The Fine Structure Constant, the Rydberg Constant and the Planck Constant

YinYue Sha*

Dongling Engineering Center, Ningbo Institute of Technology, Zhejiang University, PR China

*Corresponding Author:
Dongling Engineering Center
Ningbo Institute of Technology
Zhejiang University, PR China
Tel: +86 574 8822 9048
E-mail: [email protected]

Received date: July 12, 2017; Accepted date: September 20, 2017; Published date: September 30, 2017

Citation: Sha YY (2017) The Fine Structure Constant, the Rydberg Constant and the Planck Constant. Polym Sci Vol.3 No.2:13

 
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Keywords

Protons; Electronic; Mass; Charge; Bohr atom radius; Fine structure constant; The Rydberg constant; Planck constant

So let's say that the electron is orbiting the proton in the innermost orbital, and then, according to the equilibrium relationship of forces, there's the following formula:

F=K × Qp × Qe/(Rb × Rb)=Me × Ve × Ve/Rb (1)

The K is the electromagnetic constant; Qp is the charge of proton; Qe is the charge of electron; Rb is the Bohr atom radius; Me is the mass of the electron; Ve is the speed of electrons.

One, the fine structure constant and the Bohr atomic radius.

From the formula (1), we can obtain the formula for calculating the basic radius of the hydrogen atom:

Rb=K × Qp × Qe/(Me × Ve2) (2)

Based on the international recommendation of the basic physical constants in 2006, we take the numerical constants as follows:

K=8987551787.3681764 m/F, Qp=Qe=1.602176487 × 10-19 C, Me=9.109382145 × 10-31 kg, C=299792458 m/s, α=0.0072973 525376

The movement speed of electrons is:

Ve=α × C=2187691.25413734 m/s (3)

It is calculated by the formula (2) that the Bohr atom radius is Rb:

Rb=K × Qp × Qe/(Me × Ve2)=5.2917720859 × 10-11 m (4)

Two, The basic frequency of the Hydrogen spectrum and the Rydberg constant.

By the speed of the electrons and the basic radius of the hydrogen, we can calculate the basic frequency of the Hydrogen spectrum:

Fb=Ve/(2 × π × Rb)/2=3.2898419603609 × 1015 1/s (5)

Hydrogen spectrum basic wavelength:

λb=C/Fb=9.1126705055191143 × 10-8 m (6)

Rydberg constant is: R=1/λb=10973731.568527 1/m (7)

Three, The kinetic energy of the ground state electron and the Planck constant

The kinetic energy of the ground state electron:

Eb=1/2 × Me × Ve2=2.1798719696853 × 10-18 J=13.6056919275362 eV (8)

Planck constant is: h=Eb/Fb=6.62606896 × 10-34 Js (9)

Four, The speed limit of the electron with the limit of the X ray frequency

According to the nature of electricity and magnetism, electrons moving in the same direction at the speed of light interaction force is zero, that is to say, the electronic impossible by electricity and magnetism are accelerated to the speed of light, the speed of light is electronic speed limit [1].

According to Planck quantum mechanics and Einstein's photoelectric effect law, the speed limit of an electron is the same as the limit of the X-ray frequency:

Em=(1÷2) × Me × C × C=h × Fm=Qe × Um (10)

Em=(1÷2) × Me × C × C=4.093552189 × 10-14 J (11)

Um=Em/Qe=255499.45477 V (12)

Fm=Em/h=6.177949873 × 1019 Hz (13)

λe=C/Fm=4.852620435 × 10-12 m (14)

Compton wavelength is: λC=λb/2 × α2=λe/2=2.4263102175 × 10-12 m (15)

References

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