# How silver with greater number of free electrons has lower resistance?

My book(Concise Physics ICSE) mentions the following things about the dependence of resistance on the material of conductor:-

Dependence on the material of conductor:Different materials have different concentration of free electrons and therefore the resistance of a conductor depends on its material . Metals such as silver , copper , aluminium , lead , etc. have the concentration of free electrons in the decreasing order , so their identical wires offer resistance in the increasing order .

My doubt is regarding the following Statement:

Metals such as silver,copper , aluminium , lead , etc. have the concentration of free electrons in the decreasing order , so their identical wires offer resistance in the increasing order

This implies that since silver has high number of free electrons so it offers low resistance.My doubt arises that since silver has greater number of free electrons the number of electron collisions with the positive ions of silver would also be greater which should lead to higher resistance (since greater number of free electrons means greater numbers of collisions) but the opposite happens (ie,silver offers lower resistance rather than higher resistance). So my first question is how come silver with greater number of free electrons has low resistance? In the same way how lead with lower number of free electrons has higher resistance?

• I think you are mixing up the direction of the order of increase and decrease, see the table on resistivity of the metals here en.wikipedia.org/wiki/… Dec 26, 2021 at 6:52

The number of electrons does effect the scattering rate, but that is not significant for these metals. Rather, their scattering is generally dominated by phonons, and at lower temperatures, defects. So to a first approximation, we can take the scattering rate to be fixed. Then, the conductivity (i.e. inverse resistivity) is proportional to electron number.

Now, your book is slightly deceptive since the resistivity of those metals is proportional to the scattering rate, and who’s to say the rates are the same between them all? In fact, the scattering rates are a bit different, and the differences between resistivity cannot be entirely explained by electron number. But electron number is the most important factor, and your book is trying to be concise, not thorough.

• (+1) It is a rare textbook that does not strive for conciseness in favor of thoroughness.
– Ed V
Dec 26, 2021 at 15:46

First, the number of free electrons in silver is less than the number of free electrons in copper according to this equation: Ne= (Avagadro number * Density) / atomic weight

Second, the resistance depends on the resistivity, and the resistivity of silver is less than the resistivity of copper. Thus, the current of silver is higher.

https://www.brainkart.com/article/Solved-Problems--Conducting-Materials_6818/

• Silver and copper both have one conduction electron per atom. Mar 18, 2022 at 13:41