Binding Energy

E_b = binding energy, in MeV
Z = number of protons
m_H = mass of a hydrogen atom (1.007825 atomic mass units, or amu)
N = number of neutrons
m_n = mass of a neutron (1.008664904 amu)
m_isotope = actual mass of the isotope
931.5 Mev/amu = the conversion factor to convert mass into energy, in units of MeV

Remember how I said that the greater the binding energy per nucleon of an atom, the greater it's stability? Well, above is a graph of the relative binding energy per nucleon vs. mass number (total number of nucleons composing an atom). Notice that the nuclei of the light elements are generally less stable than the heavier nuclei up to those with a mass number around 56. The nuclei of the heaviest elements are less stable than the nuclei that have a mass number of around 56. From this, you can see that the nuclei around iron are the most stable. This information implies two methods towards the converting of mass into useful amounts of energy: fusion and fission.

Fusing two nuclei of very small mass, such as hydrogen, will create a more massive nucleus and release a small amount of mass which appears as energy. Meanwhile, fissioning elements of great mass, like uranium, will create two lower-mass and more stable nuclei while losing mass in the form of kinetic and/or radiant energy. The calculation to find the energy released in these reactions is similar to calculating, and related to, binding energy. If the reactants (the things that went into the reaction) are bound more weakly than the products (the stuff that comes out of the reaction), then the reaction releases energy. Just sum the masses of the reactants and subtract the sum of the masses of the products. As an example, lets take a look at a step in the proton-proton reaction:

(2.) 2H + 1H 3H + gamma ray (y)