There are a few things I would like to comment on here.
When you look at the periodic table, what is given is the molar mass of the atoms, which includes relative isotopic abundance. Take hydrogen, for instance. You will find that the number is 1.007 97 g/mol. That means that if you collect 1/2 mole of hydrogen gas (H2), which is the natural form for that element, such that you have a total of 1 mole of H atoms, that sample is going to have a mass of 1.007 97 g.
But if you divide that mass by Avogadro's number, you get 1.67377×10-24 g, which is not the mass of one hydrogen atom. The mass of the most common isotope of hydrogen, 1H, is actually 1.007 825 032 23 g/mol, or 1.67353×10-24 g for one atom. This is because 0.0115% of hydrogen atoms are the deuterium isotope, 2H.
While the difference is small for hydrogen, it is not far all elements. A good example is chlorine. The periodic table will give a molar mass of 35.453 g/mol, but an actual sodium atom will either have a mass of 34.969 g/mol (35Cl) or 36.966 g/mol (37Cl). A sample of naturally occurring chlorine will be 75.8% 35Cl and 24.2% 37Cl.