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Fine Structure Constant α and the Golden Section
The fine-structure constant α is
defined as
where e is the charge of an
electron, p is pi, ћ = h/(2p) is Dirac's constant, c
is the speed of light in vacuum and e0 is the
permittivity of the vacuum.
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The Sommerfeld
Fine Structure Constant, symbol α , was first shown by Arnold
Sommerfeld (1868-1951) in order to account for the actual
frequency of the spectral lines for the hydrogen atom from the
fundamental Bohr hydrogen atom equations. For brevity, the
results of central motion that made the apparent electron
orbits ellipses. These was not the full corrections required
so that the work of Walter Ritz (1878-1909) applied later
modified this to account for their calculated and measured
positions (frequency). |
A very accurate, 2006, New Value of the Fine Structure
Constant from the Electron g-Value and QED, G.
Gabrielse et al derive the value for this quantity with the (±
5) uncertainty range centered on the last two digits (36) as,
α =
0.007297352536(5).
In 2006 CODATA
recommended experimental value for this quantity is,
Concise form 7.297 352 5376(50) x 10-3
According to my research the fine structure constant has
value:
where
m = 9.109 382 15 x 10-31 kg , electron mass
c = 299 792 458 m s-1, speed of light in vacuum
h = 6.626 068 96 x 10-34 J s , Planck constant
r = 0.529 177 208 59 x 10-10 m, Bohr radius .
Using the best experimental values for m,r,h and (the value of c is fixed by definition) gives
α =
0.0072973525335357.
I am doing my own investigation of the Fine structure constant with regard to the Golden Section.I found the relation between Golden Section and Fine structure constant:
Fine structure constant value is:
α =
0.007297352539.
Planck's constant (denoted h) is a physical constant that is used to describe the sizes of quanta. It plays a central role in the theory of quantum mechanics, and is named after Max Planck, one of the founders of quantum theory.
where phi is the value of the golden section
The value of Planck's constant is:
Planck's constant has dimensions of energy multiplied by time, which are also the dimensions of action. In SI units Planck's constant is expressed in joule-seconds. The dimensions may also be written as momentum times distance (N·m·s), which are also the dimensions of angular momentum.
The quantity,
called h-bar or sometimes Dirac's constant, is also commonly encountered.The value of Dirac's constant is:
See: Fine structure constant and Fundamental Physical Constants
See: Planck`s constant and number PI
P. A. M. Dirac, Nature 139, 323 (1937)
G. Gamow, Phys. Rev. Lett. 19, 757 and 913 (1967).
Kinoshita, T. "The Fine Structure Constant." Rept. Prof. Phys. 59, 1459-1492, 1996.
Hans A.Bethe: "Intermediate Quantum Mechanics",W.A.Benjamin Inc,New York - Amsterdam (1964).
Todorovic,Milan: "Atomska fizika".Elektrotehnicki fakultet, Beograd (1973).
Ivanovic,Dragisa: "Kvantna mehanika".Naucna knjiga, Beograd (1972).
James Gilson : Fine structure
constant
Scienceworld, Wolfram: Fine structure constant
Wikipedia: The Fine-Structure Constant
Bert Schreiber: The collected works of Bert Schreiber
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