# THE UNSTABLE NUCLEUS

In this section we will look at some heavy elements where the ratio of protons and neutrons is very different from one. If this happens the nucleus may become unstable and break apart by radioactive decay or even by spontaneous fission.

This instability is due to the repulsion between the protons in the nucleus and in the case of artificially created isotopes by excess nuclear energy. We can compare a nucleus with a drop of water – this analogy is called the liquid drop model of the nucleus. An excited nucleus can be compared with a liquid drop that is shaken. As more and more energy is added the drop vibrates more and more violently and eventually will shake itself apart. This corresponds to the loss of energy by the emission of a particle or a gamma ray from an excited nucleus.

In the table we worked out the binding energy of some stable light nuclei but now suppose we try the same thing with radium 226.

 Mass of 88 protons + 138 neutrons = 227.836u Mass of "completed" radium 226 nucleus = 225.977u Mass defect = 1.8593uu Binding energy = 1732 MeV Binding energy per nucleon = 7.66 MeV

The nucleus appears to be stable but you may know that radium is very radioactive, why? What actually happens is that it emits an alpha particle to form Radon 222. The mass of the original radium nucleus is greater than that of the alpha particle and residual radon nucleus.

You can work out the energy of the alpha particle using the following equation:

This energy is shared between the alpha and the recoiling radon nucleus.

N.B in this example atomic masses have been used, the masses of the electrons cancel out on both sides of the equation. This is a very common practice when dealing with similar reactions.

Another interesting case is beryllium 8. The nucleus has a mass of 8.00421u while the four protons and four neutrons have a mass of 8.06377u. This looks as if the nucleus would be stable but in fact what happens is that it breaks up into two alpha particles with a total nuclear mass of 8.00302u - less than that of the original beryllium 8 nucleus. As we have said before the helium nucleus is a very stable particle.