Eb = (Z × mH + N × mn - misotope) × 931.5 MeV/amu
Eb = binding energy, in 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)The fusion of the deuteron (2H) and another proton (a hydrogen nucleus) resulted in the formation of 3He and a gamma ray. If you summed the masses 2H (2.0140 amu) and the proton (1.007825 amu), and subtracted the isotopic mass of 3He (3.01603 amu), you would end up with 0.005795 amu of missing mass. This is equivalent to 5.398MeV of released energy (not including any kinetic energy the reactants had), in this case taking the form of a gamma ray and any additional kinetic energy of the products.
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