# Why is silver the best conductor of electricity?

I've been wondering why silver is the best conductor of electricity for a while now, and I've observed that in Group 11 transition metals where silver is located, copper and gold too are also one the best conductors of electricity (Cu, Ag, Au are all in Group 11). I believe that Cu Ag and Au share some physical similarities that makes them a very good conductor of electricity as they are in the same group. More importantly, why is silver, specifically silver (not gold nor copper) the BEST conductor of electricity?

• An answer to your question can be found here answers.yahoo.com/question/index?qid=20080220111633AAz8DWZ – Farcher Nov 16 '16 at 13:29
• Looks like graphene can be a better conductor than silver (en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity) – akhmeteli Nov 16 '16 at 13:56
• @Farcher : I'm not convinced. That answer talks about 'ripeness for conduction' arising from electron affinity or ionization potential. Conduction does not require ionization. – sammy gerbil Nov 16 '16 at 14:28
• How is a metallic bond formed? By an electron leaving an atom to form an ion. – Farcher Nov 16 '16 at 14:40
• One element will be, almost by definition, the best conductor (amongst the elements). You have ignored superconductivity mind you... – Jon Custer Nov 16 '16 at 16:01

How much of a difference is there, in fact? The conductivities of Ag, Cu, Au are respectively 6.3, 6.0 and 4.5 x $10^7$ S/m. These are the highest among bulk metals. Closely followed by Al, Ca and Be with conductivities of 3.5, 2.82 and 2.5 in the same units. Fe is 1.0 and Hg is 0.1. By comparison the conductivity of semiconductors Ge and Si are 2.17 and 0.00156 S/m - a factor of more than $10^7$ lower.

So on the scale of conductivity, the difference between Ag, Cu and Au is insignificant. Trying to explain such small differences is difficult. As Jon Custer's comment implies, the difference may depend on a variety of factors, with no one factor being dominant.

Notice, for example, the difference of 0.19 between Cu and annealed Cu, which is about the same as between Ag and Cu. Notice also the large differences between pure metals and alloys : eg nichrome 0.067 compared with Ni 1.43 and Cr 0.51.

According to the classical Drude Model, conductivity depends on electron density $n$ (number of conduction electrons per $m^3$) and mean time $\tau$ between collisions. The latter could be presumed to depend on interactomic spacing, but this is remarkably uniform for many metals : Ag 0.2888, Au 0.2882, Cu 0.2556, Al 0.2962 nm. Number densities ought to depend on atomic number density (approximately constant because spacing is constant) and valency, the latter being where position in the periodic table comes into it. With a valency of 3, Al should be the best conductor. Measured number densities vary within 1 power of 10, ranging from 18.1 for Al to 3.15 for Ba, in units of $10^{28}/m^3$, with Ag, Au and Cu at 5.86, 5.8 and 6.87 respectively. So classically Al, Fe, Sn and Pb should be the best conductors.

• Not iron: there is a lot of electron scattering with the $3d$ band. Lead and tin are in column IV, below germanium in the periodic system. In fact, grey tin is a semiconductor. – user137289 Nov 28 '16 at 23:20

I will not work out the details, but just give an overview, simply because I'm not an expert in solid state physics.

First of all, the property of electrical conduction of metals, can be explained upto a certain degree of accuracy by Band Theory*. In single atoms, electron reside in atomic orbitals, while in molecules, these electrons reside in molecular orbitals(formed by various overlaps of atomic orbitals). In a solid(eg: some metallic crystal), many of these MOT's superpose to form 'bands' , which can be visualized as extended molecular orbitals. There are band gaps between them, corresponding to forbidden energy zones. In a metal, the distribution of these bands w.r.t its Fermi energy level, determines(partially) how good a conductor it can be. Transition metals like Cu,Au and Ag, form different types of these bands,w.r.t their corresponding Fermi energy levels. I cannot explain the mathematical analysis of this, as it involves some really complicated statistical mechanics, but if you happen to work out the band distributions right from the wave functions, i believe you would get the perfect answer to your question. Anyway, i suggest you wait for other answers.

• Is there a missing link to "Band Theory*"? – sammy gerbil Nov 16 '16 at 16:49
• Umm, no, i just wanted to add that its generally not used frequently at present, due to certain materials behaving anomolously(as per band theory) – Lelouch Nov 16 '16 at 16:51

Electron-electron scattering is lower in silver. Conduction in the coinage metals is in the $sp$-band that are wide and quite free-electron-like. But there is scattering with the $d$-electrons. This is least important in silver where the $4d$-electrons are about 4 eV away from the Fermi-level (which is also why silver is colorless). But the $3d$ bands in copper and and the $5d$ bands in gold are closer to the Fermi level (absorption in the blue) and they cause more scattering with the $sp$ electrons.

• I have read in some textbook(s) that the electron-electron interaction does not impact on the conductivity of metals. Because any momentum lost for an electron is gained for another, so that in average there is no momentum change due to this interaction, and hence, no increase or decrease in the current. Could you comment on this? – AccidentalBismuthTransform Jun 8 '19 at 20:28
• @thermomagneticcondensedboson Clearly, the transition metals with their partially filled $d$-band have higher resistivities than the coinage metals and simple metals. Momentum in solids is crystal momentum, for theoretical explanations a new question would be a better place. – user137289 Jun 8 '19 at 23:20