No, it is not possible to use a fission reactor to split mercury (Hg) into gold (Au) and hydrogen (H). The process you described involves changing the number of protons in the nucleus of an atom, which is not achievable through fission reactions.
Fission reactions involve the splitting of heavy atomic nuclei, such as uranium or plutonium, into two or more lighter nuclei, along with the release of energy. Fission reactions typically occur with isotopes that are much heavier than mercury, such as uranium-235 or plutonium-239.
The transformation of one element into another, specifically changing the number of protons, involves nuclear reactions such as fusion or specific decay processes. These processes are different from fission reactions and are typically associated with extreme conditions such as those found in stars or specific particle accelerators.
To convert mercury into gold and hydrogen, one would need to consider other nuclear processes, such as nuclear transmutation through particle bombardment or nuclear decay series. However, such transformations are highly impractical or inaccessible for elements like mercury under normal conditions.