# Speed of electrons in batteries

i have read around the forum that the speed of electrons in a conductor is somewhat 1mm/s
if that is true , then how do galvanic cells operate ? by that rate , about 1000 electrons would come out of the conductor / sec , not only this , but it would seem like the velocity of electrons is irrelevant of the current intensity * i know i should not be treating charges and electrons the same *

but for a current of 1 ampere , thats 1 couloumb / sec , 6.24*10^18 electrons * if i recall correctly * must come out of the conductor to precepitate 1.118 grams of silver * the amount of silver precipiptated by the passage of a couloumb in a solution of silver * so it does not make any sense
( this might seem like it should be posted somewhere in chemistry forum , but i am asking about a physical phenomena which is how the electrons travel in a conductor "

The answer is simple, there is a very large number of free electrons in even a tiny quantity of a metallic conductor like copper. Apparently much more than you think. There's one free electron for every copper atom.

There are 6.022*10^23 copper atoms in 1 mole (63.5 grams) of copper.

If you have a conductor with a 1 (mm)^2 cross section and the drift speed of the electrons is 1 mm/s, the number of electrons passing through the cross section will be the same number of free electrons as are present in a volume of 1 mm^3 copper.

1 mm^3 copper weighs 8.96 * 10^-3 gram, so there are 0,14 * 10^-3 moles of copper atoms in it, so there are
6.022 * 10^23 * 0,14 * 10^-3 = 8.4 * 10^19 copper atoms, and the same number of free electrons.
This corresponds to a current of 8.4 * 10^19 / 6.24 * 10^18 = 13.5 A

Willem2. A little clarification of "drift" speed? The energy is transmitted at a percentage of light speed yet the drift speed of the electrons is no where near a percentage of light speed. Saying the electrons that flow out of one battery post to power a car's starter take about 4 hours to return to the negative post shows a slow movement of electrons that have a generally chaotic motion in all directions, the "free" ones. But en masse there is a flow and that combined flow across an area of conductor is the drift. Been a while. Listening for any correction.

The answer is simple, there is a very large number of free electrons in even a tiny quantity of a metallic conductor like copper. Apparently much more than you think. There's one free electron for every copper atom.

There are 6.022*10^23 copper atoms in 1 mole (63.5 grams) of copper.

If you have a conductor with a 1 (mm)^2 cross section and the drift speed of the electrons is 1 mm/s, the number of electrons passing through the cross section will be the same number of free electrons as are present in a volume of 1 mm^3 copper.

1 mm^3 copper weighs 8.96 * 10^-3 gram, so there are 0,14 * 10^-3 moles of copper atoms in it, so there are
6.022 * 10^23 * 0,14 * 10^-3 = 8.4 * 10^19 copper atoms, and the same number of free electrons.
This corresponds to a current of 8.4 * 10^19 / 6.24 * 10^18 = 13.5 A
thats 27 amp since there are 2 electrons for each copper atom , anyway that was really really helpful , so does the voltage affect the drift velocity ? if not then what determines the amount of electrons coming out of the conductor ?

thats 27 amp since there are 2 electrons for each copper atom , anyway that was really really helpful , so does the voltage affect the drift velocity ? if not then what determines the amount of electrons coming out of the conductor ?

Copper has 1 electron for each atom

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html#c2

All of that should be taken with a huge grain of salt. Electron conductivity in metals is essentially a quantum effect.

sophiecentaur
Gold Member
2020 Award
All of that should be taken with a huge grain of salt. Electron conductivity in metals is essentially a quantum effect.

Could we have that printed in large flashing letters at the top of every screen of PF?
People still want electrons to be like grains of sand or drops of water. Grrrrr!

I just realized that the initial question was also about galvanic cells. In galvanic cells, conductivity is not just electronic, it also involves ions. So it is even more of a hairball.

