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## Homework Statement

Using specific heat data for a nitrogen molecule, estimate then vibrational frequency of the diatomic molecule

## Homework Equations

C= 3N_a k = 3R

## The Attempt at a Solution

unable to attempt a solution

- Thread starter bull0sees
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Using specific heat data for a nitrogen molecule, estimate then vibrational frequency of the diatomic molecule

C= 3N_a k = 3R

unable to attempt a solution

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thank you for your input shamone. I would also love to find out the answer

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- #5

Andrew Mason

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You could start by treating the diatomic molecule as two masses joined by a spring with a certain spring constant. (this may be correct only for small vibrations). You can express the frequency of vibration using the "spring constant", which is a function of the bond strength, and the mass of the N atom. The trick is to find the "spring constant" from the specific heat. I'll have to think about that one.## Homework Statement

Using specific heat data for a nitrogen molecule, estimate then vibrational frequency of the diatomic molecule

## Homework Equations

C= 3N_a k = 3R

## The Attempt at a Solution

unable to attempt a solution

AM

Last edited:

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Andrew Mason

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[tex]E_{vib} = (n + 1/2)h\nu[/tex]

At low energies (low temperature < 500K) the energy of vibration is [itex]h\nu/2[/itex] (n=0). The addition of thermal energy is not sufficient to allow many molecules to reach the next energy level (n=1) which is [itex]3h\nu/2[/itex] (ie the number of molecules in the Boltzmann distribution for that temperature with that amount of energy).

However, as T increases the number of molecules able to acquire additional vibrational energy ie. to jump from [itex]h\nu/2 \text{ to } 3h\nu/2[/itex] increases so the specific heat starts increasing. At about 6000 K the specific heat, Cv reaches 3.5R. This means that the addition of any amount of thermal energy adds vibrational energy to the molecules which, I think, means many of the higher n levels are excited.

That should help you figure out the frequency [itex]\nu[/itex]. From that you could figure out the force holding the atoms together, too.

AM

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