nucleus, in physics: Mass Defect, Binding Energy, and Nuclear Reactions

Mass Defect, Binding Energy, and Nuclear Reactions

When nuclear masses are measured, the mass is always found to be less than the sum of the masses of the individual nucleons bound in the nucleus. The difference between the nuclear mass and the sum of the individual masses is known as the mass defect and is due to the fact that some of the mass must be converted to energy in order to make the nucleus stable. This nuclear binding energy is related to the mass defect by the famous formula from relativity, E = mc2, where E is energy, m is mass, and c is the speed of light. The binding energy of a nucleus increases with increasing mass number.

A more interesting property of a nucleus is the binding energy per nucleon, found by dividing the binding energy by the mass number. The average binding energy per nucleon is observed to increase rapidly with increasing mass number up to a mass number of about 60, then to decrease rather slowly with higher mass numbers. Thus, nuclei with mass numbers around 60 are the most stable, and those of very small or very large mass numbers are the least stable.

Two important phenomena result from this property of nuclei. Nuclear fission is the spontaneous splitting of a nucleus of large mass number into two nuclei of smaller mass numbers. Nuclear fusion, on the other hand, is the combining of two light nuclei to form a heavier single nucleus, again with an increase in the average binding energy per nucleon. In both cases, the change to a stable final state is accompanied by the release of a large amount of energy per unit mass of the reacting materials as compared to the energy released in chemical reactions (see nuclear energy).

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