Which of the following is a wrong description of binding energy of a nucleus?

Options

A. It is the energy required to break a nucleus into its constituent nucleons.
B. It is the energy released when free nucleons combine to from a nucleus
C. It is the sum of the rest mass energies of its nucleons minus the rest energy of the nucleus
D. It is the sum of the kinetic energy of all the nucleons in the nucleus

Explanation

To determine which of the statements regarding the binding energy of a nucleus is incorrect, let's analyze each statement step by step:

1. **Statement A**: "It is the energy required to break a nucleus into constituent nucleons."
- **Analysis**: This statement is correct. The binding energy is indeed the energy required to separate the nucleons (protons and neutrons) that make up the nucleus. It reflects how tightly the nucleons are held together.

2. **Statement B**: "It is the energy released when free nucleons combine to form a nucleus."
- **Analysis**: This statement is also correct. When nucleons come together to form a nucleus, energy is released due to the conversion of mass into energy (as per Einstein's equation \(E=mc^2\)). This energy released is equal to the binding energy of the nucleus.

3. **Statement C**: "It is the sum of the rest mass energy of the nucleons minus the rest mass energy of the nucleus."
- **Analysis**: This statement is correct as well. The binding energy can be calculated by taking the difference between the total rest mass energy of the individual nucleons and the rest mass energy of the nucleus itself. This difference represents the energy that was released when the nucleons formed the nucleus.

4. **Statement D**: "It is the sum of the kinetic energy of the nucleons in the nucleus."
- **Analysis**: This statement is incorrect. The binding energy does not relate to the kinetic energy of the nucleons. Instead, it is a measure of the energy that holds the nucleus together, which is derived from the mass defect and the energy released during the formation of the nucleus.

**Conclusion**: The wrong description of the binding energy of a nucleus is given in **Statement D**.