Re: Proof for atoms?

["John S. Denker" <jsd@MONMOUTH.COM>]

Savinainen Antti asked for:
> ... experiments which could provide convincing evidence for the existence of
> atoms without having initially decided that idea of atoms is used to analyze
> the data.

It depends on what you mean by "convincing" evidence and
"without having initially decided".

If the doubter is not willing even to entertain the hypothesis
of atoms, there's not much you can do to convince him.

So let's assume everybody is being reasonably scientific.  We
will not assume the existence of atoms, but we will entertain
the hypothesis and evaluate it relative to competing hypotheses.

A particularly incisive version of this question is to find not
only evidence of atoms, but also an estimate of their size.  I
once was challenged (over lunch) to do this, subject to the
constraint of not using any high-tech scientific equipment.  It
took me a while to come up with a good answer.

1) The best answer I could come up with is to compare the speed
of sound to the speed of smell.  The speed of sound has to do
with the typical velocity of air molecules, and is more-or-less
independent of the mean free path.  The rate of diffusion of a
small smelly molecule like ammonia depends on the velocity and
on the mean free path, which in turn depends on the scattering
cross section.  The math (random walk) is pretty easy to work
out, and the kids can do a simulation by tossing a coin and
moving a marker accordingly:  the marker moves short distances
in short times, but doesn't get very far unless you take a
verrry large number of steps.

If you do the experiment, take care to prevent convection.

2) When I was in high school we did an experiment to estimate the
size of molecules by putting some oleic acid on the surface of
water and measuring the size of the oil slick.  I didn't much
like the experiment, because we weren't told enough about what
oleic acid was.  A key part of the analysis involved assuming
that the oleic acid formed a _monolayer_ on the water, and it
wasn't at all obvious why it should do that (and why other
substances wouldn't).  I now understand how and why that works,
but it was pretty mysterious back then.  I was however impressed
by how big the oil slick was.  Atoms are pretty darn small!

3) The fact that the sky is blue is further evidence that the air
is not a homogeneous fluid.  The molecules of gas are distributed
pretty much at random, and this leads to random fluctuations in
the number of molecules in any small region.  Light scatters off
the density fluctuations.  Blue light is more strongly scattered.
If atoms were much smaller, the fluctuations would average out
better, so the fluid would be more uniform and the sky would be
black.  If atoms were much larger, the fluctuations would be larger
and there would be multiple scattering at all wavelengths, and
the sky would be grayish-white (like it is on overcast days).  An
overview of the physics involved can be found at
  http://mailgate.nau.edu/cgi-bin/wa?A2=ind0104&L=phys-l&P=R17793
More details can be found in Jackson's _Classical Electrodynamics_
section 9.7.  You might also want to read Einstein's "Theorie der
Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen
in der Nähe des kritischen Zustandes", Annalen der Physik, 33,
1910, pp. 1275-1298.  (Otherwise beware; there are lots and lots
of incorrect explanations floating around.  Anything that concentrates
on "fluctuations in a region of size lambda cubed" should be
distrusted.)

4) If you're allowed to use a microscope, you can observe
Brownian motion.  That gives you kT in terms of something
you can see.  Then kT and the speed of sound gives you the
mass of atoms.

5) A battery tells you that typical atomic energy scales are
on the order of a volt.  Spark-gap voltages tell you the
field necessary to develop an atomic-scale voltage across
a mean free path.

*) Et cetera.

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

No one of these by itself constitutes an absolute proof.  You
can always contrive alternative explanations.  But eventually
the weight of evidence accumulates.  The atomic hypothesis is
the simplest way to explain the data.