Why don't high-voltage electrons in a metal wire escape?

[Mayan Fung]

The work function of a metal is typically several eV. When we transmit electricity through cables of some 10-100kV, how come the electrons not having enough energy to escape from the metal?

 

[Vanadium 50]

Can you write down an equation relating wire voltage to electron emission?

 

[Mayan Fung]

Can you write down an equation relating wire voltage to electron emission?

Sorry I don't understand what you are asking exactly. What I am thinking is that under an electric potential difference, an electron would eventually gain enough kinetic energy to escape from the metal.

 

[DaveE]

It may help for you to think of the electric field strength (V/m) at the electron in question rather than just the potential difference (V). If you have two wires at different potentials the electrons will jump if they get close enough to each other.

 

[sophiecentaur]

The work function of a metal is typically several eV.

That's true (though it's quite a bit higher for all but the Alkali Metals) but that amount Energy cannot 'get to' an electron near the surface of a metal. You need a photon of incident radiation to single out just one particular electron. Just because the energy is stated in terms of eV, doesn't actually mean that those volts can have an effect to a bound electron. Despite the very low average drift velocity of electrons inside a metal, there is a huge range of velocities of the electrons actually within the metal, including some very fast ones so, by your argument, you could expect those electrons to be constantly escape the surface yet they don't.

If you look up Photoelectric Effect you will see that photoelectrons can be affected by such small potentials and can be 'stopped' by an electrode with only a volt or two (search in the link for "stopping potential".

 

[anorlunda]

Are you thinking about corona discharge? That is caused by ionization in the air, not the electrons in the wire, and in the range 100-1000 kV
https://en.wikipedia.org/wiki/Corona_discharge

 

[sophiecentaur]

not the electrons in the wire

Each electron in the metal is is a nice cosy bed of almost neutral charge and any external field will just cause a huge number of them to shift just a little bit until the fields balance. Otoh, being an insulator, the air can experience very high fields locally. Some the atoms in the nearby air can be subjected to very high fields (around spikes and corners on the metal surface) which can ionise them and then you have a spark. The ions in the spark can take individual electrons out of the metal (or give them) due to high (atomic scale) local fields.

 

[Vanadium 50]

What I am thinking is that under an electric potential difference, an electron would eventually gain enough kinetic energy to escape from the metal.

Potential difference between where are where?

I'm trying to get you to ask a clear question, rather than have us all guess what you mean.

 

[ZapperZ]

The work function of a metal is typically several eV. When we transmit electricity through cables of some 10-100kV, how come the electrons not having enough energy to escape from the metal?

That potential difference is across the wire, not between the wire and some other external surface. So the electrons will take the easiest route and flow through the wire.

If this is an isolated piece of metal (or a grounded one), and another surface at a different potential is next to it, then YES, the electrons can escape into the air. That's how we get the phenomenon of field emission. That's why you get a spark when you reach for a metal door nob during winter or when the air is very dry.

What you are being asked to think about is WHERE is the potential difference being applied. You cannot just say that there is a 10-100 kV potential difference but not think of the two locations that indicate such a potential difference.

Zz.

 

[sophiecentaur]

f this is an isolated piece of metal (or a grounded one), and another surface at a different potential is next to it, then YES, the electrons can escape into the air. That's how we get the phenomenon of field emission. That's why you get a spark when you reach for a metal door nob during winter or when the air is very dry.

It's not straightforward though because it's a non-linear system. Before any current flows, you have an insulator between the two pieces of metal so all the Field is in the air and can cause ionisation. What happens when the two conductors are in a vacuum is very different and a much higher voltage is necessary to drag electrons off one surface than when there is some ionisable air in between. (Vacuum Capacitors are great for use at very high voltages)

 

[ZapperZ]

It's not straightforward though because it's a non-linear system. Before any current flows, you have an insulator between the two pieces of metal so all the Field is in the air and can cause ionisation. What happens when the two conductors are in a vacuum is very different and a much higher voltage is necessary to drag electrons off one surface than when there is some ionisable air in between. (Vacuum Capacitors are great for use at very high voltages)

I'm not sure why we are getting into the details of this and why this is relevant to the thread.

Field emission occurs, in principle at any forward bias voltage, because it is a tunneling phenomenon. I can have a sharp protrusion on the metal surface or grain boundary, that topology can create a huge localized field-enchancement (grain boundaries can enhance the field by 100's). Those are field-emission sources.

