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2014-06-07T05:44:50Z

Dating maintenance tags: {{Unreferenced}}

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	~~The '''Bjerrum length''' (after Danish chemist [[Niels Bjerrum]] 1879–1958~~		Careers Counsellor Anton Lester from Timmins, usually spends time with pastimes for instance listening to music, property developers in singapore and hot rods. Has signed up for a global contiki journey. Is extremely excited in particular about visiting Works of Antoni Gaudí.<br><br>Feel free to surf to my page [http://www.englishandtranslationsinaction.com/?q=node/20 englishandtranslationsinaction.com]
	~~<ref>http://www.rsc.org/delivery/_ArticleLinking/DisplayArticleForFree.cfm?doi=TF959550X001&JournalCode=TF</ref>)~~
	~~is the separation at which the [[electrostatic]] interaction between two~~
	~~[[elementary charge]]s is comparable in magnitude~~ to ~~the thermal energy scale~~,
	~~<math>k_B T</math>, where <math>k_B</math> is the [[Boltzmann constant]]~~ and ~~<math>T</math> is the~~
	~~[[absolute temperature]] in [[Kelvin]]~~. ~~This length scale arises naturally~~ in ~~discussions~~ of ~~electrostatic,~~
	~~electrodynamic and electrokinetic phenomena in [[electrolyte]]s, [[polyelectrolyte]]s and [[DLVO theory\|colloidal dispersions]]~~.
	~~<ref>{{cite book \| last1=Russel \| first1=William B. \| first2=D. A. \| last2=Saville \| first3=William R. \| last3=Schowalter \|~~
	~~title=Colloidal Dispersions \| publisher=Cambridge University Press \| location=New York \| year=1989}}~~<~~/ref~~>

	~~In [[SI units\|standard units]], the Bjerrum length is given by~~

	<~~math~~>~~\lambda_B = \frac{e^2}{4\pi \varepsilon_0 \varepsilon_r \ k_B T},</math>~~

	~~where <math>e</math> is the~~ [~~[elementary charge]], <math>\varepsilon_r<~~/~~math> is the relative [[dielectric constant]] of the medium~~
	~~and <math>\varepsilon_0<~~/~~math> is the [[vacuum permittivity]]~~.
	~~For water at~~
	~~room temperature (<math>T = 300 \mbox{ K}</math>), <math>\varepsilon_r \approx 80</math>, so that~~
	~~<math>\lambda_B \approx 0~~.~~7 \mbox{nm}<~~/~~math>.~~

	~~In [[Gaussian units]], <math>4\pi\varepsilon_0~~ = 1</~~math> and the Bjerrum length has the simpler form~~

	~~<math>\lambda_B = \frac{e^2}{\varepsilon_r k_B T}~~.~~</math>~~

	~~==References==~~
	~~{{Reflist}}~~

	~~[[Category:Physical chemistry]~~]

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The '''Bjerrum length''' (after Danish chemist [[Niels Bjerrum]] 1879–1958
<ref>http://www.rsc.org/delivery/_ArticleLinking/DisplayArticleForFree.cfm?doi=TF959550X001&JournalCode=TF</ref>)
is the separation at which the [[electrostatic]] interaction between two
[[elementary charge]]s is comparable in magnitude to the thermal energy scale,
<math>k_B T</math>, where <math>k_B</math> is the [[Boltzmann constant]] and <math>T</math> is the
[[absolute temperature]] in [[Kelvin]]. This length scale arises naturally in discussions of electrostatic,
electrodynamic and electrokinetic phenomena in [[electrolyte]]s, [[polyelectrolyte]]s and [[DLVO theory|colloidal dispersions]].
<ref>{{cite book | last1=Russel | first1=William B. | first2=D. A. | last2=Saville | first3=William R. | last3=Schowalter |
title=Colloidal Dispersions | publisher=Cambridge University Press | location=New York | year=1989}}</ref>

In [[SI units|standard units]], the Bjerrum length is given by

<math>\lambda_B = \frac{e^2}{4\pi \varepsilon_0 \varepsilon_r \ k_B T},</math>

where <math>e</math> is the [[elementary charge]], <math>\varepsilon_r</math> is the relative [[dielectric constant]] of the medium
and <math>\varepsilon_0</math> is the [[vacuum permittivity]].
For water at
room temperature (<math>T = 300 \mbox{ K}</math>), <math>\varepsilon_r \approx 80</math>, so that
<math>\lambda_B \approx 0.7 \mbox{nm}</math>.

In [[Gaussian units]], <math>4\pi\varepsilon_0 = 1</math> and the Bjerrum length has the simpler form

<math>\lambda_B = \frac{e^2}{\varepsilon_r k_B T}.</math>

==References==
{{Reflist}}

[[Category:Physical chemistry]]

Isotropic manifold - Revision history

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