These diagrams represent the potential energy `U` of a diatomic molecule as a function of the inter-atomic distance `r`. The diagram corresponds to stable molecule found in nature is.

Options

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D.

Explanation

To determine which diagram represents the potential energy \( U \) of a diatomic molecule as a function of the inter-atomic distance \( r \) for a stable molecule found in nature, we can analyze the characteristics of potential energy graphs.

### Step-by-Step Solution:

1. **Understanding Potential Energy and Inter-Atomic Distance**:
- The potential energy \( U \) of a diatomic molecule varies with the distance \( r \) between the two atoms. Typically, as the atoms approach each other, the potential energy decreases until it reaches a minimum value at the equilibrium bond length.

2. **Identifying Stable Molecules**:
- A stable molecule corresponds to a potential energy curve that has a minimum point. At this minimum, the force between the atoms is zero, indicating that the atoms are in a stable equilibrium position.

3. **Analyzing the Graphs**:
- Look for a graph where:
- The potential energy \( U \) decreases as the distance \( r \) decreases until it reaches a minimum.
- After reaching the minimum, as \( r \) increases further, the potential energy \( U \) should increase again.
- This behavior indicates that the molecule is stable at the minimum point.

4. **Choosing the Correct Diagram**:
- Among the provided diagrams, identify the one that shows a clear minimum in the potential energy curve. This is the diagram that corresponds to a stable diatomic molecule found in nature.

5. **Conclusion**:
- Based on the analysis, select the diagram that meets the criteria of having a minimum potential energy, indicating a stable molecular configuration.