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