Why don't polyatomic gases rotate nor vibrate at low temperature?Because the energy available to them is less than that required to get them to rotate or vibrate.
Is vibrational energy also quantized?Yes.
QM is not important.Yes it is.
What's the minimum non-zero quantity of of rotational energy?It depends on the molecule.
For N2 I think it's about 10^-4 eV.
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