|
The velocity of the first Bohr`s electron and the speed of light ratio is called The Fine Structure Constant.
|
|
The Sommerfeld Fine Structure Constant, 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.
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. The standard definition of fine structure constant in terms of other fundamantal
physical constants are:
|
where e is the elementary charge, h is the Planck constant,
is the magnetic constant (permeability of vacuum).
Also the fine structure constant is,
The fine structure square is the ratio of the Bohr`s electron frequency and the Compton`s electron frequency:
From the theory of Hydrogen atom we find for the fine structure constant this amusing relation:
Where R is Rydberg constant, and r(Bohr) is radius of the first Bohr`s electron.
So, the velocity of the first Bohr`s electron is
The frequency of this electron according to the theory of Hydrogen atom is
The Bohr`s electron wavelength is
The Compton`s wavelength of electron is
From the Bohr`s fundamental relation
Where m is electron rest mass and h is Planck constant, we get famous De Broglie relation
Also we have another form of Bohr`s fundamental relation:
From which we have next relation for the fine structure constant
Where
Is Dirac`s constant.
Also, the fine-structure constant is defined as
Where e is electron`s elementary charge. The connection between the fine structure constant and the golden section constant is
Where
phi is the golden section constant.
As of 2007, the best determination of the value of the fine-structure constant is α = 7.297352570(5)×exp(-3) = 1/137.035999070(98). The standard error is enclosed in parentheses.
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
Encyclopædia Britannica.2009: Fine-structure constant
Wikipedia: The Fine-Structure Constant
CODATA Value: Fine-Structure Constant
| 
