Question: how many oxygen atoms are present in 1.00 mole of oxygen molecules?
Answer: For elements that exist as molecules, it is best to explicitly state whether molecules or atoms are meant. Thus "1 mole of oxygen molecules" means 6.022 x 1023 O2 molecules, or 2 x 6.022 x 1023 O atoms; "1 mole of oxygen atoms" means 6.022 x 1023 O atoms.