Diagonal matrix - Revision history

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	~~{{infobox~~		I will demonstrate and explain how to get to the most effective of the SERPS where your organization can utilize tons of search traffic. It Is mysterious to exhibit up number-one, when someone types in the phrase you need.<br><br>Analysis your present social media activities might convey the recognition that you would be better-off switching your social media activities within the coming year to activities that put you facing your target readers.<br><br>Referrals are easy-to get. I've spent very little time hoping to get referrals and I have above a 100 and all of it extends back to reason number 1. Individuals are willing to register and at the very least attempt it, leading me to my next reason Since it's free.<br><br><br><br>The quicker you are able to target your potential customer with effectively published articles and reviews that support the keywords and keyword phrases that people in your niche are searching for, the more traffic you will be getting to your internet site.<br><br>+Direct client interaction. [http://20thstreetblockparty.com/2014/jordan-kurland-intro/ Jordan Kurland] is just a way to directly relate to consumers and potential clients on a regular basis. Enterprise is about building relationships. Develop relationships and your company will prosper.<br><br>The short version of how-to use twitter for organization will be to contemplate it like a short electronic PR release to direct visitors to events, a new blog post, a website, a printed report, a YouTube video, a SlideShare demonstration, a Facebook Lover page, etc. To use Twitter effectively, a company must have a number of social media items in-place, the very least being truly a website.<br><br>If you are an agent anywhere on the planet your agency may presently provide free web-marketing by providing a contact and collection platform and an internet site to you. If not you can contact a web-design agency to have you started.<br><br>Just remember, never quit. No matter what type of business you're required, it requires plenty of time and work to develop and build your business. Don't quit. If you stop, you crash. Do not expect you'll be described as a success overnight. After you put in the effort and hard-work, you will be greatly honored when it pays off.
	~~\| above = Bohr radius~~
	~~\| label1 = Symbol:~~
	~~\| data1 = ''a''<sub>0</sub>~~
	~~\| label2 = Named after:~~
	~~\| data2 = [[Niels Bohr]]~~
	~~\| label3 = Value in [[meter]]s:~~
	~~\| data3 = ≈ 5.29{{e\|-11}}[[meter\|m]]~~
	~~\| label4 = Value in [[picometer]]s:~~
	~~\| data4 = ≈ 52.9 [[meter\|pm]]~~
	~~\| label5 = Value in [[angstrom]]s:~~
	~~\| data5 = ≈ 0.529 [[angstrom\|Å]]~~
	}}
	~~The '''Bohr radius''' is a [[physical constant]], approximately equal~~ to the most ~~probable distance between~~ the ~~[[proton]] and [[electron]] in a [[hydrogen atom]] in its [[ground state]]~~. It ~~is named after [[Niels Bohr]]~~, ~~due to its role~~ in the ~~[[Bohr model]] of an atom~~. ~~The precise definition of the Bohr radius is:~~<~~ref~~>~~[[David J. Griffiths]], ''Introduction~~ to ~~Quantum Mechanics'', Prentice-Hall, 1995, p~~. ~~137. ISBN 0-13-124405-1~~<~~/ref~~>
	:<~~math~~>~~a_0 = \frac{4 \pi \varepsilon_0 \hbar^2}{m_{\mathrm{e}} e^2} = \frac{\hbar}{m_{\mathrm{e}}\,c\,\alpha}</math>~~

	~~where:~~
	~~:<math> \varepsilon_0 \ </math> is the [[permittivity~~ of ~~free space]]~~
	~~:<math> \hbar \ </math> is~~ the ~~[[reduced Planck~~'s ~~constant]]~~
	:<~~math~~> ~~m_{\mathrm{e}} \~~ <~~/math~~> ~~is the [[mass of electron\|electron rest mass]]~~
	:<~~math~~> ~~e \~~ <~~/math~~> is the ~~[[elementary charge]]~~
	~~:<math> c \ </math> is the [[speed of light]]~~ in ~~vacuum~~
	~~:<math> \alpha \ </math> is~~ the ~~[[fine structure constant]]~~.

