THE BOHR ORBIT - Chapter 23 Physics of the Universe Copyright (c)
1998 by Gerald Grushow
Let us calculate the velocity of the electron in the first Bohr
Orbit state and the radius as well. Bohr did an excellent job of bringing
an understanding of the hydrogen atom to man. He compared the light spectra
and simple equations to relate the electric field and the centripital
force to arrive at a set of equations which he fit into each other. He
did not explain the binding energy of the hydrogen atom. He merely used
the 13.58 electron volts in his work.
Let us now calculate the Bohr orbit without any need to study the
light spectra. Bohr studied the spectra and came to his great conclusions.
However this method of emperical analysis which fits the data into the
equations lacks the understanding of what is happening in the process.
This chapter will show the reader the exact workings of the hydrogen
atom and how it was produced from the neutron.
In Chapter 16, Electron in Neutrons Orbit, it was shown that the
binding force for the neutron was due to the electron in an orbit of
radius 1.409E-15 with a gravitational mass of 2.4537 times the rest
mass of the electron. The characterists are as follows:
Me = 2.4537 Meo (23-1)
Re = 1.409E-15 (23-2)
Ve= 0.91318C (23-3)
In equations 23-1,2,and 3 we see that the mass of the electron in the
neutron orbit is about 2.5 times the rest mass of the electron. The
orbit of 1.409E-15 was chosen as the root mean square distance of
an exponential sinusoid moving downward from the radius Rp*, the common
radius in the universe of 1.457E-15 and the radius of the proton which
equals its wavelength of 1.321E-15. As a simplification this was
approximated by an upside down half sinewave. The velocity was then
calculated using the standard equality between the centripital force
and the coulomb attraction. Thus:
KQQ/Rb^2 = Meo (V^2) / Rb [1-V/C)^2]^0.5 (23-4)
In equation 23-4 we find that the electric force equals the
centripital force when corrected for the gravitational mass increase
as per Einsteins formula of the Doppler formula. In addition to this
there is an additional increase in inertial energy when we use the
inertial formula:
Mei = Meo/[1-(V/C)^2] (23-5)
The inertial mass calculates to:
Mei = 4.076 Me (23-6)
The energy in MEV of the gravitational and inertial masses are:
Meg = 2.4537 Me (1.2538 MEV) (23-7)
Mei - 4.076 Me (2.0828 MEV) (23-8)
We see in equation 23-7 that the gravitational mass which gives
the neutron weight has a surplus energy of 0.7428 MEV.The
neutron also has surplus photon energy which is non gravitational
and equals 1.5718 MEV. Together there is sufficient energy to
radiate photons and to produce the Bohr orbit.
Let us now look at the Bohr orbit. The neutron will radiate
its surplus energy and the velocity of the electron will move from
relativistic speeds to ordinary speeds. Bohr deduced that the
orbit would be at C/137 and Rb at 0.528E-10. He showed that
there was a constant relationship between the square of the velocity of the
orbit and the radius such that:
Me(Vb ^2)Rb = Constant (23-9)
Thus for an orbit of the series Rb, 4Rb, 9Rb... the velocities
would be Vb, Vb/2, Vb/3. The proton electric field attracts the
electron and the electron heads toward the proton. Bohr had no
explanation as to why the electron would not be captured by the
proton. Yet his answers were great.
As we saw in the chapter on Electron in neutron orbit, the
high speed of the electron carries the binding energy for all the
molecules. Thus binding energy is due to Einsteins formula.When
the electron moves toward the proton, the mass of the electron
increases. The AC electric field within the electron interacts with
the protons AC electric field to produce standing wave patterns
which prevent the electron from heading right into the proton.
The amount of energy in MEV required to push the electron into the
neutron orbit is from the inertial formula :
2.0828 - 0.511 = 1.5718 MEV (23-10)
Thus the electron cannot fall into the proton. It must be pushed
into it.And it must be a spherical pressure like an atomic bomb
to do the trick.Thus the minute the electron starts to gather mass
it resists the orbit. This is because the electric force and the
centripital force are basically equal. The increase of mass damages
the relationship. Thus the hydrogen atom is proof of Einsteins formula.
