According to the law of equipartition of energy, the energy associated with each degree of freedom is :

Options

A. `(1)/(3)K_(B)T`
B. `(1)/(2)K_(B)T`
C. `K_(B)T`
D. `(3)/(2)K_(B)T`

Explanation

To solve the question regarding the law of equipartition of energy, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Law of Equipartition of Energy**:
- The law states that in a system at thermal equilibrium, the energy is distributed equally among all degrees of freedom.

2. **Identify Degrees of Freedom**:
- Degrees of freedom refer to the independent ways in which a system can possess energy. For a monatomic gas, there are three translational degrees of freedom (movement in x, y, and z directions).

3. **Energy Contribution per Degree of Freedom**:
- According to the law, each degree of freedom contributes an amount of energy given by:
\[ \text{Energy per degree of freedom} = \frac{1}{2} k_B T \]
- Here, \( k_B \) is the Boltzmann constant and \( T \) is the absolute temperature in Kelvin.

4. **Conclusion**:
- Therefore, the energy associated with each degree of freedom is \( \frac{1}{2} k_B T \).

5. **Final Answer**:
- The correct answer to the question is:
\[ \frac{1}{2} k_B T \]