Question

Explain the meaning of binding energy of a nucleus. Write the dependency of binding energy per nucleon on the mass number of the nucleus.

Hint:

The binding energy per nucleon is typically highest for elements near iron (Fe). The higher the binding energy per nucleon, the more stable the nucleus. For light elements, fusion increases the binding energy per nucleon, while for heavy elements, fission does.

Answer 1

Binding energy of a nucleus is the energy required to separate a nucleus into its constituent nucleons (protons and neutrons). It is the energy that holds the nucleus together and is a measure of the stability of the nucleus. The binding energy is negative, indicating that energy must be supplied to break the nucleus apart. The higher the binding energy, the more stable the nucleus is.
The binding energy per nucleon is the total binding energy of the nucleus divided by the number of nucleons. It is an important quantity as it gives an idea of how tightly bound the nucleons are in a nucleus. The binding energy per nucleon typically increases with the atomic number up to iron (Fe) and then decreases for heavier nuclei.
The dependency of binding energy per nucleon on the mass number \(A\) (the number of nucleons in the nucleus) can be approximated by the following empirical relationship:
\[ \text{Binding energy per nucleon} = \frac{aV A - aS A^{2/3} - aC Z^2 A^{-1/3} - aA (A-1)}{A}, \] where:
- \( A \) is the mass number of the nucleus,
- \( Z \) is the atomic number (number of protons),
- \( aV, aS, aC, \) and \( aA \) are constants.
This equation shows that the binding energy per nucleon depends on the size of the nucleus (related to \(A\)) and the nuclear force binding the nucleons. For light nuclei, binding energy increases with the number of nucleons, and for heavier nuclei, it tends to decrease due to the repulsive forces between protons.