Read the given statements and decide which is are correct on the basis of kinetic theory of gases
(I) Energy of one molecule at absolute temperature is zero
(II) r.m.s. speeds of different gases are same at same temperature
(III) For one gram of all ideal gas kinetic energy is same at same temperature
(IV) For one mole of all ideal gases mean kinetic energy is same at same temperature

Options

A. All are correct
B. I and IV are correct
C. IV is correct
D. None of these

Explanation

To determine which statements are correct based on the kinetic theory of gases, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement I: Energy of one molecule at absolute temperature is zero.**
- At absolute zero (0 Kelvin), the kinetic energy of a gas molecule is theoretically zero. This is because the kinetic energy is given by the formula \( KE = \frac{3}{2} k T \), where \( k \) is the Boltzmann constant and \( T \) is the absolute temperature. When \( T = 0 \), \( KE = 0 \).
- **Conclusion**: This statement is **correct**.

2. **Statement II: r.m.s. speeds of different gases are the same at the same temperature.**
- The root mean square (r.m.s.) speed of a gas is given by the formula \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( R \) is the ideal gas constant, \( T \) is the temperature, and \( M \) is the molar mass of the gas. Since different gases have different molar masses, the r.m.s. speed will vary with the type of gas even at the same temperature.
- **Conclusion**: This statement is **incorrect**.

3. **Statement III: For one gram of all ideal gases, kinetic energy is the same at the same temperature.**
- The kinetic energy for one gram of an ideal gas can be expressed as \( KE = \frac{3}{2} \frac{RT}{M} \), where \( M \) is the molar mass. Since the molar mass \( M \) varies for different gases, the kinetic energy will also vary for one gram of different gases at the same temperature.
- **Conclusion**: This statement is **incorrect**.

4. **Statement IV: For one mole of all ideal gases, mean kinetic energy is the same at the same temperature.**
- The mean kinetic energy for one mole of an ideal gas is given by \( KE = \frac{3}{2} RT \). Since \( R \) and \( T \) are constants for a given temperature, the mean kinetic energy will be the same for one mole of any ideal gas at the same temperature.
- **Conclusion**: This statement is **correct**.

### Final Evaluation:
- **Correct Statements**: I and IV
- **Incorrect Statements**: II and III

### Summary:
- **Correct Answers**: I and IV are correct based on the kinetic theory of gases.