Pointed space: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Paul A
m Reverted edits by 75.170.29.78 (talk) to last version by Brad7777
 
en>Monkbot
Line 1: Line 1:
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)]]

Revision as of 18:23, 28 January 2014

29 yr old Orthopaedic Surgeon Grippo from Saint-Paul, spends time with interests including model railways, top property developers in singapore developers in singapore and dolls. Finished a cruise ship experience that included passing by Runic Stones and Church. Template:Expert-subject 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.[1]

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.

The electronic polarizability α is defined as the ratio of the induced dipole moment p of an atom to the electric field E that produces this dipole moment.

p=αE

Polarizability has the SI units of C·m2·V−1 = A2·s4·kg−1 while its cgs unit is cm^3. Usually it is expressed in cgs units as a so-called polarizability volume, instead of cm^3 it is sometimes expressed in Å3 = 10−24 cm3. One can convert from SI units to cgs units as follows:

α(cm3)=1064πε0α(Cm2V1)

where ε0 is the vacuum permittivity. If the polarizability volume is denoted α the relation can also be expressed generally[2] (in SI) as 4πε0α=α.

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

Note that the polarizability α as defined above is a 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 x-direction can only produce an x component in p. However, it can happen that an electric field in the x-direction, produces a y or z component in the vector p. In this case α is described as a tensor of rank 2, which is represented with respect to a given system of axes (frame of reference) by a 3×3 matrix.

Tendencies

Generally, polarizability increases as volume occupied by electrons increases.[3] In atoms, this occurs because larger atoms have more loosely held electrons in contrast to smaller atoms with tightly bound electrons.[3][4] On rows of the periodic table, polarizability therefore increases from right to left.[3] Polarizability increases down on columns of the periodic table.[3] Likewise, larger molecules are generally more polarizable than smaller ones.

Though water is a very polar molecule, alkanes and other hydrophobic molecules are more polarizable. Alkanes are the most polarizable molecules.[3] 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.[3] This results because of alkene's and arene's more electronegative sp2 carbons to the alkane's less electronegative sp3 carbons.[3]

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.[3]

<Magnetic polarizability>...</Magnetic polarizability>Magnetic polarizability

Magnetic polarizability defined by spin interactions of nucleons is an important parameter of deuterons and hadrons. In particular, measurement of tensor polarizabilities of nucleons yields important information about spin-dependent nuclear forces.[5]

The method of spin amplitudes uses quantum mechanics formalism to more easily describe spin dynamics. Vector and tensor polarization of particle/nuclei with spin Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. are specified by the unit polarization vector p and the polarization tensor P`. 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 Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. .[5]

See also

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

Template:Particles

  1. Template:Cite web
  2. 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
  3. 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 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[1]
  4. 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[2]
  5. 5.0 5.1 Template:Cite web