[mrorganiclover]

Good day ladies and gentlemen

I'm currently studying chemistry and I have a spectroscopy module (which I'm finding rather tricky). I'm not sure if this is allowed on here, but I couldn't think of a better way to get help at this precise moment. So here goes....

Can you good people please help me understand how I get the answers to the following questions (I don't want the answers, more the concepts involved).

4. The energy levels of a rigid diatomic rotor are given by:

E = BJ(J+1).

(a)What are the rotational energies of the first 4 levels of this system?

(b)The selection rule governing rotational transitions is J = 1

Show that the rotational energy change associated with the excitation of a diatomic molecule from J J+1 is given by:- 2B(J+1) where J is the rotational quantum number of the lower level.

(c)What is the energy change associated with the first three rotational transitions?

Much thanks in advance

[Borek]

You have to show your attempts at solving the question to receive help. This is a forum policy.

[mrorganiclover]

Okay thanks for letting me know. The thing is, I have no idea where to start, thus my reasoning for the post.   Like I said previously, I dont actually want the answers just help with getting there....

[Borek]

You do know a little bit about quantum chemistry, and you do know what quantum numbers are?

What is B, what is J?

[mrorganiclover]

Thanks I have spent the day reading into it yes, but I can't actually find anything that relates directly to the questions. Or to put it better, I'm not seeing how the info relates due to my lack of understanding. I have a strong understanding of n, l, ml and ms but not B or J.

[Corribus]

n, l, and ml are the quantum numbers for the hydrogen atom.  J is a the usual designation for the quantum numbers of the simplest, rigid rotating object. The quantum numbers help to specify what the solutions to the Schrodinger equation are - that is, what the energy levels of the system are allowed to be. Quantum numbers are integer numbers (usually 1, 2, 3.... ) As J gets bigger, the energy gets bigger - the molecule in this case is spinning faster because it has more energy. B is just a constant that is specific to a given molecule, because different molecules have different moments of inertia (the way their mass is spread around the rotating axis).

You are given an energy formula that allows you to determine the energies as a function of the rotational constant, B, and the quantum numbers J. You are asked what the first four (lowest) energy levels are for a generic system (in terms of B). This should be easy for you to figure out now. Then we can worry about parts 2 and 3.

[mrorganiclover]

By jove I think I've got it (please let me know if I'm wrong).

E = BJ(J+1).

J=0 - E=0B
J=1 - E=2B
J=2 - E=6B
J=3 - E=12B

And so on...

[Corribus]

Ok, good. These are your allowed rotational states.

While it may seem like you should be able to go between any two states, in reality there are restrictions to which state you can go to from any given starting state. This "selection rule" for the simple rigid rotor is that ΔJ has to be ±1. This means you can go from J = 1 to J = 2 or J = 3 to J = 2, but not J = 1 to J = 3. What (B) is asking is to determine what the allowed transition energies are. If you always have to go from J to J + 1, then you can determine the allowed transition energies as ΔE(J :rarrow:J+1) = E(J+1) - E(J).  You should be able to solve this by using your equation E(J) = BJ(J+1).

From this, finding the first three allowed transitions should be trivial.

[mrorganiclover]

Just so you don't think I'm ignoring you Corribus, I'm going to wait until I have more time to study this subject. As I have an inorganic exam on Thursday which is currently taking up all of my time and I don't want to come to an answer on this without a solid understanding of the concepts involved.

Speak to you soon

Thanks

[Corribus]

No problem, especially since I pretty well botched this already by not paying attention.