As the mass number `A` increases, the binding energy per nucleon in a nucleus.

Options

A. increases
B. decreases
C. remains the same
D. varies in a way that depends on the actual value of `A`

Answer

To solve the question regarding how the binding energy per nucleon (EBN) changes as the mass number (A) increases, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Binding Energy per Nucleon (EBN)**:
- The binding energy per nucleon is defined as the total binding energy of the nucleus divided by the number of nucleons (protons and neutrons) in the nucleus. It indicates how tightly the nucleons are bound together.

2. **Analyzing the Relationship with Mass Number (A)**:
- The mass number (A) is the total number of protons and neutrons in a nucleus. As A increases, we need to observe how EBN behaves.

3. **Plotting EBN vs. A**:
- A graph of binding energy per nucleon (EBN) versus mass number (A) typically shows a curve. Initially, as A increases from low values, EBN increases. This indicates that nuclei become more stable with increasing mass number.

4. **Identifying the Peak**:
- The curve reaches a maximum around A = 56, which corresponds to iron (Fe). At this point, the binding energy per nucleon is at its highest.

5. **Behavior Beyond the Peak**:
- After reaching the peak at A = 56, as A continues to increase (for heavier nuclei), the binding energy per nucleon starts to decrease. This indicates that heavier nuclei are less stable compared to those around iron.

6. **Conclusion**:
- Therefore, the behavior of binding energy per nucleon as mass number A increases is not uniform. It increases up to a certain point (around A = 56) and then starts to decrease for heavier nuclei. Thus, the binding energy per nucleon varies depending on the value of A.

### Final Answer:
The binding energy per nucleon in a nucleus varies in a way that depends on the actual value of A.