# NUCLEAR FISSION

In the late nineteen thirties two German scientists Hahn and Strassman were doing a series of experiments to study the affects of firing neutrons at some uranium compounds. The result was a very radioactive product that they thought was a nucleus of a very heavy element, formed when the neutrons joined onto the uranium nucleus. However, when they analysed the products they found not elements heavier than uranium but two about half the mass number of the original uranium, a solution that had been suggested in 1938 by Lisa Meitner and Otto Frisch.

The uranium nucleus had split in half - this was the first evidence of what is called nuclear fission. If a nucleus is made unstable it may lose the extra energy in two ways. It can emit radiation (alpha, beta or gamma) or undergo fission. You can think of fission as rather like a wobbly jelly that has been shaken about too much and simply split up.
In all nuclei there are two forces, the strong nuclear force (acting between all the neutrons and protons) trying to hold the nucleus together and the electrostatic repulsion trying to push the protons apart.

## Neutron induced fission and the chain reaction

When a neutron is fired at a uranium 238 nucleus, uranium 239 is formed, this is unstable and the nuclear fission occurs.

(This only occurs with fast neutrons; slow neutrons are captured giving neptunium and then plutonium)

There are many possible results of the nuclear fission of another isotope of uranium, uranium 235 nucleus, one possible reaction is:

 235U + 1n giving 236U giving 148La     +   85Br    +    31n + energy 235.044 + 1.0087 147.961 + 84.938 + 3.0261

This reaction has a mass defect of 0.1276u

Energy is given out by the reaction because the mass of the products is less than the total mass of the original nucleus and the neutron.

A full treatment of the equation shows that this energy is 118 MeV or 1.90 x 10-11J. This is a very small amount of energy but when you work out how many nuclei there are in 1kg of uranium you can understand why nuclear fission is so important.

Using Avogadro's number we can calculate the number of uranium atoms (N) in 1kg of the metal.
N = [1000x6.02x1023]/235.004 = 2.56x1024
This means that if we could fission all the nuclei in 1kg of U235 we would release 2.56x1024 x 1.90x10-11 = 4.9x1013J of energy!

Put in every day terms this is sufficient to heat a house, with a 5kW heater, 24 hours a day, 7 days a week, 52 weeks a year for over 300 years! It is not quite that simple because it's difficult to get ALL the nuclei to split.

However once one nucleus has fissioned neutrons are released and these can go on to split further nuclei. If this fission can be sustained a chain reaction is produced. A diagram of such a reaction is shown in the diagram above. This reaction will proceed at high speed, the time for an emitted neutron to collide with another nucleus to produce a second fission is about 0.01 microsecond.

### schoolphysics: Nuclear fission animation

To see an animation of nuclear fission click on the animation link.

Problems
1. Assuming that the nuclei split into two equal halves and produce three neutrons calculate the energy available from the fission of:
(a) 235U (b) 239Pu (c) 233Th (d) 205Hg
if these nuclei could be made to fission.

2. Use the data in the data section to show that energy would not be released by fission of the following nuclei:
(a) 55Mn (b) 43Ca (c) 39K (d) 27Al