Difference between revisions of "Bohr radius"
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[[Bohr radius]] is fundamental physical constant |
[[Bohr radius]] is fundamental physical constant |
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| − | + | \(\displaystyle a_0={\hbar\over\alpha \mu c} |
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| − | = \frac{\hbar^2}{\mu e^2} \approx 5.2917721067(12) \times 10^{-11} \rm m |
+ | = \frac{\hbar^2}{\mu e^2} \approx 5.2917721067(12) \times 10^{-11} \rm m\) |
where <br> |
where <br> |
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| − | + | \(\hbar\) is the [[Planck constant]], \(\hbar \approx 1.054571800(13)\times 10^{-34}\, \rm Joule\, second\)<br> |
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| − | + | \(e\) is [[elementary charge]], <br> |
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| − | + | \(\mu\) is [[electron mass]], \(\mu = 9.10938356(11)\times 10^{−31}\, \rm kg\); |
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| − | + | \(\alpha = \frac{e^2}{\hbar c}\) is [[thin structure constant]],<br> |
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| − | + | \(c\) is [[speed of light]], |
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The [[Bohr radius]] appear as scale of the solution of the [[Radial equation for hydrogen atom]]; roughly, it determines the size of all atoms to be of order of several picometers. |
The [[Bohr radius]] appear as scale of the solution of the [[Radial equation for hydrogen atom]]; roughly, it determines the size of all atoms to be of order of several picometers. |
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This article is to elaborate unified notations, because of lack of letters in the Latin alphabet. The mode detailed description can be found at Wikipedia. |
This article is to elaborate unified notations, because of lack of letters in the Latin alphabet. The mode detailed description can be found at Wikipedia. |
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| − | Usually, letters |
+ | Usually, letters \(a\) and \(c\) are used to denote coefficients of some polynomial and/or asymptotic expansions. |
In this case, it worth ro denote the Bohr radius with |
In this case, it worth ro denote the Bohr radius with |
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| − | + | \(r_{\rm b}\) or \(r_{\rm B}\) or \(R_\rm B\) |
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While no unified system of notation is elaborated, each article should define the notations at the beginning. |
While no unified system of notation is elaborated, each article should define the notations at the beginning. |
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Latest revision as of 18:46, 30 July 2019
Bohr radius is fundamental physical constant
\(\displaystyle a_0={\hbar\over\alpha \mu c} = \frac{\hbar^2}{\mu e^2} \approx 5.2917721067(12) \times 10^{-11} \rm m\)
where
\(\hbar\) is the Planck constant, \(\hbar \approx 1.054571800(13)\times 10^{-34}\, \rm Joule\, second\)
\(e\) is elementary charge,
\(\mu\) is electron mass, \(\mu = 9.10938356(11)\times 10^{−31}\, \rm kg\);
\(\alpha = \frac{e^2}{\hbar c}\) is thin structure constant,
\(c\) is speed of light,
The Bohr radius appear as scale of the solution of the Radial equation for hydrogen atom; roughly, it determines the size of all atoms to be of order of several picometers.
This article is to elaborate unified notations, because of lack of letters in the Latin alphabet. The mode detailed description can be found at Wikipedia.
Usually, letters \(a\) and \(c\) are used to denote coefficients of some polynomial and/or asymptotic expansions. In this case, it worth ro denote the Bohr radius with \(r_{\rm b}\) or \(r_{\rm B}\) or \(R_\rm B\)
While no unified system of notation is elaborated, each article should define the notations at the beginning.
References
http://quantummechanics.ucsd.edu/ph130a/130_notes/node233.html
https://en.wikipedia.org/wiki/Bohr_radius
Keywords
Bohr radius, Fundamental constant, Hydrogen atom, Planck constant, Quantum mechanics, Speed of light