I forgot to add that I think there should be something else. There maybe 100 or so discrete thermally populated states from which the molecule can be excited. That's only 2 orders of magnitude instead of 9.
My best answer, which I didn't want to put in the original post to corrupt future responses, was the molecule has many possible ground states and the absorption cross section includes the probability the excitation electron happens to be in that vibrational and rotational state.
Is that what...
Why are absorption cross sections for atoms so much larger than that of molecules.
For example, the absorption cross section for the D2 line in Rubidium is ~1E-9 cm^2. Specifically, the cross section is basically σ~λ^2
The absorption cross sections for say, I2, is 9 orders of magnitude...
Thank you for the response.
Isn't that integral far more general though? I guess what I'm asking is, where in that integral do we specify 2 quadratic degrees of freedom?
The Equipartition Theorem states that each quadratic degree of freedom contributes 1/2 kT of energy. This can be derived for the translational degrees by integrating the average kinetic energy multiplied by the Maxwell velocity distribution:
\int_{-\infty }^{\infty } \frac{m v^2}{2}...
As I said, I can do the math.
The question is why is there an exact symmetry.
Is your answer that there is simply no reason for there not to be an exact symmetry?
An electromagnetic plane wave has an electric field and a magnetic field. Each component contributes equally to the energy density. Mathematically it is very straight forward to show this is true.
The question is, "Fundamentally, why is this true?" Again, I'm not looking for a derivation...