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3-1: The Origin of the Nuclear Energy

[Exothermic Chemical Reactions]
Heat is evolved in the chemical reaction in which hydrogen and oxygen are combined to be water; i.e. the combustion of hydrogen. Such chemical reaction in which heat is evolved is called exothermic reaction. The chemical equation of this reaction for one mol of hydrogen is written

Namely, when one mol of hydrogen burns, 286 kJ of heat is evolved.
Another example is

where one mol of carbon is oxidated to be carbon dioxide with producing 394 kJ of heat.
The above chemical equations, (1) and (2), are for one mol of hydrogen and carbon, respectively. In order to compare these chemical reactions with nuclear reactions, it is convenient to rewrite these equations "for one molecule". For this, let us divide the heat production by the Avogadro constant

Then they are rewritten as


Equation (3) means that the process in which two hydrogen and one oxygen molecules combine to be one water molecule generates 3.0 eV energy emission. And Eq. (4) says that, when a carbon atom combines with an oxygen molecule to be a carbon dioxiside molecule, 4.1 eV energy is released.
As learned before, eV is a unit of energy extensively used in the atomic and nuclear world. It is the work done on an electron that is accelerated through a potential difference of one volt. Its value is

Moreover, the units of energy, keV and MeV, are often used in the nuclear world; the former is 1,000 times eV and the latter 1,000,000 times eV.
We can understand that "the energy evolved from one process of an exothermic chemical reaction is about 3 or 4 eV".

[Exothermic Nuclear Reactions]
Nuclei show various types of reaction: For example, one nuclide splits into two or more fragments. This type of reaction is called nuclear fission. Contrarily, two nuclides sometimes combine with each other to be a new nuclide. This type of reaction is called nuclear fusion. There are many other types of reaction processes; they are generally called nuclear reaction.
Among these various types of nuclear reactions, there are some types of exothermic reactions which are sometimes called "exoergic" reaction in nuclear physics.
The nucleus of deuterium atom is called deuteron which consists of a proton and a neutron. It is represented by a symbol "d". The nuclear reaction in which two deuterons bind with each other is an example of nuclear fusion. This exoergic reaction is written as

If a neutron is absorbed in the uranium-235 nucleus ( ), it would split into two fragments of almost equal masses and evolves some number of neutrons and energy Q. One of the equations for the processes is written

This is an example of nuclear fission.
Here it is quite interesting how much the amount of the energy emission Q is. It must be about 200 MeV. Let us explain below why it is so. The details of the mechanism of nuclear fission and fusion will be given on the following pages.

[The Origin of the Nuclear Energy]
Let us take up the d-d fusion reaction shown by the above Eq. (5) as an example. Since the experimental value of the binding energy of deuteron is 2.2246 MeV, the sum of the binding energies of the two deuterons before the reaction (on the left-hand side of Eq.(5)) is 4.449 MeV. On the other hand, the experimental value of the binding energy of is 7.719 MeV. Therefore the total binding energy after the reaction (on the right-hand side of Eq. (5)) is 3.27 MeV (= 7.719 - 4.449) larger than the binding energy before the reaction (on the left-hand side of Eq. (5)). Thereby the total mass decreases after the reaction and the mass defect corresponding to the above increase of the binding energy occurs. This mass defect is released as the heat (or energy) production in this exothermic (or exoergic) process.
Next, we shall discuss the change of the binding energy before and after the fission of uranium-235 ( ) shown by Eq. (6). As seen in the figure on Page 2-4, [Comparison between Mass formula and Experiment] , the binding energy per nucleon in nuclei around A = 240 is about 7.5 MeV. On the other hand, that in nuclei around A = 120 is about 8.5 MeV. Accordingly, if a uranium nucleus splits into two fragments with almost equal masses, the binding energy per nucleon would increase by about 1 MeV and the total mass of the fission fragments would decrease by the corresponding amount. This loss of mass (or mass defect) is converted into the heat (or energy) product Q. Since an energy of about 1 MeV per nucleon is released, the total energy Q would be more than 200 MeV.
According to the above discussions, it becomes clear that "the origin of nuclear energy is the change of nuclear masses", and it is based on the principle of Einstein's Mass-Energy Equivalence.
If the total binding energy after the reaction is larger than before, the total sum of the masses of the reaction products becomes smaller than that before the reaction. This decrease in mass is converted into an energy, so that the process would be an exothermic (exoergic) reaction.

[The Origin of the Heat in Exothermic Chemical Reaction, Law of Energy Conservation]
We have learned that, if hydrogen and carbon burn in oxygen gas, heat or energy is evolved. What is the origin of this heat or energy? The principle of the heat production in chemical reaction is just the same as that in the nuclear reaction.
The hydrogen molecule is a bound system of two hydrogen atoms. The mass of a hydrogen molecule is slightly smaller than the sum of the masses of two hydrogen atoms. Converting this difference (= mass defect) into an energy with Einstein's Mass-Energy Equivalence, we have the binding energy of the hydrogen molecule.
In the process of combustion of hydrogen represented by Eq. (3), the total mass after the reaction is slightly smaller than before, and this decrease in mass is transformed into the heat emission in the exothermic reaction.
Strictly speaking, conservation of mass does not hold even in a chemical reaction. Both in chemical and nuclear reactions, the energy of the total system with converting mass into energy conserves before and after the reaction.

[Huge Amount of Nuclear Energy]
Comparing Eq. (3) with (5), and Eq. (4) with (6), we can easily understand that the nuclear reactions yield a huge amount of energy in comparison with ordinary combustion processes.
As explained above, "the energy evolved from an exothermic chemical reaction like combustion of hydrogen or carbon is about 3 or 4 eV". In contrast, d-d fusion reaction shown by Eq. (5) releases 3.27 MeV of energy. It is about several million times as large as the ordinary combustion.
In the fission of uranium-235 shown by Eq. (6), the more energy than 200 MeV is emitted. It is about several 100 million times as large as an ordinary chemical reaction.
Thus, the nuclear energy released in nuclear fission and fusion is several million or 100 million times as large as an ordinary chemical reaction like a combustion process.
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