Assertion : The root mean square velocity of an ideal gas at constant pressure varies with density as `1//sqrtd`.
Reason : Average kinetic energy of a gas is directly proportional to the absolute temperature.

Options

A. Assertion and reason both are correct statements and reason is correct explanation for assertion.
B. Assertion and reason both are correct statements but reason is not correct explanation for assertion.
C. Assertion is correct statement but reason is wrong statement.
D. Assertion is wrong statement but reason is correct statement.

Answer

To analyze the given assertion and reason, we will break down the concepts step by step.

### Step 1: Understanding the Assertion
The assertion states that the root mean square velocity (Vrms) of an ideal gas at constant pressure varies with density (d) as \( \frac{1}{\sqrt{d}} \).

**Explanation:**
- The formula for root mean square velocity is given by:
\[ V_{rms} = \sqrt{\frac{3RT}{M}} \]
where \( R \) is the universal gas constant, \( T \) is the absolute temperature, and \( M \) is the molar mass of the gas.
- At constant pressure, we can use the ideal gas law \( PV = nRT \) or \( P = \frac{nRT}{V} \).
- Rearranging gives us \( RT = PV \).
- Substituting this back into the Vrms equation leads us to express Vrms in terms of density:
\[ V_{rms} = \sqrt{\frac{3P}{\frac{M}{V}}} = \sqrt{\frac{3P}{d}} \]
where \( d = \frac{M}{V} \) is the density.
- This shows that \( V_{rms} \) varies as \( \frac{1}{\sqrt{d}} \).

### Step 2: Understanding the Reason
The reason states that the average kinetic energy of a gas is directly proportional to the absolute temperature.

**Explanation:**
- The average kinetic energy (KE) of a gas is given by:
\[ KE = \frac{3}{2}RT \]
- This indicates that the average kinetic energy is directly proportional to the absolute temperature \( T \).
- Therefore, this statement is also true.

### Step 3: Analyzing the Relationship
Now, we need to analyze the relationship between the assertion and the reason.

- Both the assertion and the reason are true statements.
- However, the reason does not provide a correct explanation for the assertion. The assertion is about the relationship between Vrms and density, while the reason discusses kinetic energy and temperature.

### Conclusion
- The assertion is correct.
- The reason is correct.
- However, the reason does not explain the assertion.

Thus, the answer to the question is:
**Assertion is correct, Reason is correct, but Reason is not the correct explanation for Assertion.**