What Temperatures Contribute to Air's Heat Capacity Due to Vibration?

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Homework Statement

Air is mostly composed of diatomic nitrogen, N₂. Assume that we can model the gas as an oscillator with an effective spring constant of 2.3 x 10³ N/m and and effective oscillating mass of half the atomic mass. For what temperatures should vibration contribute to the heat capacity of air?

Homework Equations

\omega=\sqrt{\frac{\kappa}{m}}
E=\hbar\omega
K=\frac{3}{2}k_{B}T

The Attempt at a Solution

\omega=\sqrt{\frac{\kappa}{m}}=1.67\times10^{15} rad/s
E=\hbar\omega=1.76\times10^{-19} J

I am not sure what to do next.

 

[glebovg]

Can anyone help?