The total energy of a body equals the sum of its rest energy and its kinetic energy

In nuclear reactions where two particles collide, a change occurs in their total kinetic energy and in their total mass. The increase of total kinetic energy is accompanied by an equal decrease of internal energy. Thus the total energy, kinetic plus internal, remains constant.

Now let’s consider the relationship between mass and potential energy. Let us assume a system of interacting mass points, all of them being in state of rest. In this case the potential energy of interaction does exist, but the kinetic energy is null.

The total energy consists of the sum of rest energy of all the particles constituting the system, , and their potential energy of interaction, ,

We get

.

Here is called the difference of mass (or mass difference), it is the difference between the total mass of the system and the sum of masses of all the individual particles constituting this system. The difference of mass is a measure of the binding energy of particles (that is the energy needed to take all the particles apart so that they are completely separated).

Thus Einstein demonstrated in his Special Theory of Relativity that energy would release from an object when its mass decreased. Einstein's mass-energy relation states that if the mass decreases by kg, the energy released in joule, , is given by

.

Experiments in radioactivity on nuclear reactions demonstrated that Einstein’s relation was true. It shows that even if a small change of mass occurs, a relatively large amount of energy is produced.

Thus, a very simple and universal relation between the mass and energy is found:

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