Electron transmission through a condutor

[bbarrett]

Can anyone give me any details on exactly how an electron travels trough a conductor? Is the electron passed from one outer valence of an atom to another, ( basically hops aride from one atom to the next) if this is the case then there would be two electrons on one orbit, is this possible? Or does the electron "knock" off existing electron, and that electron does the same thing to his neighbor and continues the process. Has anyone done any research to determine that an electron entering a conductor is the same electron that comes out at the end? Or better question still,,,, well I 'll save it for now.

What About BOB

 

[chroot]

In a normal conductor, the electrons are more or less completely free to move about. They are not tied to anyone atom in any respect at all. The electrons that are free to move about have thermal energies high enough to put them into a continuum of states called the 'conduction band' which is larger than the binding energy of the atoms in solid. As a first approximation, you can actually consider the electrons in a conductor as a free gas. This approximation is actually even pretty good for many metals.

The electrons that flow into one end of a conductor probably do realistically come out the other end eventually, but it's not physically possible (or meaningful) to tag an electron to try to tell one from another. Electrons are all exactly identical.

Current is conducted through a conductor by the biased random thermal motion of the free electrons in the conduction band. The electrons have average thermal energies of 3/2 kT, corresponding to a mean velocity of about 100,000 meters per second. They bounce around pretty much randomly inside a conductor.

When you apply an external potential difference of, say, 1 V to the conductor, the electrons experience a small force which propels them towards the positive terminal of the battery. They do not go directly towards the battery, but only drift very slowly in the direction of the positive terminal. The drift velocity is

$$v_d = \frac{J}{n e}$$

Where J is the current density, n is the number density of electrons in the conductor, and e is the charge on an electron. For usual currents in usual wires, this drift velocity is only a few tens of centimeters per hour. If you apply a potential difference across a small block of metal, it literally can take hours for electrons to move all the way across it.

This makes sense if you consider how many electrons there are in a cube of copper 1 cm on a side: 8.46 * 10²² per cm³, a truly staggering number. You only need 6.25 * 10¹⁸ electrons per second emerging from the end of your wire to carry one ampere of current.

Feel free to let me know if you have any more questions.

- Warren

 

[ZapperZ]

Can anyone give me any details on exactly how an electron travels trough a conductor? Is the electron passed from one outer valence of an atom to another, ( basically hops aride from one atom to the next) if this is the case then there would be two electrons on one orbit, is this possible? Or does the electron "knock" off existing electron, and that electron does the same thing to his neighbor and continues the process. Has anyone done any research to determine that an electron entering a conductor is the same electron that comes out at the end? Or better question still,,,, well I 'll save it for now.

What About BOB

Chroot is correct in pointing out that the electrons in a metal are "almost free", meaning they are not tied to any particular atom. The only correction I would like to point out is that these electrons are already in the conduction band even at T=0K, i.e. the ground state is already in the conduction band without any need for thermal energies.

What you are looking for is what is known as the Drude Model, which is essentially covered in the early chapters (typically the first chapter) of a Solid State Physics textbook. This model is purely classical statistical physics. While it is successful at explaining simple properties of a conductor, it is quite limited in explaining others. For a summar, read here:

http://people.deas.harvard.edu/~jones/es154/lectures/lecture_2/drude_model/drude_model_cc/drude_model_cc.html

Also, for future cultural references, we don't technically call this "electron transmission". It is called either simply electronic conduction or electronic transport.

Zz.

 

[bbarrett]

Thanks, how does the advent of super cooling effect these conduction bands?
If at all . I realize the result to be superconductivity but what is occurring to reduce the resistive nature of the conductor and how is it allowing the electrons to flow unimpeded? I had read somewhere that at near absolute zero that oscillations or resonace of the atoms slows down, does this have an effect on the conduction bands ? sorry for so many questions but I am trying to get an accurate understanding of superconductivity one step at a time before I delve into exotic high temp SC's. Again thanks

Bob

 

[chroot]

At very low temperatures, the thermal excitations (phonons) are quieted down enough so that electrons can form pairs, called Cooper pairs. An individual electron is a fermion, and obeys the Pauli exclusion princinple. A pair of electrons acts as a boson, and is not subject to the exclusion principle. Quite the opposite, in fact -- all the Cooper pairs try to be in the same quantum mechanical state. This means that instead of a bump in the road (e.g. a phonon) scattering just one electron as it would at high temperature, the bump would have to change the quantum mechanical state of trillions of electrons at all once. The energy requirement to change so many electron states at once is very high -- so high the bump can't do it. The electrons thus do not interact with the bump and flow without resistance.

Superfluid helium can flow without viscosity through very small pores for the same reason.

- Warren

 

[ZapperZ]

Thanks, how does the advent of super cooling effect these conduction bands?
If at all . I realize the result to be superconductivity but what is occurring to reduce the resistive nature of the conductor and how is it allowing the electrons to flow unimpeded? I had read somewhere that at near absolute zero that oscillations or resonace of the atoms slows down, does this have an effect on the conduction bands ? sorry for so many questions but I am trying to get an accurate understanding of superconductivity one step at a time before I delve into exotic high temp SC's. Again thanks

Bob

Here's the problem. You can't go from "free electron gas" to "superconductivity. This is because, as I have said, the Drude model is purely classical. It doesn't take into account the fermionic nature of the electrons and the many-body interactions between the electrons to create the Fermi sea. To be able to understand superconductivity, you have to do a bit more studying to connect the two, i.e. bringing in the quantum effects of the conduction electrons.

