About the smallest thing I can think of in my house is baby powder. Just how many molecules are in a little teeny tiny fleck of baby powder?
Million?
Billion?
Trillion?
I want to get a sense of scale.
I doesn’t answer your question exectly, but this should give you an idea (Talc is down there somewhere).
Talcum powder is Mg(3)Si(4)O(10)OH(2) and has a molecular weight of 379.27g.
My bottle of baby powder is 22oz =624g.
If I took 1/1000th of that bottle (should be easy) and then took 1/1000th of that (kinda hard) I would have 0.000624g.
This would contain 990,000,000,000,000,000 molecules (give or take a couple).
I don’t know how much a fleck of baby powder weighs, so I can’t figure that one out.
I can figure out how many molecules are in a drop of water though.
Let’s say that 20 drops = 1 teaspoon
1 teaspoon = 5 grams
molecular weight of water is 18 Atomic mass units (AMU)
Avogadro says that 6*10^23 molecules of water weighs 18 grams, so
1 drop * (1 tsp/20drops) * (5 gr/1 tsp) * (6*10^23/18 gr) = 8.333 * 10^21 molecules of water
That’s 8,333,333,333,333,333,333,333 molecules
We need a few numbers:
talc is Mg3Si4O10(OH)2 or thereabouts. It’s molecular weight is ~378.
The density of soapstone (talc) is 2.6-2.8 gm/cc http://www.tesarta.com/www/resources/library/weights.html
A grain of table salt is about 100 microns. A grain of talcum powder is 10 microns. The average human cannot see anything smaller than a 40 micron particle. A red blood cell is ~ 8 microns in diameter.
http://www.jlhermon.com/filtration.htm
http://www.webcom.com/~bi/particle-size.htm
So what you are calling a tiny fleck of baby powder is probably really a clump of 50 or 100 flecks of baby powder. The single flecks are too small to see.
A spherical 10 micron speck would have a volume of 5.2e-10 cubic cm, and a mass of about 1.4 nanograms.
A 40 micron, visible, speck would have a volume of 3.4e-8 cubic cm, and a mass of about 92 nanograms.
Converting mass to moles, and moles to molecules: (1.4e-9/378 X 6.02e23)
The 10 micron spec contains about 2.2 trillion molecules of talc. The larger 40 micron speck contains about 146 trillion molecules.
Some baby powder is cornstarch instead of talc. Cornstarch “feels” finer, but is it actualy smaller?
slight technicality. Talc does not exist as discrete molecules. Rather it is a layered structure consisting of infinitely linked chains and sheets of atoms. In theory, one speck of talc could contain one “molecule”, though that is stretching the definition of molecule.
oh and heres a link to the structure of talc with pictures if anyone might be remotely interested
http://mineral.gly.bris.ac.uk/Mineralogy/clayminerals/clayminerals.html
According to a random web page I found with Google:
So a grain of talcum powder is about 10^-9 cubic centimeters and should weigh roughly 10^-9 grams. That would have roughly 10^10 molecules, or 10 trillion. The smallest visible particle at 40 microns will have almost 100 times that. (I don’t even remember what comes after trillion…) Either case, zigaratten’s number is at least 3 orders of magnitude off.
I’m sure you can imagine something smaller: smoke. Those particles are only a few microns, some smaller. Of course you can’t see individual particles, but you can see how a collection of them behaves. Incidentally, at least one early astronomical paper talked about “interstellar smoke” which is a much more appropriate description than “dust.”