Question

The binding energy per nucleon initially increases and then decreases with mass number because:

• A. The force of attraction between nucleons increases initially and then decreases.
• B. The strong nuclear force between nucleons increases with mass number.
• C. The size of the nucleus increases with mass number, leading to decreased binding energy per nucleon.
• D. The weak nuclear force has no significant effect on the binding energy.

Answer 1

The Correct Option is C

To address the problem, it's essential to understand the relationship between binding energy per nucleon and a nucleus's mass number.

1. Understanding Binding Energy Per Nucleon:

- Binding energy per nucleon represents the average energy binding each nucleon (proton or neutron) within the nucleus.
- A higher binding energy per nucleon signifies a more stable nucleus.
- The graph of binding energy per nucleon versus mass number shows an initial sharp increase for light nuclei, peaking around iron (mass number ~56), followed by a gradual decline for heavier nuclei.

2. Initial Increase:

- In smaller nuclei, the addition of more nucleons enhances the strong nuclear force interactions, thereby increasing the binding energy per nucleon.
- The strong nuclear force, a short-range interaction, binds nucleons together tightly.

3. Decrease After a Point:

- As nuclei grow larger, their overall size increases.
- The electrostatic (Coulomb) force causes protons to repel each other, and this force has a longer range.
- This proton repulsion diminishes the overall binding energy per nucleon in larger nuclei.
- Additionally, the short-range nature of the strong nuclear force means that nucleons farther apart experience weaker attraction.

4. Option Analysis:

• Option 1: "The force of attraction between nucleons increases initially and then decreases." - This statement is partially correct but lacks completeness by omitting the influence of nucleus size and proton repulsion.
• Option 2: "The strong nuclear force between nucleons increases with mass number." - This is incorrect; the strong force is short-range and does not scale with mass number.
• Option 3: "The size of the nucleus increases with mass number, leading to decreased binding energy per nucleon." - This accurately explains the decline in binding energy per nucleon beyond a certain point.
• Option 4: "The weak nuclear force has no significant effect on the binding energy." - While true, this does not account for the observed variations in binding energy per nucleon.

Final Answer:

Binding energy per nucleon initially rises and then falls with increasing mass number primarily because the size of the nucleus increases with mass number, resulting in a decrease in binding energy per nucleon.