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### Topic: Birge Sponer  (Read 1125 times)

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#### summer

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##### Birge Sponer
« on: September 15, 2019, 08:37:40 AM »
Hi, I have to solve this exercise and I don't know how:
I have to calculate the anharmonicity constant from the slope m of the line

#### Corribus

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##### Re: Birge Sponer
« Reply #1 on: September 16, 2019, 10:04:02 AM »
Well why don't you start with what you DO know, because to receive help here you have to show some effort that you have expended to solve the problem.

For example, how do you think the anharmonicity constant relates to the plot?

Also, have you been given any additional information, or were you just thrown a plot with some points on it?
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

#### summer

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##### Re: Birge Sponer
« Reply #2 on: September 16, 2019, 11:06:07 AM »
Well why don't you start with what you DO know, because to receive help here you have to show some effort that you have expended to solve the problem.

For example, how do you think the anharmonicity constant relates to the plot?

Also, have you been given any additional information, or were you just thrown a plot with some points on it?

I tried to apply the Birge-Sponer formula
Xe=-(S/2*vo)
I have m, that's s and different wavenumbers (do I have to calculate them with everyone or do I have to use ONE?)

#### Corribus

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##### Re: Birge Sponer
« Reply #3 on: September 16, 2019, 01:13:41 PM »
First,  can you think of how the slope should change as a function of increasing anharmonicity?
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

#### summer

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##### Re: Birge Sponer
« Reply #4 on: September 16, 2019, 03:29:10 PM »
First,  can you think of how the slope should change as a function of increasing anharmonicity?

The function gets steeper

#### Corribus

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##### Re: Birge Sponer
« Reply #5 on: September 16, 2019, 04:07:42 PM »
Right, good.

To solve quantitatively, start with the energy levels, Ev, of the Morse potential:

$$E(\nu)=(\nu+\frac{1}{2})\tilde{\nu}-(\nu+\frac{1}{2})^2\chi_e\tilde{\nu}$$

The Birge Sponer plot is a plot of ΔE(ν+1 ν) as a function of ν+1. So using the expression above, you should be able to determine an expression for ΔE in terms of the various parameters. (Hint: put in ν+1 for ν in the above expression, and then subtract the one from the other to get ΔE). From this expression, you can use the slope of the B-S plot to determine χe and etc.

If you are using Atkins, this is solved for you, but it's a quick and good exercise to show yourself. (Atkins uses G instead of E, at least my version does... but G becomes confusing with Gibbs energy so I don't really like that.)
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

#### summer

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##### Re: Birge Sponer
« Reply #6 on: September 16, 2019, 04:18:09 PM »
I found this on my book, how should i apply the formula? I don't have v and De
« Last Edit: September 16, 2019, 04:34:39 PM by summer »

#### Corribus

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##### Re: Birge Sponer
« Reply #7 on: September 16, 2019, 05:24:01 PM »
I gave you the solution in my hint. You need to convert that first expression into one for ΔE (or ΔG, using your expression). The energy gaps are given by v+1 to v.

So find an expression for G(v) and G(v+1), and subtract one from the other to get ΔG(v+1 v). This is the origin of the Birge Sponer plot. Then you should be able to see what slope and intercepts are equal to.

What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman