Bohr radius

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