Why don't electrons leave a metal surface?

[jklfabc]

TL;DR Summary

Why does attraction always prevail over repulsion in keeping electrons from leaving the metal? (Even if the metal surface is negatively charged)

Why don't electrons leave the metal surface? I have searched the internet for the answer and from my teachers they all say that electrons are attracted to the positive ion crystal lattice. I know that, but the problem is why is that attraction so much greater than the repulsion from other free electrons? While obviously, with an electrically neutral surface, that repulsion must balance out the attraction. Even when placing metal in an external electric field or giving it a negative charge, the repulsion from other free electrons can be even greater than the attraction from the ions. But reality proves that the repulsive force is many times smaller than the attraction force(?). Can someone please show why the attraction is greater than the repulsion? This problem bothers me a lot. Hope someone can solve this problem for me

 

[Baluncore]

Welcome to PF.

Why don't electrons leave the metal surface?

The free electrons do, until the positive nuclear charge is neutralised, which is how you find it.

... my teachers they all say that electrons are attracted to the positive ion crystal lattice.

The fixed count of protons in a stable atomic nucleus define the chemistry of the atoms by attracting about the same number of electrons to that atom's vicinity. Those electrons are shared, which makes the chemical bonds that hold the nuclei together, to form the crystal lattice, that you call a solid metal.

If you remove too many electrons from the surface cloud, the metal crystal will fall apart, as the proton charges of the nucleus repel each other. To remove a "free" electron from the surface of a metal object, you must provide energy. That is called the Photoelectric effect.
https://en.wikipedia.org/wiki/Photoelectric_effect

 

[PeroK]

TL;DR Summary: Why does attraction always prevail over repulsion in keeping electrons from leaving the metal? (Even if the metal surface is negatively charged)

Why don't electrons leave the metal surface? I have searched the internet for the answer and from my teachers they all say that electrons are attracted to the positive ion crystal lattice. I know that, but the problem is why is that attraction so much greater than the repulsion from other free electrons? While obviously, with an electrically neutral surface, that repulsion must balance out the attraction. Even when placing metal in an external electric field or giving it a negative charge, the repulsion from other free electrons can be even greater than the attraction from the ions. But reality proves that the repulsive force is many times smaller than the attraction force(?). Can someone please show why the attraction is greater than the repulsion? This problem bothers me a lot. Hope someone can solve this problem for me

There is no valid model of the atom using classical EM. You need QM to explain atomic structure. The electrons form a bound energy state that satisfies the Schrodinger equation, rather than Maxwell's equations.

Likewise, the reason for chemical bonding is that the two or more atoms form a lower overall energy state.

And, the behavior of free electrons in a metal is governed by QM:

https://en.m.wikipedia.org/wiki/Free_electron_model

 

[hutchphd]

What keeps a Hydrogen atom from collapsing? Why does it take energy ionize a Hyrogen atom? These are simpler systems than chunk of metal but still require Quantum Mechanics to provide the answers. You should be equally confused about these simpler systems.

 

[tech99]

I think the answer to your exact question is that the charges within the metal are, on average, in equilibrium until we supply energy, when electrons will be emitted. As an example of the action, when we heat tungsten, as with the cathode of a vacuum tube, electrons in the metal acquire sufficient energy to be emitted from the surface. They are then attracted back to the surface because they leave behind a positive charge. We end up with a cloud - a space charge - above the surface. If a positive anode is then introduced, electrons are drawn from the space charge and form a current flowing across the space.

 

[Drakkith]

Even when placing metal in an external electric field or giving it a negative charge, the repulsion from other free electrons can be even greater than the attraction from the ions. But reality proves that the repulsive force is many times smaller than the attraction force(?). Can someone please show why the attraction is greater than the repulsion?

There's no mystery here. The positive charges in the lattice attract the electrons very strongly and it takes a very large force to counteract them. The exact 'why' is hard to put into words if that doesn't already make sense. Perhaps remember that the electrons are spread out and able to move in response to adding more electrons. So when you add some extra electrons the extra negative charge alters the distribution slightly, but not much else. The negative charges are spread out and don't entirely 'screen' the positive charge from the nucleus at short ranges. This is also one reason you can add extra electrons to an atom/molecules to get anions.

