densityelectrical-resistanceelectricitymaterial-science
I just read this answer on EE.SE and that triggered a doubt in me.
If I were asked whether there is any relationship between the electrical resistivity and the density of a substance I'd answer negatively, but is it really so?
Is there really no (relevant) relationship between those two bulk properties of a material? Can anyone confirm or disprove this and give some explanation thereof?
Different molecules and different crystalline structures have frequency dependent absorption/reflection/transmission properties. In general, light in the human visible range can travel with little absorption through glass, but not through brick. UV can travel well through plastic, but not through silicate-based glass. Radio waves can travel through brick and glass, but not well through a metal box. Each of these differences has a slightly different answer, but each answer is based on molecular resonance or crystalline structure (or lack thereof) or electrical conductivity.
Bottom line: There isn't one general answer for why $\lambda_A$ goes through material X but $\lambda_B$ doesn't.
There's no general mathematical relation between stiffness (as parameterized by an elastic modulus such as Young's modulus) and density for all materials, but a relationship can be defined for an ideal gas, and a general trend exists for condensed matter.
For fluids such as gases and liquids, Young's modulus is zero; you won't encounter any resistance if you slowly pull on these materials uniaxially. However, the bulk modulus (i.e., the resistance one encounters when trying to compress these materials using pressure) is not zero; for an ideal gas, it is exactly equal to the pressure. One can relate this relation to the density $m/V$ using the ideal gas law $PV=nRT$ and the molecular weight of the gas.
For condensed matter, the stiffness generally scales up with the density:
The reason is that both properties depend on the pair potential between atoms; if the atoms are strongly bonded, then their spacing is generally small; thus, the density is high. In addition, the curvature of the pair potential at the equilibrium position is large, which is exactly equivalent to saying that the material is stiff:
(A third implication to strong bonding is that the pair potential dips deep and that the material is refractory, i.e., it has a high melting temperature):
An active area of research is to precisely define the pair potential in condensed matter to theoretically predict both stiffness and density; this is something you might pursue in an academic or industry environment.
Best Answer
There is no relationship between the density of a metal and its electrical resistivity.
There is a big database of material properties called MatWeb which is recommend as a legitimate source of data by UCSD's and Stanford's library systems, Rose-Hulman, etc.
I took data from around 60 different metals and graphed them:
As you can see there is no empirical relationship. From a theory perspective, density has to do with atomic packing and resistivity has to do with electronic structure.
I will admit, however, that gaseous copper is an extremely poor conductor.