Talha's Physics Academy
Nuclear Fusion in Sun and Stars
Nuclear Fusion
Definition: When two light nuclei are combined to form a heavy nucleus, the mass of the product nucleus is slightly less than the sum of the masses of the light nuclei fusing together. The process of combining two light nuclei to form a heavy nucleus with the release of a huge amount of energy due to mass defect is known as nuclear fusion.
This mass defect results in the release of a huge amount of energy according to the relation $E = mc^2$. When two nuclei of heavy hydrogen or deuterium ($_{1}^{2}\text{H}$) are combined, the following reaction is possible:
The nucleus of tritium ($_{1}^{3}\text{H}$) so formed can again fuse with a deuterium nucleus ($_{1}^{2}\text{H}$) to give the following reaction:
The net result of these two nuclear reactions is that three deuterium ($_{1}^{2}\text{H}$) nuclei fuse together to form a helium nucleus ($_{2}^{4}\text{He}$) and a neutron with the release of $21.6 \text{ MeV}$ ($4.0 + 17.6 = 21.6 \text{ MeV}$). This energy of $21.6 \text{ MeV}$ is obtained in the form of kinetic energy of a proton ($_{1}^{1}\text{H}$) and a neutron only.
Note that energy released in the fusion reaction is $21.6 \text{ MeV}$, which is very much less than the energy of about $200 \text{ MeV}$ released in the fission of a $_{92}\text{U}^{235}$ nucleus. But this does not mean that fusion is a weaker energy source than fission. The sun and other stars are very hot, so nuclei are moving fast enough for fusion to take place, and the energy released keeps the temperature high so that further fusion reactions can occur. But on Earth, such high temperatures are not attained in a controlled manner. However, the temperature produced by a fission bomb (atom bomb) is close to $10^8\text{ K}$. Therefore, a fission bomb can be used to cause the fusion process. The practical problems involved in producing energy from fusion to make a practical and cost-effective form of power are: Temperature, Pressure, and Confinement.
Nuclear Fusion in Sun and Stars
The sun is a star which is primarily made up of hydrogen (about 75%), helium (about 25%), and trace amounts of other elements. It produces energy through a process called nuclear fusion, where hydrogen atoms combine to form helium atoms, releasing light and heat in the process. The fusion in the sun can take place in two different reaction sequences: the most common is the Proton-Proton (PP) Cycle, and the other is the Carbon-Nitrogen-Oxygen (CNO) Cycle.
1. The Proton-Proton Cycle
It involves the fusion of protons (hydrogen nuclei) to form helium. The PP cycle is a very efficient way to generate energy in the Sun. In the pp chain, two protons first fuse to produce a deuterium nucleus, which combines with another proton to yield $^3\text{He}$. Two $^3\text{He}$ nuclei fuse and form $^4\text{He}$ and two protons.
These reactions can be represented by the equations:
$_{1}^{2}\text{H} + {}_{1}^{1}\text{H} \to {}_{2}^{3}\text{He} + \gamma$
$_{2}^{3}\text{He} + {}_{2}^{3}\text{He} \to {}_{2}^{4}\text{He} + 2({}_{1}^{1}\text{H})$
The net Q value of the chain reactions is about $26 \text{ MeV}$.
2. The Carbon-Nitrogen-Oxygen (CNO) Cycle
The CNO cycle is a series of nuclear fusion reactions that convert hydrogen into helium, and it is the primary source of energy in stars that are more than 1.3 times as massive as the Sun. This cycle uses carbon, nitrogen, and oxygen as catalysts to convert hydrogen to helium:
$_{7}^{13}\text{N} \to {}_{6}^{13}\text{C} + e^+ + \nu$
$_{6}^{13}\text{C} + {}_{1}^{1}\text{H} \to {}_{7}^{14}\text{N} + \gamma$
$_{7}^{14}\text{N} + {}_{1}^{1}\text{H} \to {}_{8}^{15}\text{O} + \gamma$
$_{8}^{15}\text{O} \to {}_{7}^{15}\text{N} + e^+ + \nu$
$_{7}^{15}\text{N} + {}_{1}^{1}\text{H} \to {}_{6}^{12}\text{C} + {}_{2}^{4}\text{He}$
In the CNO cycle, four protons fuse, using carbon, nitrogen, and oxygen isotopes as a catalyst, to produce one alpha particle, two positrons, and two electron neutrinos. Combining all the above reactions, the net reaction for the CNO cycle comes out to be:
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