 

[Dale]

TL;DR Summary: Why does attraction always prevail over repulsion in keeping electrons from leaving the metal? (Even if the metal surface is negatively charged)

Why don't electrons leave the metal surface?

They do leave.

There is a characteristic of a given surface called the “work function”. It is the amount of work that is required to remove an electron from the metal surface to the vacuum immediately outside the metal. For copper this is around 4.8 eV.

When electrons have the energy of the work function then they can and do leave the surface. For example, if the metal is heated enough then some of the thermally excited electrons can reach that energy. Or if there are incident photons with enough energy they can exceed work function.

 

[vanhees71]

Of course one should stress that one can understand this only using quantum mechanics!

 

[tech99]

Do you know if tunneling is involved in this case?

 

[vanhees71]

Sure. The electrons leak out with some probability beyond the limits given by the classical model. A simple toy model is to consider an electron in a finitely deep potential pot. You have a certain finite number of bound states, and the wave functions have support till infinity, exponentially decaying outside of the "classically allowed" region.

 

[apostolosdt]

They do, like in photoemission effect. The theoretical description of such phenomena is not yet complete. Not only because metal surface—external probe interactions are many-particle QFT effects; the metal surfaces are restructured over a number of crystal layers, making the metal very difficult to model.

On the other hand, there’s a plethora of experimental, non-evasive techniques, so we know a lot about metals’ surface physics.

 

[Baluncore]

The OP required respect and acceptance, followed by a safe crossing from the classical to the quantum.
Beginners retreat every time they see a statement like; "one can only understand this using quantum mechanics".
Where is the OP now ?

 

[hutchphd]

Hopefully deciding that she needs to understand Quantum Mechanics.
What was the nature of the "disrespect" and how is it to be ameliorated? Sometimes half-truths are not better.

 

[vanhees71]

The OP required respect and acceptance, followed by a safe crossing from the classical to the quantum.
Beginners retreat every time they see a statement like; "one can only understand this using quantum mechanics".
Where is the OP now ?

It's no disrepect giving an honest answer!

 

[Baluncore]

What was the nature of the "disrespect" and how is it to be ameliorated?

They get respect from me.
The OP is a critical thinker, who understood and questioned their teachers. They have an existing science foundation and an interest in Physics. Be gentle.

While "one can only understand this using quantum mechanics" may be true, it undermines their existing educational foundation and confidence. In effect, it tells them that they have been misled in their exploration, that they now understand nothing and must start again, or change from STEM to the Arts. I believe it is better to show them the next page, than to tell them that they have been going the wrong way.

The concept of quantum mechanics does not yet exist in the mind of the beginner. Using the as yet meaningless term can only confuse them. We must live our education forwards, but it can only be understood backwards. If they get there, they too will know that "one can only understand this using quantum mechanics".

 

[hutchphd]

Why is it off-putting to tell them it is a fact that they will understand later should they so desire?

 

[Baluncore]

Why is it off-putting to tell them it is a fact that they will understand later should they so desire?

When they are put in their place, and treated like a child, it disrespects and belittles them.

 

[apostolosdt]

The OP required respect and acceptance, followed by a safe crossing from the classical to the quantum.
Beginners retreat every time they see a statement like; "one can only understand this using quantum mechanics".
Where is the OP now ?

I humbly agree with you! My post was even worse than the "quantum-mechanical" ones.

 

[TeethWhitener]

But reality proves that the repulsive force is many times smaller than the attraction force(?).

It doesn’t require quantum mechanics to understand why this can’t be true. The B-level answer is that the metal is in equilibrium, so all the forces must sum to zero. The only thing that changes when we switch to quantum mechanics is that the expectation values of the forces sum to zero. If there were a net force on the metal, it would be changing in some way. If the attractive force were greater, the metal would contract, and if the repulsive force were greater, the metal would expand.

