Energy of photon from rotational state with angular momentum quantum number l

[Vitani11]

Homework Statement

A certain molecule has a characteristic rotational energy of 8.81x10^-4 eV. What is the energy of the decay photon towards the state with angular momentum quantum number l?

Homework Equations

E = E_rot (L(L+1))

The Attempt at a Solution

Why would this not be 12 multiplied by the characteristic energy?

 

[Simon Bridge]

Is there a good reason to think that it would be? Shouldn't the answer depend on the angular momentum quantum number (not provided)?

Please demonstrate your reasoning...

 

[Vitani11]

I'm sorry the angular momentum quantum number was given as 3.

 

[Vitani11]

So everything is provided. My reasoning is that by using the equation to find the characteristic energy, then plugging in the numbers given, should give me the characteristic energy since I have all of the information.

 

[Simon Bridge]

You are given the characteristic energy, you are not asked to find it. You are asked to find the energy of the "decay photon".
If you have an equation that relates the characteristic energy to the energy of the decay photon, then it is numbers in numbers out.
What is the problem?

 

[Vitani11]

I've solved this now - but the problem was that it wasn't 12 times the characteristic energy. That is for a particle going towards the L =3 (or n =4) state from a lower state...since the photon is going towards the L = 3 state from a higher state (decaying implies from a higher state to a lower state) it is going from L = 4 to L=3 and so you had to do a difference in energies using L = 4 then L = 3. Anyway, thank you for the help.

 

[Simon Bridge]

I've solved this now - but the problem was that it wasn't 12 times the characteristic energy. That is for a particle going towards the L =3 (or n =4) state from a lower state

Is it the same photon energy for transition from any lower state?
Can there be an L=3 state for energy states other than n=4?

...since the photon is going towards the L = 3 state from a higher state (decaying implies from a higher state to a lower state) it is going from L = 4 to L=3 and so you had to do a difference in energies using L = 4 then L = 3.

But not from L=5 or L=6? What are you talking about?

You are not being clear. One of the purposes of these forums is to help people with scientific communication skills.

Basically, you did not provide the full problem statement or your reasoning - if you had, then the reason why you thought it should be 12x, and it was not, would have been clear. In future, please just write out the whole problem statement as you got it, then show your annotated working.

 

[Vitani11]

I'm sorry for the way I word things - I'm fresh in the physics major and I still have a lot to work on. I thought this reasoning was sound. I didn't think it would be the same photon energy for transition from any lower state, but is that what you are saying? Anyway, that was the exact problem statement verbatim I promise that. I wish I was given more information also. I had to go to a tutor to figure this out. Referring to the L= 5 and 6 state I am not referring to them because this problem only asked about from L = 4 to L = 3 which I agree was not so clear because it wasn't explicitly stated.

 

[Simon Bridge]

I am not saying your reasoning was not sound, just that you did not present it - not enough to know what you were talking about.
ie. you did not say which state was transitioned to or from. That would have an effect on the energy of the photon.
Initially you made no reference to state at all, then you only talked about the final state - not the initial one - and, even then, you just said "L=3" and not how this fits in with the problem statement.
Sure, if $L=3$ then $E_l = 12E_{rot}$ ... but what did that have to do with the problem? You didn't say.

I could have assumed you did not use initial state in your reasoning and corrected you accordingly - but would that have been correct? I cannot tell.
You cannot get good advise if you do not provide good information.
Don't just assume people know what you mean.

It is a standard in presenting homework problems to write out the entire problem as it is presented to you ... copy it out.
Did you do this? Is post #1 what you have written down in your homework problems?
There is a reason this is how you are asked to do things.

 

[Vitani11]

Yes, this was posted verbatim. The problem didn't tell me which state it was initially in. I blame the lon capa HW system. Anyway, thank you for the help.

 

[DrClaude]

I have to agree with @Simon Bridge on this. You say that you copied the problem verbatim, but already in the OP you consider $L=3$, which is additional information you had.

Next time, please give all the information you have, don't make helpers fish for it!

Glad your question was answered. Time to close the thread.