Zz.

 

[Algr]

My understanding is that if an electron escaped like that, the wire would then have a positive charge, and it would just suck in another electron from somewhere else. Then it would be as if nothing happened. Is that right?

 

[ZapperZ]

My understanding is that if an electron escaped like that, the wire would then have a positive charge, and it would just suck in another electron from somewhere else. Then it would be as if nothing happened. Is that right?

If the wire is isolated, yes. In a typical field-emission setup, the wire or field-emitter is not isolated, such as grounded, if you do not want charging effects.

Zz.

 

[sophiecentaur]

I'm not sure why we are getting into the details of this and why this is relevant to the thread.

Field emission occurs, in principle at any forward bias voltage, because it is a tunneling phenomenon. I can have a sharp protrusion on the metal surface or grain boundary, that topology can create a huge localized field-enchancement (grain boundaries can enhance the field by 100's). Those are field-emission sources.

Zz.

Current flowing from a piece of metal by any mechanism is surely relevant?

I was looking around the topic and, of course, as well as photo emission, thermionic emission came into what I read. At room temperature, the field required is much higher than for a 'hot cathode'. I get the impression that the energy required for an electron to leave the surface is highest for Field Emission, then thermally assisted Field Emission, Field assisted thermionic Emission and Thermionic Emission, when the electrons are continually 'boiling off'.
I found the https://www.researchgate.net/figure/Paschens-breakdown-voltage-Eq-8-the-field-emission-breakdown-voltages-in_fig8_224141072 which shows (afaics) that field emission will dominate for very small gaps but the Paschen curve for air breakdown seems to go below the field emission curve as gap size increases.

the wire would then have a positive charge,

The electrons around the outside of the metal under these conditions can form a 'cloud'. It's referred to as a space charge which hangs around unless conducted away. (Much the same situation as for thermionic emission)

 

[ZapperZ]

Current flowing from a piece of metal by any mechanism is surely relevant?

I was looking around the topic and, of course, as well as photo emission, thermionic emission came into what I read. At room temperature, the field required is much higher than for a 'hot cathode'. I get the impression that the energy required for an electron to leave the surface is highest for Field Emission, then thermally assisted Field Emission, Field assisted thermionic Emission and Thermionic Emission, when the electrons are continually 'boiling off'.
I found the https://www.researchgate.net/figure/Paschens-breakdown-voltage-Eq-8-the-field-emission-breakdown-voltages-in_fig8_224141072 which shows (afaics) that field emission will dominate for very small gaps but the Paschen curve for air breakdown seems to go below the field emission curve as gap size increases.
View attachment 268126The electrons around the outside of the metal under these conditions can form a 'cloud'. It's referred to as a space charge which hangs around unless conducted away. (Much the same situation as for thermionic emission)

What exactly is the point in all of this again?

Zz.

 

[sophiecentaur]

What exactly is the point in all of this again?

I'm sorry this isn't to your taste but did you read the OP recently?
Is PF not allowed to explore around a subject (which concerns electrons escaping from a metal surface)? My posts are not exactly off-topic, compared with many other posts from other members that you can read in many threads.

 

[Vanadium 50]

Yes, but the OP is confused about something very basic - that potential difference is measured between two well-specified points. Does bringing thermionic emission in help with that understanding?

 

[ZapperZ]

I'm sorry this isn't to your taste but did you read the OP recently?
Is PF not allowed to explore around a subject (which concerns electrons escaping from a metal surface)? My posts are not exactly off-topic, compared with many other posts from other members that you can read in many threads.

I agree with @Vanadium 50 . This discussion on field emission is a total distraction and from my perspective, is not on topic.

For your info, I investigated field emission, since it is something we were trying to mitigate both in our photocathodes in a photoinjector and in our PMT. So it isn't something that ".. isn't to my taste..". I can talk about it for days! But I don't see this as being pertinent to the OP's question because there is a confusion there in what the potential difference mean in a wire, but not external to it.

Zz.

 

[sophiecentaur]

there is a confusion there in what the potential difference mean in a wire,

There was - because the question was put in a naive way. I think we all know what was actually meant but no one thought to dig him out of that one. (I was not on PF at the time). PF has a habit of leaping on a question that's not put in just the right way, rather than gently helping to re state that question better first.

