[lopazz]

So for a project im working on as a part of my class i have chosen to work out why different pure elements have different resistivities. originally i thought it was down to their amount of valence electrons but since they all have 1 that couldnt be the reason. My next conclusion was that it was due to atomic size/amount of shells but that doesnt explain why sliver is a better conductor and has a lower resistivity than copper. My final conclusion was that it was down to the structure and amount of atoms in X amount of area. from my calculations i have not come to a conclusive answer as the amount of moles in 1 cm3 of copper, silver and gold came to 0.141 mols cm-3, 0.097 mols cm-3 and 0.098 mols cm-3. from that reasoning gold would have a better conductivity than copper and a lower resistivity but from other sources its shown to not.

If anyone has a reason as to why the resistivity goes from silver being the best then copper then gold being the worst please reply so that i can understand it better.

[Corribus]

I'm assuming we are talking electrical conductivity here. So first, some data. Here are a few I pulled of the web. First column is resistivity (Ω m) and the second is conductivity (S/m):

https://www.thoughtco.com/electrical-conductivity-in-metals-2340117

Copper    1.68x10^-8    5.98x10⁷               
Silver    1.59x10^-8    6.30x10⁷
Gold    2.44x10^-8    4.52x10⁷

So we see that going down the column, in terms of conductivity, silver is more conductive than copper, but then gold is less conductive than silver, a sort of inverted V trend.

Conductivity is a complex property that depends on a lot of things, so you may expect that trends across (or in this case down) the periodic table are difficult to explain in any simple way. Certainly this trend suggests at least two factors are at play, possible more.

Were I to hazard a complete guess, though: electrical conductivity depends a lot on electron mobility against the crystalline lattice of the metal. In turn, this depends on how well various atomic orbitals overlap. In going from copper to silver, silver's electrons are more diffuse, further from the nucleus, and perhaps more mobile, explaining its higher conductivity. The metals all crystallize in the same group but the unit cell in silver is much larger than copper. Why isn't gold more conductive than silver than? Perhaps gold has some anomalous behavior due to the fact that relativistic effects cannot be neglected on account of its very high nuclear mass, which accelerates electrons to significant fractions of the speed of light. This has the effect of, as one example, contracting certain atomic orbitals compared to what they would be in the absence of relativistic effects. For instance, the unit cell of gold and silver are nearly identical, despite gold being much heavier. A hand-wavy argument might then be made that valence electrons in relativity-contracted orbitals are less mobile, manifesting as reduced macroscopic conductivity for gold compared to silver, which exhibits fewer relativistic effects. Hence the Λ pattern going down the table.

I have no data or sources to support that hypothesis, but it's not too outlandish to suspect that relativity plays some role here, as it is well known that relativity is responsible for other weird behavior in gold and other heavy elements that defy periodic trends observed in the lighter elements.