Imagine that you're an air molecule and an EM wave comes by, with a
frequency that's too low to excite your electrons into excited
states. Your electrons are pulled back and forth by the alternating
electric field of this wave, and your nuclei are pulled back and
forth in opposite directions. Both oscillate at the same frequency
as the wave itself. But now your electrons (and nuclei), being
accelerated charged particles, are going to emit their own EM
wave (dipole radiation). The rate at which they emit energy is
proportional to their acceleration squared (look up the Larmor
formula), and their acceleration, for an incident wave of a given
amplitude, is proportional to the square of the frequency
because their position is proportional to cos(omega t) and
acceleration is the second derivative of position. So the rate
at which your electrons emit energy is proportional to the
fourth power of the frequency of the wave. By energy conservation,
this energy must be removed from the incident wave. Hence we
have scattering of the incident wave into other directions,
at a rate that's proportional to the frequency to the fourth
power, or wavelength to the -4 power. That means that blue light
gets scattered much more efficiently than red light. The scattered
blue-rich light is the blue sky, and the unscattered red-rich light
is the red sunset.
I think I've now explained everything in pretty elementary terms
except the larmor formula, which says that for an accelerated
charged particle, the power radiated is proportional to the
acceleration squared. If you'd like to see an elementary derivation
of this fact, look in Purcell's E&M book, or download the materials
that I've posted at "http://physics.weber.edu/schroeder/mrr/MRR.html";.
It's hard to explain without a picture, but basically the idea is
that the greater the acceleration, the more abrupt the kink in the
electric field lines where the near field (which already knows
about the acceleration) joins the far field (which doesn't yet
know). The transverse (non-Coulomb) component of the field is
proportional to the acceleration, so the energy carried away
by the field is proportional to the square of the acceleration.