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

I think one of the simplest effects demonstrating the atomic size i=
s the spread of a droplet on an adhesive substrate. A well known exam=
ple is the spread of an oil drop on the water surface. Generally, a c=
hain molecule of an organic material may stand vertically on the wate=
r surface, with its hydrophilic end submerged and hydrophobic one sti=
cking out. Assuming that a drop of such material will spread until it=
flattens down to the monolayer, we can find its thickness as the rat=
io of the initial volume to the area of the formed spot. The spot may=
be visible due to change of the optical properties of the surface co=
vered by it. It works for some organic materials with long molecules =
provided we have a large enough surface of still water available. Unf=
ortunately, I do not remember the source describing the details. But =
in principle, this method could be applied for estimation of the atom=
ic size as well in experiments with microdroplets put onto an appropr=
iate substrate. But this may be difficult to show as a lecture demo.=
=20
I also agree with Jack that another straightforward demonstration c=
omes from the scattering experiments. For estimation of the atomic si=
ze the scattering in the two oncoming low-energy atomic beams may be =
relevant. I disagree, however, that a sharply defined surface will re=
sult in the rapid fall-off in the corresponding diffraction peak. Qui=
te the contrary, in the Fraunhofer-type diffraction corresponding to =
the scattering experiments, the sharper the surface (all other things=
equal), the wider the peak, and vice versa. In a special case, when =
the surface fuzziness is Haussian, so is the diffraction peak, but th=
eir respective widths are, again, reciprocal. The nature of this rela=
tionship is the same as the indeterminacy relationship between the po=
sition and momentum in Quantum Mechanics.

Moses Fayngold,
NJIT=20


-----Original Message-----
=46rom:=09Forum for Physics Educators on behalf of Jack Uretsky
Sent:=09Fri 7/8/2005 1:55 PM
To:=09PHYS-L@LISTS.NAU.EDU
Cc:=09
Subject:=09Re: Sizes of atoms (was evidence for non-classical behavio=
r)


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 an=
d
noting that they involve deecreasing exponentials. I think of decayi=
ng
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 densit=
ies
of elemental substances. With a few marked exceptions, these are
surprisingly (to me) constant. This fact tells me that most atoms ar=
e
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 tha=
t
termininates abruptly. Size is a macroscopic concept that seems to
have little precise meaning microscopically.
As pointed out diffraction techniques give information about period=
ic
spacings, not size. Even something like scanning tunnelling micros=
copy
does not show atom size, if such a term were really meaningful, rat=
her
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 valle=
ys,
but I think that is a different issue than the really microscopic o=
ne.

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 Cle=
yet
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 betwe=
en
scattering centers (atoms) and not sizes of atoms? To estimate si=
zes of
atoms one can assume that (in solids) they "essentially touch eac=
h
others."

The size of an atomic nucleus can be operationally defined in ter=
ms of
ranges of nuclear forces. Can the size of an atom be operationall=
y
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 Val=
ley
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