How many atoms are in the human head?

We can calculate the number of atoms in your head if we know the density and a constant called Avogadro's number. This is really just an estimate, but it's going to be a good one. The equation is fairly simple. The number of atoms of ANY substance in a volume is:

# of atoms = N * (density) * volume / (Molecular Weight).

N is a constant called Avogadro's number and its equal to 6.022*10^{23} atoms/mole. It can also be molecules per mole. In the above formula density times volume is just the mass. If you know how heavy something is or what its volume and density are you can easily do this.

Lets start with a simple problem. A liter of water is 1000 cubic centimeters. Water is easy because each cubic centimeter has 1 gram of mass. Water is made up of 2 hydrogen atoms and one oxygen atom. Hydrogen has an atomic weight of 1 and oxygen has an atomic weight of 16. The water has a molecular weight of 18. The liter of water has 1000 grams. The number of moles is 1000/18 = 55.556 moles. The number of molecules is therefore 6.022*10^{23} * 55.556 = 3.346*10^{25} molecules. The number of atoms is 3 times larger because each molecule has three atoms, so there are 1.0038*10^{26} atoms in a liter of water.

Now we know enough to answer your question. A typical human head weighs about 10 - 12 pounds. We are mostly made up of water. When you go swimming you probably noticed that almost everybody floats with just part of their head out of water. This observation will lead you to conclude that our density is very close to the density of water. Armed with all this we can estimate the number of atoms in your head. A pound is 454 grams so a 10 pound human head is 4,540 grams. If I assume that we are mostly water on the average because our average density is approximately that of water then I can use the above information on water to get the answer.

Moles per head = (4,540 grams) / (18 grams/mole) = 252.22 moles

Molecules per mole = 6.022*10^{23} * 252.22 moles = 1.519*10^{26} molecules

Atoms per head = 3 * molecules = 4.56*10^{26}

This is 456 trillion trillion atoms!

I'll conclude on a historical note. Avogadro was an Italian Physicist who first described the Avogadro constant as a hypothesis in 1811. He was trying to understand why in chemical reactions involving gases the observation that equal volumes of different gases had the same number of moles. This was found true even when the masses were very different. The idea that a mole of any substance has exactly the same number of atoms (or molecules) no matter what the substance is made of was explained by Avogadro and his name has stuck to his number ever since.

Author:

Paul Brindza, Experimental Hall A Design Leader (Other answers by Paul Brindza)

This page is maintained by Steve Gagnon.