Vibrating Charges Revisited
Let's step back from the Bohr model for a moment and look at an earlier model for the atom
don't worry, you've seen this before. Remember when you were playing around with
orbits, and I said you'd created a simplified
version of an atom?
So does the Rutherford model relate to the "charge on a spring" idea?
So if an electron is orbiting, you could say it's "vibrating" at a certain frequency, which
depends on the radius of its orbit. That makes sense. But when we discussed the "charge on a
spring," you said that if an electron vibrates at a particular frequency, it must produce
electromagnetic radiation at that same frequency. So if you had, say, a hydrogen atom with an
electron orbiting at some fixed radius, it would always be giving off radiationthat
can't be right.
Yes, Rutherford's picture of the atom has a couple of fundamental problems. First of all,
there's no apparent reason why an electron's orbit couldn't have just any old radius, and thus
any old frequency. That flatly contradicts the experimental evidence of
spectral lines.
Well, isn't that why Bohr came up with the idea of electrons' being restricted to certain
special orbits?
Yes, that's a partial solution. Let's assume that an electron's orbit, for some mysterious
reason, can only have certain discrete radii. Now suppose that an electron is happily
cruising along in one of these legal orbits. As you've said, the electron is "vibrating," so
it ought to be producing radiation. So, let's say our electron emits an electromagnetic wave
of the proper frequency. That's all well and good until you start to think about the
energy contained in that wave...
Waves have energy?
If the wave made that second charge move, then it must have carried energy from the + charge
to the  charge.
And meanwhile the electron would still be wiggling, so it would give off another wave (at a
different frequency), which would make its orbit decay even more...when would this
ever end?
It wouldn't. The electron would keep right on spiraling inward until it crashed into the
nucleus, at which point there would be no more atom. So if this classical picture were
correct, atoms would be highly unstable, and nothing made of atoms could possibly exist
for more than a fraction of a second. You and I couldn't be having this conversation if
it weren't for quantum mechanics.
Okay, so it sounds like you're saying that the Bohr model and the Rutherford model
actually have nothing to do with each other. Rutherford's classical picture was just
completely wrong, so Bohr had to come up with something entirely new.
Well...yes and no. This classical model is inaccurate, but there are cases in
which the correspondence principle applies. Just as Newtonian mechanics is a good
approximation to relativity at low velocities, Rutherford's model is a good approximation
to the Bohr model for closely packed energy levels.

