### Author Topic: How long would it take to replace all the electrons in a piece of wire?  (Read 6631 times)

0 Members and 1 Guest are viewing this topic.

#### raspberrypi

• Frequent Contributor
• !
• Posts: 361
• Country:
##### How long would it take to replace all the electrons in a piece of wire?
« on: February 07, 2017, 04:53:36 am »

Say you had a meter of 16ga wire. At what amps for how long would it take for each electron to be bumped out of one end and replaced in the other end? Or at what speed would a single electron make the journey though the wire?
I'm legally blind so sometimes I ask obvious questions, but its because I can't see well.

The following users thanked this post: Vtile

#### switchedmodepsu

• Regular Contributor
• !
• Posts: 80
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #1 on: February 07, 2017, 04:58:12 am »

Say you had a meter of 16ga wire. At what amps for how long would it take for each electron to be bumped out of one end and replaced in the other end? Or at what speed would a single electron make the journey though the wire?

At the speed of light, I'd think.

#### Brumby

• Supporter
• Posts: 9591
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #2 on: February 07, 2017, 05:04:27 am »
At the speed of light, I'd think.

Actually, no.

The speed of causality is getting up there, but the physical electron movement speed - called Drift Velocity - is actually quite slow.

• Super Contributor
• Posts: 6239
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #3 on: February 07, 2017, 05:18:56 am »
Yeah, Drift Velocity depends on cross section of a conductor and for typical wire and normal currents, it is in single digits of mm/second.
Alex

#### onlooker

• Frequent Contributor
• Posts: 385
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #4 on: February 07, 2017, 05:20:02 am »
To be more precise, according to https://en.wikipedia.org/wiki/Drift_velocity#Numerical_example
"Assume a current I = 1 ampere, and a wire of 2 mm diameter,... the electrons are flowing at the rate of -0.000023 m/s"

#### Rick Law

• Super Contributor
• Posts: 2733
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #5 on: February 07, 2017, 05:24:20 am »

Say you had a meter of 16ga wire. At what amps for how long would it take for each electron to be bumped out of one end and replaced in the other end? Or at what speed would a single electron make the journey though the wire?

At the speed of light, I'd think.

EM field would move at the speed of light, but electrons not being mass-less will by laws of physics move below the speed of light.

Getting a good guess is not hard.  Getting a precise answer is good bit harder.

The speed of electricity over copper average about 0.5c to 0.9c according to this guy:
https://www.quora.com/What-is-the-speed-of-electric-current

That sounds within reason.  I would have guess unobstructed (by EM field) around 0.7c.  Your 16AWG or whatever wire, the material property of the wire is unknown, so you don't know would it be 0.5c or 0.9c speed.

1Amp (pre SI unit) is approx 1Coulomb @ 6.2 x 1018 x e
From that, you can figure out (after you find the material property of your wire) how many electrons are in that piece of wire of X mm long, and how many Amps does it take to pass the equivalent amount of electrons over that wire.  If it is pure copper you know from the periodic table how much each copper atom weights and how many electrons are in that copper atom.  But of course pure copper is impossible -  at least you would have a copper oxide outer layer among other impurities.

Note I carefully avoided saying the electrons are now all replaced.  You are merely passing the equivalent number of electrons through the wire.  Some electrons in the wire are never moved.  Mostly, only the outer shell get shuffled around.

The path is not direct.  Electron get shuffled near atom A, atom A with an extra electron hanging around has its outer-shell over-charged resulting in another electron in the outer shell leaving to atom B, then the same things happens an another electron got captured by atom C...