	~~Or, in [[Gaussian units]] the Bohr radius is simply~~
	:<~~math~~>~~a_0=\frac{\hbar^2}{m_e e^2}~~<~~/math~~>
	~~According to 2010 [[CODATA]] the Bohr radius has a value of 5.2917721092(17){{e\|−11}} m (i.e., approximately 53 [[1 E-12 m\|pm]] or 0~~.~~53 ~~[~~[angstrom]]s).<ref>{{cite web \|url=~~http://~~physics~~.~~nist.gov~~/~~cgi~~-~~bin/cuu~~/~~Value?bohrrada0 \|title=CODATA Value: Bohr radius \|author= \|work=Fundamental Physical Constants \|publisher=[[National Institute of Standards and Technology\|NIST~~]~~] \|accessdate=3 July 2011}}</ref><ref>The number in parenthesis (36) denotes the [[standard deviation\|uncertainty]] of the last digits.</ref>~~

	~~In the [[Bohr model]] of the structure of an [[atom]], put forward by [[Niels Bohr]] in 1913, [[electrons]] orbit~~ a ~~central [[atomic nucleus\|nucleus]]. The model says that the electrons orbit only at certain distances from the nucleus, depending~~ on ~~their energy. In the simplest atom, [[hydrogen]],~~ a ~~single electron orbits the nucleus and its smallest possible orbit, with lowest energy, has an orbital radius almost equal to the Bohr radius~~. ~~(It~~ is ~~not ''exactly'' the Bohr radius due to the [[reduced mass\|reduced mass effect]]. They differ by~~ about 0.1%.)

	~~Although the Bohr model is no longer in~~ use~~, the Bohr radius remains very useful in [[atomic physics]] calculations, due in part~~ to ~~its simple relationship with other fundamental constants. (This is why~~ it ~~is defined using the true electron mass rather than the reduced mass, as mentioned above.) For example, it is the unit of length in [[atomic units]].~~

	~~According~~ to ~~the modern~~, ~~[[quantum mechanics\|quantum-mechanical]] understanding of the hydrogen atom~~, ~~the average distance −its [[expectation value (quantum mechanics)\|expectation value]]− between electron and proton is ≈1.5a<sub>0</sub>~~,~~<ref>[http://books.google.com/books?id=Yfo3rnt3bkEC&pg=PA234 Modern physics~~, ~~by Serway~~, ~~Moses~~, ~~Moyer~~, ~~Example 8~~.9, p284] The value 1.5a<sub>0</sub> is approximate, not exact, because it neglects [[reduced mass]], [[fine structure]] effects (such as relativistic corrections), and other such small effects.</ref> somewhat different than the value in the Bohr model (≈''a~~''<sub>0</sub>), but certainly the same [[order of magnitude]].~~

	~~The Bohr radius of the electron is one of~~ a ~~trio~~ of ~~related units of length~~, the ~~other two~~ being ~~the [[Compton wavelength]] of the electron <math> \lambda_{\mathrm{e}} \ </math> and the [[classical electron radius]] <math> r_{\mathrm{e}} \ </math>~~. ~~The Bohr radius is built from the [[electron mass]]~~ <~~math~~>~~m_{\mathrm{e}}~~<~~/math~~>~~, [[Planck's constant]] <math> \hbar \ </math> and~~ the ~~[[electron charge]] <math> e \ </math>. The Compton wavelength is built from <math> m_{\mathrm{e}} \ </math>, <math> \hbar \ </math>~~ and ~~the speed of light <math> c \ </math>. The classical electron radius is built from <math> m_{\mathrm{e}} \ </math>, <math> c \ </math>~~ and ~~<math> e \ </math>~~. ~~Any one of these three lengths~~ can ~~be written in terms of any other using the fine structure constant <math> \alpha \ </math>:~~

	~~:<math>r_{\mathrm{e}} = \frac{\alpha \lambda_{\mathrm{e}}}{2\pi} = \alpha^2 a_0~~.<~~/math~~>

	~~The Compton wavelength is about 20 times smaller than the Bohr radius, and the classical electron radius is about 1000 times smaller than the Compton wavelength.~~

	~~==Reduced Bohr radius==~~
	~~The Bohr radius including the effect of [[reduced mass]] in the hydrogen atom can be given by the following equation:~~

	:<~~math~~> ~~\ a_0^* \ = \frac{\lambda_{\mathrm{p}} + \lambda_{\mathrm{e}}}{2\pi\alpha}~~,~~</math>~~

	~~where:~~

	~~:<math> \lambda_{\mathrm{p}} \ </math> is the Compton wavelength of the [[proton]]~~.
	~~:<math> \lambda_{\mathrm{e}} \ </math> is the Compton wavelength~~ of ~~the electron.~~
	~~:<math> \alpha \ </math> is the fine structure constant.~~

	~~In the above equation~~, ~~the effect~~ of ~~the [[reduced mass]] is achieved by using the increased Compton wavelength, which is just the Compton wavelengths of the electron~~ and ~~the proton added together~~.

