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What is binding energy?

The binding energy of the nucleus is the work that must be done to separate the nucleus into its constituent protons and neutrons.


Seperating nucleons:

Increase their potential energy as work must be done to overcome the nuclear strong force.


If a nucleus is formed from separate protons and neutrons:

Binding energy is released as the strong force pulls the nucleons together.

As a result, mass of the nucleus < mass of the separate nucleons


What is the mass defect?

Mass defect, ∆m, of a nucleus is the difference between the mass of the separated nucleons and the mass of the nucleus.


Mass defect, ∆m, =

  Zmp + (A-Z)mn - MNUC


Binding energy = ∆E =



Binding energy per nucleon of a nucleus is:

The average work done per nucleon to remove all the nucleons from a nucleus. Higher binding energy/nucleon means a nucleus is more stable.


Describe the features of the graph.

Q image thumb

  • Curve has a steep rise 
  • A maximum of 8.7 between A = 50  60 
  • IIron is the most stable nucleus 
  • have a gradual fall of approx. 20% 
  • go up to A, approx. 250.


Fusion can occur when:

Two smaller nuclei combine together to form a larger nucleus. If fusion occurs, the product nucleus (A < 50) has more binding energy per nucleon than the smaller nuclei. Fusion starts with two small nuclei on the left and moves to the right upwards towards the peak.


Fission can occur when:

Larger nuclei split into two smaller nuclei. If fission occurs, the smaller nuclei (A > 50) has more binding energy per nucleon than the original nucleus. Fission starts with a large nucleus on the right and moves to the left upwards towards the peak. The fragments are more stable than the original nucleus.


Explain why small nuclei can’t be split and why large nuclei can’t be fused.

  • Small nuclei have stronger nuclear force due to higher binding energy per nucleon. It is energetically favourable for them to fuse together to make a bigger nucleus.
  • Large nuclei have a weaker nuclear force and a lower energy per nucleon. It is energetically favourable for them to split into smaller nuclei with nucleons with higher binding energy per nucleon.