According to the law of equipartition of energy, internal energy of an ideal gas at a given temperature, is equally distributed in translational and rotational kinetic energies.
Rotational kinetic energy of a monoatomic gas is zero.

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 solve the problem, we need to analyze the statements given in the question regarding the law of equipartition of energy and the properties of a monoatomic gas.

### Step-by-Step Solution:

1. **Understanding the Law of Equipartition of Energy**:
The law of equipartition of energy states that the internal energy of an ideal gas at a given temperature is distributed equally among all degrees of freedom. For a monoatomic gas, the degrees of freedom include translational motion only.

2. **Degrees of Freedom for Monoatomic Gas**:
- A monoatomic gas has 3 translational degrees of freedom (corresponding to motion along the x, y, and z axes).
- It has 0 rotational degrees of freedom because monoatomic gases consist of single atoms that do not rotate.

3. **Translational and Rotational Kinetic Energy**:
- The translational kinetic energy for a monoatomic gas can be expressed as \( KE_{trans} = \frac{3}{2} kT \), where \( k \) is the Boltzmann constant and \( T \) is the temperature.
- Since there are no rotational degrees of freedom for a monoatomic gas, the rotational kinetic energy \( KE_{rot} = 0 \).

4. **Conclusion on Internal Energy Distribution**:
- According to the law of equipartition, if there were rotational degrees of freedom, the internal energy would be equally distributed among translational and rotational kinetic energies.
- However, since the rotational kinetic energy for a monoatomic gas is zero, the internal energy is not equally distributed. It is solely in the translational kinetic energy.

5. **Evaluating the Statements**:
- The assertion states that the internal energy is equally distributed between translational and rotational kinetic energies. This is **false** for a monoatomic gas because the rotational kinetic energy is zero.
- The reason states that the rotational kinetic energy of a monoatomic gas is zero. This statement is **true**.

### Final Answer:
- The assertion is **false**, but the reason is **true**.