Question

Which of the following statement(s) is/are true in respect of nuclear binding energy?
(i) The mass energy of a nucleus is larger than the total mass energy of its individual protons and neutrons.
(ii) If a nucleus could be separated into its nucleons, an energy equal to the binding energy would have to be transferred to the particles during the separating process.
(iii) The binding energy is a measure of how well the nucleons in a nucleus are held together.
(iv) The nuclear fission is somehow related to acquiring higher binding energy.

• A. Statements (i), (ii), and (iii) are true
• B. Statements (ii), (iii), and (iv) are true.
• C. Statements (ii) and (iii) are true.
• D. All four statements are true

Hint:

In nuclear binding energy, the total mass of the nucleus is always less than the sum of the masses of its individual nucleons. This mass difference is the binding energy.

Answer 1

The Correct Option is B

Statement (i): The mass energy of a nucleus is actually smaller than the sum of the mass energies of individual protons and neutrons due to the binding energy. Therefore, this statement is false.

Statement (ii): When a nucleus is separated into its nucleons, energy equal to the binding energy must be supplied to overcome the nuclear forces holding the nucleons together. This statement is true.

Statement (iii): The binding energy is indeed a measure of how strongly the nucleons (protons and neutrons) are held together within the nucleus. This statement is true.

Statement (iv): Nuclear fission involves the splitting of a heavy nucleus into lighter nuclei, which results in a release of binding energy, leading to a higher binding energy per nucleon in the fragments. This statement is true.

Thus, the correct answer is that statements (ii), (iii), and (iv) are true.

Answer 2

Statements about Nuclear Binding Energy

Let's evaluate the truthfulness of the given statements regarding nuclear binding energy:

1. (i) The mass energy of a nucleus is larger than the total mass energy of its individual protons and neutrons.

False. The mass of a nucleus is less than the sum of the masses of its individual nucleons. This mass defect is converted into binding energy ($BE = \Delta m c^2$), meaning the mass energy of the nucleus is actually smaller.

1. (ii) If a nucleus could be separated into its nucleons, an energy equal to the binding energy would have to be transferred to the particles during the separating process.

True. The binding energy represents the energy holding the nucleons together. To separate them, an equivalent amount of energy must be supplied to overcome the nuclear forces.

1. (iii) The binding energy is a measure of how well the nucleons in a nucleus are held together.

True. A higher binding energy per nucleon indicates a stronger attraction between the nucleons and a more stable nucleus.

1. (iv) The nuclear fission is somehow related to acquiring higher binding energy.

True. In nuclear fission, a heavy nucleus splits into lighter nuclei that have a higher binding energy per nucleon, releasing a significant amount of energy in the process as the system moves towards a more stable state.

Conclusion

Based on the evaluation, statements (ii), (iii), and (iv) are true.

Answer: (2) Statements (ii), (iii) and (iv) are true