Assertion : The molecules of a monatomic gas has three degrees freedom.
Reason : The molecules of a diatomic gas has five degrees of freedom.

Options

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

Explanation

To analyze the assertion and reason provided in the question, we will break down the concepts of degrees of freedom for monatomic and diatomic gases step by step.

### Step 1: Understanding Degrees of Freedom
Degrees of freedom refer to the number of independent ways in which a system can move. For gas molecules, this includes translational, rotational, and vibrational motions.

### Step 2: Degrees of Freedom for Monatomic Gas
Monatomic gases consist of single atoms (e.g., helium, neon). The only motion they can exhibit is translational motion.

- **Translational Motion**: In three-dimensional space, a monatomic gas can move in three directions: along the x-axis, y-axis, and z-axis.
- Therefore, the total degrees of freedom for a monatomic gas is **3** (only translational).

### Step 3: Degrees of Freedom for Diatomic Gas
Diatomic gases consist of two atoms bonded together (e.g., oxygen O₂, nitrogen N₂). These molecules can exhibit both translational and rotational motions.

- **Translational Motion**: Like monatomic gases, diatomic gases can also move in three dimensions, contributing **3 degrees of freedom**.
- **Rotational Motion**: Diatomic molecules can rotate about two axes perpendicular to the bond between the two atoms. This contributes an additional **2 degrees of freedom**.
- Therefore, the total degrees of freedom for a diatomic gas is **3 (translational) + 2 (rotational) = 5**.

### Step 4: Evaluating the Assertion and Reason
- **Assertion**: "The molecules of a monatomic gas have three degrees of freedom." This statement is **correct**.
- **Reason**: "The molecules of a diatomic gas have five degrees of freedom." This statement is also **correct**.

### Step 5: Conclusion
Both the assertion and reason are correct. However, the reason does not provide a direct explanation for the assertion. Therefore, while both statements are true, the relationship between them does not hold.

### Final Answer
- Assertion: True
- Reason: True
- Conclusion: Both are correct, but the reason does not explain the assertion.

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