Fission and Fusion

We've talked in the past about radioactive decay and transmutation of elements. At this point, let's take a look at two nuclear processes that provide tremendous amounts of energy: fission and fusion.

Fission is a process where an element (generally enriched uranium 235) is struck by a neutron and in turn is split yielding daughter nuclides, more neutrons, and a great deal of energy. Enrico Fermi, Otto Hahn, Lise Meitner, Otto Frisch, and Fritz Strassman are the names generally associated with the discovery and recognition of what fission was. The Liquid Drop Model (try http://physics.bu.edu/cc104/liquid_drop_model.html) is generally used to explain why fission takes place: a nucleus of U235 is struck by a low energy (or slow, or thermal) neutron and absorbed, becoming U236. This provides extra internal energy to the nucleus and elongates it like a liquid drop being stretched. At this point, the strong force at the ends is no longer able to overcome the electromagnetic force of the protons, and the drop breaks into smaller drops (daughter nuclides) releasing more neutrons and energy.

A chain reaction is a series of nuclear fissions that take place as a result of neutrons available from fission the generation before. In a nutshell, when a fission takes place from a single neutron, more than one neutron is produced. For a neutron to induce the next fission, it must lie within a certain energy band to cause the fission - otherwise it may either be absorbed or have no effect at all. Some neutrons escape out of the reactor or are captured by other materials in the reactor, such as control rods, moderators, fission product "poisons" and the materials that go into reactor construction. The key is to design and build a reactor so that there are just enough neutrons available to cause fission each generation. When this is accomplished, we have a stable reactor. The amount of uranium required to sustain this chain reaction is called a critical mass. When more than enough neutrons are available and used for fission, the reactor power will increase and the reactor could run out of control. If, in certain materials and configurations this chain reaction happens completely and quickly enough, we have a bomb.

A typical fission reaction involves U-235. (U-235 only exists in nature as about .7% of natural uranium, the rest being made up of mostly U-238. As a result, U-235 must be produced in a process known as enrichment.) A neutron hits U-235 and is absorbed, transforming the element to U-236. U- 236 has a very short life cycle = on the order of 10-12 seconds. This is so short, in fact, that when writing a nuclear fission reaction, we generally leave out the intermediate step involving U 236. The U-236 is transformed to 2 daughter nuclides (there are many possible combinations) and an average of 2.4 neutrons per fission. For example,

shows a fission that results in Barium-Krypton daughter products. Note that total atomic number and atomic mass are conserved. Another reaction yields Strontium-Xenon products as shown:

To calculate how much energy is achieved from this reaction, we add the products before, subtract the products after, and multiply the mass defect by c2.

 Our mass before = n + U235, or 1.008665u + 235.043924u = 236.052589 u.

Our products after are Sr (87.905618u) + Xe(135.90721u) + 12 n(1.008665u) = 235.916808u.

The difference is .135781u. At 931.5 MeV/u, this gives an energy yield of 126.5 MeV per fission.

The average energy released from a single fission of a U-235 atom is about 200 MeV. This is huge for a single nuclear reaction, and when multiplied by the number of fissions taking place in a critical reactor at any given time, can easily yield thermal output on the order of 1000 Megawatts. We can do some quick calculations to figure out just how much uranium is required for a power reactor in order to operate for a year.

One use of fission is the generation of heat in order to boil water to drive turbine generators. Above is a schematic of a commercial nuclear power plant. Not all reactors are used to produce power, however. Some reactors operate at very low power and are used for experimentation and to produce radionuclides for research and medicine. (Image from http://www.nrc.gov/images/reading-rm/basic-ref/students/student-bwr.gif)

Fusion is a process that takes advantage of the fact that the sum of the masses of the individual components on a nucleus are always less than the whole nucleus. Thus, fusion is a form of energy released when we build a nucleus from protons and neutrons or from smaller nuclei. Stars derive their energy from nuclear fusion. Fusion has a great deal of attraction to those interested in long term prospects for power generation. A typical reaction involves isotopes of Hydrogen (Deuterium and Tritium) and produces a Helium nucleus and a neutron.

The fuel supply is plentiful, and the end products do not have the radioactive disposal problems associated with typical fission reactions. Unfortunately, a sustainable fusion reaction has not been achieved, but research continues.

For more on Fusion, try:

http://fusedweb.pppl.gov/

http://www.fusion.org.uk/

I cannot stress enough the importance in Physics of the history involved in fission. For an outstanding (in my personal opinion) source of this history, I recommend "The Making of the Atomic Bomb" by Richard Rhodes.

http://www.lbl.gov/abc/

http://physics.nist.gov/PhysRefData/Compositions/

For Practice Problems, Try: Giancoli Multiple Choice Practice Questions