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I believe that the speed of visible light we should know c=3.00 x 10^8 which is one of the things they made us memorize in high school as well but as far as the diameter of an atom I don't think we're expected to memorize. Also, I'm not sure what you mean by the number associated with the human eye?
It would benefit for you to know the diameter of an atom is on the order of few angstroms, but you do not have to know the exact numbers since these numbers will vary atom to atom. Not really sure by what you mean by human eye.