Number of degrees of freedom in a molecule

In a molecule, the degrees of freedom represent the different ways in which the atoms can move. The total number of degrees of freedom can be calculated using the formula:

F = 3N - R

where F is the total number of degrees of freedom, N is the number of atoms in the molecule, and R is the number of constraints.

Given constraints

In the given scenario, the HBr molecule is constrained to translate along a straight line. This means that the molecule is free to move in a straight line without any rotation or vibration. Let's analyze the different types of motion in a molecule and determine the constraints for each.

Translation
Translation refers to the movement of the entire molecule as a whole. In this case, the molecule is constrained to move only along a straight line.

Rotation
Rotation refers to the movement of the molecule around its center of mass. In this scenario, there are no constraints on the rotation of the molecule.

Vibration
Vibration refers to the motion of atoms within a molecule. It involves stretching and bending of bonds. However, in this scenario, there are no constraints on the vibration of the HBr molecule.

Calculating the degrees of freedom

Since the molecule is constrained to translate along a straight line, there is only one constraint, which is the translation constraint. Therefore, we can substitute the values into the formula to calculate the total number of degrees of freedom.

N = 2 (H and Br atoms)
R = 1 (translation constraint)

F = 3(2) - 1
F = 6 - 1
F = 5

Therefore, the total number of degrees of freedom in the HBr molecule, which is constrained to translate along a straight line but doesn't have any constraint for rotation or vibration, is 5.