Velocity of Orbiting Electron
It is possible to find the velocity of an electron in its orbit using:
To shorten the calculations, the words in the equations will be converted to symbols:
The following calculations are based on de Broglie’s speculative equation:
(1) 
(2) 
(3) 
(A) 




(1)

(2)

(3)

(1)

(3)

(A )


(4) (2) 
(B) (3) 

(5) (3, 4) 
(C) (A, B) 

(6) (1, 5) 
(D) (C) 

(7) (6) 
(E) (1, D) 

(8) (7) 
(F) (E) 

(G) (F) 

(H) (G) 
(9)
(7, G)
(10)
(9)
(11)
(10)
v is the velocity of the electron in the orbital λ = 1.
Size of a Hydrogen Atom
From the electron velocity you can determine the size of a hydrogen atom.



meters 
Ionization Energy of Hydrogen
You can also determine the ionization energy of hydrogen.


This gives a voltage of:
(Experimental 13.595 electron volts)
and a frequency of
Second Ionization Constant of Helium
The second ionization constant of helium may also be calculated from
=
(Experimental 54.403 ev)
Third Ionization Constant for Lithium
You can determine the third ionization constant for lithium in the same way as above.
=
(Experimental 122.418 ev)
Frequency of Light Emitted When a Hydrogen Atom Forms
The frequency of light emitted when a hydrogen atom forms (from ) is
This is just half the frequency of the hydrogen atom’s electron in its orbit
The same is true of the ion.
Frequencies of Light in the Hydrogen Emission Spectrum
You can also determine the frequencies of light in the hydrogen emission spectrum from the ionization energy of hydrogen. Niels Bohr hypothesized (1913) that electrons only occupied orbits where λ was an integer.












The frequencies of light in the hydrogen spectrum correspond to the differences between these energies as the electron goes from one orgit to another. If an electron goes from orbit 2 to orgit 1, a photon with the energy of 13.6 ev 3.40 ev = 10.20 ev is emitted. You can construct a chart showing the energies and frequencies of light emitted in the hydrogen spectrum:
Initial Orbit 
Final Orbit 
ev 
ν 
∞ 
1 
13.6 

4 
1 
13.6  .85 = 12.75 

3 
1 
13.6 1.51 = 12.09 

2 
1 
13.6 3.4 = 10.2 

∞ 
2 
3.40 

4 
2 
3.40  .85 = 2.55 

3 
2 
3.40 1.51 = 1.89 

These correspond closely with the observed frequencies.
Content of this paper may be freely used so long as credit is given to the author, Brian Stedjee
First publication date: September, 2003