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 solve the problem, we need to understand why the binding energy per nucleon varies with the mass number of a nucleus.

1. Understanding Binding Energy Per Nucleon:

- Binding energy per nucleon is the average energy that holds each nucleon (proton or neutron) together in the nucleus.
- It indicates the stability of a nucleus; higher values mean greater stability.
- When plotting binding energy per nucleon against mass number, the graph rises sharply for light nuclei, reaches a peak around iron (mass number ~56), and then gradually decreases for heavier nuclei.

2. Why Does It Increase Initially?

- For small nuclei, adding more nucleons means more strong nuclear force interactions, which increases the binding energy per nucleon.
- The strong nuclear force is a short-range force attracting nucleons tightly together.

3. Why Does It Decrease After a Point?

- As the nucleus gets larger, the size of the nucleus increases.
- Protons repel each other due to electrostatic (Coulomb) force, which acts over longer distances.
- The repulsive force among protons reduces overall binding energy per nucleon as the nucleus grows larger.
- Also, the strong nuclear force acts effectively only over short distances, so nucleons farther apart feel less attraction.

4. Analyze the Options:

• Option 1: "The force of attraction between nucleons increases initially and then decreases." - This is partially true but incomplete as it does not mention the effect of nucleus size and proton repulsion.
• Option 2: "The strong nuclear force between nucleons increases with mass number." - False; the strong force is short-range and does not increase with mass number.
• Option 3: "The size of the nucleus increases with mass number, leading to decreased binding energy per nucleon." - This correctly explains why binding energy per nucleon decreases after a point.
• Option 4: "The weak nuclear force has no significant effect on the binding energy." - True, but it does not explain the variation of binding energy per nucleon.

Final Answer:

Binding energy per nucleon initially increases and then decreases with mass number because the size of the nucleus increases with mass number, leading to decreased binding energy per nucleon.