Chroot has given you some idea on what is involved in a conventional superconductivity. It isn't just zero resistance. It is a phase transition. So it is more complex than just something being a "perfect conductor". Copper, for example, being a good conductor at room temperature, does NOT become a superconductor even at the lowest temperature attainable. So already this tells you there's something more to superconductivity than having no resistance.

High Tc superconductors are of a different beasts entirely. I highly recommend we don't delve into it because it will drive you mad.

Zz.

 

[Dr Transport]

Not to mention that they still have not figured out why theoretically high Tc superconductors are superconding. "Normal" BCS theory isn't applicable, the most credible theory I have seen deals with the 2-d planes in the structure. I have been away from teh subject for a while, so if there is a better explanation out there, please pass it along...

dt

 

[Chronos]

Picture electrons as spinning billiard balls. The original electron does not have a chance. It transfers energy to the ball it hits. The ball it hits randomly carries away momentum and spin. Superconductivity occurs when the balls are spinning so slowly there is a near perfect transfer of momentum.

 

[ZapperZ]

Picture electrons as spinning billiard balls. The original electron does not have a chance. It transfers energy to the ball it hits. The ball it hits randomly carries away momentum and spin. Superconductivity occurs when the balls are spinning so slowly there is a near perfect transfer of momentum.

Whaaaaaaaat?!

Zz.

 

[bbarrett]

As for the mad part your correct, it has already driven me there!
Thats why I posed the question and figured I 'd better start back at square...
or should I say electron 1.Thanks for input, it reinforces what I 've
thought all along.As for the dropping of temp, I merely wanted to state the correlation between temputure and the decrease in resistance in all condutors,
I think,,, well maybe I need a vacation! Better yet I 'm going to shot some billiards and have a beer!Again thanks

BoB

 

[bbarrett]

Dr T, has hit the proverbial nail on the head, everything we've all been taught and studied starts to fall apart or clash with the classical theories once Superconductivity enters the picture, and vice versa. Even the scientists that
have and are currently developing high temp SC's cannot precisely explain
how they superconduct. 2-d plane starts to make sense of it but also has its short comings. I guess (no pun intended) this is why the are called theories. Maybe its flawed from the word go, maybe not. Enjoy the weekend
and have a beer on me!

Regards, Bob

 

[ZapperZ]

Dr T, has hit the proverbial nail on the head, everything we've all been taught and studied starts to fall apart or clash with the classical theories once Superconductivity enters the picture, and vice versa. Even the scientists that
have and are currently developing high temp SC's cannot precisely explain
how they superconduct. 2-d plane starts to make sense of it but also has its short comings. I guess (no pun intended) this is why the are called theories. Maybe its flawed from the word go, maybe not. Enjoy the weekend
and have a beer on me!

Regards, Bob

Hey, I told you not to bring in high-Tc superconductors into this. What do I have to do, spank you? :)

The 2-D plane isn't the "mechanism", it is the geometry that the charge carriers are confined to. Even THAT is disputed if you buy into Anderson's resonance valence band model, or Emery-Kivelson's stripe model.

Let's not go into this...

Zz.

 

[Dr Transport]

I'm outta here...

 

[bbarrett]

Nah, no spankin required, this question has been spankin me for the better part of 15 years, just wanted to see if anyone has made any progress. Seems like when ever I bring the subject up with colleagues their "electron"
hairs stand on end also.

Regards, BoB
(Los Alamos flunky)

 

[what_are_electrons]

In a normal conductor, the electrons are more or less completely free to move about. They are not tied to anyone atom in any respect at all. The electrons that are free to move about have thermal energies high enough to put them into a continuum of states called the 'conduction band' which is larger than the binding energy of the atoms in solid. As a first approximation, you can actually consider the electrons in a conductor as a free gas. This approximation is actually even pretty good for many metals.

The electrons that flow into one end of a conductor probably do realistically come out the other end eventually, but it's not physically possible (or meaningful) to tag an electron to try to tell one from another. Electrons are all exactly identical.

Current is conducted through a conductor by the biased random thermal motion of the free electrons in the conduction band. The electrons have average thermal energies of 3/2 kT, corresponding to a mean velocity of about 100,000 meters per second. They bounce around pretty much randomly inside a conductor.

When you apply an external potential difference of, say, 1 V to the conductor, the electrons experience a small force which propels them towards the positive terminal of the battery. They do not go directly towards the battery, but only drift very slowly in the direction of the positive terminal. The drift velocity is

$$v_d = \frac{J}{n e}$$

Where J is the current density, n is the number density of electrons in the conductor, and e is the charge on an electron. For usual currents in usual wires, this drift velocity is only a few tens of centimeters per hour. If you apply a potential difference across a small block of metal, it literally can take hours for electrons to move all the way across it.

This makes sense if you consider how many electrons there are in a cube of copper 1 cm on a side: 8.46 * 10²² per cm³, a truly staggering number. You only need 6.25 * 10¹⁸ electrons per second emerging from the end of your wire to carry one ampere of current.

Feel free to let me know if you have any more questions.
- Warren

Since Copper is considered to have 11 valence electrons (9 from 3d and 2 from 4s) should we multiply 8.46 * 10²² atoms per cm³ by 11 to get the number of free electrons/cm3, or is there another way to determine the number of free electrons/cm3 ?

If this is the way to estimate the number of free electrons/cm3, then I am wondering if that is true then why when copper reacts with other elements does it only give up 1 or 2 of its free (valence) electrons? Sounds like the number of free electrons/cm3 should be between 1 and 2 times 8.46 * 10 ²² atoms per cm³ and not the 11X that I wrote above.