Hello Ernest Rogers ,

You have posed a very simple sounding question for which I do not believe I have ever seen a satisfactory explanation. I have seen confusion about such elementary things as to which of these three metals has the highest electrical conductivity (lowest resistivity). Someone came to a company I was working for at the time, and gave an extended course on the control of DC motors, and claimed that gold had the highest electrical conductivity! What was so surprising about this erroneous assertion is that they could simply have looked up the correct answer (silver) in any chemistry textbook or the "CRC Handbook of Chemistry and Physics". I suppose they might have thought that since gold is used to coat PCB (Printed Circuit Board) contacts, it must have been used for that purpose because it had a higher electrical conductivity than copper (it doesn't), instead of the correct reason that gold does not oxidize in the presence of air unlike copper. Charles Kittel mentions in the 4th edition (1971) of his "Introduction to Solid State Physics" textbook, p. 295, that E. M. McMillan once remarked that the observed resistivity values for insulators and conductors spans a range of about 1032, which is wider that any other physical parameter. But why?

Of course, there is also the question of why the best conducting metallic elements are the group IB elements (Cu, Ag, and Au), which are transition metals, and not the group IA akali metals with their weakly bound outer electron. Even quantum mechanics does not seem to be of much help in the sense that it cannot tell you a priori, i.e., in the absence of experience, which elements are metals, and of those metals, which have the highest conductivity. Physicists and quantum chemists have been trying for a long time to calculate the material properties of elements from first principles using quantum mechanics, but as Robert B. Laughlin mentioned in his 2005 book "A Different Universe", it is usually just easier to simply measure the property of interest. I mean when superconducting metal elements were first discovered, and for decades afterwards - even after the BCS theory, no one thought that high-temperature superconductors, if and when they would be discovered, would turn out not even to be metals but, rather, ceramic-like materials.

Anyway, I really like your question. Good luck in your search.

Regards,

Tom Cuff

Probably not the right answer Prof. Ernest Rogers, since it depends on how they are obtained, I mean the concentration ni of impurities.

For Silver, resistivity strongly depends on scattering from dislocations and grain boundaries, and it is in the middle of the transition metals between the noble gasses and the alkali metal.

In Gold oxidation is low, that is, few impurities that destroy electrical conductivity, it is used in contacts.

Ag, Cu and Au belong to the transition metals Group 11 in the periodic table.

Dear Ernest Rogers ,

All metals have energy band structure such that the valence band is partially filled with valence electrons. Thanks to this energy band structure, these valence electrons are free to move and when one applies electric field these fee electrons are drift under the electric field such that the drift velocity is proportional to the the electric field E.

vd= mu E where mu is the mobility.

Assuming that the concentration of the valence electrons is equal n then

the current I in the conductor can be expressed by

I= AqunE = A sigma E, sigma is the conductivity

Ais the area, and q is the electron charge.

You see that as the conductivity increases the material conducts more current for the same applied electric field.

The free election concentration is major factor affecting the conductivity, then comes the mobility. The mobility results from the free electron impedance by the scattering centers and obstacles in the material or at its surface.

It depends strongly on temperature.

If the metal is cooled down the mobility gets larger and the conductivity increases.

There is a temperature below which the material is no longer impart any resistance to the motion of the electrons. The material becomes then a superconductor. There is research to find materials whose superconducting temperature is relatively high. I did not follow the research in this important area.

Best wishes

Thank you, everyone, for your answers. I apologize for my slow response. I guess I have asked a hard one, and If I am to go further, I will have to hit the literature. I imagined that if I am to make progress toward a better conductor it would be through a deeper understanding of phonon scattering.

I will have to work on this. /Ernie