Degrees of freedom of a monatomic gas due to its rotational motion will be

Options

A. 3
B. 5
C. 0
D. 6

Answer

To determine the degrees of freedom of a monatomic gas due to its rotational motion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Monatomic Gases**: A monatomic gas consists of single atoms, such as noble gases (e.g., helium, neon). Each atom is treated as a point mass.

2. **Degrees of Freedom Concept**: The degrees of freedom of a system refer to the number of independent ways in which the system can move or store energy. For gases, these can be translational, rotational, and vibrational.

3. **Translational Motion**: Monatomic gases have three degrees of freedom due to translational motion. This means they can move in three-dimensional space (x, y, and z directions).

4. **Rotational Motion**: For rotational motion, we consider how the molecules can rotate around their axes. However, since a monatomic gas consists of single atoms, they do not have a structure that allows for rotation in the same way that diatomic or polyatomic molecules do.

5. **Inertia Consideration**: The moment of inertia for a single atom about any axis is effectively zero because it has no shape or size that contributes to rotational inertia. Therefore, it cannot rotate in a meaningful way.

6. **Conclusion**: Since a monatomic gas has no rotational degrees of freedom, the degrees of freedom due to rotational motion is zero.

### Final Answer:
The degrees of freedom of a monatomic gas due to its rotational motion will be **0**.

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