Nuclear binding energy
The binding energy of a nucleus is defined as the amount of energy required to pull it apart (much like pulling apart a bunch of grapes, energy is required to break the stems that bind the grapes together). The binding energy is always positive because energy always needs to be added to pull apart a nucleus.
Binding energy is essentially a debt of energy (or potential energy). The greater the binding energy a nucleus has, the less actual energy it has (in the same sense that having more debt equates to having less money).
It follows from this that nucleons bound in a nucleus must have less energy than they would have if they were free. They therefore must also have less mass. The binding energy E and the mass deficit m of a nucleus are simply related by the familiar equation:
Binding energy is essentially a debt of energy (or potential energy). The greater the binding energy a nucleus has, the less actual energy it has (in the same sense that having more debt equates to having less money).
It follows from this that nucleons bound in a nucleus must have less energy than they would have if they were free. They therefore must also have less mass. The binding energy E and the mass deficit m of a nucleus are simply related by the familiar equation:
Binding energy per nucleon
Below is a graph of the binding energy per nucleon vs. number of nucleons:
The graph starts out as you might expect. As more nucleons are added to a nucleus, more bonds are formed between nucleons, thus the binding energy per nucleon increases.
The binding energy then reaches a peak at Fe, and thereafter steadily decreases as the nuclei become larger.
To explain this we must consider the two opposing forces acting inside a nucleus:
The binding energy then reaches a peak at Fe, and thereafter steadily decreases as the nuclei become larger.
To explain this we must consider the two opposing forces acting inside a nucleus:
- The coulomb force acts between the positively charged protons. Because like-charges repel, this force is repulsive and acts to push the nucleus apart.
- The nuclear force acts between all nucleons (both protons and neutrons). It is an attractive force and acts to bind the nucleus together.
The nuclear force is much stronger than the coulomb force, however, it is very short ranged. Consequently, at larger distances the coulomb force becomes stronger than the nuclear force. This effect becomes prominent in larger nuclei, which become less bound the larger they become.