Write the nuclear equation for the fusion of H-3 with H-1 to form He-4.

Nuclear fusion is a powerful reaction where two light atomic nuclei merge to form a heavier nucleus. This is the process that powers stars, including our Sun, providing them with immense energy. During fusion, the combined mass of the resulting nucleus and any released particles is slightly less than the mass of the original nuclei. The missing mass is converted into energy, as explained by Einstein's famous equation, \(E = mc^2\), where \(E\) is energy, \(m\) is mass, and \(c\) is the speed of light.

The fusion of isotopes of hydrogen is a typical example of such a reaction and efficiently releases energy. Scientists are interested in harnessing this energy for use on Earth, which could provide a nearly inexhaustible and clean energy source. To accomplish a controlled fusion reaction for energy production, laboratories and reactors around the world are working on replicating the high-pressure and high-temperature conditions found inside stars.

Isotopes are variations of chemical elements that have the same number of protons but different numbers of neutrons. The number of protons defines the element itself, while the neutron number can vary, giving rise to different isotopes of the same element with unique physical properties but identical chemical behavior.

In the context of the exercise, H-1, or protium, and H-3, or tritium, are both isotopes of hydrogen. They share a single proton but differ in their neutron count—the former has none, and the latter has two. He-4, or helium-4, is an isotope of helium with two protons and two neutrons. Understanding isotopes is crucial because the characteristics of different isotopes affect how they interact in nuclear reactions, such as fusion.

To balance a nuclear equation, one must ensure that the total number of protons and neutrons (the mass number) and the number of protons (the atomic number) are conserved from the reactants side to the products side of the equation. This reflects the Law of Conservation of Mass-Energy, indicating that while mass and energy can interconvert, their total quantity in an isolated system remains constant.

Following these principles, when writing a nuclear fusion equation, you start by listing the reactants and their respective mass and atomic numbers. Then, you identify the products — in our case, helium-4. Finally, you confirm that the sum of mass and atomic numbers is the same on both sides. If the equation balances, you have successfully represented the nuclear process. For the exercise provided, the nuclear equation for the fusion of H-3 with H-1 to form He-4 is correctly balanced as \(^1_1H + ^3_1H \rightarrow ^4_2He\).