Pointed space - Revision history

en>AnomieBOT: Dating maintenance tags: {{Cleanup}}

2014-07-29T02:51:15Z

Dating maintenance tags: {{Cleanup}}

← Older revision		Revision as of 04:51, 29 July 2014
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	~~{{About\|\|electromagnetic waves\|Polarization (waves)\|other uses\|Polarization (disambiguation)}}~~		She is known by the title of Myrtle Shryock. To gather cash is what her family members and her enjoy. Puerto Rico is where he's been living for years and he will by no means transfer. Since she was eighteen she's been working as a meter reader but she's always wanted her own business.<br><br>Look at my web site ... [http://www.jesusvibes.com/members/aleadela/activity/19218/ std testing at home]
	~~{{expert-subject\|Chemistry\|article\|date=May 2010}}~~
	~~'''Polarizability''' is the ability for a molecule to be polarized. It~~ is a property of matter. Polarizabilities determine the dynamical response of a bound system to external fields, and provide insight into a molecule's internal structure.<ref name="CERN">{{cite web \|author=L. Zhou \|coauthors=F. X. Lee, W. Wilcox, J. Christensen \|title=Magnetic polarizability of hadrons from lattice QCD \|url=http://cdsweb.cern.ch/record/581347/files/0209128.pdf \|publisher=European Organization for Nuclear Research ([[CERN]]) \|year=2002 \|format=[[PDF]] \|accessdate=25 May 2010}}</ref>

	~~=={{anchor\|Electric polarizability\|Electronic polarizability}}Electric polarizability==~~

	~~===Definition===~~
	Electric polarizability is the relative tendency of a charge distribution, like the [[electron cloud]] of an [[atom]] or [[molecule]], to be distorted from its normal shape by an external [[electric field]], which is applied typically by inserting the molecule in a charged parallel-plate [[capacitor]], but may also be caused by the ~~presence of a nearby [[ion]] or [[Dipole#Field_from_an_electric_dipole\|dipole]].~~

	The electronic polarizability <math>\alpha</math> is defined as the ratio of the induced [[Electric dipole moment\|dipole moment]] <math>\boldsymbol{p}</math> of an atom to the electric field <math>\boldsymbol{E}</math> that produces this dipole moment.

	~~<math>\boldsymbol{p} = \alpha \boldsymbol{E}</math>~~

	Polarizability has the [[SI units]] of C·m<sup>2</sup>·V<sup>−1</sup> = A<sup>2</sup>·s<sup>4</sup>·kg<sup>−1</sup> while its cgs unit is cm<sup>^3</sup>. Usually it is expressed in cgs units as a so-called polarizability volume, instead of cm<sup>^3</sup> it is sometimes expressed in [[Angstrom\|Å]]<sup>3</sup> = 10<sup>−24</sup> cm<sup>3</sup>. One can convert from SI units to cgs units as follows:

	~~<math>\alpha (\mathrm{cm}^3) = \frac{10^{6}}{ 4 \pi \varepsilon_0 }\alpha (\mathrm{C} \cdot \mathrm{m}^2 \cdot \mathrm{V}^{-1})</math>~~

	where <math>\varepsilon_0 </math> is the [[permittivity\|vacuum permittivity]]. If the polarizability volume is denoted <math>\alpha'</math> the relation can also be expressed generally<ref name=Atkins>{{cite book\|title=Atkins' Physical Chemistry\|year=2010\|publisher=Oxford University Press\|isbn=978-0-19-954337-3\|page=622-629\|last1=Atkins\|first1=Peter\|last2=de Paula\|first2=Julio\|chapter=17}}</ref> (in SI) as <math>4\pi\varepsilon_0 \alpha' = \alpha</math>.

