Nuclear Forces and Binding Energy

Nuclear Forces: There are four known types of field forces that we are aware of. We are already familiar with gravitational force and electromagnetic force. Since the nucleus of an atom is comprised of positively charged protons and neutrally charged neutrons, we might expect that the electromagnetic force between the protons would tend to blow the nucleus apart. But we also know that this does not routinely happen, so there must be another force acting in the nucleus to hold it together. The strong nuclear force is this force, named so because it is stronger than either the electromagnetic or gravitational forces. We don't know the nature of the strong nuclear force, but we do know that it is a short range force (on the order of 10-15 m) while gravity and the electromagnetic force act over long ranges. Thus, for very large nuclei, there is a potential for the electromagnetic force of the
protons to overcome the strong nuclear force and make the nucleus unstable. This manifests itself in a couple of ways. First, since the protons are the only nucleon that exert electromagnetic force and neutrons and protons have strong nuclear forces holding them together, we find that atoms tend to have the same number of neutrons as protons up to the point where the atomic number is between 30 and 40. Above that, the nucleus will have additional neutrons to hold it together. There is a point, however, when there cannot be enough neutrons added to overcome the em force, and the nuclides become unstable. There are no completely stable nuclides above Lead (atomic number 82).

A fourth force, the weak nuclear force, manifests itself in radioactive decay. It is named the weak nuclear force because it is significantly weaker than the strong force. But of the four forces that act to bind a nucleus together, the very weakest is in fact the gravitational force.

Binding Energy is the energy that must be put into a nucleus in order to break it apart. The mass of a nucleus is always less than the mass of its individual protons and neutrons. The difference in mass has gone into some form of energy, such as kinetic energy or radiation. We call this difference mass defect. For example, we can find the Binding Energy of a helium nucleus (Helium 4). Helium weighs 4.002602 u. (We get this number from tables.) It is composed of 2 protons (mp = 1.007276 u) and 2 neutrons (mn = 1.008665 u). The 4 nucleons add to 4.032980 u. The difference, 0.030378 u has been converted to energy:

(0.030378 u)(931.5 MeV/u) = 28.30 MeV.

This would be the amount of energy necessary to break up a Helium nucleus.

The total binding energy is the energy of the constituent parts less the energy of the formed nucleus, as computed above. The average binding energy per nucleon is the total binding energy divided by the atomic mass number. For Helium, the average binding energy per nucleon is 28.30 MeV/4 = 7.1 MeV.

For more on the topic, try:

A useful applet:

For Practice Problems, Try: Giancoli Multiple Choice PracticeQuestions (Don't worry if you can't solve all of them just yet!)