Binding Energy and Stability

The binding energy of an atom is the energy required to rip it apart into its component particles. These particles are held together, in the nucleus by the strong nuclear force, so it takes a lot of work to separate them. When we talk about the binding energy of an atom or nucleus remember that it is a negative quantity.

We can calculate the binding energy of an atom by looking at the difference in mass between the atom and its bits. Consider helium 4.

So it takes 26.9 MeV of energy to rip a helium atom to pieces. Because the energy required to separate the nucleons is so much bigger than the energy to remove the electrons (ionisation energy) this is approximately the binding energy of the nucleus.

A very interesting quantity is the binding energy per nucleon, B.E. / A.  For helium this is 26.9 / 4 = 6.73 MeV

As a rule of thumb, the greater the binding energy per nucleon the more stable a nucleus is.

We can learn much by plotting this quantity against nucleon number A

1. Medium sized nuclei are the most stable. Iron turns out to be the most stable nucleus.

2. If a very large nucleus split in two then energy would be released as B.E./A increased. This is the basis of fission.

3. If very small nuclei stuck together then energy may be released for the same reason. This is fusion.

4. Two protons and two neutrons seem to form a very stable configuration which doesn't fit the general trend.

Mass and Energy

Did you know that a stretched rubber band is heavier than one that isn't stretched? Because we have to give energy to the system to get from one state to the other its total mass increases.

A hot cup of tea is heavier than a cold one.

A person running is heavier than a person stood still.

Use E = m c² to estimate the difference in mass of the examples above and you'll realise why we don't notice the difference.