	~~The polarizability of individual particles is related to the average [[electric susceptibility]]~~ of ~~the medium by the [[Clausius-Mossotti relation]].~~

	Note that the polarizability <math>\alpha</math> as defined above is a [[scalar (physics)\|scalar]] quantity. This implies that the applied electric fields can only produce polarization components parallel to the field. For example, an electric field in the <math>x</math>-direction can only produce an <math>x</math> component in <math>\boldsymbol{p}</math>. However, it can happen that an electric field in the <math>x</math>-direction, produces a <math>y</math> or <math>z</math> component in the vector <math>\boldsymbol{p}</math>. ~~In this case <math>\alpha</math>~~ is ~~described as a [[tensor]] of rank 2, which is represented with respect to a given system of axes (frame of reference) by a <math>3 \times 3</math> [[Matrix (mathematics)\|matrix]].~~

	~~===Tendencies===~~
	Generally, polarizability increases as volume occupied by electrons increases.<ref name="anslyn"/> In atoms, this occurs because larger atoms have more loosely held electrons in contrast to smaller atoms with tightly bound electrons.<ref name="anslyn"/><ref name="Schwerdtfeger">{{cite book\| last1 = Schwerdtfeger \| first1 = Peter \| title = Atomic Static Dipole Polarizabilities \| editor = G. Maroulis \| volumetitle = Computational Aspects of Electric Polarizability Calculations: Atoms, Molecules and Clusters \| publisher = IOS Press \| year = 2006 }}[http://www.worldscibooks.com/etextbook/p464/p464_chap01.pdf]</ref> On rows of the [[periodic table]], polarizability therefore increases from right to left.<ref name="anslyn"/> Polarizability increases down on columns of the periodic table.~~<ref name="anslyn"/> Likewise, larger molecules are generally more polarizable than smaller ones.~~

	~~Though water~~ is a very [[chemical polarity\|polar]] molecule, [[alkanes]] and other [[hydrophobic]] molecules are more polarizable. Alkanes are the most polarizable molecules.<ref name="anslyn"/> Although [[alkenes]] and [[arenes]] are expected to have larger polarizability than alkanes because of their higher reactivity compared to alkanes, alkanes are in fact more polarizable.<ref name="anslyn"/> This results because of alkene's and ~~arene~~'s ~~more electronegative sp<sup>2</sup> carbons to the alkane~~'s ~~less electronegative sp<sup>3</sup> carbons~~.<~~ref name="anslyn"/~~>

	It is important to note that ground state electron configuration models are often inadequate in studying the polarizability of bonds because dramatic changes in molecular structure occur in a reaction.<~~ref name="anslyn"~~>{{cite book\| last1 = Anslyn\| last2 = Dougherty\| first1 = Eric\| first2 = Dennis \| authorlink2 = Dennis Dougherty \| title = Modern Physical Organic Chemistry \| publisher = University Science \| year = 2006 \| isbn = 978-1-891389-31-3}}[http://books.~~google~~.com/books?id=gY-Sxijk_tMC&pg=PA25&dq=organic+chemistry+polarizability&hl=en&ei=NasLToOwF8Ta0QG7kq2iAQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC0Q6AEwAA#v=onepage&q=organic%20chemistry%20polarizability&f=false]</ref>

	~~=={{anchor\|Magnetic polarizability}}Magnetic polarizability==~~
	~~Magnetic polarizability defined by [[Spin (physics)\|spin]] interactions of [[nucleon]]s is an important parameter of [[deuteron]]s and [[hadron]]s~~. ~~In particular, measurement of [~~[tensor]] polarizabilities of nucleons yields important information about spin-dependent nuclear forces.<ref name="Silenko">{{cite web \|author=A. J. Silenko \|title=Manifestation of tensor magnetic polarizability of the deuteron in storage ring experiments \|url=http://www.~~springerlink~~.com/~~content/m2744373305l24m7/ \|publisher=Springer Berlin / Heidelberg \|date=18 Nov 2008 \|doi=10.1140/epjst/e2008-00776-9 \|accessdate=25 May 2010}}</ref>~~

