Question

Total number of degrees of freedom of a rigid diatomic molecule is

• A. 3
• B. 6
• C. 5
• D. 2
• E. 7

Hint:

At normal temperatures, diatomic molecules (like $H_2, O_2, N_2$) are treated as rigid with $f=5$. At very high temperatures, 2 vibrational degrees are added, making $f=7$.

Answer 1

The Correct Option is C

Concept: The degree of freedom ($f$) is the number of independent ways a molecule can store energy through motion in space.
• Translational Degrees of Freedom: Movement of the molecule's center of mass along the three axes ($x, y, z$). Every gas molecule, regardless of its structure, has 3 translational degrees of freedom.
• Rotational Degrees of Freedom: Rotation of the molecule about independent axes.
• Rigid Constraint: In a "rigid" molecule, the distance between atoms is fixed, meaning no energy is spent on internal vibrations 71, 78].

Step 1: Evaluate the molecular geometry.
A diatomic molecule is linear. It possesses 3 translational degrees of freedom as it moves in 3D space.

Step 2: Calculate the rotational contribution.
For a linear molecule, rotation can occur about three axes. However, rotation about the inter-nuclear axis itself is negligible because the moment of inertia for point-mass atoms is effectively zero. Therefore, it only possesses 2 rotational degrees of freedom about the axes perpendicular to the bond.

Step 3: Determine the total for a rigid structure.
For a rigid molecule, vibrational modes are not counted. \[ f_{total} = f_{translational} + f_{rotational} = 3 + 2 = 5 \]