Question

The number of degrees of freedom for monoatomic gas molecule is

• A. \(3 \)
• B. \(4 \)
• C. \(5 \)
• D. \(7 \)
• E. \(1 \)

Hint:

Monoatomic → only translation → 3 DOF.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The "degrees of freedom" of a system refer to the number of independent ways in which a particle or system can move, or more formally, the number of independent coordinates required to specify its configuration. For a gas molecule, this relates to translational, rotational, and vibrational motion.
Step 2: Detailed Explanation:
A monoatomic gas molecule (like Helium, Neon, or Argon) can be considered as a single point mass.
Translational Motion: It can move independently along the three perpendicular axes (x, y, and z). This gives it 3 translational degrees of freedom.
Rotational Motion: Since it's treated as a point mass, its moment of inertia about any axis passing through it is negligible. Therefore, its rotational kinetic energy is considered zero, and it has 0 rotational degrees of freedom.
Vibrational Motion: As a single atom, it cannot vibrate with respect to other atoms. So it has 0 vibrational degrees of freedom.
The total number of degrees of freedom is the sum of these, which is \(3 + 0 + 0 = 3\).
Step 3: Final Answer:
The number of degrees of freedom for a monoatomic gas molecule is 3.