The energy associated with each degree of freedom of a molecule

Options

A. 1/2RT
B. 1/2 KT
C. 3/2 RT
D. 3/2KT

Explanation

To solve the question regarding the energy associated with each degree of freedom of a molecule, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Degrees of Freedom**:
- Degrees of freedom refer to the number of independent ways in which a molecule can move or store energy. For a gas molecule, these can include translational, rotational, and vibrational motions.

2. **Recall the Equipartition Theorem**:
- The equipartition theorem states that energy is equally distributed among all degrees of freedom. According to this theorem, each degree of freedom contributes an amount of energy to the total energy of the system.

3. **Identify the Energy Contribution per Degree of Freedom**:
- According to the equipartition theorem, the energy associated with each degree of freedom is given by the formula:
\[ E = \frac{1}{2} kT \]
- Here, \( k \) is the Boltzmann constant, and \( T \) is the absolute temperature in Kelvin.

4. **Evaluate the Given Options**:
- The options provided are:
- (A) \(\frac{1}{2} RT\)
- (B) \(\frac{1}{2} kT\)
- (C) \(\frac{3}{2} RT\)
- (D) \(\frac{3}{2} kT\)
- From our understanding of the equipartition theorem, the correct expression for the energy associated with each degree of freedom is \(\frac{1}{2} kT\).

5. **Select the Correct Answer**:
- Based on the analysis, the correct answer is option (B) \(\frac{1}{2} kT\).

### Final Answer:
The energy associated with each degree of freedom of a molecule is \(\frac{1}{2} kT\).