	The method of spin amplitudes uses [[Mathematical formulation of quantum mechanics\|quantum mechanics formalism]] to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin {{math\|<big>S</big> ≥ 1}} are specified by the unit polarization vector <math>\boldsymbol{p}</math> and the polarization tensor ''P''<sub>`</sub>. Additional tensors composed of products of three or more spin matrices are needed only for the exhaustive description of polarization of particles/nuclei with spin {{math\|<big>S</~~big> ≥ {{frac\|3\|2}}}} .<ref name="Silenko"~~/>

	~~==See also==~~
	* [[Polarization density]]
	* [[MOSCED]], an estimation method for activity ~~coefficients; uses polarizability as parameter~~

	~~==References==~~
	~~{{reflist}}~~

	~~==External links==~~
	* [http://books.google.com/books?id=bI-ZmZWeyhkC&pg=PA290&lpg=PA290&dq=Magnetic+polarizability&source=bl&ots=G5kn6PLhSr&sig=ZJKTzwW-YZhTKtOLjbEHcRzdVfA&hl=en&ei=13z8S8HGG8KBlAfbx-nGDw&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBQQ6AEwATgK#v=onepage&q=Magnetic%20polarizability&f=false The theory of the electromagnetic field] by David M. Cook
	* [http://arxiv.org/abs/hep-ph/9309211 Consistent Calculation of the Nucleon Electromagnetic Polarizabilities in Chiral Perturbation Theory Beyond Next-to-Leading Order]
	* [http://bearspace.baylor.edu/Walter_Wilcox/www/LHPCPresentation-Dell.pdf Hadron polarizabilities and magnetic moments with background field methods] ([[PDF]])

	~~{{particles}}~~

	~~[[Category:Atomic physics]]~~
	~~[[Category:Chemical physics]]~~
	~~[[Category:Electric and magnetic fields in matter]]~~
	~~[[Category:Polarization (waves)]~~]

en>Monkbot: /* References */Fix CS1 deprecated date parameter errors

2014-01-28T17:23:08Z

References: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 19:23, 28 January 2014
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	~~She~~ is ~~recognized~~ by the ~~name~~ of ~~Myrtle Shryock~~. One of the ~~issues she enjoys most~~ is to ~~do aerobics and now she~~ is ~~trying~~ to ~~earn money~~ with it. ~~North Dakota~~ is ~~exactly where me~~ and ~~my husband live~~. ~~Bookkeeping~~ is ~~what I do~~.<br><br>~~Review my webpage~~; [http://~~Www~~.~~Twinurl~~.com/~~mealdeliveryservice77873~~ http://~~Www~~.~~Twinurl~~.~~com~~/]		{{About\|\|electromagnetic waves\|Polarization (waves)\|other uses\|Polarization (disambiguation)}}
			{{expert-subject\|Chemistry\|article\|date=May 2010}}
			'''Polarizability''' is the ability for a molecule to be polarized. It is a property of matter. Polarizabilities determine the dynamical response of a bound system to external fields, and provide insight into a molecule's internal structure.<ref name="CERN">{{cite web \|author=L. Zhou \|coauthors=F. X. Lee, W. Wilcox, J. Christensen \|title=Magnetic polarizability of hadrons from lattice QCD \|url=http://cdsweb.cern.ch/record/581347/files/0209128.pdf \|publisher=European Organization for Nuclear Research ([[CERN]]) \|year=2002 \|format=[[PDF]] \|accessdate=25 May 2010}}</ref>

			=={{anchor\|Electric polarizability\|Electronic polarizability}}Electric polarizability==

			===Definition===
			Electric polarizability is the relative tendency of a charge distribution, like the [[electron cloud]] of an [[atom]] or [[molecule]], to be distorted from its normal shape by an external [[electric field]], which is applied typically by inserting the molecule in a charged parallel-plate [[capacitor]], but may also be caused by the presence of a nearby [[ion]] or [[Dipole#Field_from_an_electric_dipole\|dipole]].

