# Nuclear stability and binding energy

Binding energy is not possessed by a nucleus, but instead is released when the nucleus formed.

Binding energy is often wrongly defined as the energy that holds a nucleus together. The nucleus is held together by the nuclear force. Binding energy is the energy required to separate the nucleons.

Key Concepts

Building a nucleus

Not all combinations of protons and neutrons are possible as they form nuclei that are unstable.

Small nuclei are most stable if the number of protons and neutrons are equal. Larger nuclei require a higher ratio of neutrons as these do not create electrostatic repulsion.

Nuclear force

The nuclear force is very strong but has a short range. Unlike gravity and electric force it only acts between neighbours. This leads to the constant density of all nuclei.

Essentials

Binding energy

Binding energy is the energy released when a nucleus is formed. It is equal to the work done that would need to be added to separate the nucleus into individual nucleons.

This leads to an increase in mass: $$E = mc^2$$

Splitting a nucleus require work to be done, equal to the binding energy.

Potential well

Putting nucleons together is like throwing balls into a bucket. They will only stay in the bucket if they can lose energy to reach a position of stability.

Calculation - the binding energy of helium

Binding energy is calculated by finding the difference in mass between the nucleus and it constituents.

The mass defect in u is multiplied by 931.5 MeVu-1 to convert to MeV.

Summary

#### Binding energy per nucleon curve

This curve indicates the relative stability of nuclei.

Test Yourself

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