[Phys-l] "filling" the space in an atom

[John Denker <jsd@av8n.com>]

On 10/25/2006 03:16 PM, Roger Haar wrote:
>   My reasoning is that the electrons are not 
> localized, thus electrons "fill" the space in an atom.

The question is ill-posed.  It is tempting to say the question
is unanswerable, but in fact it is just the opposite:  the
question has an irreducible multiplicity of answers.

This has to do with a fundamental feature of our quantum-mechanical
world, namely that the answer you get depends on the details of how
you ask the question.  If you ask whether the electron is in the 1s
orbital, then you might get the answer, yes, it is in the 1s orbital.
If instead you ask for the position of the electron, you will get
some information about the position of the electron.  You cannot,
however, answer both questions at the same time.

As to delocalization in particular, if you ask whether the electron
in a hydrogen atom is "a little bit here" *and* "a little bit there"
at any particular time, the answer is absolutely no.

   This is an entirely nontrivial result, because it is directly
   connected to the electrostatic self-energy.  One part of the
   "electron cloud" does not repel other parts.  It's the same
   electron after all, and it cannot repel itself.

Also, if you pick any particular small region within the atom, and
ask whether the electron is in that region, the answer is very,
very likely to be no.  If there are N such regions, N-1 of them
will be empty at any given time.

Bottom line:  depending on details of how you ask the question, it
is usually not safe to conclude that the electron "fills" the space
in the atom.