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

[glebovg]

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?