« Last Edit: February 07, 2017, 05:27:34 am by Rick Law »

#### helius

• Super Contributor
• Posts: 2871
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #6 on: February 07, 2017, 05:51:59 am »
It would take a long long time.
16awg is 1.31 mm2. The number of electrons in a wire is equal to its length, times cross-sectional area, times the number of electrons per unit volume. The valence orbitals of copper are such that there is one electron per atom that is free to move. So the number of electrons is equal to the number of copper atoms per unit volume.
The number of atoms per cubic meter is equal to the density of copper, times Avogadro's number, divided by copper's atomic mass. Copper's atomic mass is 64, and its density at STP is 9000 kg/m3. So there are 8.5 x 1028 electrons per cubic meter in copper wire.
That makes 0.00000131 m2 * 1 m = 1.31 x 10-6 m3 of copper, times 8.5 x 1028 e/m3, is 1.11 x 1023 electrons. A coulomb is 6.25 x 1018 electrons, so that is 17800 coulombs.
An amp is a coulomb per second, so at 1A, that would take nearly 5 hours. However, that is not "All the electrons in a piece of wire". That is only the valence electrons that are free to move; the others stay where they are.

The speed component of the valence electrons due to current is called the drift speed. The drift speed equals the current density divided by the number of mobile charges per unit volume. We already know there are 8.5 x 1028 electrons per cubic meter, so we need the current density J.
J = I/A, the current per cross-sectional area. At 1 amp, that is 1/0.00000131 m2 = 763000 A/m2.
But amps are coulombs per second, and we want the speed of an electron. So we should multiply J by 6.25 x 1018, then divide by 8.5 x 1028 electrons per cubic meter, to get the speed of an electron, 5.6 x 10-5 meters per second, or 56 microns/s. About the thickness of a human hair per second.

#### Rick Law

• Super Contributor
• Posts: 2733
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #7 on: February 07, 2017, 06:25:00 am »
Helius just shown how many damn electrons are involved in a tiny wire.  Which actually points out something far more interesting you can ponder (than speed of electrons traveling)...

One might have imagined, if I make moon-shine, and my alcohol droplet condensed from vapor will vary in size depending on humidity in the air, air temperature...

How did the universe managed to make so many identical electrons?

A Chinese made electron is going to be exactly like an electron made in the USA.  They can use their own high energy collider to create an electron using power from the world's largest dam; we could use powered from diesel generator to power a collider in the (never constructed) Texas super collider.  Yet if we both made an electron, they will be exactly the same...

How did the universe do that?

Well, may be those cheap LiIon cells from China do put out smaller electrons just to save a few bucks.
« Last Edit: February 07, 2017, 06:27:02 am by Rick Law »

#### Ian.M

• Super Contributor
• Posts: 8183
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #8 on: February 07, 2017, 06:32:25 am »

#### Brumby

• Supporter
• Posts: 9591
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #9 on: February 07, 2017, 06:33:24 am »
String theory.

You want proof? ..... How about string cheese.

#### Vgkid

• Super Contributor
• Posts: 2547
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #10 on: February 07, 2017, 06:39:57 am »
I had never heard about the "String Theory" until a guy mentioned it in one of my college math classes. We never discussed it(or got that far) in my university physics class.
If you own any North Hills Electronics gear, message me. L&N Fan

#### Rick Law

• Super Contributor
• Posts: 2733
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #11 on: February 07, 2017, 07:13:19 am »
https://en.wikipedia.org/wiki/One-electron_universe

I learned of this "one electron universe" in 1973.  It was fascinating but an unsatisfactory explanation then.  The trouble only got worst.

Neither it, nor string theory can survive the inflation phase of the universe formation.  To survive means it has to take hold before inflation (so information can be passed along to the entire universe to make them consistent), and the results has to remain consistent post-inflation.  If it is to occur post-inflation, than information must be passed from one end of the universe to the other end at speed faster than the speed of light.

I like to see (one of the) string theory takes hold and develop to a point where it is the model to explain everything at least in particle physics, but it isn't there yet.  To fully explain formation, we will now have to factor in dark energy and dark matter.

There is so much to learn, yet even if I am just 1 year old today, there is not enough time left to understand them all.

#### Halcyon

• Super Contributor
• Posts: 3828
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #12 on: February 07, 2017, 07:40:36 am »
I think you guys are onto a audiophool winner here. "Fast Electron Replenishing Cable". Think of all the good you could do ;-)
Beats the crap out of "directional" cables as the electrons can travel either direction!

