# Why is the electron mobility 'irrelevant' in metallic conductors?

This Wikipedia article states in the introduction

Conductivity is proportional to the product of mobility and carrier concentration. For example, the same conductivity could come from a small number of electrons with high mobility for each, or a large number of electrons with a small mobility for each. For metals, it would not typically matter which of these is the case, since most metal electrical behavior depends on conductivity alone. Therefore mobility is relatively unimportant in metal physics.

As we know, conductivity does depend on mobility $$\sigma = \rho \mu$$

where $$\rho$$ is the electronic charge density. The sentences in bold state the electron mobility $$\mu$$ is irrelevant when dealing with metallic conductors because the exhibited electrical behavior depends solely on the conductivity $$\sigma$$ of the material in question.

Why is mobility 'irrelevant' in metal physics? Even though conductivity, which is a very important parameter in metal physics, does depend on this irrelevant quantity?

• I believe what this means is that Wikipedia is not the most definitive nor the most self-consistent source of knowledge about physics. – The Photon Sep 23 at 18:34
• It does seem a bit odd of a way to phrase it, but... I think they may be trying to distinguish normal metal properties from various semiconductor cases. For example, I don't think one worries much about ballistic electrons in a metal but they are important for high-electron mobility devices. – Jon Custer Sep 23 at 18:36
• Your suspicion is justified. This passage does not make much sense. – my2cts Sep 23 at 20:42

I think you have misinterpreted the Wikipedia passage. It states that: "most metal electrical behavior depends on conductivity alone". Therefore, it is saying that the underlying physical phenomena that are responsible for the conductivity are irrelevant to the electrical behavior.

The same conductivity could arise because a small number of electrons have high mobility, or because there are a large number of electrons with low mobility. Doesn't matter - all we care about is the conductivity (to paraphrase Wikipedia).

• "same conductivity could arise because a small number of electrons have high mobility, or because there are a large number of electrons with low mobility" Why would this logic be exclusive to metals? – Hilbert Sep 23 at 18:48
• @Hilbert I don't know; however, most non-metals tend to not be very conductive in the first place, and the mechanisms behind their conductivity may be different. Really, the purpose of my answer was to provide an interpretation of the given passage. I am not necessarily saying that I agree with it (interpretation does not equal endorsement). – Time4Tea Sep 23 at 18:56