			The electronic polarizability <math>\alpha</math> is defined as the ratio of the induced [[Electric dipole moment\|dipole moment]] <math>\boldsymbol{p}</math> of an atom to the electric field <math>\boldsymbol{E}</math> that produces this dipole moment.

			<math>\boldsymbol{p} = \alpha \boldsymbol{E}</math>

			Polarizability has the [[SI units]] of C·m<sup>2</sup>·V<sup>−1</sup> = A<sup>2</sup>·s<sup>4</sup>·kg<sup>−1</sup> while its cgs unit is cm<sup>^3</sup>. Usually it is expressed in cgs units as a so-called polarizability volume, instead of cm<sup>^3</sup> it is sometimes expressed in [[Angstrom\|Å]]<sup>3</sup> = 10<sup>−24</sup> cm<sup>3</sup>. One can convert from SI units to cgs units as follows:

			<math>\alpha (\mathrm{cm}^3) = \frac{10^{6}}{ 4 \pi \varepsilon_0 }\alpha (\mathrm{C} \cdot \mathrm{m}^2 \cdot \mathrm{V}^{-1})</math>

			where <math>\varepsilon_0 </math> is the [[permittivity\|vacuum permittivity]]. If the polarizability volume is denoted <math>\alpha'</math> the relation can also be expressed generally<ref name=Atkins>{{cite book\|title=Atkins' Physical Chemistry\|year=2010\|publisher=Oxford University Press\|isbn=978-0-19-954337-3\|page=622-629\|last1=Atkins\|first1=Peter\|last2=de Paula\|first2=Julio\|chapter=17}}</ref> (in SI) as <math>4\pi\varepsilon_0 \alpha' = \alpha</math>.

			The polarizability of individual particles is related to the average [[electric susceptibility]] of the medium by the [[Clausius-Mossotti relation]].

			Note that the polarizability <math>\alpha</math> as defined above is a [[scalar (physics)\|scalar]] quantity. This implies that the applied electric fields can only produce polarization components parallel to the field. For example, an electric field in the <math>x</math>-direction can only produce an <math>x</math> component in <math>\boldsymbol{p}</math>. However, it can happen that an electric field in the <math>x</math>-direction, produces a <math>y</math> or <math>z</math> component in the vector <math>\boldsymbol{p}</math>. In this case <math>\alpha</math> is described as a [[tensor]] of rank 2, which is represented with respect to a given system of axes (frame of reference) by a <math>3 \times 3</math> [[Matrix (mathematics)\|matrix]].

			===Tendencies===
			Generally, polarizability increases as volume occupied by electrons increases.<ref name="anslyn"/> In atoms, this occurs because larger atoms have more loosely held electrons in contrast to smaller atoms with tightly bound electrons.<ref name="anslyn"/><ref name="Schwerdtfeger">{{cite book\| last1 = Schwerdtfeger \| first1 = Peter \| title = Atomic Static Dipole Polarizabilities \| editor = G. Maroulis \| volumetitle = Computational Aspects of Electric Polarizability Calculations: Atoms, Molecules and Clusters \| publisher = IOS Press \| year = 2006 }}[http://www.worldscibooks.com/etextbook/p464/p464_chap01.pdf]</ref> On rows of the [[periodic table]], polarizability therefore increases from right to left.<ref name="anslyn"/> Polarizability increases down on columns of the periodic table.<ref name="anslyn"/> Likewise, larger molecules are generally more polarizable than smaller ones.

