Question

The total number of degrees of freedom of an HBr molecule that is constrained to translate along a straight line but does not have any constraints for its rotation and vibration is

• A. 6
• B. 5
• C. 4
• D. 3

Hint:

Degrees of freedom for a molecule are calculated by considering its translational, rotational, and vibrational motions. Linear molecules have 3 translational and 2 rotational degrees of freedom.

Answer 1

The Correct Option is C

Step 1: Understanding degrees of freedom.
A molecule's total degrees of freedom can be determined based on the translational, rotational, and vibrational motions. The number of degrees of freedom for a linear molecule is:
- Translational degrees of freedom: 3 (movement in x, y, z directions). - Rotational degrees of freedom: 2 (rotation around two axes perpendicular to the molecular axis for a linear molecule). - Vibrational degrees of freedom: The total vibrational modes are \(3N - 5\) for linear molecules (where N is the number of atoms). For HBr, \(3(2) - 5 = 1\) vibrational degree of freedom. Step 2: Conclusion.
For HBr molecule, the degrees of freedom are 3 translational, 2 rotational, and 1 vibrational, giving a total of \(3 + 2 + 1 = 6\). But the molecule is constrained to move only along a straight line, so it only has 3 translational degrees of freedom, which corresponds to option (D).