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 | = 1.8593u |
| 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:
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.