Correct statement -

Options

A. At constatn temperature, the KE of all the gas molecules is the same
B. At constant temperature, averge KE of gas molecules remains constant but KE of individual molecule may differ
C. At constant temperature , the KE is less for heavier gas molecules
D. At constatn temperature , the KE is less for heavier gas molecules

Answer

To solve the question regarding the correct statement about the kinetic energy of gas molecules, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Kinetic Energy in Gases:**
- The kinetic energy of gas molecules is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
- Here, \(m\) is the mass of the molecule and \(v\) is its velocity.

2. **Analyzing the First Option:**
- The first option states that "at constant temperature, the kinetic energy of all the gas molecules is the same."
- This statement is incorrect because, although the average kinetic energy of gas molecules at a given temperature remains constant, individual molecules can have different kinetic energies due to variations in their velocities.

3. **Analyzing the Second Option:**
- The second option states that "at constant temperature, the average kinetic energy of gas molecules is the same."
- This statement is correct. At a constant temperature, the average kinetic energy of gas molecules is constant and is directly proportional to the temperature.

4. **Analyzing the Third Option:**
- The third option states that "at constant temperature, the kinetic energy is less for heavier gas molecules."
- This statement is incorrect. While heavier gas molecules have a greater mass, they can have higher kinetic energy if their velocity is sufficiently high. The average kinetic energy is dependent on temperature, not directly on mass.

5. **Analyzing the Fourth Option:**
- The fourth option is similar to the third and states that "heavier gas molecules have less kinetic energy."
- This statement is also incorrect for the same reasons as the third option. Kinetic energy depends on both mass and velocity.

6. **Conclusion:**
- After analyzing all the options, the only correct statement is option 2, which asserts that at constant temperature, the average kinetic energy of gas molecules is the same.

### Final Answer:
The correct statement is **Option 2**: At constant temperature, the average kinetic energy of gas molecules is the same.