Quantized conductance behavior of gold nano wires was studied under electrochemical potential control. We fabricated 1 nm long mono atomic wires in solution at room temperature. Electrochemical potential significantly affected the stability of the mono atomic wire and fractional conductance peak occurrence in the conductance histogram. We revealed that the hydrogen adsorption on gold mono atomic wires was a decisive factor of the fractional peak, which was originated from the dynamic structural transition between two bistable states of the mono atomic wire showing the unit and the fractional values of the conductance. We could tune the stability of these bistable states to make the fractional conductance state preferable.