Re: IONS on metals/dielectrics

["Tim Folkerts" <tfolkert@bigcat.fhsu.edu>]

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.