			Though water is a very [[chemical polarity\|polar]] molecule, [[alkanes]] and other [[hydrophobic]] molecules are more polarizable. Alkanes are the most polarizable molecules.<ref name="anslyn"/> Although [[alkenes]] and [[arenes]] are expected to have larger polarizability than alkanes because of their higher reactivity compared to alkanes, alkanes are in fact more polarizable.<ref name="anslyn"/> This results because of alkene's and arene's more electronegative sp<sup>2</sup> carbons to the alkane's less electronegative sp<sup>3</sup> carbons.<ref name="anslyn"/>

			It is important to note that ground state electron configuration models are often inadequate in studying the polarizability of bonds because dramatic changes in molecular structure occur in a reaction.<ref name="anslyn">{{cite book\| last1 = Anslyn\| last2 = Dougherty\| first1 = Eric\| first2 = Dennis \| authorlink2 = Dennis Dougherty \| title = Modern Physical Organic Chemistry \| publisher = University Science \| year = 2006 \| isbn = 978-1-891389-31-3}}[http://books.google.com/books?id=gY-Sxijk_tMC&pg=PA25&dq=organic+chemistry+polarizability&hl=en&ei=NasLToOwF8Ta0QG7kq2iAQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CC0Q6AEwAA#v=onepage&q=organic%20chemistry%20polarizability&f=false]</ref>

			=={{anchor\|Magnetic polarizability}}Magnetic polarizability==
			Magnetic polarizability defined by [[Spin (physics)\|spin]] interactions of [[nucleon]]s is an important parameter of [[deuteron]]s and [[hadron]]s. In particular, measurement of [[tensor]] polarizabilities of nucleons yields important information about spin-dependent nuclear forces.<ref name="Silenko">{{cite web \|author=A. J. Silenko \|title=Manifestation of tensor magnetic polarizability of the deuteron in storage ring experiments \|url=http://www.springerlink.com/content/m2744373305l24m7/ \|publisher=Springer Berlin / Heidelberg \|date=18 Nov 2008 \|doi=10.1140/epjst/e2008-00776-9 \|accessdate=25 May 2010}}</ref>

			The method of spin amplitudes uses [[Mathematical formulation of quantum mechanics\|quantum mechanics formalism]] to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin {{math\|<big>S</big> ≥ 1}} are specified by the unit polarization vector <math>\boldsymbol{p}</math> and the polarization tensor ''P''<sub>`</sub>. Additional tensors composed of products of three or more spin matrices are needed only for the exhaustive description of polarization of particles/nuclei with spin {{math\|<big>S</big> ≥ {{frac\|3\|2}}}} .<ref name="Silenko"/>

			==See also==
			* [[Polarization density]]
			* [[MOSCED]], an estimation method for activity coefficients; uses polarizability as parameter

			==References==
			{{reflist}}

			==External links==
			* [http://books.google.com/books?id=bI-ZmZWeyhkC&pg=PA290&lpg=PA290&dq=Magnetic+polarizability&source=bl&ots=G5kn6PLhSr&sig=ZJKTzwW-YZhTKtOLjbEHcRzdVfA&hl=en&ei=13z8S8HGG8KBlAfbx-nGDw&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBQQ6AEwATgK#v=onepage&q=Magnetic%20polarizability&f=false The theory of the electromagnetic field] by David M. Cook
			* [http://arxiv.org/abs/hep-ph/9309211 Consistent Calculation of the Nucleon Electromagnetic Polarizabilities in Chiral Perturbation Theory Beyond Next-to-Leading Order]
			* [http://bearspace.baylor.edu/Walter_Wilcox/www/LHPCPresentation-Dell.pdf Hadron polarizabilities and magnetic moments with background field methods] ([[PDF]])

			{{particles}}

			[[Category:Atomic physics]]
			[[Category:Chemical physics]]
			[[Category:Electric and magnetic fields in matter]]
			[[Category:Polarization (waves)]]

en>Paul A: Reverted edits by 75.170.29.78 (talk) to last version by Brad7777

2012-05-17T04:11:03Z

Reverted edits by 75.170.29.78 (talk) to last version by Brad7777

New page

She is recognized by the name of Myrtle Shryock. One of the issues she enjoys most is to do aerobics and now she is trying to earn money with it. North Dakota is exactly where me and my husband live. Bookkeeping is what I do.<br><br>Review my webpage; [http://Www.Twinurl.com/mealdeliveryservice77873 http://Www.Twinurl.com/]