	~~==See also==~~
	*[[Bohr model]]

	~~==Notes and references==~~
	~~{{Reflist}}~~

	~~== External links ==~~
	* [http://math.~~ucr~~.~~edu/home/baez/lengths~~.~~html#bohr_radius Length Scales~~ in ~~Physics:~~ the ~~Bohr Radius]~~

	~~[[Category:Units of length]]~~
	~~[[Category:Atomic physics]]~~
	~~[[Category:Physical constants]]~~

en>ClueBot NG: Reverting possible vandalism by 111.69.198.186 to version by 217.28.15.192. False positive? Report it. Thanks, ClueBot NG. (1617573) (Bot)

2013-05-01T09:57:07Z

Reverting possible vandalism by 111.69.198.186 to version by 217.28.15.192. False positive? Report it. Thanks, ClueBot NG. (1617573) (Bot)

← Older revision		Revision as of 11:57, 1 May 2013
Line 1:		Line 1:
	~~Garfield Murtagh~~ is ~~my name like when people use my full name but I don~~'t. ~~Tennessee will be~~ the ~~place I really like most~~. In ~~my professional life I am planning officer~~ and ~~a production~~. ~~My wife does~~ not ~~like~~ it ~~just how I do~~ but ~~what I actually like doing~~ is ~~acting but I~~'~~ve been taking over new things lately~~.<br><br>~~Look into my blog post;~~ [http://~~20thstreetblockparty~~.~~com~~/~~2014~~/~~jordan-kurland-intro~~/ ~~Jordan Kurland~~]		{{infobox
			\| above = Bohr radius
			\| label1 = Symbol:
			\| data1 = ''a''<sub>0</sub>
			\| label2 = Named after:
			\| data2 = [[Niels Bohr]]
			\| label3 = Value in [[meter]]s:
			\| data3 = ≈ 5.29{{e\|-11}}[[meter\|m]]
			\| label4 = Value in [[picometer]]s:
			\| data4 = ≈ 52.9 [[meter\|pm]]
			\| label5 = Value in [[angstrom]]s:
			\| data5 = ≈ 0.529 [[angstrom\|Å]]
			}}
			The '''Bohr radius''' is a [[physical constant]], approximately equal to the most probable distance between the [[proton]] and [[electron]] in a [[hydrogen atom]] in its [[ground state]]. It is named after [[Niels Bohr]], due to its role in the [[Bohr model]] of an atom. The precise definition of the Bohr radius is:<ref>[[David J. Griffiths]], ''Introduction to Quantum Mechanics'', Prentice-Hall, 1995, p. 137. ISBN 0-13-124405-1</ref>
			:<math>a_0 = \frac{4 \pi \varepsilon_0 \hbar^2}{m_{\mathrm{e}} e^2} = \frac{\hbar}{m_{\mathrm{e}}\,c\,\alpha}</math>

			where:
			:<math> \varepsilon_0 \ </math> is the [[permittivity of free space]]
			:<math> \hbar \ </math> is the [[reduced Planck's constant]]
			:<math> m_{\mathrm{e}} \ </math> is the [[mass of electron\|electron rest mass]]
			:<math> e \ </math> is the [[elementary charge]]
			:<math> c \ </math> is the [[speed of light]] in vacuum
			:<math> \alpha \ </math> is the [[fine structure constant]].

