The equilibrium energy of the energy state consists of the energy of all the particles in the system minus the energy of the free state, which can be expressed numerically by the equation
In our example, we must assume that none of the particles are in the free state. This is the only energy state that could be produced by nuclear fusion. However, the energy of the free state is not a zero energy. One may use the following definition of the energy of the free state for a certain energy (see Figure 5.4 on the Wikipedia page on Nuclear Fusion for more details).
The total energy is that of the sum of all of the energy states, the number of which can be calculated as, for each particle,
where is the energy and is the probability of that particle having energy. (A particle of energy is called a Higgs particle and a Higgs boson is referred to as a “standard model Higgs particle”. For another good description of these particles, it is helpful to read the paper: “A Standard Model of Particle Physics”.).
Figure 5.4: Nuclear Fusion Energy Calculator
Using our examples as example, I will calculate the equation for the “normal” energy of the state, i.e., the energy in terms of mass, density, time as in equation, E = mc2, to obtain
This equation is easy to verify! I will use the following equations and the results will be the same regardless of the choice of units. The nuclear fusion energy will be given in J/kg and is the energy required to create the fusion reaction between a nucleus and a proton plus more.
A single proton contains approximately 1034 kg, and since we will assume that the nucleus will have mass = 1034g and the proton’s mass is 1034kg, we can convert E by the expression
E = J/kg. This gives
where and is the energy. The mass can be calculated as
and is the energy of the particle in terms of the total mass. The mass of the Higgs is given by the formula
Now let’s plug in the mass of the proton, 1034kg, and the proton’s mass in terms of the mass of the nucleon and the proton we want to produce, 1034 + 1034g = 1034kg, the mass of the Higgs, and use a similar equation to find
The energy is also given in J/kg.
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