# Voltage between electron and proton in ground state hydrogen atom?

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• epotratz
In summary: I'm guessing the actual voltage between the proton and electron must be higher because coulombs law says the voltage (electric potential) is 29 volts at 50 pm from the proton.
epotratz
TL;DR Summary
Is it possible to determine the “voltage” between an electron and a proton in a ground state hydrogen atom?
I’m not sure if this belongs in classic or quantum physics... but here it is...Is it possible to calculate the “voltage” between an electron and a proton in a ground state hydrogen atom?I know the ionization energy is 13.6 eV, so I assume it's safe to say the voltage is 13.6 volts at a certain distance of separation of the point charges (i.e., 105 pm)... but I don’t know what's going on once the electron and proton close the distance... going to negative voltage or ?Do i need to be factoring for a centripetal factor? Thanks,

Why do you think you are in an eigenstate of voltage?

epotratz said:
I know the ionization energy is 13.6 eV, so I assume it's safe to say the voltage is 13.6 volts

No, it isn't. 13.6 electron volts just means the ionization energy is the same, numerically, as the energy it would take to push one unit of electric charge through a potential change of 13 volts. It does not mean that ionizing a hydrogen atom is the same process, physically, as pushing one unit of electric charge through a potential change of 13 volts.

Also, the energy change of 13.6 electron volts for ionizing a hydrogen atom is the change between the electron being bound in the atom and separated from the atom. It is not the change between the electron being bound in the atom in its normal bound state and the electron being next to the proton, which is what "voltage between the electron and proton" would imply.

epotratz said:
at a certain distance of separation of the point charges (i.e., 105 pm)

The electron and proton aren't point charges. They're quantum objects. They don't even have a well-defined "distance of separation" while they're bound in a hydrogen atom.

It looks like you are trying to use classical concepts in a regime where they are not meaningful.

PeterDonis said:
No, it isn't. 13.6 electron volts just means the ionization energy is the same, numerically, as the energy it would take to push one unit of electric charge through a potential change of 13 volts. It does not mean that ionizing a hydrogen atom is the same process, physically, as pushing one unit of electric charge through a potential change of 13 volts.

Also, the energy change of 13.6 electron volts for ionizing a hydrogen atom is the change between the electron being bound in the atom and separated from the atom. It is not the change between the electron being bound in the atom in its normal bound state and the electron being next to the proton, which is what "voltage between the electron and proton" would imply.

Hey Peter,

It sounds like centripetal force (kinetic energy) of the electron is reducing the energy required to remove it from hydrogen, thus only requiring 13.6 eV, so I'm guessing the actual voltage between the proton and electron must be higher than 13.6 volts because coulombs law says the voltage (electric potential) is 29 volts at 50 pm from the proton.

Is this valid? Or do you know of a better way to calculate voltage at different separation distances?

PeterDonis said:
The electron and proton aren't point charges. They're quantum objects. They don't even have a well-defined "distance of separation" while they're bound in a hydrogen atom.

It looks like you are trying to use classical concepts in a regime where they are not meaningful.

Yes, I'm making a few assumptions that might be wrong, but assuming the separation distance is 50 pm in the ground state, there must be some way to estimate the electric potential, no?

epotratz said:
It sounds like centripetal force (kinetic energy) of the electron is reducing the energy required to remove it from hydrogen

Where are you getting that from?

Once again, the electron is not a point charge orbiting the proton. It's a quantum object. It looks like you are trying to use classical concepts in a regime where they are not valid.

epotratz said:
I'm guessing the actual voltage between the proton and electron must be higher

I guess I wasn't clear enough before. There is no such thing as "the actual voltage between the proton and the electron". It's not a meaningful concept. You're trying to use a classical concept in a regime where it's not valid.

epotratz said:
coulombs law says the voltage (electric potential) is 29 volts at 50 pm from the proton

The Coulomb potential does appear in the quantum Hamiltonian for the electron (in the common approximation where the proton is considered to be at rest), but it doesn't have an interpretation as a classical voltage between the electron and the proton.

PeterDonis said:
Where are you getting that from?
Hey David,

Sorry, was referred to whatever the center-fleeing force would be, not centripetal force.

I don't know what the "quantum Hamiltonian" is. I only have a basic qualitative understanding of quantum stuff.

Yes, I am trying to apply classical concepts to an electron and proton. I'm willing to control any variables to get an electric potential here...

epotratz said:
Hey David

As you can see from the header on my posts, my name is Peter Donis.

epotratz said:
I don't know what the "quantum Hamiltonian" is. I only have a basic qualitative understanding of quantum stuff.

Then I would strongly recommend taking some time to work through a textbook on basic QM. I personally think Ballentine is a decent one to start with. Or even the Feynman Lectures on Physics, which are available online, and have a pretty good treatment of the basics of QM.

epotratz said:
I am trying to apply classical concepts to an electron and proton.

