Tunneleffekt und quantenverteilung der energie bei der elektrochemischen entladung von protonen und deuteronen

Abstract

The role of the tunnel effect in electrode processes has been studied in a series of earlier papers assuming a continuous energy distribution of the dissolved ions. In particular the probable shape and the permeability of the potential barrier for the discharge of protons and deuterons on a mercury cathode have been determined in this way on the basis of Post and Hiskey's experimental values.In the present paper the same problem is treated assuming a quantum distribution of the vibrational energy of the H+-OH2 bond. The calculations were carried out using a recently found expression for the permeability of a generalized Eckart barrier. It is found that the parameters of the barrier do not differ much from those determined previously. It is also shown that practically all particles penetrate this barrier at the quantum level n = 2 (for protons) or n = 3 (for deuterons). Actually these energy levels correspond approximately to the mean values of the energy of the protons or deuterons penetrating the barrier because the strictly quantized energy spectrum is strongly smeared out due to the interactions of the particles in the solution.