Assertion: Average kinetic energy per molecule of any ideal monoatomic gas is `3/2k_(B)T`
Reason: Aveerage kinetic energy depends only on temperature and is independent of the nature of the gas.

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.

Answer

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

### Step 1: Analyze the Assertion
The assertion states that the average kinetic energy per molecule of any ideal monoatomic gas is given by the formula:

\[ \text{Average Kinetic Energy} = \frac{3}{2} k_B T \]

where \( k_B \) is the Boltzmann constant and \( T \) is the absolute temperature.

This statement is true for ideal monoatomic gases because they have three degrees of freedom (corresponding to motion in three dimensions), and the average kinetic energy is derived from the kinetic theory of gases.

### Step 2: Analyze the Reason
The reason states that the average kinetic energy depends only on temperature and is independent of the nature of the gas.

This statement is partially true but misleading. While it is true that the average kinetic energy of an ideal gas depends on temperature, it also depends on the degrees of freedom, which vary with the type of gas (monoatomic, diatomic, etc.). For example, diatomic gases have additional degrees of freedom (rotational), which means their average kinetic energy is different from that of monoatomic gases at the same temperature.

### Step 3: Conclusion
- The assertion is **true**: The average kinetic energy for an ideal monoatomic gas is indeed \( \frac{3}{2} k_B T \).
- The reason is **false**: The average kinetic energy does depend on the nature of the gas due to the different degrees of freedom.

### Final Answer
- Assertion: True
- Reason: False