# Binding energy

## Binding energy

When you make a nucleus from its constituent parts, you give out energy (lose mass). That means that to break up a nucleus you will need to put back in the same amount of energy you took out (to convert back into mass). This energy is called the Binding Energy of the nucleus, as it is the energy involved in binding the nucleus together.

Obviously, the bigger the nucleus you make the more energy you get out (every time you add another proton or neutron (smack - flash of light!) you get more mass going missing). So the bigger nuclei have bigger mass defects. But if you look at the binding energy per nucleon involved in the nucleus, you notice that certain atoms have higher values than others. This is interesting as it suggests that some nuclei are more stable than others.

Tip: To find the binding energy per nucleon simply find the energy of the entire nucleus and divide by the number of nucleons (protons + neutrons) - its that easy!

The graph below shows the binding energy per nucleon for a range of elements increasing in atomic number.

If we imagine the original protons and neutrons separated then energy is lost as we assemble the nucleus (remember the flash of light?) We say that the protons and neutrons have zero energy when separated and therefore as energy is lost in assembling them the binding energy per nucleon is negative. We can put the same amount of energy back in to break the nucleus apart again and thus we return to the original zero energy situation.

It is helpful to imagine the graph as a nuclear valley. At the bottom sits the iron nucleus. This nucleus requires the most energy (-8.8 MeV) to break apart and move up the valley and out. The other elements sit on the slopes of the valley and need less energy to break up and escape. Iron is therefore the most stable nucleus of all.