The Energy of Nuclear Reactions

Photo courtesy of National Nuclear Security Administration / Nevada Site Office

The first atomic artillery shell fired from a 280-mm artillery gun, May 25, 1953, Nevada Proving Grounds, USA.

Nuclear reactions involve vast amounts of energy, either creating massive fireballs in a chain reaction or slowly releasing significant amounts of energy over many years in a nuclear reactor.  Recall that particles (nucleons) make up a nucleus and they are held together by a strong nuclear force.  Both nuclear fission and fusion reactions change the number of nucleon particles, so work must be done against the strong nuclear force during any nuclear reaction.
The amount of work required to separate all the nucleons in a given atom is referred to as the binding energy .  Binding energy is equal to the difference between the energy of all the nucleons when they are free compared to when they are contained in the nucleus.
binding energy: the net energy required to liberate all of the protons and neutrons in a nucleus (overcome the strong nuclear force)

Ebinding = Enucleons - Enucleus

Dividing the binding energy of the nucleus by the number of nucleons gives a value for the binding energy of each nucleon.

Stable nuclei have greater binding energy per nucleon than unstable nuclei.  Nuclei with atomic masses in the range of 58-62 (iron-nickel) are the most stable, with the highest binding energy per nucleon.  Smaller atoms, such as hydrogen-2, have a very small amount of binding energy per nucleon, making them less stable.  At the same time, much larger atoms such as uranium-238 also have a reduced binding energy per nucleon making it unstable.  To become more stable, very small nuclei can become larger by combining in the process of fusion, and very large nuclei can become smaller by breaking down into smaller nuclei in the process of fission.  The result in either process is to move toward a medium-sized stable nucleus with the greatest amount of binding energy per nucleon.

For both fission and fusion reactions, the energy released is equal to the difference between the total binding energy of the original nucleus or nuclei and the final binding energy of the nucleus or nuclei.

For both fission and fusion, the binding energy of the final (resulting) atom(s) is much larger than the binding energy of the initial atom(s), leading to both a more stable nucleus and the release of a large amount of energy.

The change in binding energy also corresponds exactly to the change in mass between the original and new nuclei, according to Einstein's mass-energy equivalency ( E = mc2 ).  In this respect, the energy released in a nuclear reaction is based on the change in mass before and after the reaction.

According to this equation, even a very small change in mass multiplied by the square of the speed of light (9 × 1016 ) will result in a large release of energy.

fission: reaction in which a nucleus with more than 120 nucleons splits into smaller nuclei with greater binding energy per nucleon

 

fusion: reaction in which a nucleus with fewer than 60 nucleons combines with another to form a larger nucleus with greater binding energy per nucleon