			Or, in [[Gaussian units]] the Bohr radius is simply
			:<math>a_0=\frac{\hbar^2}{m_e e^2}</math>
			According to 2010 [[CODATA]] the Bohr radius has a value of 5.2917721092(17){{e\|−11}} m (i.e., approximately 53 [[1 E-12 m\|pm]] or 0.53 [[angstrom]]s).<ref>{{cite web \|url=http://physics.nist.gov/cgi-bin/cuu/Value?bohrrada0 \|title=CODATA Value: Bohr radius \|author= \|work=Fundamental Physical Constants \|publisher=[[National Institute of Standards and Technology\|NIST]] \|accessdate=3 July 2011}}</ref><ref>The number in parenthesis (36) denotes the [[standard deviation\|uncertainty]] of the last digits.</ref>

			In the [[Bohr model]] of the structure of an [[atom]], put forward by [[Niels Bohr]] in 1913, [[electrons]] orbit a central [[atomic nucleus\|nucleus]]. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy. In the simplest atom, [[hydrogen]], a single electron orbits the nucleus and its smallest possible orbit, with lowest energy, has an orbital radius almost equal to the Bohr radius. (It is not ''exactly'' the Bohr radius due to the [[reduced mass\|reduced mass effect]]. They differ by about 0.1%.)

			Although the Bohr model is no longer in use, the Bohr radius remains very useful in [[atomic physics]] calculations, due in part to its simple relationship with other fundamental constants. (This is why it is defined using the true electron mass rather than the reduced mass, as mentioned above.) For example, it is the unit of length in [[atomic units]].

			According to the modern, [[quantum mechanics\|quantum-mechanical]] understanding of the hydrogen atom, the average distance −its [[expectation value (quantum mechanics)\|expectation value]]− between electron and proton is ≈1.5a<sub>0</sub>,<ref>[http://books.google.com/books?id=Yfo3rnt3bkEC&pg=PA234 Modern physics, by Serway, Moses, Moyer, Example 8.9, p284] The value 1.5a<sub>0</sub> is approximate, not exact, because it neglects [[reduced mass]], [[fine structure]] effects (such as relativistic corrections), and other such small effects.</ref> somewhat different than the value in the Bohr model (≈''a''<sub>0</sub>), but certainly the same [[order of magnitude]].

			The Bohr radius of the electron is one of a trio of related units of length, the other two being the [[Compton wavelength]] of the electron <math> \lambda_{\mathrm{e}} \ </math> and the [[classical electron radius]] <math> r_{\mathrm{e}} \ </math>. The Bohr radius is built from the [[electron mass]] <math>m_{\mathrm{e}}</math>, [[Planck's constant]] <math> \hbar \ </math> and the [[electron charge]] <math> e \ </math>. The Compton wavelength is built from <math> m_{\mathrm{e}} \ </math>, <math> \hbar \ </math> and the speed of light <math> c \ </math>. The classical electron radius is built from <math> m_{\mathrm{e}} \ </math>, <math> c \ </math> and <math> e \ </math>. Any one of these three lengths can be written in terms of any other using the fine structure constant <math> \alpha \ </math>:

			:<math>r_{\mathrm{e}} = \frac{\alpha \lambda_{\mathrm{e}}}{2\pi} = \alpha^2 a_0.</math>

			The Compton wavelength is about 20 times smaller than the Bohr radius, and the classical electron radius is about 1000 times smaller than the Compton wavelength.

			==Reduced Bohr radius==
			The Bohr radius including the effect of [[reduced mass]] in the hydrogen atom can be given by the following equation:

			:<math> \ a_0^* \ = \frac{\lambda_{\mathrm{p}} + \lambda_{\mathrm{e}}}{2\pi\alpha},</math>

			where:

			:<math> \lambda_{\mathrm{p}} \ </math> is the Compton wavelength of the [[proton]].
			:<math> \lambda_{\mathrm{e}} \ </math> is the Compton wavelength of the electron.
			:<math> \alpha \ </math> is the fine structure constant.

			In the above equation, the effect of the [[reduced mass]] is achieved by using the increased Compton wavelength, which is just the Compton wavelengths of the electron and the proton added together.

			==See also==
			*[[Bohr model]]

			==Notes and references==
			{{Reflist}}

			== External links ==
			* [http://math.ucr.edu/home/baez/lengths.html#bohr_radius Length Scales in Physics: the Bohr Radius]

			[[Category:Units of length]]
			[[Category:Atomic physics]]
			[[Category:Physical constants]]

en>Rgdboer: /* Uses */ update link

2012-08-07T22:40:59Z

Uses: update link

New page

Garfield Murtagh is my name like when people use my full name but I don't. Tennessee will be the place I really like most. In my professional life I am planning officer and a production. My wife does not like it just how I do but what I actually like doing is acting but I've been taking over new things lately.<br><br>Look into my blog post; [http://20thstreetblockparty.com/2014/jordan-kurland-intro/ Jordan Kurland]