Assertion: The pressure of a fixed amount of an ideal gas is proportional to its temperature.
Reason: Frequency of collisions and their impact both increase in proportion of the square root of temperature.

Options

A. If both (`A`) and (`R`) are correct and (`R`) is the correct explanation of (`A`).
B. If both (`A`) and (`R`) are correct, but (`R`) is not the correct explanation of (`A`).
C. If (`A`) is correct, but (`R`) is incorrect.
D. If (`A`) is incorrect, but (`R`) is correct.

Explanation

To solve the assertion and reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that "The pressure of a fixed amount of an ideal gas is proportional to its temperature."

- According to the ideal gas law, \( PV = nRT \), where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles of gas
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

For a fixed amount of gas (constant \( n \)), if the volume \( V \) is also constant, we can rearrange the equation to show that:
\[ P \propto T \]
This means that the pressure is indeed proportional to the temperature when the amount of gas and volume are held constant.

### Step 2: Understanding the Reason
The reason states that "Frequency of collisions and their impact both increase in proportion to the square root of temperature."

- From the kinetic theory of gases, the root mean square (RMS) speed \( u_{rms} \) of gas molecules is given by:
\[ u_{rms} = \sqrt{\frac{3RT}{M}} \]
where \( M \) is the molar mass of the gas. This indicates that \( u_{rms} \) is proportional to the square root of temperature \( T \).

- The frequency of collisions is related to the speed of the gas molecules and the density of the gas. Thus, as the temperature increases, the speed of the molecules increases, leading to a higher frequency of collisions.

### Conclusion
- The assertion is **true** because pressure is proportional to temperature for a fixed amount of gas.
- The reason is also **true** because the frequency of collisions increases with the square root of temperature.

### Final Answer
Both the assertion and the reason are true, but the reason does not explain the assertion. Therefore, the correct answer is:
- Assertion: True
- Reason: True