Question

The number of rotational degrees of freedom of a monatomic molecule is:

• A. 2
• B. 0
• C. 3
• D. 1

Hint:

For monatomic molecules, the degrees of freedom are only translational (3 degrees), and they do not exhibit rotational or vibrational degrees of freedom.

Answer 1

The Correct Option is B

Monatomic molecules (e.g., helium, neon) only have translational degrees of freedom. They do not have rotational degrees of freedom because they are spherical and cannot rotate around their center of mass in the way that non-spherical molecules (like diatomic molecules) can. Hence, the number of rotational degrees of freedom for a monatomic molecule is \( \boxed{0} \).

Answer 2

Step 1: Understanding degrees of freedom
Degrees of freedom refer to the number of independent ways in which a molecule can move or rotate.

Step 2: Types of molecules
- Monatomic molecules consist of a single atom.
- Diatomic and polyatomic molecules consist of two or more atoms.

Step 3: Translational and rotational motion
- Monatomic molecules have 3 translational degrees of freedom (movement along x, y, z axes).
- For rotational degrees of freedom:
    • Diatomic molecules have 2 rotational degrees of freedom.
    • Polyatomic molecules have 3 rotational degrees of freedom.

Step 4: Rotational degrees of freedom of monatomic molecules
Since a monatomic molecule is a single point mass, it cannot rotate about its own axis meaningfully.
Therefore, the number of rotational degrees of freedom for a monatomic molecule is 0.

Step 5: Conclusion
Monatomic molecules have 0 rotational degrees of freedom.