BINDING ENERGY FORMULA - Chapter 23 Physics of the Universe
Copyright (c) 1998 by Gerald Grushow BSEE (Summa Cum Laude)
In Chapter 22, we saw that the binding energy of the electron in the
Bohr Orbit of 13.58 electron volts was due to the change of mass of the
electron as it moves at 1/137 times the speed of light. The change of mass
of the electron was only 50 parts per million according to Einsteins mass
formula. Thus:
Energy = 50 PPM X 511,000EV = 13.59 EV (1)
This is well within the measured accuracy. In our universe anything
with an accuracy of 0.2% accuracy tends to be correct since this factor
always exists in many various relationships. This factor is most likely
due to the Earths total speed within the universe, the gravitational
field which distorts things, and some other factors which the author is
no aware of right now.
When the speed is 1.274 C, the energy from Einsteins formula is:
Energy = 6.56 PPM x 511,000 MEV = 3.4 EV (2)
We can now work backwards and derive the binding energy from Einsteins
formula directly.The binding energy of atoms and of the hydrogen atom in
particular is the mass gain of the electron in the Bohr Orbit. For the
neucleus, the binding energy of the neucleus is the mass gain in the
neutron orbit.
In heavy atoms, the electron travels at greater than
90 percent of the speed of light. This provides the 8MEV of binding energy
per neuclei. In the neutron the speed was 0.91318 C at a root mean square
radius of 1.4087E-15 meters. This gives us a gravitational mass of 2.45 Me.
As previous stated, not all energy from light is gravitational. Thus the
total inertial energy of the electron in the Neutron Orbit is 4.076MEV.
Thus there is a lot of energy to bind the deuteron and when we move to
heavier atoms the electron speed is even higher, thus giving us the
8 MEV. Atomic scientists find a lot of particles and subparticles in the
process. This is merely produced by the energy within the electrons
themselves. There are no particles and subparticles within the neutron.
Thus everything you find in atom smashers are produced by the
experiment themselves or are products of the photon energy released by
the electrons after the collision. Thus the experiment produces its own
results. The more you smash, the more you make. However, all you are
doing is recreating products from exploding stars. Within the protons,
you will only find dots.
Thus the proton and the electron are all you need to produce
everything you see in the universe.The antiproton and antielectron
are really the same thing but at a 180 degree phase angle and with
the opposite excess of dots of total value Q. Thus Q* is 180 degrees
phase shifted for the antimatter protons and electrons.
Let us now calculate the binding energy from the speed of the
electron in the Bohr orbit.The mass difference of the electron is:
delta Me = Me/[(1-(V/C)^2]^0.5 - Me (23-3)
The binding energy is the mass difference times the speed of
light and then divided by the charge Q for electron volts.
BE = [(MeC^2)/Q] . (1/J* - 1) (23-4)
In equation 23-4 J* is used for Einsteins correction formula.
BE = [(MeC^2)/Q] . (1 - J*)/ J* (23-5)
In equation 23-5 we see that since J* is almost equal to unity in
the Bohr orbit the expression can be simplified as follows:
BE= [(MeC^2)/Q] . (1 - J*) (23-6)
Thus:
BE = [(MeC^2)/Q] . 1 - [1 - (V/C)^2]^0.5 (23-7)
Equation 23-7 shows the binding energy formula for the electron in
the Bohr orbit. It is the same formula for the binding energy of the
electron in the neutron orbit, however for high speeds, equation 23-5
must be used and the approximation discarded. Likewise it is the same
formula for the binding energy of the heavy atoms. In each case, all that is
necessary is to know is the velocity of the electron. Likewise we can
calculate the velocity of the electron using this formula.
The inertial energy of the electron at the higher speeds can
be found using the inertial formula:
Inertial Energy = [Me C^2] / [ 1 - (V/C)^2] (23-8)
The difference in energy adds momentum to the freed electrons
or produces additional products such as neutrinos etc.
Photon Energy = [(MeC^2)/Q] . [1- k*] / k* (23-9)
where K* is the inertial correction factors which is the arithmetic
mean of the Doppler masses. Einsteins formula is the geometric mean of
the Doppler masses. The Doppler masses are the masses seen in front
of the moving object and behind the moving object as per the Doppler
formula previously discussed.
For the Bohr atom in the lowest outside shell, the photon
energy also equals 27.22 EV. Some of this is part of the binding
energy and the rest represents orbital energy.
Surplus Energy = Photon Energy - Binding Energy (23-10)
Surplus Energy = 27.22 - 13.61 = 13.61 (23-11)
We notice that for the Bohr Orbit the surplus energy equals the
binding energy. When we go to very high speed electrons in the heavy
atoms, the surplus energy is much larger than the binding energy.gg