STATEMENT-1 : The average translational kinetic energy per molecule of the gas per degree of freedom is 1/2 KT.
STATEMENT-2 : For every molecule there are three rotational degree of freedom.

Options

A. If both the statement are TRUE and STATEMENT-2 is the correct explanation of STATEMENT-1
B. If both the statement are TRUE but STATEMENT-2 is NOT the correct explanation of STATEMENT-1
C. If STATEMENT-1 is TRUE and STATEMENT-2 is FALSE
D. If STATEMENT-1 is FALSE and STATEMENT-2 is TRUE

Answer

To analyze the given statements, we will break down each statement and evaluate its validity based on the principles of kinetic theory and molecular motion.

### Step 1: Evaluate Statement 1
**Statement 1:** The average translational kinetic energy per molecule of the gas per degree of freedom is \( \frac{1}{2} kT \).

- According to the kinetic theory of gases, the average translational kinetic energy of a gas molecule is given by the formula:
\[ KE = \frac{3}{2} kT \]
where \( k \) is the Boltzmann constant and \( T \) is the absolute temperature in Kelvin.
- Since there are three translational degrees of freedom (movement in x, y, and z directions), the average kinetic energy per degree of freedom is:
\[ \text{Average KE per degree of freedom} = \frac{KE}{\text{Number of degrees of freedom}} = \frac{\frac{3}{2} kT}{3} = \frac{1}{2} kT \]
- Therefore, Statement 1 is **True**.

### Step 2: Evaluate Statement 2
**Statement 2:** For every molecule, there are three rotational degrees of freedom.

- The number of rotational degrees of freedom depends on the type of gas molecule:
- **Monoatomic gases** (e.g., Helium, Neon) have **0** rotational degrees of freedom because they are spherical and do not rotate.
- **Diatomic gases** (e.g., Oxygen, Nitrogen) have **2** rotational degrees of freedom (rotation about two axes perpendicular to the bond axis).
- **Linear triatomic gases** (e.g., Carbon Dioxide) also have **2** rotational degrees of freedom.
- **Non-linear triatomic gases** (e.g., Water) have **3** rotational degrees of freedom.
- Therefore, the statement that "for every molecule there are three rotational degrees of freedom" is **False**.

### Conclusion
- **Statement 1 is True.**
- **Statement 2 is False.**

### Final Answer
- Statement 1 is correct, while Statement 2 is incorrect.

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