Write the nuclear equation for the fusion of two H-2 atoms to form He-3 and one neutron.

Deuterium fusion, also known as D-D fusion, is a process where two deuterium atoms, which are isotopes of hydrogen with one proton and one neutron, combine to form new elements and particles. Deuterium is represented by the symbol \(^2_1H\text{ or }D\text{.}\) When two deuterium nuclei fuse, they typically produce a helium-3 nucleus and a free neutron, releasing a significant amount of energy. This process is of great interest as a possible source of clean energy because deuterium can be readily extracted from seawater, making it a potentially abundant fuel for fusion reactors. The power of fusion comes from the fact that the mass of the resulting particle is slightly less than the total mass of the two deuterium nuclei, and according to Einstein's famous equation \(E = mc^2\text{,}\) this mass difference is converted into energy.

Writing nuclear equations is essential for illustrating and understanding nuclear reactions, such as fusion, fission, and radioactive decay. In nuclear equations, the elements are represented by their nuclear symbols, which include the element symbol, the atomic number as a subscript, and the atomic mass as a superscript. For instance, deuterium is written as \(^2_1H\text{.}\) To balance a nuclear equation, one must ensure that the total number of protons and neutrons (the atomic numbers and mass numbers, respectively) are equal on the reactant and product sides. This is due to the principle of conservation of mass and charge. For example, when writing the equation for deuterium fusion, the sum of mass numbers and atomic numbers should be the same on both sides: \(2(2_1H) \rightarrow ^3_2He + ^1_0n\)indicating that two deuterium atoms (each with mass-number 2 and atomic-number 1) produce a helium-3 atom (mass-number 3, atomic-number 2) and a neutron (mass-number 1, atomic-number 0).

Nuclear chemistry is the subfield of chemistry dealing with radioactivity, nuclear processes, and the changes in the nucleus of atoms. It encompasses the study of both natural and artificial changes in atoms' nuclei and is key in various applications, such as energy generation through nuclear power, radiopharmaceuticals for medical diagnosis and therapy, and understanding cosmological processes in the universe like star formation and supernovae. A fundamental aspect of nuclear chemistry is understanding how the strong nuclear force and electrostatic repulsion dictate stability and reactions in atomic nuclei, including fusion processes like those with deuterium. The pursuit of controlled nuclear fusion for energy production is a prime focus in nuclear chemistry because of the potential to harness immense amounts of energy efficiently and with far less hazardous waste compared to nuclear fission.