[Ciara]

Going through past paper questions and cant figure this out please help  Smiley
Explain the physical reason that the vibrational contribution to the heat capacity Cv is different from those of the translational and rotational contributions at ambient temperatures.
Why is the (Cv)vib not an integral or half integral multiple of R as it is for the translational and rotational components?

[tamim83]

It is because the energy of each vibrational level only depends linearly on the quantum number. 
For translation (particle in a box) and rotation (rigid rotor), the energy is quadratically dependent on the quantum number.