See here: http://education.jlab.org/qa/mathatom_05.html – roughly speaking, a “1” followed by 50 “0”s. It’s steadily increasing, I think, because in the core of a nuclear (fission) reactor, as well as in naturally occuring radioactive elements, big atoms break up into smaller ones. But this doesn’t happen enough to make much of a dent on the overall number! I seem to remember the estimate for the entire observable universe is a “1” with about 80 “0”s following.
As David says, but in terms of different *types* of atoms, there actually aren’t that many! There are only 118 elements (that we know of), and then the isotopes (different chemical forms) of their atoms.
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