Let us now calculate the Bohr Orbit and the Bohr velocity. The
energy difference as we move from way outside the atom toward the
proton is:
In order to improve the accuracy of the conversion process
from the neutron electron energy to the Bohr Orbit certain relationships
are helpful. If we know the RMS radius of the neutron accurately, we
can calculate the mass of the electron from:
MeC^2 = KQQ/2Rn (23-10)
Equation 23-10 states that the rest energy of the electron is equal to
half the electrical energy of a charge moving from the radius of the
universe to the root mean square radius of the neutron orbit.
Since we know Me=9.108E-31, we can calculate the Neutron radius a
little more accurately as:
Rn= 1.4087E-15 (23-11)
We previously calculated 1.409E-15 but this method is as accurate
as the measurement of the charge. The previous method used an
approximation calculation but this used the Bohr philosophy of
equating half the energy to the mass of the electron and half to
its motion. Equation 23-10 does give a very simple relationship
between the mass of the electron and its orbit within the neutron.
We now need to find a relationship between the mass of the
electron in the Bohr orbit and the near speed of light of the
electron within the neutron together with the radius of the
neutron and the radius of the Bohr orbit.The equations generated
must match the Bohr results.
In the modified MKS system shown in chapter 22. The gravitational
constant had the units of Met^3 / Kg Sec^2. Thus the term Met^3/sec^2
denotes a constant related to the gravitational field. Evidently
there is a property of space and time such that an important
constant relationship exists between the cube of velocity times
distance. Thus we can formulate the equation between the Bohr
orbit and the neutron orbit as follows:
[Me/2] [(C/A)^2] Rb = Me (C^2) Rn (23-11)
Vb = C/A (23-12)
In equation 23-11 states that the kinetic energy of the electron in
the Bohr orbit times the radius of the Bohr orbit is equal the energy
of the electron times the radius of the neutron. Thus we have an
equation which relates the neutron radius and the Bohr orbit.
In equation 23-12 we specify that Vb is the speed of light C
divided by the constant A. We can now solve for A:
A =(Rb/2Rn)^0.5 (23.12)
Using Rb= 0.528E-10 and Rn=1.4087E-15 we get:
A= 136.8966 (23.12)
Here we used the more accurate Rn in order to determine if the
A=137 is really 137.0 or 16 pi e = 136.636. At this point we still
do not know. We see that the relationships in equation 23-11 do
produce correct results.
We know from this analysis that the energy within the neutron
produces frequencies which when multiplied by the neutron radius
matches the frequencies of the electron within the Bohr orbit times
the radius of the Bohr orbit. This would be the basis of Bohr's
quantum wavelengths.
Let us now look a little more carefully at the electron in
the Bohr orbit at V= C/137 to see if 137 is the correct answer or
if some other answer is correct. Let us use Einsteins formula:
Correction = [1-(V/C)^0.5] (23-13)
and look at the differential mass as we change the velocity around C/137.
The following chart shows the calculations.
Velocity Correction Error Energy {EV)
C/274 0.9999933 6.56PPM 3.4 EV
C/200 0.9999874 12.5PPM 6.387EV
C/137 0.999732 26.6PPM 13.59EV
C/100 0.999499 50.0PPM 25.55EV
C/10 0.9949 5012PPM 2561EV
From the Chart we see that a velocity of C/10 produces a relativity
mass error of 5012 parts per million, PPM of 2561 electron volts, EV.
Even at C/274 we get a small error in mass due to Einsteins equation.
At C/137 we see that the differential relativistic mass has an
error of 26.6 PPM or 13.59 electron volts.
Now we know where the binding energy of the hydrogen atom
comes from. It comes from the gain in relativistic gravitational
mass as per Einsteins formula. Thus the above chart is the proof
that binding energy is caused by the electrons mass increase with
velocity as per Einsteins formula.gg