: Is the mass of the particle, and S is the spin angular momentum of the particle (with magnitude ħ /2 for Dirac particles). Protons, neutrons, nuclei, and other composite baryonic particles have magnetic moments arising from their spin (both the spin and magnetic moment may be zero, in which case the g -factor is undefined). Conventionally, the associated g -factors are defined using the nuclear magneton, and thus implicitly using

874-421: Is the total magnetic moment resulting from both spin and orbital angular momentum of an electron, J = L + S is its total angular momentum, and μ B is the Bohr magneton . The value of g J is related to g L and g s by a quantum-mechanical argument; see the article Landé g -factor. μ J and J vectors are not collinear, so only their magnitudes can be compared. The muon, like

920-435: Is unambiguous: it refers to a quantity of charge equal to that of a proton. 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. It is currently unknown why isolatable particles are restricted to integer charges; much of the string theory landscape appears to admit fractional charges. The elementary charge

966-660: Is − μ B m l For a finite-mass nucleus, there is an effective g value g L = 1 − 1 M {\displaystyle g_{L}=1-{\frac {1}{M}}} where M is the ratio of the nuclear mass to the electron mass. Thirdly, the Landé g-factor , g J , is defined by | μ J | = g J μ B ℏ | J | {\displaystyle |{\boldsymbol {\mu _{\text{J}}}}|=g_{J}{\mu _{\text{B}} \over \hbar }|\mathbf {J} |} where μ J

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1012-447: The 2019 revision of the SI , the seven SI base units 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 4.803 2047 ... × 10   statcoulombs . Robert A. Millikan and Harvey Fletcher 's oil drop experiment first directly measured the magnitude of

1058-541: The Fermilab Muon g −2 collaboration presented and published a new measurement of the muon magnetic anomaly. When the Brookhaven and Fermilab measurements are combined, the new world average differs from the theory prediction by 4.2 standard deviations. The electron g -factor is one of the most precisely measured values in physics. Elementary charge The elementary charge , usually denoted by e ,

1104-591: The First Solvay Conference in November that year, Paul Langevin obtained a value of e ℏ / ( 2 m e ) {\displaystyle e\hbar /(2m_{\mathrm {e} })} . Langevin assumed that the attractive force was inversely proportional to distance to the power n + 1 , {\displaystyle n+1,} and specifically n = 1. {\displaystyle n=1.} The Romanian physicist Ștefan Procopiu had obtained

1150-411: The electron orbital g-factor , g L , is defined by μ L = − g L μ B ℏ L , {\displaystyle {\boldsymbol {\mu }}_{L}=-g_{L}{\mu _{\mathrm {B} } \over \hbar }\mathbf {L} ,} where μ L is the magnetic moment resulting from the orbital angular momentum of an electron, L

1196-576: The quantum Hall effect . From these two constants, the elementary charge can be deduced: e = 2 R K K J . {\displaystyle e={\frac {2}{R_{\text{K}}K_{\text{J}}}}.} The relation used by CODATA to determine elementary charge was: e 2 = 2 h α μ 0 c = 2 h α ε 0 c , {\displaystyle e^{2}={\frac {2h\alpha }{\mu _{0}c}}=2h\alpha \varepsilon _{0}c,} where h

1242-416: 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,

1288-403: The "quantum of charge" is e , with the proviso that quarks are not to be included. In this case, "elementary charge" would be synonymous with the "quantum of charge". In fact, both terminologies are used. For this reason, phrases like "the quantum of charge" or "the indivisible unit of charge" can be ambiguous unless further specification is given. On the other hand, the term "elementary charge"

1334-539: The Avogadro constant N A was first approximated by Johann Josef Loschmidt who, in 1865, estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas. Today the value of N A can be measured at very high accuracy by taking an extremely pure crystal (often silicon ), measuring how far apart the atoms are spaced using X-ray diffraction or another method, and accurately measuring

