According to kinetic theory of gases, for a datomic molecule.

Options

A. the pressure exerted by the gas, is proportional to mean velocity of the molecule
B. the pressure exerted by the gas is proportional to the root mean velocity of the molecule
C. the root mean square velocity of the molecule is inversely proportional to the temperature
D. the mean translational kinetic energy of the molecule is proportional to the absolute temperature

Explanation

To solve the question regarding the kinetic theory of gases for a diatomic molecule, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Kinetic Theory of Gases**:
The kinetic theory of gases states that gas molecules are in constant random motion and that their collisions with each other and with the walls of the container result in pressure.

**Hint**: Remember that the kinetic theory applies to ideal gases and assumes no intermolecular forces.

2. **Kinetic Energy and Temperature Relationship**:
According to the kinetic theory, the average kinetic energy of gas molecules is directly proportional to the absolute temperature (T). For a diatomic molecule, the average kinetic energy can be expressed as:
\[ KE = \frac{5}{2} RT \]
This is because a diatomic molecule has both translational and rotational degrees of freedom.

**Hint**: Diatomic molecules have more degrees of freedom compared to monatomic molecules, which affects their kinetic energy expression.

3. **Pressure and Velocity**:
The pressure exerted by a gas is related to the root mean square (RMS) velocity of the molecules. The RMS velocity (v_rms) is given by:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where M is the molar mass of the gas.

**Hint**: Remember that pressure is related to the momentum change of molecules colliding with the walls of the container.

4. **Correct Relationships**:
- The pressure exerted by the gas is directly proportional to the number of collisions with the walls, which is influenced by the RMS velocity.
- The RMS velocity is directly proportional to the square root of the temperature, not inversely.

**Hint**: Focus on how temperature affects molecular motion and, subsequently, pressure.

5. **Conclusion**:
The mean translational kinetic energy of a diatomic molecule is proportional to the absolute temperature. Therefore, the correct statement according to the kinetic theory of gases for a diatomic molecule is that the mean translational kinetic energy is proportional to the absolute temperature.

**Final Answer**: The mean translational kinetic energy of a diatomic molecule is proportional to the absolute temperature.