(Cut me in for 20% of your profits)

#### Doc Daneeka

• Contributor
• Posts: 33
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #13 on: February 07, 2017, 06:24:46 pm »
When I last brushed up on my QM, I read that all electrons are in fact absolutely identical: when you talk about a number of them you have to talk about the combined wave function which represents all of them; there are no 'individual' electrons as such. So the answer is both instantaneously and infinitely long... or some such thing....close?

#### Vtile

• Frequent Contributor
• Posts: 993
• Country:
• Ingineer
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #14 on: February 07, 2017, 08:23:14 pm »
I must admit I had forgotten the speed difference of electron and the wave.
« Last Edit: February 08, 2017, 09:18:20 am by Vtile »

#### TimFox

• Super Contributor
• Posts: 1016
• Country:
• Retired, now restoring antique test equipment
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #15 on: February 07, 2017, 08:41:30 pm »
I remember a few years ago when the Des Plaines river (in Illinois) was in flood, comparing the current (water velocity) with the time it took the crest of the flood to move a few miles, and thinking of the analogy.

#### Rick Law

• Super Contributor
• Posts: 2733
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #16 on: February 07, 2017, 09:43:09 pm »
When I last brushed up on my QM, I read that all electrons are in fact absolutely identical: when you talk about a number of them you have to talk about the combined wave function which represents all of them; there are no 'individual' electrons as such. So the answer is both instantaneously and infinitely long... or some such thing....close?

No that doesn't follow.  Even when viewed as a wave, it doesn't make it travel instantaneously.

Viewing it as a wave merely means you are looking the the wave properties of the particle.  Wave properties are properties such as formation of an interference pattern, passing from one side of the wall to the other using two holes at the same time.  Stuff like that.

The particle properties of this wave is that it is not mass-less.  So, not only can this wave not travel instantaneously, it cannot even travel at the universe's top speed which is c.

The following users thanked this post: Vtile

#### Vtile

• Frequent Contributor
• Posts: 993
• Country:
• Ingineer
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #17 on: February 07, 2017, 09:48:20 pm »
Yep, in the cable sonars/radars reflectometers that is easily seen, if I'm understood correctly. I should repair mine, to get it finally play working order.
« Last Edit: February 07, 2017, 09:51:35 pm by Vtile »

#### David Hess

• Super Contributor
• Posts: 10486
• Country:
• DavidH
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #18 on: February 07, 2017, 10:59:55 pm »
Neither it, nor string theory can survive the inflation phase of the universe formation.  To survive means it has to take hold before inflation (so information can be passed along to the entire universe to make them consistent), and the results has to remain consistent post-inflation.  If it is to occur post-inflation, than information must be passed from one end of the universe to the other end at speed faster than the speed of light.

Entanglement does not solve this?

#### T3sl4co1l

• Super Contributor
• Posts: 14551
• Country:
• Expert, Analog Electronics, PCB Layout, EMC
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #19 on: February 07, 2017, 11:21:07 pm »
It's a meaningless question, because all electrons are identical.  You could just as well ask how long it would take the electrons to be replaced from the wire into my body; the answer is the same: it doesn't matter!

If you change the problem so that identification is possible, then the answer is either the drift velocity, or the carrier diffusion velocity, whichever is higher.  (Few conductors operate with a drift velocity higher than the thermal velocity, i.e., ballistic rather than drift motion.  An example is electrons in a Gunn diode, which is really a monode: just a lump of doped GaAs that exhibits negative resistance, thanks entirely to its material properties, no junction needed!)

A possible substitute could be an ionic conductor, like heated ZrO2, which carries current through mobile O2- ions and lattice defects.

The experimental design might be like so:

Set up a ZrO2 plate, with metallized grids on either side, with an atmosphere of 18O2 on one side.  The exchange of O2 with the ceramic surface, introduces different nuclear isotopes into the composition (which starts as mostly 16O).  As 16O is displaced with 18O isotopes, labeling is achieved, and observation of the process is possible.