I am surprised you cannot see the field emission thing in the context of a hierarchy of reasons for an electron to leave a metal surface. As an expert about Field Emission, you would surely see it as 1. not being a familiar phenomenon and 2. requiring rather special circumstances. (Certainly not something needed for a good answer to the 'real' OP question.

 

[ZapperZ]

I am surprised you cannot see the field emission thing in the context of a hierarchy of reasons for an electron to leave a metal surface.

I'm not going to respond to something that I've never said, implied, and isn't true.

Zz.

 

[sophiecentaur]

Does bringing thermionic emission in help with that understanding?

The OP includes mention of the Work Function (which actually makes out fairly clear that the question was about - just badly put) so the idea of other mechanisms is relevant imo.
The question was basically "If a 3eV photon can shift an electron, why doesn't 10kV?"
The connection with thermionic emission and the energies involved is surely relevant and so is what happens as the volts are further increased above 3V.

Perhaps we should just bounce all questions that are not put in a suitably erudite way and demand that the questioners pass some sort of test first.

 

[ZapperZ]

The OP includes mention of the Work Function (which actually makes out fairly clear that the question was about - just badly put) so the idea of other mechanisms is relevant imo.
The question was basically "If a 3eV photon can shift an electron, why doesn't 10kV?"
The connection with thermionic emission and the energies involved is surely relevant and so is what happens as the volts are further increased above 3V.

Perhaps we should just bounce all questions that are not put in a suitably erudite way and demand that the questioners pass some sort of test first.

But is that the ONLY option? Why can't we just tell the OP how that 10kV is applied in the wire? I already mentioned that this is not external to the wire.

There's a simple remedy to this without going off on a tangent!

Zz.

 

[vanhees71]

Why don't you simply discuss the physics but about "politics" of PF in answering questions?

 

[Vanadium 50]

People are discussing physics. The issue is whether field emission is helpful or not to someone who wrote the words "work function" but doesn't seem to understand electrical potential.

 

[vanhees71]

Well, yes, but then simply explain it.

 

[sophiecentaur]

Well, yes, but then simply explain it.

Twenty posts earlier would have helped. But I still think it was just sloppiness in the question and not ignorance. How else could Work Function come into it?

 

[sophiecentaur]

For your info, I investigated field emission, since it is something we were trying to mitigate both in our photocathodes in a photoinjector and in our PMT. So it isn't something that ".. isn't to my taste..". I can talk about it for days!

I'm not going to respond to something that I've never said, implied, and isn't true.

?

 

[anorlunda]

The OP has not returned to PF since post #3. Does that influence the back-and-forth?

His wording in post #3, makes it sound like he visualizes a wire as being like a linear particle accelerator where a free electron continuously accelerates in the external E field. If I had seen that earlier, I might have pointed him to The Drude Model.

Sorry I don't understand what you are asking exactly. What I am thinking is that under an electric potential difference, an electron would eventually gain enough kinetic energy to escape from the metal.

 

[Mayan Fung]

Thank you all for the fruitful discussion. Sorry that I didn't go online for the weekend.

After reading all your comments, I think about it again. I shall further rephrase my question as follows:

I understand that the work function is related to the photoelectric effect. But I read on Wikipedia about the electron emission due to a high temperature - a phenomenon called "Thermionic emission" (https://en.wikipedia.org/wiki/Thermionic_emission). So according to my understanding, as long as an electron gains enough energy, no matter what form of energy (light/kinetic), an emission may occur.

Naively, I think that if an electron travels in an electric field, let's say 1000V over 1km, then after it travels 20m, it will gain 20eV energy, which is sufficient to escape. If the electron does not escape, that means it must have lost energy.

The next thing that comes to my mind is that the electron is not traveling in a vacuum but a metal. The Drude model comes to play. It describes a group of electrons drifting slowly while individual electrons bouncing the stationary ions frequently. That means the electrons may exchange energy with the ions.

Combining the above thoughts, I propose two possibilities where both contradicts to reality.
1. The electrons continually transfer kinetic energy to the ions so they cannot escape from the metal. However, it means that the energy is localised and most of the energy is dissipated as heat which is not the real case as we can transmit our electricity pretty well in the power grid. According to my logic, the maximum energy carried by the electrons cannot exceed the work function, which would mean the eventual voltage arrived at the end-user cannot be bigger than a few volts.
2. The electrons do not lose most of their energy to the ions. Then, in a short time, it shall acquire enough energy to escape from the metal wire.

I understand that I must have made some wrong arguments in the above construction. Sorry that I may not present clearly enough.

