A level revision

Binding energy

The binding energy of a nucleus is the amount of energy needed to pull the nucleons (protons and neutrons) infinitely apart. When you put energy into a nucleus to break it apart that energy 'becomes' mass of the nucleons. This means the mass of the sum of individual nucleons is more than the mass of the nucleus.

Atomic Mass Unit

Before looking at binding energy a new unit is to be introduced. The masses being dealt with in the context of protons, neutrons and nucleuses are so small that it helps to use another unit rather than kilograms. The atomic mass unit, u, is defined at 1/12 the mass of a carbon-12 atom, which is 1.66056 x 10^-27kg. Therefore the mass of a carbon atom is 12u.

Calculating binding energy

The calculation of binding energy is done in several steps. As an example we'll calculate the binding energy of a carbon-12 nucleus. Firstly calculate the mass of the nucleons, in this example that's 6 neutrons and 6 protons:

The mass of a nucleus of Carbon-12 is 12u (as above) minus the mass of the 6 electrons. This is 11.9967u. Now we work out the difference:

We now need to convert mass to energy. This requires use of the famous equation E = mc², but before we do this we need to convert the mass back to kilograms:

Typically we want the binding energy per nucleon, so divide by 12:

In general the binding energy per nucleon can be given by the equation:

Where:

• is the number of protons in the nucleus
• is the mass of a proton
• is the number of neutrons in the nucleus
• is the mass of a neutron
• is the mass of the nucleus
• is speed of light

When doing calculations involving binding energy you shouldn't round up because the differences are so small. Your figures should be given to around 6-7 significant figures

Binding energy graphs

A graph of binding energy per nucleon against nucleon number looks like this:

All binding energies are negative. Binding energy is only ever 0 when the nucleons are infinitely far apart.

Iron, at the lowest point of the graph, is the most stable atom as its nucleon are the most tightly bound.

Nuclei to the right of iron on the graph become more and more unstable as they grow in size. Uranium-235 towards the far right is so big the force which keeps the nucleons together can only just reach across the diameter of the nucleus.