For an ideal system at thermal equilibrium, the velocity distribution of the constituting particles will be governed by

Options

A. Gaussian distribution
B. Maxwell-Boltzmann distribution
C. Lorentzian distribution
D. Log-normal distribution

Explanation

To solve the question regarding the velocity distribution of particles in an ideal system at thermal equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**:
- In an ideal gas at thermal equilibrium, the distribution of velocities of the gas particles is not uniform. Instead, it follows a specific statistical distribution.

2. **Maxwell-Boltzmann Distribution**:
- The velocity distribution of particles in an ideal gas is described by the Maxwell-Boltzmann distribution. This distribution gives the probability of finding a particle with a certain velocity at a given temperature.

3. **Key Parameters**:
- The Maxwell-Boltzmann distribution can be characterized by three important velocities:
- **Most Probable Velocity (v_mp)**: The velocity at which the maximum number of particles is found.
- **Average Velocity (v_avg)**: The mean velocity of all particles.
- **Root Mean Square Velocity (v_rms)**: The square root of the average of the squares of the velocities.

4. **Formulas**:
- The formulas for these velocities are:
- Most Probable Velocity: \( v_{mp} = \sqrt{\frac{2RT}{M}} \)
- Average Velocity: \( v_{avg} = \sqrt{\frac{8RT}{\pi M}} \)
- Root Mean Square Velocity: \( v_{rms} = \sqrt{\frac{3RT}{M}} \)
- Where \( R \) is the universal gas constant, \( T \) is the absolute temperature, and \( M \) is the molar mass of the gas.

5. **Conclusion**:
- Therefore, the velocity distribution of the constituting particles in an ideal system at thermal equilibrium is governed by the Maxwell-Boltzmann distribution.

### Final Answer:
The velocity distribution of the constituting particles in an ideal system at thermal equilibrium is governed by the **Maxwell-Boltzmann distribution**.

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