[Physics] Physics Digest, Vol 11, Issue 2

[Ruud Loeffen]

Hello Carl.

I know that you don't rely on Wikipedia but there I find:
The fine-structure constant, *α*, has several physical interpretations.

   - The ratio of the velocity of the electron in the first circular orbit
   of the Bohr model of the atom
   <https://en.wikipedia.org/wiki/Bohr_model_of_the_atom>, which is
{\displaystyle
   {\frac {1}{4\pi \varepsilon _{0}}}{\frac {e^{2}}{\hbar }}}[image:
   {\displaystyle {\frac {1}{4\pi \varepsilon _{0}}}{\frac {e^{2}}{\hbar }}}]
    to the speed of light <https://en.wikipedia.org/wiki/Speed_of_light> in
   vacuum, *c*.[5]
   <https://en.wikipedia.org/wiki/Fine-structure_constant#cite_note-5> This
   is Sommerfeld's original physical interpretation. Then the square of *α* is
   the ratio between the Hartree energy
   <https://en.wikipedia.org/wiki/Hartree_energy> (27.2 eV = twice the Rydberg
   energy <https://en.wikipedia.org/wiki/Rydberg_constant> = approximately
   twice its ionization energy) and the electron
   <https://en.wikipedia.org/wiki/Electron> rest energy
   <https://en.wikipedia.org/wiki/Rest_energy> (511 keV).



See: https://en.wikipedia.org/wiki/Fine-structure_constant (2nd bullet)

Then on the 8th- bullet you find the meaning of alpha as:

   - The fine-structure constant gives the maximum positive charge of an
   atomic nucleus that will allow a stable electron-orbit around it within the
   Bohr model (element feynmanium <https://en.wikipedia.org/wiki/Feynmanium>
   ).[8] <https://en.wikipedia.org/wiki/Fine-structure_constant#cite_note-8>
For
   an electron orbiting an atomic nucleus with atomic number *Z*, *mv*2/*r* =
   1/4*πε*0 (*Ze*2/*r*2). The Heisenberg uncertainty principle
   <https://en.wikipedia.org/wiki/Uncertainty_principle> momentum/position
   uncertainty relationship of such an electron is just *mvr* = *ħ*. The
   relativistic limiting value for *v* is *c*, and so the limiting value
   for Z is the reciprocal of the fine-structure constant, 137.[9]
   <https://en.wikipedia.org/wiki/Fine-structure_constant#cite_note-9>


If you don't want to be involved with Wikipedia, I found on:
https://physics.nist.gov/cuu/Constants/alpha.html

The quantity *α* was introduced into physics by A. Sommerfeld in 1916 and
in the past has often been referred to as the Sommerfeld fine-structure
constant. In order to explain the observed splitting or fine structure of
the energy levels of the hydrogen atom, Sommerfeld extended the Bohr theory
to include elliptical orbits and the relativistic dependence of mass on
velocity. The quantity *α,* which is equal to the ratio *v*1/*c* where *v*1 is
the velocity of the electron in the first circular Bohr orbit and *c* is
the speed of light in vacuum, appeared naturally in Sommerfeld's analysis
and determined the size of the splitting or fine-structure of the
hydrogenic spectral lines. Sommerfeld's theory had some early success in
explaining experimental observations but could not accommodate the
discovery of electron spin. Although the Dirac relativistic theory of the
electron introduced in 1928 solves the main aspects of the problem of the
hydrogen fine-structure, *α* still determines its size as in the Sommerfeld
theory. Consequently, the name "fine-structure" constant for the group of
constants below has remained:

   [image: $$\alpha = \frac{e^2/\hbar c}{4 \pi \epsilon_0}= \frac{\mu_0 c
      e^2}{2 h}$$],


where e is the elementary charge, [image: h bar] = *h*/2π where *h* is the
Planck constant, ε0 = 1/*µ*0*c*2 is the electric constant (permitivity of
vacuum) and *µ*0 is the magnetic constant (permeability of vacuum). In the
International System of Units (SI), *c*, ε0, and *µ*0 are exactly known
constants.

Our view of the fine-structure constant has changed markedly since
Sommerfeld introduced it over 80 years ago. We now consider α the coupling
constant for the electromagnetic force and similar to those for the other
three known fundamental forces or interactions of nature: the gravitational
force, the weak nuclear force, and the strong nuclear force. Further, since
*α* is proportional to *e*2, it is viewed as the square of an effective
charge "screened by vacuum polarization and seen from an infinite distance.

Any comments?

Best regards.

Ruud Loeffen



On Mon, Jan 29, 2018 at 10:18 PM, <cj at mb-soft.com> wrote:

> The "Fine Structure Constant" only applies to the internal structure of
> the atomic nucleus, and it has absolutely nothing to do with any electrons
> in their orbitals.
>
> C Johnson
>
>
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-- 
*Ruud Loeffen*
Paardestraat32
6131HC Sittard
http://www.human-DNA.org
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