# Strong Force and Nuclear Binding Energies

Forces come in various forms in nature but the nature of the strong force is very peculiar in that it does not create an attraction or repulsion between any two entities. It uses mass energy as a way to create a potential energy well. This is done by the following.

Nuclei actually have atomic masses $\inline&space;M$ smaller than the masses of its individual protons and neutrons $\inline&space;\sum&space;m$. Using Einstein’s famous mass energy relation $\inline&space;E=mc^2$, it is known that the total difference in the energies of these two systems are $\inline&space;\Delta&space;E_{be}=\sum&space;{mc^2}-Mc^2$ where $\inline&space;\Delta&space;E_{be}$ is called the binding energy. This quantity merely represents the energy that was lost through the bonds created by the strong force. This means in order to separate the individual nucleons completely from the nucleus, an energy of $\inline&space;\Delta&space;E_{be}$ would have to be applied allowing for the nucleons to regain their mass and escape. In some sense, there is no force that exists but merely an interaction that strips particles of their mass using it as binding energy differentiating this “force” from the nature of other commonly known forces. The force is mass itself.

From this, one can define binding energy per nucleon as $\inline&space;\Delta&space;E_{ben}&space;=&space;\frac{\Delta&space;E_{be}}{A}$. When graphing this quantity for different mass numbers A, the following graph forms.

As seen by the graph, the binding energy per nucleon increases until around Fe-56 (Iron) and then starts to decrease again. This tendency has a profound impact on nuclear processes. Atoms tend toward more stable states which have higher binding energies per nucleon because higher energies translate to being bound stronger. When atoms are on the left side of this peak, fusion allows for atomic nuclei to be combined into a more stable state. Because this more stable state takes away more energy from the nuclei to hold them together, it releases energy because that excess energy must go somewhere. This is what allows for nuclear fusion to create energy in stars and here on earth in plants. It also explains why only elements up to Fe-56 are formed in stars. The same goes for fission but for the right side of the graph. Atoms split into more stable states that again release excess energy unnecessary for the binding of the nucleons in that smaller nucleic state.

This is all the result of the strong force’s weird property of using mass itself as a force instead of some external field like in electromagnetism or gravity.

If you want to learn more or see where I got it from, read the book “Fundamentals of Physics” by Halliday & Resnick. It should be in the “Books” category of the site.