How many atoms?

[rickg]

Recently I read about the supercomputer simulation of the 1.3 million atoms of a 10 micron aerosol droplet containing a virus particle and I realized I don't have a good intuitive understanding about how small atoms are or how many make up common items.  Take for example, how many ink molecules make up a period on a page with the smallest font size? Or how many photons are being emitted from a typical computer screen pixel, How many pixels make up a single smallest white pixel against a black background?  You get the idea. 

To continue, my laptop screen is set to the highest resolution, 1366 X 768 is 345mm X 195 mm so apparently each pixel is about 250 um square.  Anyone have have any idea how many photons are being emitted per second?

[exchemist]

35 minutes ago, rickg said:

Recently I read about the supercomputer simulation of the 1.3 million atoms of a 10 micron aerosol droplet containing a virus particle and I realized I don't have a good intuitive understanding about how small atoms are or how many make up common items.  Take for example, how many ink molecules make up a period on a page with the smallest font size? Or how many photons are being emitted from a typical computer screen pixel, How many pixels make up a single smallest white pixel against a black background?  You get the idea. 

The key to questions like this one is Avogadro's Number, which is the number of carbon atoms in 12g of carbon, or, say, the number of molecules in 18g of water.  This number is roughly 6 x 10²³, (6 followed by 23 zeros, if you write it out longhand). One can use this to work through your aerosol droplet example. 

18g of water has a volume of 18cm³ (because the density of water is 1 in these units). There are a million (10⁶) cm³ in a cubic metre, so this becomes 1.8 x 10⁻⁵ m³. 

Let's pretend your aerosol droplet is a cube rather than pear-shaped, as the error in doing this is not great and it makes the calculation simpler.  A cube with a side of 10μ has a volume of (10⁻⁶)³  = 10⁻¹⁸ m³.    So it will contain   10⁻¹⁸/1.8 x 10⁻⁵  ~ 5.5 x 10⁻¹⁴ of Avogadro's number of molecules, so the number of molecules will be  5.5 x 10⁻¹⁴ x   6 x 10²³ which is about 3.3 x 10¹⁰. This is 33 billion molecules.  That's if I have not made any blunders in my arithmetic (which is easy to do with all these powers of ten, admittedly). Each molecule of water has 3 atoms in it: 2 of hydrogen and 1 of oxygen. So the number of atoms would be of the order of 100 billion.

I'm not sure where your 1.3 million comes from but it looks far too small to to me. 

You can do similar exercises for other small volumes of other materials, but you need to know the molecular weight (molar mass) of the material and its density. 

[rickg]

Exchemist, I checked your math, it looks correct but boy, it's hard to imagine 33 billion molecules of water in 10 micron droplet.

[exchemist]

11 hours ago, rickg said:

Exchemist, I checked your math, it looks correct but boy, it's hard to imagine 33 billion molecules of water in 10 micron droplet.

Yes indeed. An atom is of the order of 0.1 nanometres in radius.  A water molecule is about 0.3nm across. So in a cubic nanometre, which is 10⁻⁹ of a cubic micron, there are about 3 molecules on a side, i.e. 30 molecules in the cube. (So that checks out with my arithmetic above, phew!)    

Edited December 20, 2021 by exchemist