## Physics Questions People Ask Fermilab

You Wrote:

Hi my question is what is the number of atoms in the world and why don't scientist agree on one number for them.

Thank you.

Hi, the answer to your question by its very nature can not be terribly accurate.

However, when I pull down my copy of a college physics book, I find that it lists the mass of the earth as (6 x 10^24 kg). The mass of a proton or neutron is (1.67 x 10^-27 kg). Consequently, you can say to mediocre accuracy that the number of protons or neutrons in the earth is (mass earth)/(mass proton) = 3.6 x 10^51.

Now it gets a bit more complicated. Each proton has an associated electron, which I have ignored, as the mass of the electron is 1/2000 that of the proton. So now I can concentrate simply on the atomic nucleus.

If the earth were made entirely of a single material (say iron), then things are pretty easy. An iron nucleus contains 26 protons and 30 neutrons. Thus the mass of an iron nucleus is (56 x mass of a proton) = 9.4 x 10^-26 kg. And then the earth would have 6.4 x 10^49 iron atoms in it.

But different materials have different weights. For instance, we know that there is a lot of silicon, water, oxygen, etc. on Earth. In order to do the calculation better, you would need to know what fraction of the Earth's mass is in each material. I'm guessing that the fact that the different fractions of these elements are not incredibly well known. On the other hand, we know that it can't be too different than iron. Silicon is half the mass of iron, so if the earth were entirely silicon, there'd be twice as many atoms. I bet we can say that the number of atoms in the earth is something like 10^49-10^50.

Cheers...

Dr. FermiGuy

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