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:

### Step 1: Analyze Statement I
**Statement I**: "The velocity at which distribution of molecules is maximum is called most probable velocity."

- The most probable velocity (v_mp) is defined as the speed at which the maximum number of molecules in a gas sample is moving. This statement is true because it accurately describes the concept of most probable velocity in kinetic theory.

### Step 2: Analyze Statement II
**Statement II**: "Most probable velocity of a gas is larger than root mean square velocity."

- The root mean square velocity (v_rms) is given by the formula:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \]
where R is the universal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

- The most probable velocity is given by the formula:
\[ v_{mp} = \sqrt{\frac{2RT}{M}} \]

- To compare these two velocities, we can see that:
\[ v_{mp} = \sqrt{\frac{2RT}{M}} \quad \text{and} \quad v_{rms} = \sqrt{\frac{3RT}{M}} \]

- Since \(\sqrt{2} \approx 1.414\) and \(\sqrt{3} \approx 1.732\), it is clear that:
\[ v_{mp} < v_{rms} \]

- Therefore, this statement is false because the most probable velocity is not larger than the root mean square velocity.

### Conclusion
Based on the analysis:
- Statement I is correct.
- Statement II is incorrect.

Thus, the correct option is that only Statement I is true.

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