Given below are two statements :
Statement I : In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.
Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.
In the light of the above statements, choose the correct answer from the options given below :

Options

A. Statement I is false but Statement II is true.
B. Both Statement I and Statement II are false.
C. Both Statement I and Statement II are true.
D. Statement I is true but Statement II is false.

Answer

To solve the problem, we need to analyze the two statements provided regarding diatomic molecules and their energy distributions.

### Step-by-Step Solution:

1. **Understanding Statement I**:
- The first statement claims that in a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution.
- Maxwell's distribution describes the distribution of speeds (or energies) of particles in a gas at thermal equilibrium.
- For diatomic molecules, which have rotational degrees of freedom, the rotational kinetic energy indeed follows this distribution.
- **Conclusion**: Statement I is **True**.

2. **Understanding Statement II**:
- The second statement claims that in a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule.
- For a diatomic gas, the degrees of freedom are as follows:
- Translational degrees of freedom: 3 (movement in x, y, and z directions)
- Rotational degrees of freedom: 2 (rotation about two axes perpendicular to the molecular axis)
- The average translational kinetic energy for a diatomic gas is given by:
\[ \text{Translational K.E.} = \frac{3}{2} kT \]
- The average rotational kinetic energy for a diatomic gas is given by:
\[ \text{Rotational K.E.} = \frac{2}{2} kT = kT \]
- Comparing these, we see that:
- Translational K.E. = \(\frac{3}{2} kT\)
- Rotational K.E. = \(kT\)
- Therefore, the translational kinetic energy is greater than the rotational kinetic energy.
- **Conclusion**: Statement II is **False**.

3. **Final Evaluation**:
- Since Statement I is True and Statement II is False, the correct answer based on the evaluation of the statements is that only Statement I is correct.

### Summary:
- **Statement I**: True
- **Statement II**: False