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### Topic: Find the moment of inertia and the energy (in kJ/mol) of a nitrogen molecule N2  (Read 18207 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 »

#### 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?

#### 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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#### 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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#### 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 »
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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#### 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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#### 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.

#### 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 »
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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#### 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 »
Do you have any idea if anybody ever tried to?

Don't know.

#### 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.

#### 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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#### 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.

#### 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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#### 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 »
Actually, no.  R is simply the whole bond length.

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