# How can electron move between two metals without the presence of electric field?

Electron can move from one location to another if it feels a force that is if there is a presence of electric field. Now suppose I have a $$\ce{Zn}$$ rod immersed in $$\ce{CuSO4}$$ solution. Electrons are transferred from $$\ce{Zn}$$ to $$\ce{Cu}$$. What results in this motion of electrons from $$\ce{Zn}$$ to $$\ce{Cu}$$. How can electron move without a field?

• Still, the question is legitimate. Electrons won't move without a field, will they? – Ivan Neretin Jun 30 at 17:28
• You might want to check: chemistry.stackexchange.com/questions/23450/… – Buck Thorn Jun 30 at 20:36
• – Buck Thorn Jun 30 at 20:44
• My interpretation of this question, which I will upvote, is that @GracemarsMars wants to know exactly what happens, and WHY it happens, when a cupric ion, in aqueous solution, gets reduced by a bulk piece of zinc metal. It obviously happens, and the thermodynamics and driving force are understood, but what is the step-by-step reaction mechanism? I do not know the answer and even doubt that people like Prof. Bard know (and I do not say this lightly). It is an extremely difficult thing to study. If I am wrong in this, I would absolutely love to see a posted answer explaining the mechanism! – Ed V Jul 1 at 2:28
• @EdV I agree that there is nothing trivial about the problem, particularly if you dwell into mechanisms of electron transfer etc, but I think that the OP might not be familiar with the Nernst equation. After all, that provides a quantitative description of the correspondence between differences in the chemical potential of the electrons at the two electrodes and the resulting voltage. Not quite "QED" but I think if you want a really detailed explanation maybe you need to roll up the sleeves and start digging into more advanced literature. There is bound to be lots of case-specific variation. – Buck Thorn Jul 1 at 7:48

## 2 Answers

The wording of the question hides the answer.

Electrons do not move from Zn to Cu. They move from neutral zinc to cupric ion Cu++. The field arises from the mix of H2O, H+, OH-, SO4--, and Cu++ all around the Zn rod. Could electrons be forced onto Zn from OH- or SO4-- ? No.There is no gain in stability; energy would be needed. Or could electrons be attracted to H+; yes, and even more so to Cu++. And the final products (Zn++ and neutral Cu) would be more stable.

How can electron move without a field?

There is a field, the field of two nuclei (shielded by some electrons, if you will). In the figure below, the top shows the potential energy (y-axis, arbitrary units) of a free electron in a homogeneous electric field (changing along the x-axis). It will move along the gradient, like in an old-style TV with a cathode ray tube.

If you treat the situation of an electron transfer in a pre-Planck way, it will look like the lower panel (again, the y-axis is the potential in arbitrary units, and the x-axis location). There are two infinitely deep wells in the potential energy landscape, and the electron would disappear in either of them.

Instead, quantum mechanics describes that the energy of the electron is quantized, and there are bound states near each nucleus. Using a one-electron approximation, if the highest occupied orbital of one atom/molecule/ion (species) has a higher energy than the lower unoccupied orbital of the other species, the electron will transfer "when given a chance" (the latter has to do with distance and other subtleties).

From which to which species electrons will transfer is described by the electrochemical series (or the reduction potential). If the two nucleic are sufficiently close, the electron can tunnel, so it can overcome a high barrier without input of energy. Rudolph A. Marcus received the 1992 Nobel prize for work on electron transfer in chemistry; you can read the Nobel lecture here.

• I think there is a misconception in your answer about what QM does or does not provide you with. Much of what you encounter in basic QM treatments is a "classical" treatment of the potential (as opposed to relativistic), what you call "pre-Planck". What is new is the dual particle/wave description of particles. What QM does is do away with the exclusively particle description of matter (it also describes the photon as a particle with zero rest mass). So those singularities remain in a "static" (eg Born-Oppenheimer) description of the potentials. – Buck Thorn Jul 2 at 14:40
• I haven't read a good explanation of why particles should not dive head first into those singularities, only that they don't because of quantization, as you point out, where quantization is a property of the standing waves that define the solutions of the time-independent SE. – Buck Thorn Jul 2 at 14:43
• But good link, will have to read! – Buck Thorn Jul 2 at 14:45