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I do not think there is an exact answer to your question, although there are some simplifying assumptions we can make to come up with an approximate number.

You may recall (or can look up in many places) that the approximate mass of the earth is 6E27 grams, and the mass of a nucleon (proton or neutron) is about 1.66E-24 grams. So if we divide the former number by the latter we get the result that the earth contains about 3.6E51 nucleons. So, the question is, how many nucleons are there in an "average molecule" of the earth?? That can't be answered precisely without knowing the exact composition of the earth, but we can make some educated approximations.

The average density of the earth is about 5.5 grams per cubic centimeter, or about 5.5 times as dense as water, and is more dense than rock at the surface of the earth. Consider also that aluminum has a density of about 2.7 grams per cubic centimeter, so let's assume that the "average earth molecule" has about twice as many nucleons as aluminum. That would take us roughly to an atomic weight of about 55, or 55 grams per mole. Recall that one "mole" of a substance contains about 6E23 molecules. If we take the mass of the earth and divide by the density of this "average earth molecule" (55 grams per mole) we obtain about 1.1E26 moles of the "average earth molecule", and multiplying that times 6E23 we obtain about 6.6E49 molecules.

For a quick check on our calculations, divide 3.6E51 nucleons by 6.6E49 molecules of our "average earth molecule", and we obtain 54.5 nucleons per molecule, which is pretty close to the atomic weight of our hypothetical "average earth molecule".

I hope this helps!!!

John Link, MadSci Physicist

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