Assertion: The ratio of rms speed and average speed of a gas molecules at a given temperture is `sqrt3:sqrt(8//pi)`
Reason: `c_(rms)c_(av.)`

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 the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that the ratio of the root mean square (RMS) speed to the average speed of gas molecules at a given temperature is \( \sqrt{3} : \sqrt{\frac{8}{\pi}} \).

2. **Formulas for RMS Speed and Average Speed**:
According to the kinetic theory of gases:
- The RMS speed (\( C_{rms} \)) is given by:
\[ C_{rms} = \sqrt{\frac{3RT}{M}} \]
- The average speed (\( C_{av} \)) is given by:
\[ C_{av} = \sqrt{\frac{8RT}{\pi M}} \]

3. **Calculating the Ratio**:
To find the ratio of RMS speed to average speed, we can set up the following equation:
\[ \frac{C_{rms}}{C_{av}} = \frac{\sqrt{\frac{3RT}{M}}}{\sqrt{\frac{8RT}{\pi M}}} \]
Simplifying this gives:
\[ = \frac{\sqrt{3RT}}{\sqrt{8RT/\pi}} = \sqrt{\frac{3RT \cdot \pi}{8RT}} = \sqrt{\frac{3\pi}{8}} \]

4. **Comparing with the Assertion**:
The assertion claims that this ratio is \( \sqrt{3} : \sqrt{\frac{8}{\pi}} \). To compare:
\[ \sqrt{3} : \sqrt{\frac{8}{\pi}} = \sqrt{3\pi} : \sqrt{8} \]
This confirms that the assertion is indeed true.

5. **Understanding the Reason**:
The reason states that \( C_{rms} > C_{av} \). From our earlier calculations, we can see that:
\[ C_{rms} = \sqrt{\frac{3RT}{M}} \quad \text{and} \quad C_{av} = \sqrt{\frac{8RT}{\pi M}} \]
Since \( \sqrt{3} > \sqrt{\frac{8}{\pi}} \), it follows that \( C_{rms} > C_{av} \), making the reason true as well.

6. **Checking the Explanation**:
However, we need to determine if the reason correctly explains the assertion. The assertion is about the ratio of speeds, while the reason simply states a comparison of their magnitudes. Thus, while both statements are true, the reason does not explain the assertion.

### Conclusion:
Both the assertion and the reason are true, but the reason is not the correct explanation of the assertion.

### Final Answer:
The correct option is: Both assertion and reason are true, but reason is not the correct explanation of assertion.

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