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My professor said that the statement "different atoms are different because the atoms have different atomic number." is inconsistent with Dalton's atomic theory.
Well, start with your textbook definition of Dalton's atomic theory. (I don't have it handy.) Then see if your statement needs changing, or if Dalton's theory is wrong, or incomplete. However:As you have stated it, there's no difference between an atom of 12C and 14C?