1380-556: The Danish physicist Niels Bohr as a consequence of his atom model . In 1920, Wolfgang Pauli gave the Bohr magneton its name in an article where he contrasted it with the magneton of the experimentalists which he called the Weiss magneton . A magnetic moment of an electron in an atom is composed of two components. First, the orbital motion of an electron around a nucleus generates a magnetic moment by Ampère's circuital law . Second,

1426-414: 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

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1472-428: 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. Any electric current will be associated with noise from a variety of sources, one of which

1518-478: The density of the crystal. From this information, one can deduce the mass ( m ) of a single atom; and since the molar mass ( M ) is known, the number of atoms in a mole can be calculated: N A = M / m . The value of F can be measured directly using Faraday's laws of electrolysis . Faraday's laws of electrolysis are quantitative relationships based on the electrochemical researches published by Michael Faraday in 1834. In an electrolysis experiment, there

1564-399: The electron, has a g -factor associated with its spin, given by the equation μ = g e 2 m μ S , {\displaystyle {\boldsymbol {\mu }}=g{e \over 2m_{\mu }}\mathbf {S} ,} where μ is the magnetic moment resulting from the muon's spin, S is the spin angular momentum, and m μ is the muon mass. That

1610-447: 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 and (through the Faraday constant ) at order-of-magnitude accuracy by Johann Loschmidt 's measurement of the Avogadro number in 1865. In some natural unit systems, such as

1656-485: The experimental measured value is 2.002 331 8416 (13) , compared to the theoretical prediction of 2.002 331 836 20 (86) . This is a difference of 3.4 standard deviations , suggesting that beyond-the-Standard-Model physics may be a contributory factor. The Brookhaven muon storage ring was transported to Fermilab where the Muon g –2 experiment used it to make more precise measurements of muon g -factor. On April 7, 2021,

1702-517: The expression for the magnetic moment of the electron in 1913. The value is sometimes referred to as the "Bohr–Procopiu magneton" in Romanian scientific literature. The Weiss magneton was experimentally derived in 1911 as a unit of magnetic moment equal to 1.53 × 10 joules per tesla, which is about 20% of the Bohr magneton. In the summer of 1913, the values for the natural units of atomic angular momentum and magnetic moment were obtained by

1748-474: The formula e = F N A . {\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

1794-435: The inherent rotation, or spin, of the electron has a spin magnetic moment . In the Bohr model of the atom, for an electron that is in the orbit of lowest energy, its orbital angular momentum has magnitude equal to the reduced Planck constant , denoted ħ . The Bohr magneton is the magnitude of the magnetic dipole moment of an electron orbiting an atom with this angular momentum. The spin angular momentum of an electron

1840-537: The muon g -factor is not quite the same as the electron g -factor is mostly explained by quantum electrodynamics and its calculation of the anomalous magnetic dipole moment. Almost all of the small difference between the two values (99.96% of it) is due to a well-understood lack of heavy-particle diagrams contributing to the probability for emission of a photon representing the magnetic dipole field, which are present for muons, but not electrons, in QED theory. These are entirely

1886-436: 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. 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

g-factor (physics) - Misplaced Pages Continue

1932-421: The proton's mass rather than the particle's mass as for a Dirac particle. The formula used under this convention is μ = g μ N ℏ I = g e 2 m p I , {\displaystyle {\boldsymbol {\mu }}=g{\mu _{\text{N}} \over \hbar }{\mathbf {I} }=g{e \over 2m_{\text{p}}}\mathbf {I} ,} where μ

1978-402: The result that e = 4 π α ε 0 ℏ c ≈ 0.30282212088 ε 0 ℏ c , {\displaystyle 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

2024-416: The system of atomic units , e functions as the unit of electric charge . The use of elementary charge as a unit was promoted by George Johnstone Stoney in 1874 for the first system of natural units, called Stoney units . Later, he proposed the name electron for this unit. At the time, the particle we now call the electron was not yet discovered and the difference between the particle electron and

2070-476: 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 ε 0 ℏ c , {\displaystyle {\sqrt {\varepsilon _{0}\hbar c}},} with

2116-527: Was used in the first direct observation of Laughlin quasiparticles , implicated in the fractional quantum Hall effect . 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

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