What is the degree of freedom in case of a monoatomic gas?

Options

A. 1
B. 3
C. 5
D. None of these

Explanation

To determine the degree of freedom for a monoatomic gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Degrees of Freedom**:
The degree of freedom in a physical system refers to the number of independent ways in which the system can store energy. For gases, this typically relates to the motion of gas molecules.

2. **Identifying the Type of Gas**:
We are dealing with a monoatomic gas, which means that each gas molecule consists of a single atom. Examples of monoatomic gases include noble gases like helium (He), neon (Ne), and argon (Ar).

3. **Translational Motion**:
Monoatomic gas molecules can move in three-dimensional space. This motion can be described in terms of three axes: x, y, and z. Each axis represents a direction in which the molecule can move.

4. **Kinetic Energy Contribution**:
The kinetic energy of a monoatomic gas molecule can be expressed as:
\[ KE = \frac{1}{2} m V_x^2 + \frac{1}{2} m V_y^2 + \frac{1}{2} m V_z^2 \]
where \( m \) is the mass of the gas molecule and \( V_x, V_y, V_z \) are the velocities along the respective axes.

5. **Counting Degrees of Freedom**:
Since the gas molecule can move independently along each of the three axes, we conclude that it has three degrees of freedom corresponding to its translational motion.

6. **Conclusion**:
Therefore, for a monoatomic gas, the total degrees of freedom is 3.

### Final Answer:
The degree of freedom in case of a monoatomic gas is **3**.

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