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| {{quantum mechanics}}
| | Hello and welcome. My title is Figures Wunder. My day occupation is a meter reader. One of the extremely best things in the world for me is to do aerobics and now I'm attempting to earn money with it. For many years he's been residing in North Dakota and his family enjoys it.<br><br>My homepage - [http://www.beasts-of-america.com/beasts/groups/curing-your-candida-how-to-do-it-easily/ std testing at home] |
| {{main|magnetic moment}}
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| In physics, mainly [[quantum mechanics]] and [[particle physics]], a '''spin magnetic moment''' is the [[magnetic moment]] induced by the [[spin (physics)|spin]] of [[elementary particles]]. For example the [[electron]] is an elementary [[spin-1/2]] [[fermion]]. [[Quantum electrodynamics]] gives the most accurate prediction of the [[anomalous magnetic moment#Anomalous magnetic moment of the electron|anomalous magnetic moment of the electron]].
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| "Spin" is a non–classical property of elementary particles, since [[classical mechanics|classically]] the "spin angular momentum" of a material object is really just the total ''orbital'' [[angular momentum|angular momenta]] of the object's constituents about the rotation axis. [[Elementary particle]]s are conceived as concepts which have no axis to "spin" around (see [[wave-particle duality]]).
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| In general, a [[magnetic moment]] can be defined in terms of an [[electric current]] and the [[area]] enclosed by the current loop. Since angular momentum corresponds to rotational motion, the magnetic moment can be related to the orbital angular momentum of the [[charge carrier]]s in the constituting the current. However, in [[magnetic material]]s, the atomic and molecular dipoles have magnetic moments not just because of their [[angular momentum (quantum mechanics)|quantized orbital angular momentum]], but the spin of elementary particles constituting them (electrons, and the [[quark]]s in the [[proton]]s and [[neutron]]s of the [[atomic nucleus|atomic nuclei]]). Particles do not necessarily have [[electric charge]] to have a spin magnetic moment; the [[neutron]] is electrically neutral but has a non–zero magnetic moment, because of its internal quark structure.
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| ==Calculation==
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| We can calculate the observable spin magnetic moment, a vector, ''{{vec|μ}}<sub>S</sub>'', for a sub-atomic particle with charge ''q'', mass ''m'', and [[spin (physics)|spin angular momentum]] (also a vector), {{vec|''S''}}, via:<ref>{{cite book| author = Y. Peleg, R. Pnini, E. Zaarur, E. Hecht| year = 2010|edition=2nd| title = Quantum Mechanics|series=Shaum's outlines|publisher=McGraw-Hill|page=181|volume=| isbn = 9-780071-623582}}</ref>
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| {{NumBlk|:|<math>\vec{\mu}_S \ = \ g \ \frac{q}{2 m} \ \vec{S} = \gamma \vec{S} </math>|{{EquationRef|1}}}}
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| where <math>\gamma \equiv g \frac{q}{2m}</math> is the [[gyromagnetic ratio]], ''g'' is a [[dimensional analysis|dimensionless]] number, called the [[g-factor (physics)|g-factor]], ''q'' is the charge, and ''m'' is the mass. The ''g''-factor depends on the particle: it is ''g'' = 2.0023 for the [[electron]], g = 5.586 for the [[proton]], and g = −3.826 for the [[neutron]]. The proton and neutron are composed of [[quarks]], which have a non-zero charge and a spin of ''ħ''/2, and this must be taken into account when calculating their g-factors. Even though the neutron has a charge ''q'' = 0, its quarks give it a [[neutron magnetic moment|magnetic moment]]. The proton and electron's spin magnetic moments can be calculated by setting ''q'' = +''e'' and ''q'' = −''e'', respectively, where ''e'' is the [[elementary charge]].
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| The intrinsic [[electron magnetic dipole moment]] is approximately equal to the [[Bohr magneton]] ''μ''<sub>B</sub> because ''g'' ≈ −2 and the electron's spin is also ''ħ''/2:
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| {{NumBlk|:|<math>\mu_S\approx -2\frac{-e}{2m_e}\frac{\hbar}{2}=\mu_B</math>|{{EquationRef|2}}}}
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| Equation ({{EquationNote|1}}) is therefore normally written as<ref>{{cite book|title=Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles|edition=2nd|page=274|author=R. Resnick, R. Eisberg|publisher=John Wiley & Sons|year=1985|isbn=978-0-471-87373-0}}</ref>
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| {{NumBlk|:|<math> \vec{\mu}_S = -\frac{g \mu_B \vec{\sigma}}{2}</math>|{{EquationRef|3}}}}
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| Just like the ''total spin angular momentum'' cannot be measured, neither can the ''total spin magnetic moment'' be measured. Equations ({{EquationNote|1}}), ({{EquationNote|2}}), ({{EquationNote|3}}) give the [[Observable|physical observable]], that component of the magnetic moment measured along an axis, relative to or along the applied field direction. Assuming a [[Cartesian coordinate system]], conventionally, the ''z''-axis is chosen but the observable values of the component of spin angular momentum along all three axes are each ±''ħ''/2. However, in order to obtain the magnitude of the total spin angular momentum, {{vec|''S''}} be replaced by its [[eigenvalue]], {{sqrt|''s''(''s'' + 1)}}, where ''s'' is the [[spin quantum number]]. In turn, calculation of the magnitude of the total spin magnetic moment requires that ({{EquationNote|3}}) be replaced by:
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| {{NumBlk|:|<math> |\vec{\mu}_S| = g \mu_B \sqrt{s(s + 1)} </math>|{{EquationRef|4}}}}
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| Thus, for a single electron, with spin quantum number ''s'' = 1/2, the component of the magnetic moment along the field direction is, from ({{EquationNote|3}}), |''{{vec|μ}}<sub>S, z</sub>''| = ''μ''<sub>B</sub>, while the (magnitude of the) total spin magnetic moment is, from ({{EquationNote|4}}), |''{{vec|μ}}<sub>S</sub>''| = {{sqrt|3}} ''μ''<sub>B</sub>, or approximately 1.73 Bohr magnetons.
