If the atoms in a diatomic molecule can vibrate, the molecule has

Options

A. two rotational degrees of freedom.
B. three rotational degrees of freedom.
C. one vibrational degree of freedom.
D. two vibrational degrees of freedom.

Answer

To determine the degrees of freedom for a diatomic molecule that can vibrate, we need to analyze the types of motion it can exhibit.

### Step-by-Step Solution:

1. **Understanding Degrees of Freedom**:
- Degrees of freedom refer to the number of independent ways in which a system can move. For molecules, this includes translational, rotational, and vibrational motions.

2. **Translational Motion**:
- A diatomic molecule can move in three-dimensional space. This gives it three translational degrees of freedom (movement along the x, y, and z axes).

3. **Rotational Motion**:
- A diatomic molecule can rotate about two axes perpendicular to the bond connecting the two atoms. It cannot rotate about the axis along the bond because that would not change the orientation of the molecule. Therefore, it has two rotational degrees of freedom.

4. **Vibrational Motion**:
- For vibrational motion, a diatomic molecule can vibrate in two ways:
- The two atoms can move towards and away from each other (stretching).
- The two atoms can also move in a bending motion (though this is less significant for diatomic molecules compared to polyatomic ones).
- This gives the diatomic molecule one vibrational degree of freedom for stretching and one for bending, totaling **two vibrational degrees of freedom**.

5. **Conclusion**:
- Therefore, if the atoms in a diatomic molecule can vibrate, the molecule has **two vibrational degrees of freedom**.

### Final Answer:
The molecule has **two vibrational degrees of freedom**.

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