AQA A-Level Physics/Binding Energy

Key Ideas
If one were to separate a nucleus into its individual nucleons, work must be done to overcome the strong force holding the nucleons together. The binding energy of a nucleus is the work that must be done to separate a nucleus into its constituent neutrons and protons.

When a nucleus forms from nucleons, energy is released as the strong force does work by pulling the nucleons together. When nucleons are separated from a nucleus, energy is used to break the strong force.

However, because Albert Einstein proved that the mass of an object increases when it gains energy and decreases when it loses energy, the mass of a nucleus is less than the mass of the separated nucleons. This is because energy is released when the nucleons form the nucleus, so the mass decreases. This difference between the mass of the separated nucleons and the mass of the nucleus is called the mass defect.

You can use mass defect to calculate the energy released when the nucleus formed from the separate nucleons i.e. its binding energy.

Binding energy of a nucleus =  (△m)(c²)

Calculation of mass defect
When calculating mass defect (△m), you are subtracting the mass of the nucleus from the combined mass of the nucleons.

To calculate the mass defect, you need  the mass of the nucleus (MNUC), the mass of a proton (mp) the mass of a neutron (mn) and the number of protons (Z) and neutrons (A-Z, where A represents atomic number i.e. all nucleons). (Remember, electrons are not involved at any point in this calculation as we are only referring to the nucleus of the atom.)

mp = 1.67(3) x10 -27 kg

mn = 1.67(5) x10 -27 kg

Therefore, a generic formula for mass defect is:

mass defect, △m =  Z(mp) + (A - Z)(mn)  -  MNUC