Rayleigh Scattering

Lord Rayleigh calculated low energy elastic scattering of light from atoms using classical electromagnetism. If the energy of the scattered photon is much less than the energy needed to excite an atom, \bgroup\color{black}$\omega«\omega_{ji}$\egroup, then the cross section may be approximated.

...}'\cdot\vec{x} \vert i\rangle}
\right] \right\vert^2 \\

For the colorless gasses (like the ones in our atmosphere), the first excited state in the UV, so the scattering of visible light with be proportional to \bgroup\color{black}$\omega^4$\egroup, which explains why the sky is blue and sunsets are red. Atoms with intermediate states in the visible will appear to be colored due to the strong resonances in the scattering. Rayleigh got the same dependence from classical physics.

Jim Branson 2013-04-22