I used this as an in class activity but it may work better as a problem set for your class. I had the students read the pertinent chapters of the textbook which go through symmetry and molecular vibrations, including using both stretches and cartesian axes as bases. In class, I divided the students up into four groups. Each group did one of the problems for 30 minutes and during the last 20 minutes of class, they reported out their solution. The students had not seen the Hooke’s law in the textbook so I included it as part of the activity. I also included a handout on applying the group theory to molecular motions.
|a handout that describes the projection operator technique for molecular motion||111 KB|
|the in class activity||142.05 KB|
A student should be able to use the Cartesian axes as a basis for molecular motion
A student should be able to use a bond vector as a basis for a molecular vibration
A student should be able to, given an IR stretch, predict a stretch after an isotopic substitution
a set of character tables (C2v, C3v and C4v at a minimum) is needed for some of the groups
I did this as an in-class activity on 3/28/2016. I had 15 students, so groups of 3-4 on each of 4 problems. I used problem 2a, 3, and the two related LOs in class.
as this was done in class, I evaluated each group's presentation in real time as they presented it to the class. I used 2a and 3 in my class this year, and will likely use the others on an exam.
for 2a, the students did not have much trouble determining the fact that the 18O peaks were shifted by the correct amount, thus verifying the assignment. They, by inspection, were able to determine that the two peaks were in-phase and out-of-phase stretches (symmetric and antisymmetric).
for 3, at first the students struggled with what the problem was asking. Some of them wanted to calculate the force constants. I didn't followup to see if that made sense but it seems likely that the force constants would indicate stronger bond to the O than the S or Se. Of course, that would be true given the relative magnitudes of the stretches, and evaluating whether or not the Mo=O linkage is "stronger than expected" is not something that I would be able to predict. However, once I got them on track of predicting the Mo=S and Mo=Se stretches from the Mo=O (and the other combinations), they agreed it made sense. They weren't sure whether 10% agreement was "close" or not, which is fair. But certainly the oxo does a worse job predicting the others.