 

[PeroK]

The only thing that changes when we switch to quantum mechanics is that the expectation values of the forces sum to zero.

Really?

 

[vanhees71]

They get respect from me.
The OP is a critical thinker, who understood and questioned their teachers. They have an existing science foundation and an interest in Physics. Be gentle.

While "one can only understand this using quantum mechanics" may be true, it undermines their existing educational foundation and confidence. In effect, it tells them that they have been misled in their exploration, that they now understand nothing and must start again, or change from STEM to the Arts. I believe it is better to show them the next page, than to tell them that they have been going the wrong way.

The concept of quantum mechanics does not yet exist in the mind of the beginner. Using the as yet meaningless term can only confuse them. We must live our education forwards, but it can only be understood backwards. If they get there, they too will know that "one can only understand this using quantum mechanics".

What a nonsense! It's not an insult nor should it be discouraging, if somebody tells you that something can't be explained with something you already know. After all, you ask questions to "experts" to learn something you don't yet know, and getting an honest answer, telling you what's needed to answer the question, is just the right answer.

When my teacher (BTW the best teacher of my entire high-school career) told me that there's something, which cannot be understood with what I have learnt so far, it was a motivation for me to learn what's needed to answer my question. Of course, she always helped pointing me to books, where I could find the topic.

We all know very little, and if there's something I don't understand, I just dig through the literature and finally try to understand it myself, working out in my own way, what I read. That's the only way to really understand something in the natural sciences. Just to give some handwaving popular-science answer is simply dishonest.

 

[TeethWhitener]

Really?

Why wouldn’t this be true? The only forces in question are Coulombic. Quantum mechanics explains why the electron doesn’t just sit right on top of the nucleus, but that has nothing to do with forces and everything to do with the uncertainty principle.

 

[vanhees71]

Well, classical electrostatics tells you that there cannot be a bound state!

 

[PeroK]

Why wouldn’t this be true? The only forces in question are Coulombic. Quantum mechanics explains why the electron doesn’t just sit right on top of the nucleus, but that has nothing to do with forces and everything to do with the uncertainty principle.

It's more like the Pauli Exclusion Principle! Atoms and molecules in QM are generally in energy eigenstates.

What you're posting is not recognizable to me as QM.

 

[Baluncore]

This is the Classical Physics forum.
Should this thread be moved to the Quantum Physics forum?

 

[hutchphd]

No. But the classical physics forum does need to recognize and acknowledge the existence of quantum mechanics.

 

[TeethWhitener]

It's more like the Pauli Exclusion Principle!

The Pauli exclusion principle applies to identical fermions. Electrons and nuclei aren’t identical.

Atoms and molecules in QM are generally in energy eigenstates.

Maybe when you’re studying them in class. But in the real world they’re almost always at the very least going to be in some sort of quasi-thermal distribution.

But none of that has anything to do with the fact that the net force (or expectation value of the force, if you insist on QM language) is zero in a body at equilibrium.

What you're posting is not recognizable to me as QM.

I said at the outset that it doesn’t require quantum mechanics to understand that saying one force is stronger than the other is incorrect in an equilibrium system.

 

[vanhees71]

It's more like the Pauli Exclusion Principle! Atoms and molecules in QM are generally in energy eigenstates.

What you're posting is not recognizable to me as QM.

In everyday matter we deal with bound states of particles in or at least close to thermal equilibrium. It's not an energy eigenstate. For that you'd have to cool down your matter to 0K temperature such that it goes into the ground state.

 

[Mister T]

TL;DR Summary: Why does attraction always prevail over repulsion in keeping electrons from leaving the metal? (Even if the metal surface is negatively charged)

You are essentially asking how a negatively charged object can remain charged. Why do the free electrons not escape and make the object neutral. Sometimes there is just no conducting path to drain off the excess electrons. Like when you rub your feet on the carpet, and then a spark flies when you do provide a path by touching a conductor.