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

Options

A. 2 rotational degree of freedom
B. 3 rotational degrees of freedom
C. 1 vibrational degree of freedom
D. 2 vibrational degree of freedom

Answer

To solve the question about the degrees of freedom in a diatomic molecule, we can break it down into steps:

### Step 1: Understand Degrees of Freedom
Degrees of freedom refer to the number of independent ways in which a system can move. For a molecule, this includes translational, rotational, and vibrational movements.

### Step 2: Calculate Translational Degrees of Freedom
For any molecule in three-dimensional space, the translational degrees of freedom are given by the three axes (x, y, z). Therefore, a diatomic molecule has:
- **Translational Degrees of Freedom = 3**

### Step 3: Calculate Rotational Degrees of Freedom
A diatomic molecule can rotate about two axes perpendicular to the line joining the two atoms. It cannot rotate about the axis along the line joining the two atoms because this does not change the orientation of the molecule. Thus, the rotational degrees of freedom are:
- **Rotational Degrees of Freedom = 2**

### Step 4: Calculate Vibrational Degrees of Freedom
For a diatomic molecule, each atom can vibrate relative to the other. The vibrational degrees of freedom can be calculated as:
- **Vibrational Degrees of Freedom = 2**
This accounts for the two modes of vibration (compression and rarefaction).

### Step 5: Total Degrees of Freedom
Now, we can sum up all the degrees of freedom:
- Total Degrees of Freedom = Translational + Rotational + Vibrational
- Total Degrees of Freedom = 3 (translational) + 2 (rotational) + 2 (vibrational) = 7

### Conclusion
If the atoms in a diatomic molecule can vibrate, the molecule has:
- 2 rotational degrees of freedom
- 2 vibrational degrees of freedom

### Final Answer
Thus, the correct answer is that if the atoms in a diatomic molecule can vibrate, the molecule has 2 rotational degrees of freedom and 2 vibrational degrees of freedom.

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