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



To make the debates more constructive: some of the discussed substan=
ces whose molecules have strong affinity to water, when put on the st=
ill water surface, will tend to spread around down to monolayer. The =
monolayer must eventually form because the corresponding state will h=
ave the lowest energy. But in this case, as I see things now, by the =
same token the monolayer itself may not retain its continuity. Whethe=
r this is true or not, can be verified experimentally, e.g., by check=
ing the optical properties of the formed surface.=20
Conceptually, a few important points that emerged in the discussion =
and which I initially overlooked, are:

1. Under discussed conditions, how long it takes for a film (or, bett=
er still, for the initial droplet) to thin down to the monolayer?=
=20
2. If it is never true that a continuous monolayer will form, then wh=
y does the spreading force stop short of forming it, and what is the =
factor that stops it from completing its action?
3. In this case the resulting final thickness of the formed film must=
correspond to the lowest free energy of the system. Accordingly, the=
re has to be a thermodynamic condition determining the final thicknes=
s as a function of the initial size, chemical compound, temperature, =
etc.=20
4. In the "phase space" of parameters determining the final thickness=
, is there a region corresponding to the monolayer-thickness?
5. If the answer to 4. is yes, then can the monolayer itself retain i=
ts continuity? If the answer to this is yes, too, then the question 1=
. reiterates.

I think these questions, even if they appear to depart from the ori=
ginal problem of the atomic size, are all interesting in their own ri=
ght, and the answers may critically depend on specific molecular char=
acteristics of the systems. I personally never saw them discussed in =
any book or paper, although there probably must be the relevant sourc=
es.

Moses Fayngold,
NJIT


-----Original Message-----
=46rom:=09Forum for Physics Educators on behalf of John Denker
Sent:=09Sat 7/9/2005 12:47 PM
To:=09PHYS-L@LISTS.NAU.EDU
Cc:=09
Subject:=09Re: Sizes of atoms (was evidence for non-classical behavio=
r)


Referring to ye olde oleic acid demo, on 07/09/05 10:10,
Fayngold, Moses wrote:

I think [it] provides with the most straightforward
and convincing demonstration for the classroom (at least for
estimation the length of a chain molecule.)

I did this experiment when I was in high school, and
found it less than entirely convincing. Here are just
some of the questions that my teacher couldn't answer:

1) What is lycopodium powder? Why are we using such an
unfamiliar substance? Why not some more-familiar powder?
2) For that matter, most high-schoolers aren't familiar
with oleic acid, either. Given that we are dealing
with *two* unfamiliar substances, how do we know the
behavior we observe tells us the size of oleic acid
molecules ... as opposed to telling us something about
lycopodium molecules? We're taking a lot on faith, here.
If obscure, peculiar substances are required, it makes
me suspect that the result is not robust, not reliable.
3) You say the oleic acid molecules are long and skinny,
and stand upright on the surface. How do you know? If
they were to lay down on the surface, how big would the
resulting systematic error be? A factor of ten? More?
4) You say the oleic acid forms a monolayer. How do you
know? There are molecules with rather similar structure
that form thicker layers. Salad oil, for instance.
5) You say the oleic acid molecules congregate densely,
side by side. How do you know? How do you know they
don't spread out and form a 2D gas, with space between
the molecules? The lycopodium powder spreads out.
6) You say the oleic acid doesn't dissolve in water. How
do you know? There are molecules with verrry similar
structure that do dissolve. Soaps and detergents, for
example.
7) What role does surface tension play in all this?
8) Does the water have to be pure? How pure? How do
you know?
9) If you answered any of the previous questions by
saying that we know the structure of oleic acid from
Xray crystallography or mass spectrometry ... then
what is the point of the experiment? Why not just
accept the Xray or mass-spec determination of the
size of atoms and be done with it?

I'm not saying those questions cannot be answered, but
I am saying they need to be answered ... and this makes
the lesson far from easy and far from straightforward.

The cited reference
http://www.stkate.edu/physics/phys100/MoleculeSize.html
states that oil in general will spread out until it is one
monolayer thick ... which is almost *never* true.
(Even when I was in HS I knew this wasn't true; you
can tell by looking at the coloful Newton rings that oil
thickness is on the order of micrometers, not nanometers.)
I don't entirely subscribe to the rule "falsus in uno,
falsus in omnibus" ... but garbage like this certainly
makes students wonder whether the whole oleic acid demo
is a swindle.

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

By way of comparison, the kinetic theory approach (using
viscosity and/or diffusion constants) is no walk in the
park, either. You would have to lay the groundwork:
+ probability
=3D=3D> random walk
+ mean free path
=3D=3D> diffusion
=3D=3D> viscosity

Alas, approximately none of that is found in the typical HS
intro physics syllabus. One could argue that it would be
"nice" to cover such things, but the syllabus is overcrowded
already.

Still, I like this approach better than the oleic acid
approach, because the groundwork steps needed here are
more generally useful than the groundwork required to
make the oleic acid convincing.

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

As another way of skinning this cat, note that if you know
the charge on the electron (=E0 la Millikan, just barely doable
in a HS class) then you can get kT (as in eV/kT) from the
I/V characteristic of a diode (measure it -- easy!) and then
get the mass of nitrogen from the speed of sound (dimensional
analysis -- easy!).

The background needed here is particularly nice and broadly
useful.

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D

If nothing else, the fact that this is a hard problem sheds
some useful light on a history-of-science issue. Some people
say
"Einstein, atoms, big deal. People have known about atoms
since the time of Democritus (2400 years ago). People in
1905 knew, or should have known, how big atoms are."
Well, that's just not right. The work on kinetic theory circa
1900 (Boltzmann, Einstein) *was* a big deal.

I'm pretty sure the Einstein relation (connecting diffusion
constant to mobility) was not known to Democritus.
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