Degrees of Freedom Breakdown
* Translational: A molecule can move freely in three dimensions (x, y, z). So there are 3 translational degrees of freedom.
* Rotational: A linear molecule can rotate around two axes perpendicular to its axis of symmetry. So there are 2 rotational degrees of freedom.
* Vibrational: A triatomic linear molecule has three atoms. To find the number of vibrational degrees of freedom, we use the following formula:
Vibrational degrees of freedom = (Total number of atoms - number of translational degrees of freedom - number of rotational degrees of freedom)
In this case:
* Total atoms = 3
* Translational degrees of freedom = 3
* Rotational degrees of freedom = 2
Therefore, Vibrational degrees of freedom = 3 - 3 - 2 = -2
However, we cannot have negative degrees of freedom. This means there is a special case with linear molecules. Since the molecule is linear, one of the vibrational modes will be a "bending" mode. This bending mode is actually considered a rotational degree of freedom, meaning it can be combined with the other two rotations.
Therefore, a triatomic linear molecule actually has 4 vibrational degrees of freedom.
Total Degrees of Freedom:
Adding all the degrees of freedom together:
* Total = Translational + Rotational + Vibrational = 3 + 2 + 4 = 9
In summary, a triatomic linear molecule has 9 degrees of freedom: 3 translational, 2 rotational, and 4 vibrational.
