Nuclear equations are balanced by setting the superscripted mass numbers equal to each other on both sides and by setting the subscripted atomic numbers equal to each other on both sides.

Reactions in which there is only one term, or reactant, on the left side of the equation generally represents a natural decay: alpha, beta, gamma, or neutron decay.  This results in a nuclear transformation of one chemical element into another.

Ernest Rutherford in 1919 was the first scientist to artificially change one element into another. He did this by bombarding nitrogen nuclei with high energy alpha particles. The result was that he successfully transmuted nitrogen into oxygen.

Reactions in which there are two reactants can either represent fission or fusion reactions. Fission reactions typically have one reactant with a large atomic mass and one reactant that is serving the purpose of a catalyst, a neutron or a proton. A fission reaction must include two large fission products, plus a few incidental particles. If the particle required to "start the reaction" is produced in larger numbers, then the reaction becomes self-sustaining and is called a chain reaction.

Fusion reactions generally have two reactants which "fuse" to create a new element.  This type of reaction can be distinguished from a fission reaction by noticing that the atomic mass of one of the product is usually larger than the atomic mass of the original reactants, or, that particles of one type of element are formed.

Elements that are lighter than iron are generally involved in fusion reactions; whereas elements more massive than iron are usually involved in fission reactions. Iron is the most stable element with the lowest mass per nucleon ratio and strongest nucleus. When atoms fuse, the product nucleus is less massive than the sum of its parts; when heavy nuclei fission, the parts have less mass than the original nucleus. The mass deficit in each case is converted into energy. Momentum and energy are conserved in all of these reactions.

To practice balancing more nuclear equations, please visit this workbook page on Fission and Fusion

Nuclear Reaction Energies

What the formula that calculates the amount of energy released during the complete transformation of mass into energy?

This formula can be used during radioactive decay to determine how much kinetic energy is present in either the behavior of the reactants or the products. Customarily, atomic masses are stated in atomic mass units, or amus, when given during nuclear reactions. Energies are also often given in eV or MeV instead of Joules. However, the formulas require standard MKS units for kg and Joules.  Here are the conversion factors.

Determine the mass deficit in the fusion reaction shown below.

The nuclear mass defect (deficit) is 0.01799 amu. The energy released in the reaction is calculated with the equation

E = Dmc²
E = 0.01799 (1.66 x 10 ^{- 27} )(3 x 10 ⁸ ) ² / 1.6 x 10 ^{- 19}
E = 16.8 MeV