The binding energy per nucleon, for nuclei with atomic mass number `A gt 100`, decreases with `A`.
The nuclear forces are weak for heavier nuclei.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false
D. If assertion is false but reason is true.

Explanation

To solve the question regarding the binding energy per nucleon for nuclei with atomic mass number \( A > 100 \), we will analyze the assertion and the reason provided in the statement.

### Step-by-Step Solution:

1. **Understanding Binding Energy per Nucleon**:
- Binding energy per nucleon is defined as the energy required to remove a nucleon from the nucleus. It is an important measure of the stability of a nucleus.
- It can be represented as \( BE/A \), where \( BE \) is the total binding energy and \( A \) is the mass number.

2. **Behavior of Binding Energy with Increasing Mass Number**:
- For nuclei with \( A > 100 \), it is observed that the binding energy per nucleon decreases as \( A \) increases.
- This trend can be attributed to the balance between the attractive nuclear forces and the repulsive electrostatic forces among protons.

3. **Graphical Representation**:
- A graph can be drawn where the x-axis represents the mass number \( A \) and the y-axis represents the binding energy per nucleon.
- The graph typically shows an initial increase in binding energy per nucleon with increasing \( A \) up to a certain point (around \( A = 56 \)), after which it starts to decrease.

4. **Nuclear Forces and Their Strength**:
- The nuclear force is a short-range force that acts between nucleons (protons and neutrons) and is responsible for holding the nucleus together.
- While the nuclear force is strong, it becomes less effective in larger nuclei due to the increasing number of nucleons, which leads to greater repulsive forces among protons.

5. **Conclusion on Assertion and Reason**:
- The assertion that the binding energy per nucleon decreases with increasing \( A \) for nuclei with \( A > 100 \) is **true**.
- However, the reason provided that "the nuclear forces are weak for heavier nuclei" is **false**. The nuclear forces themselves do not weaken; rather, the balance of forces changes due to increased repulsion among protons as the number of nucleons increases.

### Final Statement:
- The assertion is true, but the reason is false.