You might analyze the results by drawing various currents through the samples, for different times, at different temperatures, then sectioning the samples.  (The samples should be relatively stable at room temperature, because the ions freeze in place.)  An atomic fluorescence spectrometer should be able to resolve the isotopic differences without too much hardship, I think?

It would be an interesting graduate experiment, but rather useless in results, as it should be expected to give the identical result that chemical diffusion and electronic transport are known to achieve.  (And, anomalous results could depend on impurities in the materials, so you might not learn anything even from very precise measurements.)

Tim
Seven Transistor Labs, LLC
Electronic design, from concept to prototype.
Bringing a project to life?  Send me a message!

#### linux-works

• Super Contributor
• Posts: 1945
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #20 on: February 08, 2017, 12:03:30 am »

A Chinese made electron is going to be exactly like an electron made in the USA.

but there is a difference.

the chinese electrons seem ok, at first; but an hour later, you'll just need more.

(lol)

#### Gregg

• Frequent Contributor
• Posts: 695
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #21 on: February 08, 2017, 01:38:29 am »
The problem with trying to remove the electrons form your wire is that they always return; at least in our physical world.  Electrons in a wire work a lot like a string of balls in a Newton’s cradle; when you drop one in on one end another pops out the other end, only to return and eventually reach equilibrium.
Then there is the case of shorting out your 16 ga wire with something like 480 volts and hundreds of amps which results letting out the magic smoke with all of the angry pixies soaring away to deposit the wire material on any surfaces available; like sputtering a metallic coating on a silicon wafer.
Enclosed are a couple of pictures of the aftermath after some hapless electrician burned through two ¼ inch thick layers of copper bus bar with a little over 500 volts DC from a big bank of lead acid batteries of a 750 KVA UPS installation.  All electrons were present and accounted for in the final tally; they were just attached to the copper plating everything including the Fluke meter at the bottom of the enclosure that the electrician failed to use.
Tossing your wire onto the surface of the sun may disassociate the metal atoms, but I doubt you could measure the result. Here on earth, you may be able to put tiny samples of your wire into the Haldron collider and knock a few of the outer electrons off the sample.  Even the electrons from arc welding, Tesla coils and lightning always return to equilibrium.

#### TerraHertz

• Super Contributor
• Posts: 3641
• Country:
• Why shouldn't we question everything?
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #22 on: February 08, 2017, 01:43:25 am »

Say you had a meter of 16ga wire. At what amps for how long would it take for each electron to be bumped out of one end and replaced in the other end? Or at what speed would a single electron make the journey though the wire?

To replace ALL THE ELECTRONS?
Disregarding the 'all electrons are the same one' mind-bender, the answer is... forever.
Because only the outer shell electrons are free to move in the solid. Regardless that those ones only drift very slowly (less than walking pace) under an applied field, the vast majority of the metal atom electrons are not going anywhere. Short of you heating the wire into a completely disassociated plasma of nuclei and free electrons. Even then, good luck separating them significantly.

Aside: I'd never heard of the 'all electrons are one' thing before. Bizarre.
That's a lot of copy and paste, or 'electron shortcuts'. I wonder who has the copyright on the original one? Hopefully no DRM takedown notices in our future. All your electrons are belong to us.
Collecting old scopes, logic analyzers, and unfinished projects. http://everist.org

The following users thanked this post: station240

#### NiHaoMike

• Super Contributor
• Posts: 5836
• Country:
• "Don't turn it on - Take it apart!"
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #23 on: February 08, 2017, 01:52:31 am »
Why don't HVDC enclosures have plastic covers/baffles to reduce the chance of a foreign object setting off an arc flash?
Cryptocurrency has taught me to love math and at the same time be baffled by it.

Cryptocurrency lesson 0: Altcoins and Bitcoin are not the same thing.

#### anfang

• Regular Contributor
• !
• Posts: 108
• Country:
##### Re: How long would it take to replace all the electrons in a piece of wire?
« Reply #24 on: February 08, 2017, 02:06:02 am »
Someone's been swigging too much paint thinner

Smf