 

[willem2]

Combining the above thoughts, I propose two possibilities where both contradicts to reality.
1. The electrons continually transfer kinetic energy to the ions so they cannot escape from the metal. However, it means that the energy is localised and most of the energy is dissipated as heat which is not the real case as we can transmit our electricity pretty well in the power grid.
2. The electrons do not lose most of their energy to the ions. Then, in a short time, it shall acquire enough energy to escape from the metal wire.

The main thing is, between which 2 point do you have a 10-100 kV potential difference?
Normally this is between 2 wires. An electron in a vacuum that would move between 2 pieces of metal with a 100 kV difference would get 100 kV of kinetic energy, but it would need to be free of the wire before it could get that 100 kV.

If you have a 10-100 kV potential difference between 2 points with a piece of metal wire between it, you would get a current. Your piece of wire would have to be very long and thin, to get a current that is low enough to not evaporate/melt the wire. The electrons would transfer all the kinetic energy that they get from the field to the ions, and this will heat the wire. The random speeds of the electrons would depend only on the temperature, and not on the electric field in the wire, and the kinetic energies would remain small compared to the work function until about 1000K.
In the power grid you do not get large potential differences across short pieces of wire.

 

[Mayan Fung]

The main thing is, between which 2 point do you have a 10-100 kV potential difference?
Normally this is between 2 wires. An electron in a vacuum that would move between 2 pieces of metal with a 100 kV difference would get 100 kV of kinetic energy, but it would need to be free of the wire before it could get that 100 kV.

If you have a 10-100 kV potential difference between 2 points with a piece of metal wire between it, you would get a current. Your piece of wire would have to be very long and thin, to get a current that is low enough to not evaporate/melt the wire. The electrons would transfer all the kinetic energy that they get from the field to the ions, and this will heat the wire. The random speeds of the electrons would depend only on the temperature, and not on the electric field in the wire, and the kinetic energies would remain small compared to the work function until about 1000K.
In the power grid you do not get large potential differences across short pieces of wire.

I understand your point. I also agree with this point of view in the macroscopic world. But if I go down to the microscopic view, I cannot construct a comprehensive picture to comply with the macroscopic observations.

There is not a large potential difference across a short piece of wire. I agree. So the electrons only gain the energy very gently, but they accumulate energy throughout the journey in the wire. My puzzle is that I think an electron cannot carry energy more than a few eV because it would have escaped before it arrives at its destination. But if that's the case, most of the energy would be dissipated which also disagreed with reality.

 

[willem2]

So the electrons only gain the energy very gently, but they accumulate energy throughout the journey in the wire.

Electrons do not accumulate energy,and they do dissipate all of the energy. The reason that this is possible, is because electric fields in conductors are small.

 

[Mayan Fung]

Electrons do not accumulate energy,and they do dissipate all of the energy. The reason that this is possible, is because electric fields in conductors are small.

I kind of get some sense on what you mean. I shall try to self study more on that first. Thanks for the discussion and help!

 

[sophiecentaur]

The main thing is, between which 2 point do you have a 10-100 kV potential difference?
Normally this is between 2 wires. An electron in a vacuum that would move between 2 pieces of metal with a 100 kV difference would get 100 kV of kinetic energy, but it would need to be free of the wire before it could get that 100 kV.

It's a great shame that this point was not made explicitly after a couple of posts here. But. as the OP was not on the thread, no harm done.

. So the electrons only gain the energy very gently, but they accumulate energy throughout the journey in the wire.

'very gently' is putting it mildly. They travel through and 'emerge' with average velocities of only around 1mm/s under all conditions. The Resistance of the wire can be looked upon as affecting the Power dissipated in the wire. P = I²R (which comes from P=IV, which we know and love). The Power 'passed on' to the rest of the circuit is actually nothing to do with the Kinetic Energy of the electrons and this is a popular misconception when trying to understand the transfer of Power down a wire.

 

[snorkack]

Perhaps here a comparison between electricity and water helps.

A high voltage wire could be compared to a shallow ditch along the ridge of a high mountain.
The water could gain a lot of energy if it were able to cascade down the mountainside. But in order to do so, it would somehow have to get across or through the banks of the ditch. Shallow as they are compared to the water level inside the ditch, the water inside the ditch does not have free kinetic energy to spill over the banks. The huge potential energy of cascading down the mountainside remains just a potential.