Radioactive decay is a spontaneous reaction that is necessary to increase the stability of an element by increasing its neutron-to-proton ratio. It is achieved through nuclear reactions: fission and fusion. These reactions occur by either combining or breaking sub-atomic particles. As a result, it yields new elements. The binding energy of re-orienting the sub-atomic particles of the element has the formula: E = mc², where m is the mass defect and c is the speed of light equal to 300 million meters per second. Mass defect is defined as the difference of the mass of the isotope and the sum of the masses of its sub-atomic particles. For decay, the mass of the isotope is less than the sum of the sub-atomic particles because the rest of the energy is released when the nucleus is formed.
Thus, the answers are:
*E=mc²
*mass defect