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, I am going to digress a bit. One of the things that makes Einstein’s theory of relativity important is that it is universal. In fact, one of the motivations of Einstein’s 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 the 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, similarly 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

If we add the masses of the Thorium and Alpha particle, we find that it is less than the 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.