Electron speed and movement through a copper wire

[Saado]

I've recently read that the electrons move relatively slowly to what I had previously thought through a metal. That the "drift velocity" is slow, but because the electrons are plentiful, they can pass down the signal very fast. Near light speeds. Could someone explain what I'm missing and this concept in general? I always thought that the velocity increased as kinetic energy did and that electrons have relatively high speeds even withing orbitals.

 

[nsaspook]

I've recently read that the electrons move relatively slowly to what I had previously thought through a metal. That the "drift velocity" is slow, but because the electrons are plentiful, they can pass down the signal very fast. Near light speeds. Could someone explain what I'm missing and this concept in general? I always thought that the velocity increased as kinetic energy did and that electrons have relatively high speeds even withing orbitals.

The Kinetic energy of a charge carrier due to it's drift velocity is incredibly tiny in a good conductor.

http://en.wikipedia.org/wiki/Speed_of_electricity
http://webcache.googleusercontent.com/search?q=cache:rTslF-4YoGYJ:https://www.bpa.gov/PublicInvolvement/CommunityEducation/CurriculumActivities/CurriculumDocuments/ride_the_surprisingly_slow_electron_express.doc+&cd=1&hl=en&ct=clnk&gl=us&client=iceweasel-a

 

[Simon Bridge]

I think the bit you are missing is that the drift velocity of the electrons is an average velocity.
Electrons move in a wire like gas in a bottle - every which way. When there is no applied electric field, an electron is as likely to go one way as another, so the drift velocity is zero. With the electric field, there is a bigger chance of going one way than the others.

You can estimate the rms thermal speed of electrons in the wire at room temperature by treating them as an ideal gas and using the kinetic theory. That's much faster than the drift velocity.

This site has a widget to illustrate the motion of just one electron with different applied electric fields.

 

[Saado]

Okay that ideal gas description worked really well. So if I send an alternating and or direct current through a wire, I read that the speed from one end to the other would be very near c. How is this achieved? Is it due to the interactions between electrons along the way?

 

[UltrafastPED]

Okay that ideal gas description worked really well. So if I send an alternating and or direct current through a wire, I read that the speed from one end to the other would be very near c. How is this achieved? Is it due to the interactions between electrons along the way?

It's not the electrons, but the electric fields which travel rapidly ... a kind of knock-on effect.

See https://en.wikipedia.org/wiki/Speed_of_electricity
and the references.

 

[Saado]

Thanks :)

 

[Simon Bridge]

Okay that ideal gas description worked really well. So if I send an alternating and or direct current through a wire, I read that the speed from one end to the other would be very near c. How is this achieved? Is it due to the interactions between electrons along the way?

So if electrons are so slooowww... how is it that electrical signals are so fast?
Well what he said - there are a lot of references about this online.

There are two commonly experienced[1] situations that shed light on the situation:
1. if you hit one end of a pipe, the sounds gets to the other end even though the individual atoms in the metal do not travel that far. How does this happen?
2. you have a hose full of water and turn on the tap - water comes out the other end almost immediately, but it takes the water much longer than that to travel the length of the pipe.
(You can do the same fort of thing for a gas - blow in one end of a pipe full of gas and some comes out the other end well before the gas from your lips could have traveled the length of the pipe.)

Considering these common experiences, is it really all that surprising that a signal can go down a wire faster than the electrons themselves travel?

----------------------------

[1] if you have not experienced these situations - then you should arrange to soon.

 

[zhanhai]

I've recently read that the electrons move relatively slowly to what I had previously thought through a metal. That the "drift velocity" is slow, but because the electrons are plentiful, they can pass down the signal very fast. Near light speeds. Could someone explain what I'm missing and this concept in general? I always thought that the velocity increased as kinetic energy did and that electrons have relatively high speeds even withing orbitals.

The picture is semi-classical. QM describes electrons in a solid by wave functions.

I just tried a way to estimate the rate at which a carrier electron is excited by the E field that drives the current. The result is that normally it is in the order of 10**(-4) per second. But at just above superconducting transition it is as low as 10**(-21) per second. I am not sure whether such results are OK or not.

 

[Simon Bridge]

A simple model for a wire would be a bunch of electrons in a square well.
The applied potential, i.e. by connecting a battery to each end, tilts the well - the stationary state wavefunctions all crowd down the low end (treating electron PE as positive). But the battery also provides a large number of electrons in some very wide well so the states are close to continuum - at the high end of the potential; and it provides a similar but depleted well at the other end ... with a barriers corresponding to the contacts. There is a chance of tunnelling through the barrier.
Lastly, the wire is immersed in a heat bath (the room).

The effect is that an electron tunneling into one end of the wire ends up in a superpositon of the stationary states - time evolve the wavefunction, keeping track of the probability of tunnelling out.

This should allow you to work out an rms speed for the electrons.
Note: I know there are other ways to model this.

To work out the speed of propagation of changes in the electric field, you want to change the situation to where the applied potential changes with time ... say a time-step shift between 0 and V at time t=t0.
In the above setup - the changes in the potential are approximately instant ... so we need something else.

This is all a bit clunky still - I hope to show that the passage of an electric current through a wire quickly becomes unwieldy in pure QM terms.

 

[zhanhai]

I am curious why perturbation is not used for treating electron movement in solid. As electron states E(k) and E(-k) degenerate, when E field of V is applied, perturbation will lead to an energy level split relating to V. Would each energy level be splitted into two? Or do I miss anything?

 

[Simon Bridge]

How does the application of a uniform electric field split the energy levels.
This is a common introductory exercize in perturbation theory - see what the effect is for an infinite square well.

 

[zhanhai]

How does the application of a uniform electric field split the energy levels.
This is a common introductory exercize in perturbation theory - see what the effect is for an infinite square well.

I read several textbooks but did not find anything on energy level split by uniform electric field. Where can I get introduction on this?

I cannot understand how wavevectors k and -k are associated with respective new energy levels after perturbation. It seems that the association of k and -k with their respective splitted energy levels is not determined by perturbation treatment itself. Is this true?

 

[Simon Bridge]

I read several textbooks but did not find anything on energy level split by uniform electric field. Where can I get introduction on this?

... you can read the textbooks you have where they introduce perturbation theory - usually a 3rd year college physics course. Then you do the maths yourself. You will not find a formal treatment.

Use the 1D infinite square well width L and centered at x=0 for the unperturbed system (it's easy) and then apply the potential for a uniform electric field. For the theory to work, you need the change in potential across the well to be small compared with the lowest energy level.

The reason nobody talks about level splitting from a uniform electric field is because it does not happen.

I cannot understand how wavevectors k and -k are associated with respective new energy levels after perturbation. It seems that the association of k and -k with their respective splitted energy levels is not determined by perturbation treatment itself. Is this true?

That sounds like an off-topic question about perturbation theory.
In general the perturbation treatment is a way of approximating the full calculation while the level splitting is a measureable effect in nature caused by the perturbing field.
You are best to seek more information about this by posting the question in a new thread.