# Can molecules rotate on any axis?

In statistical physics, the rotation of molecules in a gas can be excited if the temperature is high enough. This rotation is excited in a quantum mechanical way. But is the axis of rotation also quantized? Could a molecule of $$N_2$$ rotate around any axis when excited?

That depends on the molecule and its symmetries. For example, a molecule of an ideal monoatomic gas cannot rotate because it is spherically symmetric. A typical diatomic gas molecule, like $$N_2$$ could rotate about two axes because it is axisymmetric so it cannot rotate about its axis of symmetry. A more complicated gas molecule, like water vapor, can rotate about all three axes since it is not symmetric at all.