Could we have that printed in large flashing letters at the top of every screen of PF?
People still want electrons to be like grains of sand or drops of water. Grrrrr!

does this imply that any of what was said above is incorrect ?
i know its a classical description of a quantum mechanical phenomena , but until i learn the real quantum mechanical description , this is pretty sufficient only if it's correct

The electric field will contribute towards the force on the charge carrier, depending on the medium the resulting current may be ohmic or have a more complicated effect. In the galvanic cells you will get an ohmic contribution, but also some nonlinear contributions based on the reaction kinetics and the diffusion speeds in the solute.

does this imply that any of what was said above is incorrect ?
i know its a classical description of a quantum mechanical phenomena , but until i learn the real quantum mechanical description , this is pretty sufficient only if it's correct

As far as I know, there is no real consensual QM description.

sophiecentaur
Gold Member
2020 Award
does this imply that any of what was said above is incorrect ?
i know its a classical description of a quantum mechanical phenomena , but until i learn the real quantum mechanical description , this is pretty sufficient only if it's correct

My post was about a comment about electron conduction in metals. I am just concerned that the quasi-mechanical model of electron conduction, as presented (without any caveats), is so attractive that it can be extrapolated way beyond reasonable bounds. For instance, the (school level) 'explanation' of resistance increasing with temperature in metals is based on the atoms 'jiggling around' more when hot and presenting a bigger target for the electrons to bump into. blah blah blah. Why not present the fact that it increases and leave it at that? I feel there is too much effort made to present a lot of Science in an approachable way. It tempts people to make totally invalid conclusions and, even worse, it confuses students who actually think at a deeper level. Dumbing down is a two edged sword. Why try to kid students that it's all, basically, pretty easy stuff? It isn't, and Science should be presented and treated with much more serious respect. An early lesson should be that it just ain't that simple. What's wrong with students being told that?

AlephZero
Homework Helper
i have read around the forum that the speed of electrons in a conductor is somewhat 1mm/s
if that is true , then how do galvanic cells operate ? by that rate , about 1000 electrons would come out of the conductor / sec

I can't see why you think "1mm/s" only gives "1000 electrons /sec". Maybe if you could explain your (wrong) logic, we could give you a better answer to correct it.

does this imply that any of what was said above is incorrect ?
i know its a classical description of a quantum mechanical phenomena , but until i learn the real quantum mechanical description , this is pretty sufficient only if it's correct

You seem to be assuming that "electric current" = "movement of electrons". That is a reasonable classical description of how current flows in metals, but it is completely wrong for current in most other materials, like the atmosphere (e.g. lightning), living organisms, semiconductor materials (e.g. electronic components like diodes and transistors), batteries, etc. "Current" can be the flow of any positively or negatively charged particles, or even both types of particles at the same time moving in opposite directions.

My post was about a comment about electron conduction in metals. I am just concerned that the quasi-mechanical model of electron conduction, as presented (without any caveats), is so attractive that it can be extrapolated way beyond reasonable bounds. For instance, the (school level) 'explanation' of resistance increasing with temperature in metals is based on the atoms 'jiggling around' more when hot and presenting a bigger target for the electrons to bump into. blah blah blah. Why not present the fact that it increases and leave it at that? I feel there is too much effort made to present a lot of Science in an approachable way. It tempts people to make totally invalid conclusions and, even worse, it confuses students who actually think at a deeper level. Dumbing down is a two edged sword. Why try to kid students that it's all, basically, pretty easy stuff? It isn't, and Science should be presented and treated with much more serious respect. An early lesson should be that it just ain't that simple. What's wrong with students being told that?

you sir deserve a nobel prize just for that comment , that is absolutely correct
it is really harder for me * or anyone who is interested in the subject* to learn things that are not physically correct than to learn complicated real physical things
that is due to the fact that physically incorrect ideas like that of atoms jiggling around more in a conductor due to heat , tend to build up more errors and problems when you think of it deeper , even though they might look appealing and intuitive on the outside , believe it or not but my chemistry book's analogy for electron orbitals is a fan , how we can not know where the electrons are due to their high speed !

I can't see why you think "1mm/s" only gives "1000 electrons /sec". Maybe if you could explain your (wrong) logic, we could give you a better answer to correct it.

You seem to be assuming that "electric current" = "movement of electrons". That is a reasonable classical description of how current flows in metals, but it is completely wrong for current in most other materials, like the atmosphere (e.g. lightning), living organisms, semiconductor materials (e.g. electronic components like diodes and transistors), batteries, etc. "Current" can be the flow of any positively or negatively charged particles, or even both types of particles at the same time moving in opposite directions.

nevermind , i for somereason thought that electrons come one at a time out of a conductor , i thought of the wire as a two dimensional object , but my logic has been corrected by some comment above . also i know that the movement of charges creates a current , i am just talking about electrons because i am addressing the idea of galvanic cells

sophiecentaur