# Estimate vibrational frequency of N2 molecule

## Homework Statement

Experimental data for the heat capacity of N2 as a function of temperature are provided.

Estimate the frequency of vibration of the N2 molecule.

## Homework Equations

Energy of harmonic oscillator = (n+1/2)ħω

C=7/2kB

Average molecular energy = C*T

But this is an expression for the total energy of a molecule.
Presumably the amount of energy within the two vibrational modes is:

E=C*T

with

C=kB

## The Attempt at a Solution

All I can think to do is equate the two expressions for the energy of the oscillator:

kBT=(n+1/2)ħω

But I have no idea where to go now. In order to find frequency I would want to solve for ω, from which frequency can be trivially determined. However, how am I to know which integer value to use for n?

I am also very unsure as to my construction of the problem.

Any help/guidance greatly appreciated.

DrClaude
Mentor
Experimental data for the heat capacity of N2 as a function of temperature are provided.
What does this curve look like?

What does this curve look like?

T (Kelvin) 170 500 770 1170 1600 2000 2440
C/NkB 2.5 2.57 2.76 3.01 3.22 3.31 3.4

Apologies, not sure how to post a table of data.

DrClaude
Mentor
Clearly, the heat capacity is not constant, whereas you expect it to be of the form C = f kB T / 2, where f is the number of quadratic degrees of freedom. What could be happening here?

You access rotational energy as well? So you have more degrees of freedom? But this doesn't answer the question "However, how am I to know which integer value to use for n?'..........

DrClaude
Mentor
You access rotational energy as well? So you have more degrees of freedom? But this doesn't answer the question "However, how am I to know which integer value to use for n?'..........
n is not necessarily an integer. There can be situations where you get an effective number of dofs that is not a whole number.