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[Phys-L] Re: Sizes of atoms (was evidence for non-classical behavior)



Hi all-
I disagree strongly with Joe. One of the great surprises to me
bout atoms and nuclei is the extent to which we can think about them as
classical systems - but with appropriate modifications.
The first clue comes from looking at atomic wave functions and
noting that they involve deecreasing exponentials. I think of decaying
exponentials as quantum mechanics' replacement for classical sharp
boundaries.
The second clue comes from looking at the ratios (a word that
many of your students don't understand) of atomic "weights" to densities
of elemental substances. With a few marked exceptions, these are
surprisingly (to me) constant. This fact tells me that most atoms are
about the same "size".
Sizes of atomic and sub-atomic objects are typically measured in
scattering experiments, with sizes given, e.g., by diffraction peaks. For
electron scattering on noble gases see, e.g. (again), the graphs in
Purcell, et al., Phys Rev A 3 (1971) 508.
Rapid fall-off from a diffraction peak correspond to "abrupt"
termination of a sub-atomic object. That's what we observe in almost all
cases.
Regards,
Jack

On Wed, 6 Jul 2005, jbellina wrote:

Since these are not particles as we usually think of them, they don't
have a well defined size...it isn't that they occupy some space that
termininates abruptly. Size is a macroscopic concept that seems to
have little precise meaning microscopically.
As pointed out diffraction techniques give information about periodic
spacings, not size. Even something like scanning tunnelling microscopy
does not show atom size, if such a term were really meaningful, rather
it shows the spacial distribution of electron density.

Of course when one thinks that way, real objects don't terminate
abruptly, they all have some sort of roughness with hills and valleys,
but I think that is a different issue than the really microscopic one.

cheers,

joe
On Jul 6, 2005, at 2:14 PM, Ludwik Kowalski wrote:

On Wednesday, Jul 6, 2005, at 14:15 America/New_York, Bernard Cleyet
wrote:

. . . I must be msng. something here, as I thought booth LEED
and old ordinary X-ray diff. would do this. . . .

Is it not true that X-ray crystalography gives as distances between
scattering centers (atoms) and not sizes of atoms? To estimate sizes of
atoms one can assume that (in solids) they "essentially touch each
others."

The size of an atomic nucleus can be operationally defined in terms of
ranges of nuclear forces. Can the size of an atom be operationally
defined in the same way?

Ludwik Kowalski
Let the perfect not be the enemy of the good.


Joseph J. Bellina, Jr. Ph.D.
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556



--
"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley
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