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Re: IONS on metals/dielectrics



Tim makes a crucial point here. The first job of QM is to construct a
NEUTRAL atom/molecule/object by keeping equal and opposite charges APART!
This is the first defiance of Earnshaw. Only if this is first done is
there even at all a question of how an added, unbalanced charge can be
"stably" added.

It looks like in the very process of holding equal charges apart - and
thus producing a neutral, stable object - additional, as yet unoccupied,
bound states are created for the capture of additional charges
(electrons).

There will still remain the implications of Gauss' law which demand - on
the basis of a simple line of classical logic - that the net
electrostatic force of the universe on a charged conducting surface area
is non-zero and always OUTWARD. Is this experimentally always true?
What is it that we will give up - if anything?

-Bob

Bob Sciamanda
Physics, Edinboro Univ of PA (ret)
trebor@velocity.net
http://www.velocity.net/~trebor
-----Original Message-----
From: Tim Folkerts <tfolkert@bigcat.fhsu.edu>
To: phys-l@atlantis.uwf.edu <phys-l@atlantis.uwf.edu>
Date: Friday, October 09, 1998 6:05 PM
Subject: Re: IONS on metals/dielectrics


It seems to me we are looking at this whole question from the wrong end.
Its not a question of the extra electrons don't leave, its a question of
why
the whole thing doesn't collapse!


The most basic, stable system involving more than one electron is the
Helium atom. It occurs to me that its ground state is a pointed
illustration of how quantum mechanics can over-ride Maxwellian
repulsion
of like charges. In the (singlet) helium ground state the spatial
wave
functions of the two electrons are identical - they are "on top of
each
other" (they have opposite spins to satisfy Pauli).

-Bob


I would say that helium is an example of quantum mechanics over-riding
maxwellian ATTRACTION. The maxwellian system can continue to lower its
potential energy by getting smaller and smaller. It is only the QM
postulate of quantization of the orbitals that explains the lack of
complete collapse.

Consider the overly simplified system of three stationary electrons
around a
nucleus of two protons (assume that nuclear forces hold the protons
together
and ignore wave properties). Putting the electrons as far apart as
possible,
at the corners of an equilateral triangle, the potential energy is
-(attraction of electrons to the protons) + (mutual repulsion of
electrons). This actually leads to a significant attraction.

The point is (extrapolating to a metal) that even with a few extra
electrons
around, the attraction to the nuclei can be significantly greater than
the
repulsion of the other electrons. Only quantum mechanics keeps the
sphere
with these few extra electrons from collapsing, not flying apart.

In solid state physics terms, I would say that there are still plenty of
unoccupied states that have lower energy than a free electron.

Tim Folkerts





So classically, three electrons would be mutually attracted to a He
nucleus. In fact, I seem to find that even 4 electrons would be
mutually
attracted to a He nucleus. Six electrons (at the corners of a cube) are
definitely repelled.