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



On 10/25/2006 05:35 PM, Karim Diff wrote:

Can the question "Is the electron in that region?" be answered with a definite "Yes" or "No" ?
(unless I misunderstand what "very likely to be no" means here). It seems to me the best we can
do is to say what the probability of finding the electron in that region is.

That's an interesting and tricky question. Some possible answers
include:

-- If you look closely enough, almost everything is a probability.
But sometimes the probability is so close to 0% or to 100% that
we can usefully speak in non-probabilistic terms.

-- In the nonrelativistic limit, you *can* know that an electron
is in a particular region of space, with probability approaching
100% as closely as you like. You give me an epsilon and I'll
give you a delta, such that the probability is (1-epsilon) or
better, for any epsilon greater than zero, no matter how small.

In particular, there are states that come as close as you want
to being position eigenstates. Verrry narrow Gaussians. If
you prepare the system in such a state, and come back a short
time later, the system will still be in the position where
you left it.

-- If we consider the more general case (not just nonrelativistic)
then to first order in alpha (the fine structure constant) you
can know where the electron is. So it is a decent approximation
to say we know where the electron is.

-- To higher order in alpha, there can be virtual electron/positron
pairs popping up here, there, and everywhere, so you can never
know exactly how many electrons you've got, let alone where they
are.

Therefore if you want to get really picky, you could answer
question 32 by saying the solid is "filled" with something
like 10^96 virtual particles whizzing around.

======================

A deeper problem with question 32 is that is a compound question,
with two clauses connected by "and".

If you keep reading, no matter what you think of the first clause,
the second clause is indefensible. The solidity of solids does
not depend "only" on electrical repulsion forces. There are also
electrical attraction forces ... as well as kinetic-energy terms
("degeneracy pressure") that are just as significant, i.e.
significant to leading order.

http://www.av8n.com/physics/degeneracy.htm

32) A solid object like a rock is almost entirely filled with empty space and only feels solid
due to electrical repulsion forces ... true or false?


BC wrote:

a case of being penalized for knowing too much.

Yeah, I reckon so.

It's little wonder that students tend to exhibit rote memorization
and not exhibit thinking or initiative or independence in school.

The rule for getting along in school is don't think about the
right answer; think about what the /expected/ answer is.