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Topic: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule N2  (Read 17326 times)

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camariela

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Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule N2
« on: April 12, 2006, 11:22:42 PM »
Hello,
I'm confused about the formulas to use and combine to find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule (N2) in its first excited rotational state.

Thanks
camariela
« Last Edit: April 13, 2006, 12:38:29 AM by Mitch »
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Offline Mitch

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Re: Moment of Inertia
« Reply #1 on: April 13, 2006, 12:35:48 AM »
What's the equation for moment of inertia?
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camariela

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule
« Reply #2 on: April 13, 2006, 12:40:33 AM »
I = mr^2

i have the mass, but what do i use for r?
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Offline Mitch

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule N2
« Reply #3 on: April 13, 2006, 12:43:13 AM »
The radius of a Nitrogen atom I suppose.
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Offline Borek

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule N2
« Reply #4 on: April 13, 2006, 03:25:57 AM »
I would rather go for half a triple bond length (or even better for half a N2 length). Atomic radius is for free atom and is of no use here.
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Offline Mitch

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule N2
« Reply #5 on: April 13, 2006, 04:16:13 AM »
Quote from: Borek on April 13, 2006, 03:25:57 AM
I would rather go for half a triple bond length

I was thinking of rotation down the central axis. Which is the more meaningful?
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Offline Borek

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule N2
« Reply #6 on: April 13, 2006, 04:47:42 AM »
Not sure what you mean, but only A variant has any meaning. In B both masses (both nuclei to be precise) lie on the rotation axis and moment of inertia of the particle is zero.
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Offline pantone159

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule
« Reply #7 on: April 13, 2006, 02:37:49 PM »
Yeah, for the B base the only off-axis masses are the electrons and the fact that the nucleus isn't really a point.
Both of these would be some effort to calculcate.

For the A case, the N nuclei masses dominate the calculation, so you can ignore the above complications.
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Offline Borek

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule
« Reply #8 on: April 13, 2006, 02:51:39 PM »
Quote from: Mark Kness on April 13, 2006, 02:37:49 PM
Both of these would be some effort to calculcate.

Do you have any idea if anybody ever tried to? AFAIR (but QM and spectroscopy were never my favourite subjects) only A was always taken into account. Assuming electron cloud have some moment of inertia changes in rotational energy could be observable in spectroscopy (although probably for wavelengths comparable with astronomical unit :) ).
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Offline pantone159

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule
« Reply #9 on: April 13, 2006, 03:54:36 PM »
Quote from: Borek on April 13, 2006, 02:51:39 PM
Do you have any idea if anybody ever tried to?

Don't know.
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Offline plu

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule
« Reply #10 on: April 14, 2006, 02:17:23 PM »
To calculate the moment of inertia of a diatomic molecule, one must use the formula I = mR2, where m is the reduced mass of the molecule (m1m2/m1+m2) and R is the bond length.
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Offline Mitch

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule N2
« Reply #11 on: April 14, 2006, 04:12:02 PM »
You mean half the bond length?
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Offline plu

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule
« Reply #12 on: April 15, 2006, 09:38:17 AM »
Actually, no.  R is simply the whole bond length.
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Offline Mitch

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule N2
« Reply #13 on: April 15, 2006, 03:45:20 PM »
Good to know. :)
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Offline pantone159

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Re: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule
« Reply #14 on: April 17, 2006, 03:08:35 AM »
Quote from: plu on April 15, 2006, 09:38:17 AM
Actually, no.  R is simply the whole bond length.

Using the 'reduced mass' takes care of these halves, as well as counting both nuclei.
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