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| The analysis is readily extended to the spin-only magnetic moment of an atom. For example, the total spin magnetic moment (sometimes referred to as the ''effective magnetic moment'' when the orbital moment contribution to the total magnetic moment is neglected) of a [[transition metal]] [[ion]] with a single [[d shell]] electron outside of closed [[Electron shell|shell]]s (e.g. [[Titanium]] Ti<sup>3+</sup>) is 1.73 ''μ''<sub>B</sub> since ''s'' = 1/2, while an atom with two unpaired electrons (e.g. [[Vanadium]] V<sup>3+</sup>) with ''S'' = 1 would have an effective magnetic moment of 2.83 ''μ''<sub>B</sub>.
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| ==Spin in chemistry==
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| {{main|Quantum chemistry}}
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| Spin magnetic moments create a basis for one of the most important principles in chemistry, the [[Pauli exclusion principle]]. This principle, first suggested by [[Wolfgang Pauli]], governs most of modern-day chemistry. The theory plays further roles than just the explanations of [[Doublet (physics)|doublet]]s within [[electromagnetic spectrum]]. This additional quantum number, spin, became the basis for the modern [[standard model]] used today, which includes the use of [[List of Hund's rules|Hund's rules]], and an explanation of [[beta decay]].
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| ==History==
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| The idea of a spin angular momentum was first proposed in a 1925 publication by [[George Eugene Uhlenbeck|George Uhlenbeck]] and [[Samuel Abraham Goudsmit|Samuel Goudsmit]] to explain [[hyperfine splitting]] in atomic spectra.<ref>Earlier the same year, [[Ralph Kronig]] discussed the idea with [[Wolfgang Pauli]], but Pauli criticized the idea so severely that Kronig decided not to publish it.{{harv|Scerri|1995}}</ref> In 1928, [[Paul Dirac]] provided a rigorous theoretical foundation for the concept in the [[Dirac equation]] for the [[wavefunction]] of the [[electron]].<ref>{{harv|Dirac|1928}}</ref>
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| ==See also==
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| *[[Nuclear magneton]]
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| *[[Pauli principle]]
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| *[[Nuclear magnetic resonance]]
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| *[[Multipole expansion]]
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| *[[Relativistic quantum mechanics]]
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| ==References==
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| ===Notes===
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| {{reflist}}
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| ===Selected books===
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| *{{cite book| author=B. R. Martin, G.Shaw|title=Particle Physics|edition=3rd|publisher=Manchester Physics Series, John Wiley & Sons|pages=5–6|isbn=978-0-470-03294-7}}
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| *{{Cite book|title=Physics of Atoms and Molecules|author=Bransden, BH|coauthors=Joachain, CJ|year=1983|publisher=Prentice Hall|edition=1st|page=631|isbn=0-582-44401-2}}
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| *{{cite book|title=Quanta: A handbook of concepts|author=[[Peter Atkins|P.W. Atkins]]|publisher=Oxford University Press|year=1974|isbn=0-19-855493-1}}
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| *{{cite book| author = E. Merzbacher| year = 1998|edition=3rd| title = Quantum Mechanics|publisher=|volume=| isbn = 0-471-887-021}}
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| *{{cite book|title=Molecular Quantum Mechanics Parts I and II: An Introduction to Quantum Chemistry|volume=1|author=[[Peter Atkins|P.W. Atkins]]|publisher=Oxford University Press|year=1977|isbn=0-19-855129-0}}
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| *{{cite book|title=Molecular Quantum Mechanics Part III: An Introduction to Quantum Chemistry|volume=2|author=[[Peter Atkins|P.W. Atkins]]|publisher=Oxford University Press|year=1977|isbn=0-19-855130-4}}
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| *{{cite book|title=Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles|edition=2nd|author=R. Resnick, R. Eisberg|publisher=John Wiley & Sons|year=1985|isbn=978-0-471-87373-0}}
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| ===Selected papers===
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| *{{cite journal | last=Dirac | first=P. A. M. |authorlink=Paul Dirac| title=The Quantum Theory of the Electron | journal=[[Proceedings of the Royal Society A]] | date=1928-02-01 | volume=117 | issue=778 | pages=610–624 | doi=10.1098/rspa.1928.0023 |bibcode = 1928RSPSA.117..610D }}
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| *{{cite journal|last=Scerri|first=Eric R.|title = The exclusion principle, chemistry and hidden variables| journal = [[Synthese]]|volume = 102|number=1|pages=165–169|year=1995|doi=10.1007/BF01063903}}
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| ==External links==
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| * [http://www.chemistry.mcmaster.ca/esam/Chapter_4/section_2.html An Introduction to the Electronic Structure of Atoms and Molecules] by Dr. Richard F.W. Bader ([[McMaster University]])
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| [[Category:Magnetism]]
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| [[Category:Rotational symmetry]]
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| [[Category:Spintronics]]
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Hello and welcome. My title is Figures Wunder. My day occupation is a meter reader. One of the extremely best things in the world for me is to do aerobics and now I'm attempting to earn money with it. For many years he's been residing in North Dakota and his family enjoys it.
My homepage - std testing at home