This is a fairly rough estimate, from classroom data. We took squares of aluminum
foil, measured the surface area and mass. By dividing the mass by a known density
value, we obtained the volume of aluminum foil in our sample. By dividing that by the
surface area, we found the thickness of the aluminum foil in cm. (The value was 2.86
*10^-3 cm.) The value converted to be 2.86*10^5 angstroms. Each aluminum atom is about
1.48 angstroms, so we can divide. Assuming that each aluminum atom is stacked directly
on another one (which they aren't, but we can't measure without making this
assumption), we come up with 1.93 * 10^5 atoms thick. There may be different types of
aluminum foil, but these results were fairly precise among our class's data, so I hope
it is at least somewhat helpful.
Answered by: Andy Clemons, High School Student

'Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.'