Assertion : The rms velocity and most probable speeds of the molecules in a gas are same.
The Maxwell distribution curve for the speed of the molecules in a gas is symmetrical.

Options

A. If both assertion and reason are true and reason is the correct explanation os assertion.
B. If both assertion and reason are true but reason is not be correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that the root mean square (rms) velocity and the most probable speed of the molecules in a gas are the same.

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

- The formula for the most probable speed (v_mp) is given by:
\[ v_{mp} = \sqrt{\frac{2RT}{M}} \]

### Step 2: Compare the Two Speeds
Now, we need to compare the two speeds:

- From the formulas, we can see:
\[ v_{rms} = \sqrt{\frac{3RT}{M}} \quad \text{and} \quad v_{mp} = \sqrt{\frac{2RT}{M}} \]

- Clearly, \( v_{rms} \) is not equal to \( v_{mp} \) because:
\[ \sqrt{3} \neq \sqrt{2} \]

Thus, the assertion that rms velocity and most probable speed are the same is **false**.

### Step 3: Understand the Reason
The reason states that the Maxwell distribution curve for the speed of the molecules in a gas is symmetrical.

- The Maxwell-Boltzmann distribution curve is actually **not symmetrical**; it is skewed to the right. The peak of the curve represents the most probable speed, while the rms speed is located to the right of this peak.

### Step 4: Conclusion
Since both the assertion and the reason are false, we conclude that:

- **Assertion**: False
- **Reason**: False

### Final Answer
Both the assertion and the reason are false.

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