Select the correct statement(s).
I. The velocity at which distribution of molecules is maximum is called most probable velocity
II. Most probable velocity of a gas is larger than root mean square velocity .
The correct option is:

Options

A. I
B. II
C. I , II
D. None of these

Explanation

To solve the question, we need to evaluate the two statements provided:

**Statement I**: The velocity at which the distribution of molecules is maximum is called most probable velocity.

**Statement II**: Most probable velocity of a gas is larger than root mean square velocity.

Now, let's analyze each statement step by step.

### Step 1: Analyze Statement I
- The most probable velocity is defined as the velocity at which the maximum number of molecules in a gas are moving at a given temperature.
- This means that Statement I is correct because it accurately describes the concept of most probable velocity.

### Step 2: Analyze Statement II
- The most probable velocity (denoted as \( v_p \)) is given by the formula:
\[ v_p = \sqrt{\frac{2RT}{M}} \]
where \( R \) is the universal gas constant, \( T \) is the absolute temperature, and \( M \) is the molar mass of the gas.

- The root mean square velocity (denoted as \( v_{rms} \)) is given by the formula:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]

- To compare \( v_p \) and \( v_{rms} \), we can look at their respective formulas:
- \( v_p = \sqrt{\frac{2RT}{M}} \)
- \( v_{rms} = \sqrt{\frac{3RT}{M}} \)

### Step 3: Compare the Two Velocities
- We can see that:
\[ v_{rms} = \sqrt{3} \cdot \sqrt{\frac{RT}{M}} \quad \text{and} \quad v_p = \sqrt{2} \cdot \sqrt{\frac{RT}{M}} \]

- Since \( \sqrt{3} \) (approximately 1.732) is greater than \( \sqrt{2} \) (approximately 1.414), it follows that:
\[ v_{rms} > v_p \]

- Therefore, Statement II is incorrect because it states that the most probable velocity is larger than the root mean square velocity, which is not true.

### Conclusion
- **Correct Statement**: Only Statement I is correct.
- **Final Answer**: The correct option is Statement I.

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