The electrical conductance through an atomic scale metal nano constriction is quantized. The conductance quantization has attracted wide attention not only for fundamental science but also for technological application. We have studied the conductance of metal nano constriction in solution. Metal nano constrictions were prepared by pressing a scanning tunneling microscopy (STM) tip into a substrate and then pulling out of contact in an electrochemical cell. For Au nano constriction, the Au STM tip and Au(111) substrate is used. For the preparation of nano constrictions using other metals (Ni, Pd, Cu, Ag), electrochemical metal deposition was carried out on to both Au substrate and STM Au tip in solution. In case of Au nano contact, a 1 nm long mono atomic wire is fabricated in solution at room temperature, and its stability is controlled by electrochemical potential. As well as unit value of G0, additional fractional values also appeared in the conductance histogram, when the electrochemical potential of the system was kept below the hydrogen evolution potential. The intensity of the fractional conductance peak increased when the system was polarized at the negative potential. The result implies that adsorbed hydrogen contributes to stabilize the certain atomic configuration of mono atomic wire. It was proved that the electrochemical potential can control the stability of the mono atomic wire, and its structure. For other metals, we also observed change in the conductance quantization behavior depending on the electrochemical potential. In case of Pd, clear conductance quantization appeared at the negative polarization. It is the first observation of the conductance quantization of Pd mono-atomic contact prepared at room temperature.