Two fusion reactions mentioned in the text are \(n+^{3} \mathrm{He} \rightarrow^{4} \mathrm{He}+\gamma\) and \(n+^{1} \mathrm{H} \rightarrow^{2} \mathrm{H}+\gamma\). Both reactions release energy, but the second also creates more fuel. Confirm that the energies produced in the reactions are 20.58 and \(2.22 \mathrm{MeV}\), respectively. Comment on which product nuclide is most tightly bound, \(^{4} \mathrm{He}\) or \(^{2} \mathrm{H}\).

Nuclear physics is a field of physics that studies the constituents and interactions of atomic nuclei. The most fundamental particles in a nucleus are protons and neutrons, collectively known as nucleons. The behavior and properties of these nucleons are governed by the strong nuclear force, which is one of the four fundamental forces of nature. Understanding nuclear physics is essential for explaining phenomena such as radioactivity, nuclear fission, and nuclear fusion.

Nuclear fusion reactions, like the ones mentioned in the exercise, involve the combination of lighter atomic nuclei to form a heavier nucleus, accompanied by the release of energy. These reactions are the source of immense power, which fuels stars and offers the potential for clean energy on Earth. To calculate the energy produced during fusion, one must first understand the concept of mass-energy equivalence and nuclear binding energy, which are core principles within nuclear physics.

Mass-energy equivalence is a principle famously encapsulated in Albert Einstein's equation, \(E=mc^2\), where \(E\) represents energy, \(m\) represents mass, and \(c\) is the speed of light in a vacuum. This equation reveals that mass can be converted into energy and vice versa, which is a fundamental concept in nuclear physics and a key to understanding how energy is produced in nuclear reactions.

In the context of the exercise provided, the mass-energy equivalence principle allows us to calculate the energy released in nuclear fusion reactions by converting the mass difference between the reactants and products into energy. This is a critical step in confirming whether the energies produced are indeed 20.58 MeV and 2.22 MeV for the two reactions described. A small amount of mass converted into energy can equate to a significant amount of energy, which illustrates the immense power of nuclear processes.

Nuclear binding energy refers to the energy required to separate a nucleus into its individual protons and neutrons. It is also the energy released when a nucleus is formed from these nucleons. A higher binding energy generally indicates a more stable and tightly bound nucleus. In the reactions outlined in the exercise, energy is released when the product nuclei are formed, which means that the product nuclei have a higher binding energy than the separate nucleons that formed them.

By comparing the energy released in each reaction, we can determine which final product, \(^4\mathrm{He}\) or \(^2\mathrm{H}\), is more tightly bound. The greater the amount of energy released, the more binding energy the resulting nucleus has. Therefore, if one reaction releases more energy than the other, it suggests that the product nucleus of that reaction is more tightly bound. As such, binding energy is a profound indicator of the stability of an atom's nucleus and is intricately related to the mechanism of nuclear fusion.