# Peter Lux

## Nuclear Power – Converting Mass Into Energy?

One of the things that most people know about nuclear power is that it about turning mass into energy – E= mc2. Although this is not wrong it is extremely misleading.

First of all I am going to digress a bit. One of the things that makes Einsteins theory of relativity important is that it is universal. In fact one of the motivations of Einsteins work was that he wanted the laws of physics that are universal . Galileo worked out a system where the laws of physics were true irrespective of motion (although this turned out to only be true if the speed was small compared with the velocity of light). Newton worked out laws that were true on Earth and dictated the movement of planets. Einstein devised laws of physics where were true if the speed approached the speed of light with uniform motion – Special Relativity – and when they system is accelerating – General Relativity.

What E=mc2 tells us is that when there is an energy change there is always a mass change. It is not something that only happens in nuclear physics but also when there are other energy changes. For example there is a mass change when I stir a cup of tea or burn a piece of coal. However, in nuclear physics the energy changes are about a million time larger than chemical changes – e.g. burning a piece of coal (but see here why this is often misinterpreted). This means that the differing energy levels of different nuclei can actually be measured by their masses and this can be converted into differences in energies by using E=mc2.

Although the concept of  ‘turning mass into energy’  gives us a way of measuring the energy changes it tells us nothing of what is going on or calculating what those energy changes will be. To do this we need to understand the different energy levels of the nuclei and how those change during a nuclear reaction in a similar way that we can understand the energy changes during a chemical reaction by looking how the different energy levels of the electrons change.

I am not going to go into details here but will give a quick example.

238U undergoes alpha decay to 234Th: If we look up the masses then we find

 238U 238.051 234Th 234.044 alpha 4.0026

If we add the masses of the Thorium and Alpha particle we find that it is less than mass of the Uranium by 0.004577 atomic mass units. We can then use E=mc2 and calculate that the energy change is 4.264MeV. This is the energy of the alpha particle that is emitted (4.26975MeV) to quite a good approximation.

However, it tells us nothing about why the energy of the Uranium is unstable with respect to decay into a Thorium atom and an alpha particle.