Spacing/population of rotational states

• dscot
In summary, the conversation revolved around a two-part question involving calculating the spacing between the ground rotational state and j = 6 in a scenario where the bond length of OH was not provided. The conversation also discussed using the population ratio equation to find the energy spacing, but it was noted that the 308nm wavelength may not be relevant to the question. The conversation ultimately concluded with the acknowledgement that the question was difficult and potentially required further research or assistance.
dscot

Homework Statement

This is a two part question I can do about half of each but get a little lost when trying to finish.

I have written all the values below but just in case the full question is here (sorry about clarity) - http://screencast.com/t/jHQTMFnYOhp

λ = 308nm
T = 2000K

population of ground state (j=0) is 3.6*1010 cm

(i) So we are trying to calculate the spacing (in cm-1) between the ground rotational state and the j =6.

(ii) The population of the rotational state j =6

Homework Equations

(i)
εj = BJ(J+1)
gj = 2J+1

(ii)
Nj/Nd = gj exp( -εj / KT)

The Attempt at a Solution

(i)
gj = (2*6) + 1 = 13 but this is only degeneracy

can also try:

wave number = 1 /λ = 1/308*10-9 but this is only the wave number of j=0 and not he distance between j = 0 --> 6?(ii)
use:
Nj/Nd = gj exp( -εj / KT)

We know gj, K, T Just need εj but how as we don't have a value for B?

Sorry if this is confusing and please let me know if I can clear anything up!
Thanks
David

Last edited by a moderator:
Hello, dscot. If you know the bond length of OH then you can calculate B. Then you could get the energy spacing between J = 0 and J = 6.

Hi TSny =)

I think I understand what you are saying but it doesn't look like the bond length was provided in the question? I'm just guessing here but maybe a clue is that its an OH radical? I could try google but this was a past exam question so I think there must be a way to figure it out?

Thanks!

I can't see a way to get B without knowing the bond length.

I also don't see the relevance of the 308 nm wavelength. That seems to me to be the wavelength corresponding to some electronic excitation of OH. I don't see how to use it to help answer the question.

Maybe someone else can help.

Hi TSny,

This does seem to be a tricky one, I'll keep trying and hopefully someone else might know :)

Thanks for trying!
David

1. What is the spacing of rotational states?

The spacing of rotational states refers to the energy difference between adjacent rotational energy levels in a molecule. It is determined by the moment of inertia and the rotational constant of the molecule.

2. How is the spacing of rotational states calculated?

The spacing of rotational states can be calculated using the formula E = BJ(J+1), where E is the energy, B is the rotational constant, and J is the quantum number for rotational states.

3. Why is the spacing of rotational states important?

The spacing of rotational states is important because it provides information about the molecular structure and bonding of a molecule. It also affects the rotational spectra and can be used to identify and study different molecules.

4. How does the population of rotational states change with temperature?

As temperature increases, the population of higher energy rotational states increases. This is because at higher temperatures, molecules have more thermal energy and can overcome the energy barrier to reach higher rotational states.

5. Can the population of rotational states be controlled?

Yes, the population of rotational states can be controlled by changing the temperature or by using techniques such as laser cooling or optical pumping. These methods can selectively excite or de-excite certain rotational states, altering their population.

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