Re: Orbitals as Orbits: The Return of Bohr

On 2005-04-17, Oz <Oz@xxxxxxxxxxxxxxxxxxxx> wrote:
> whopkins@xxxxxxxxxxx writes
>>Contrary to the impression one might gain from a textbook development
>>of quantum theory, the Bohr model was not only NOT superseded by the
>>later development of the Hydrogen atom from the Schroeding equation,
>>but in fact the latter development (when rendered in the Heisenberg
>>picture) CONSOLIDATED the earlier approach.
>
> There is one question that needs answering in this scenario.
>
> Its glibly stated that the orbiting electron would radiate energy away.
>
> However what would be the frequency of such radiation?
> What would the energy of such a photon be?

It radiates away in the continuum approximation, under the rules of
classical E&M. Under those rules, the E&M field isn't composed of
photons. The frequency of such radiation is just the frequency
of the orbit. Of course, if it's continuously radiating away, the
frequency constantly changes...

> I suspect that it would in fact be significantly greater than the energy
> available from the orbital, in which case no emission can ever occur.
> There simply would not be enough energy available to excite such a mode.

Well the energy available to the orbital depends on what other
available states the electron can drop down to. If we're dealing
with a continuous case, all orbital radii are allowed. An orbit
arbitrarily close to the nucleus is allowed, with an arbitrary low
energy value (and hence arbitrarily high allowed energy extraction from
a given orbit).

There aren't really any numbers to run in the classical, continuous
case.

In the quantum case, we already have a solution: there is a lowest
state, the ground state, which must be stable. Since the electron can't
drop down to a lower state, the most extracted energy is 0, and of
course that means no radiated photons. Further, in the lowest state,
the electron isn't exactly "moving around", so there isn't really any
acceleration radiation to explain. L = 0.

--
Aaron Denney
-><-

.

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