Write the nuclear equation for the fusion of \(\mathrm{H}-3\) with \(\mathrm{H}-1\) to form \(\mathrm{He}-4 .\)

Nuclear chemistry is a fascinating field that explores the processes and changes that occur in the nucleus of an atom. Unlike chemical reactions that involve the electrons surrounding the nucleus, nuclear reactions such as fusion and fission involve changes in the actual nucleus itself. These reactions can release or absorb significant amounts of energy, often much more than chemical reactions. In the context of nuclear fusion, a process central to the energy production in stars, lighter nuclei combine under extreme temperatures and pressures to form heavier nuclei, releasing vast quantities of energy. The study of these reactions has broad applications, from the generation of clean energy in nuclear power plants to the understanding of how elements are formed in the universe.

Nuclear reactions must obey the law of conservation of mass-energy and the conservation of charge, which means that the number of protons and neutrons must balance on both sides of the reaction equation. This careful balancing act enables scientists and educators to predict the products of nuclear reactions and their accompanying energy changes.

Tritium, denoted as \( \mathrm{H}-3 \) or \( {}^3_1H \), is a radioactive isotope of hydrogen containing one proton and two neutrons within its nucleus. With a relatively short half-life of about 12.3 years, tritium decays into helium-3 through beta decay. It's less commonly found in nature compared to other hydrogen isotopes due to its radioactivity but can be produced in nuclear reactors. An intriguing property of tritium is its ability to undergo nuclear fusion reactions with other isotopes, such as protium, a process that is key to some proposed forms of fusion energy. Tracking the behavior of tritium is crucial in both environmental science, given its potential health risks, and in fusion research, where it forms the basis of many experimental reactions.

Protium is the most common isotope of hydrogen, represented by \( \mathrm{H}-1 \) or simply \( H \). It's composed of a single proton and a single electron, with no neutrons in the nucleus. Due to its abundance, protium is often just referred to as hydrogen. It is the primary fuel for the sun's fusion reactions and serves as the basic building block for most of the universe's observable matter. When we speak of the fusion reaction involving hydrogen, we're usually referring to reactions using protium. Its simplicity and stability make it a cornerstone element in scientific research, providing a fundamental component in the study of both chemistry and nuclear physics.

Helium-4, symbolized as \( \mathrm{He}-4 \) or \( {}^4_2He \), is a stable, non-radioactive isotope of helium that makes up most of the helium in the universe. It contains two protons and two neutrons. Helium-4 is created in enormous quantities during the process of nuclear fusion in stars, which includes the sun, when lighter hydrogen nuclei combine through high temperatures and pressures. This isotopic form of helium is not just an interesting subject for astrophysics; it's also used in cryogenics, for its superfluid properties at low temperatures, and many practical applications ranging from welding to deep-sea diving.

Balancing nuclear reactions is similar to balancing chemical equations, but it focuses on balancing atomic nuclei rather than atoms or molecules. The primary goal is to ensure that the total number of protons, which are the atomic numbers, and the total number of nucleons, or mass numbers (protons plus neutrons), remain consistent before and after the reaction. A correctly balanced nuclear equation is essential for understanding the reaction's behavior and potential energy output.For instance, in the fusion of tritium and protium, we must make sure that the number of protons and neutrons in the reactants equates to those in the products. Here's the balanced fusion equation for this reaction: \[ \mathrm{^3_1H} + \mathrm{^1_1H} \rightarrow \mathrm{^4_2He} + \mathrm{^1_0n} \]. An additional neutron is often released to conserve momentum and energy, highlighting the importance of precision in nuclear reaction balancing for predicting by-products and calculating energy yields.