How Do You Assign Rotational Quantum Numbers Using Wavenumbers?

[helpmeplease1]

Homework Statement

Hey people, I'm in dire need of help for this question.
Say you are given a list of wavenumbers (eg. 80, 90, 100, 110 cm^-1) for rotational transitions, and you are asked to assign rotational quantum numbers J to the transitions, how would you do that?

Homework Equations

What I thought of is to use the equation V(J+1<--J) =2B(J+1) - 4D(J+1)^3
Then divide by J+1 to make it a straight line plot. Then I know that the separation of the transitions is 2B = 10 cm^-1. Know, my tutor hinted us that we should start by guessing a value of J (ie. J=0, 1, 2, ...) and plot a graph until we got a straight line plot for a certain value of J, that would mean that transition corresponds to that value of J. I don't see what I need to do...

The Attempt at a Solution

 

[Jhero]

your approach is on the right track. To assign rotational quantum numbers (J) to the given wavenumbers, you would need to use the following equation:

V(J+1<--J) = 2B(J+1) - 4D(J+1)^3

This equation relates the wavenumber (V) to the rotational quantum number (J) for a given transition. To use this equation, you would first need to calculate the value of the rotational constant (B) and the centrifugal distortion constant (D) for the molecule in question. These values can often be found in reference books or online databases.

Once you have calculated the values of B and D, you can start by guessing a value of J (e.g. J=0, 1, 2, etc.) and using the equation to calculate the corresponding wavenumber for that transition. Plot these calculated wavenumbers against the guessed values of J on a graph. If the plot shows a straight line, then that value of J is likely the correct one for the given transition.

If the plot does not show a straight line, you can try a different value of J and repeat the process until you find a value that gives a straight line plot. This value of J would then correspond to the rotational quantum number for that transition.

In summary, to assign rotational quantum numbers to the given wavenumbers, you would need to use the equation relating wavenumber to J, calculate the values of B and D, and plot the calculated wavenumbers against guessed values of J until you find a straight line plot. This will give you the correct value of J for each transition.