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Measuring N_A

I had the idea at the recent Theorynet meeting that we have 3
different ways to measure Avogadro's number using equipment that we've
been discussing:

1.  Use the election diffraction apparatus to measure the spacing of
atoms in a crystal.  Cube, multiply by some factor for crystal structure,
divided into the volume of a crystal of known weight.

2.  Use the proposed Milliken experiment to measure the charge on one
electron.  Divide into the total quantity of charge that it takes to
transport a known mass of material in an electrolytic cell.

3.  Consider that the heat of vaporization of water is the surface
tension times the area required to surround each atom by a surface.
This requires no advanced apparatus; I've heard the claim that it
could have been done by the Greeks if they'd thought of it.

Perhaps some brilliant student would like to do these 3 experiments
and compare the results.