Binding Energy (AQA A Level Physics): Revision Note

Binding energy per nucleon graph

• In order to compare nuclear stability, it is useful to look at the binding energy per nucleon

• The binding energy per nucleon is defined as:

The binding energy of a nucleus divided by the number of nucleons in the nucleus

• A higher binding energy per nucleon indicates a higher stability

• In other words, more energy is required to separate the nucleons contained within a nucleus

Key features of the graph

• At low values of $A$:

  • Nuclei have lower binding energies per nucleon than at large values of $A$, but they tend to be stable when $N=Z$

  • This means light nuclei have weaker electrostatic forces and will undergo fusion

  • The gradient is much steeper compared to the gradient at large values of $A$

  • This means that fusion reactions release a greater binding energy than fission reactions

• At high values of $A$:

  • Nuclei have generally higher binding energies per nucleon, but this gradually decreases with $A$

  • This means the heaviest elements are the most unstable and will undergo fission

  • The gradient is less steep compared to the gradient at low values of $A$

  • This means that fission reactions release less binding energy than fusion reactions

• Iron ($A=56$) has the highest binding energy per nucleon, which makes it the most stable of all the elements

• Helium (⁴He), carbon (¹²C) and oxygen (¹⁶O) do not fit the trend

  • Helium-4 is a particularly stable nucleus hence it has a high binding energy per nucleon

  • Carbon-12 and oxygen-16 can be considered to be three and four helium nuclei, respectively, bound together

Comparing fusion and fission

Similarities

• In both fusion and fission, the total mass of the products is slightly less than the total mass of the reactants

• The mass defect is equivalent to the binding energy that is released

• As a result, both fusion and fission reactions release energy

Differences

• In fusion, two smaller nuclei combine into a larger nucleus

• In fission, an unstable nucleus splits into two smaller nuclei

• Fusion occurs between light nuclei ($A<56$)

• Fission occurs in heavy nuclei ($A>56$)

• In light nuclei, attractive nuclear forces dominate over repulsive electrostatic forces between protons, and this contributes to nuclear stability 

• In heavy nuclei, repulsive electrostatic forces between protons begin to dominate over attractive nuclear forces, and this contributes to nuclear instability

• Fusion releases much more energy per kg than fission

• Fusion requires a greater initial input of energy than fission