# Nuclear Binding Energy

Physics

## definition

### Mass defect

The difference in mass of a nucleus and its constituents, , is called mass defect and is given by

## definition

### Variation in binding energy per nucleon with mass number

• The force is attractive and sufficiently strong to produce a binding energy of a few MeV per nucleon.
• The constancy of the binding energy in the range 30 < A < 170 is a consequence of the fact that the nuclear force is short-ranged.
• A very heavy nucleus, say A = 240, has lower binding energy per nucleon compared to that of a nucleus with A = 120. Thus if a nucleus A = 240 breaks into two A = 120 nuclei, nucleons get more tightly bound. This implies energy would be released in the process.
• Consider two very light nuclei (A10) joining to form a heavier nucleus. The binding energy per nucleon of the fused heavier nuclei is more than the binding energy per nucleon of the lighter nuclei.This means that the final system is more tightly bound than the initial system. Again energy would be released in such a process of fusion.

## definition

### Binding energy and binding energy per nucleon

If a certain number of neutrons and protons are brought together to form a nucleus of a certain charge and mass, an energy will be released in the process. The energy is called the binding energy of the nucleus.

The ratio of the binding energy of a nucleus to the number of the nucleons, A, in that nucleus is called the binding energy per nucleon, .

## definition

### Exoergic and Endoergic Reactions

Nuclear reactions are reactions in which either two nuclei collide with one another or a small particle such as a neutron collides with the nucleus of some atom.
Nuclear reactions can be described using energy changes as follow :
An exothermic (exoergic) nuclear reaction is a reaction that releases energy while an endothermic (or endoergic) reaction is one that requires an input of energy to take place.
The changes in kinetic energy during a nuclear reaction is defined as the reaction energy (or Q-value).
If the reaction energy is positive, the reaction is exothermic but if the reaction energy is negative, the reaction is endothermic.