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

Options

A. `E=k_(B)T`
B. `E=(1)/(2)k_(B)T`
C. `E=3k_(B)T`
D. `E=(3)/(2)k_(B)T`

Answer

To solve the question regarding the energy associated with each degree of freedom according to 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 thermal equilibrium, the energy of a system is distributed equally among its degrees of freedom.

2. **Identify Degrees of Freedom**:
Each degree of freedom corresponds to a way in which a system can store energy. For a monatomic ideal gas, there are three translational degrees of freedom (movement in x, y, and z directions).

3. **Energy per Degree of Freedom**:
According to the law, the energy associated with each degree of freedom is given by:
\[ \text{Energy per degree of freedom} = \frac{1}{2} k_B T \]
where \( k_B \) is the Boltzmann constant and \( T \) is the absolute temperature.

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

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

---