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{{quantum mechanics}} | |||
{{main|magnetic moment}} | |||
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]]. | |||
"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]]). | |||
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. | |||
==Calculation== | |||
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> | |||
{{NumBlk|:|<math>\vec{\mu}_S \ = \ g \ \frac{q}{2 m} \ \vec{S} = \gamma \vec{S} </math>|{{EquationRef|1}}}} | |||
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]]. | |||
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: | |||
{{NumBlk|:|<math>\mu_S\approx -2\frac{-e}{2m_e}\frac{\hbar}{2}=\mu_B</math>|{{EquationRef|2}}}} | |||
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> | |||
{{NumBlk|:|<math> \vec{\mu}_S = -\frac{g \mu_B \vec{\sigma}}{2}</math>|{{EquationRef|3}}}} | |||
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: | |||
{{NumBlk|:|<math> |\vec{\mu}_S| = g \mu_B \sqrt{s(s + 1)} </math>|{{EquationRef|4}}}} | |||
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. | |||
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>. | |||
==Spin in chemistry== | |||
{{main|Quantum chemistry}} | |||
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]]. | |||
==History== | |||
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> | |||
==See also== | |||
*[[Nuclear magneton]] | |||
*[[Pauli principle]] | |||
*[[Nuclear magnetic resonance]] | |||
*[[Multipole expansion]] | |||
*[[Relativistic quantum mechanics]] | |||
==References== | |||
===Notes=== | |||
{{reflist}} | |||
===Selected books=== | |||
*{{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}} | |||
*{{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}} | |||
*{{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}} | |||
*{{cite book| author = E. Merzbacher| year = 1998|edition=3rd| title = Quantum Mechanics|publisher=|volume=| isbn = 0-471-887-021}} | |||
*{{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}} | |||
*{{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}} | |||
*{{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}} | |||
===Selected papers=== | |||
*{{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 }} | |||
*{{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}} | |||
==External links== | |||
* [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]]) | |||
[[Category:Magnetism]] | |||
[[Category:Rotational symmetry]] | |||
[[Category:Spintronics]] | |||
Revision as of 17:05, 2 January 2014
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In physics, mainly quantum mechanics and particle physics, a spin magnetic moment is the magnetic moment induced by the 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 of the electron.
"Spin" is a non–classical property of elementary particles, since classically the "spin angular momentum" of a material object is really just the total orbital angular momenta of the object's constituents about the rotation axis. Elementary particles are conceived as concepts which have no axis to "spin" around (see wave-particle duality).
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 carriers in the constituting the current. However, in magnetic materials, the atomic and molecular dipoles have magnetic moments not just because of their quantized orbital angular momentum, but the spin of elementary particles constituting them (electrons, and the quarks in the protons and neutrons of the 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.
Calculation
We can calculate the observable spin magnetic moment, a vector, Template:VecS, for a sub-atomic particle with charge q, mass m, and spin angular momentum (also a vector), Template:Vec, via:[1]
where is the gyromagnetic ratio, g is a dimensionless number, called the 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 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.
The intrinsic electron magnetic dipole moment is approximately equal to the Bohr magneton μB because g ≈ −2 and the electron's spin is also ħ/2:
Equation (Template:EquationNote) is therefore normally written as[2]
Just like the total spin angular momentum cannot be measured, neither can the total spin magnetic moment be measured. Equations (Template:EquationNote), (Template:EquationNote), (Template:EquationNote) give the 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, Template:Vec be replaced by its eigenvalue, Template:Sqrt, where s is the spin quantum number. In turn, calculation of the magnitude of the total spin magnetic moment requires that (Template:EquationNote) be replaced by:
Thus, for a single electron, with spin quantum number s = 1/2, the component of the magnetic moment along the field direction is, from (Template:EquationNote), |Template:VecS, z| = μB, while the (magnitude of the) total spin magnetic moment is, from (Template:EquationNote), |Template:VecS| = Template:Sqrt μB, or approximately 1.73 Bohr magnetons.
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 shells (e.g. Titanium Ti3+) is 1.73 μB since s = 1/2, while an atom with two unpaired electrons (e.g. Vanadium V3+) with S = 1 would have an effective magnetic moment of 2.83 μB.
Spin in chemistry
Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.
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 doublets within electromagnetic spectrum. This additional quantum number, spin, became the basis for the modern standard model used today, which includes the use of Hund's rules, and an explanation of beta decay.
History
The idea of a spin angular momentum was first proposed in a 1925 publication by George Uhlenbeck and Samuel Goudsmit to explain hyperfine splitting in atomic spectra.[3] In 1928, Paul Dirac provided a rigorous theoretical foundation for the concept in the Dirac equation for the wavefunction of the electron.[4]
See also
- Nuclear magneton
- Pauli principle
- Nuclear magnetic resonance
- Multipole expansion
- Relativistic quantum mechanics
References
Notes
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Selected books
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My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
Selected papers
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Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
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A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang - One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
External links
- An Introduction to the Electronic Structure of Atoms and Molecules by Dr. Richard F.W. Bader (McMaster University)
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ 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.Template:Harv
- ↑ Template:Harv