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"Atomic Mass" varies depending on the isotope. However, the AVERAGE atomic mass, (what's printed on most periodic tables) depends on the frequency with which different isotopes occur in nature. Therefore, if one element has a higher atomic mass than another, it doesn't mean that that element IS more massive, it just means that the more massive isotopes of that element occur more frequently in nature. It is a much more constant and reasonable method of organization to organize based on the number of protons in an atom of the element, since if the number of protons changes, you've got a different element.

Also, an atoms properties are largely dependent upon the number of protons it contains, for the reason stated in the last sentence above.

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