You are trying to apply classical concepts to an electron and proton bound in a hydrogen atom. That doesn't work. Physicists spent the first few decades of the 20th century finding that out and developing quantum mechanics to treat this very case.

PeterDonis said:
As you can see from the header on my posts, my name is Peter Donis.

Then I would strongly recommend taking some time to work through a textbook on basic QM. I personally think Ballentine is a decent one to start with. Or even the Feynman Lectures on Physics, which are available online, and have a pretty good treatment of the basics of QM.

You are trying to apply classical concepts to an electron and proton bound in a hydrogen atom. That doesn't work. Physicists spent the first few decades of the 20th century finding that out and developing quantum mechanics to treat this very case.

Peter,

Are you saying its not possible to get an electric potential between an proton and electron in a hydrogen atom?

epotratz said:
Are you saying its not possible to get an electric potential between an proton and electron in a hydrogen atom?

Not the way you are using the term "electric potential".

It seems like you are missing Peter's main point. It's not that your assumptions are wrong, it's not even that you are using the wrong approach. The point is that the question doesn't really make sense in the QM world, that's not how atoms actually work.
When people like Niels Bohr tried to deal with these questions, they had to reinvent physics to get anywhere. You also need to reinvent the way you approach this question.

Dave and Peter,

I probably should have given some context. I'm writing an article. The"voltage in a hydrogen atom" is just a small point to complement a much larger topic based on the omnipresence of electric tension (voltage) in general. I'm writing it in layman's terms, and just need to be accurate enough to communicate some basic ideas. The article is full of disclosures.

So I understand it's a strange question to ask, and perhaps not even an appropriate question on a quantum mechanics forum. I also understand that several rules would have to be broken to approximate such a value. But I know an electric potential exists between a proton and electron, or at least between the electron and some other nearby atom. But my bootstrap approximation is not close enough. I figured the more advanced members here could provide a better approximation of the anwer.

Thank you.

epotratz said:
I'm writing an article. The"voltage in a hydrogen atom" is just a small point to complement a much larger topic based on the omnipresence of electric tension (voltage) in general.

Perhaps you shouldn't, since you don't understand it.

You completely ignored my Message #2, where I asked the critical question: essentially, how do you frame the question in a quantum mechanical way., Maybe it's because you don't know quantum mechanics, but if that's the case, maybe you shouldn't be arguing with those that do.

It is possible for a hydrogen atom to be in a state with a well-defined voltage potential between the proton and the electron. However, such an atom will not be in the ground state. In fact, it won't even have a well-defined energy.

weirdoguy
Interesting! Can you give a hint, how to construct a state of "well-defined voltage potential" (I guess you mean the electrostatic interaction potential in non-relativistic QM)? Wouldn't this simply be a "position eigenstate"? Last but not least, what should such a state be good for concerning the description of the hydrogen atom?

epotratz said:
I'm writing an article. The"voltage in a hydrogen atom"

As @Vanadium 50 said, you shouldn't.

epotratz said:
I'm writing it in layman's terms, and just need to be accurate enough to communicate some basic ideas.

But presumably you don't want to communicate wrong ideas. If you write about "the voltage in a hydrogen atom", you will be.

epotratz said:
I know an electric potential exists between a proton and electron, or at least between the electron and some other nearby atom.

You do? How do you know this? What measurements tell you this? (Hint: there aren't any.)

epotratz said:
my bootstrap approximation is not close enough. I figured the more advanced members here could provide a better approximation of the anwer

We can't provide a better approximation to something that doesn't exist.

It is possible for a hydrogen atom to be in a state with a well-defined voltage potential between the proton and the electron.

What state will this be? And what "voltage potential" observable will it be an eigenstate of?

Are you trying to discourage another guy from learning physics?

The OP has an interesting question and has basic understanding of physics. He also is aware of his limited knowledge of the subject, so he came here.

Also, dismissing any though experiments and analogies in favour for pure maths is totally dishearting. Pure abstract maths works only for a tiny percentage of people. Most of homo sapiens specimen think in terms of images and analogies.

If the OP's idea doesn't make sense in quantum physics then please give him the closest idea that makes sense.

Hey, this thread is labelled "basic".

The "voltage between electron and proton" means change of electron's potential energy in the presence of proton should the electron be pressed into the proton (divided by the unit charge). Unfortunately, pushing the electron into the proton, yielding a neutron, is not purely electromagnetic phenomenon. Better process to analyze would be decay of positonium. The energy emitted in a decay of positionium, minus particles kinetic and rest masses could be an analogy to the energy of the classical "voltage" between the electron and positon.

Hello, epotrarz. Keep learning, don't let yourself scared with maths and keep asking questions. And welcome to PF :).

<< Mentor Note -- profanity deleted from this post >>

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epotratz
haael said:
Are you trying to discourage another guy from learning physics?

No, we're trying to correct a misunderstanding he has. Correcting misunderstandings is an essential part of learning any subject.

haael said:
The OP has an interesting question

And a wrong answer to it, which we are trying to correct.

haael said:
Why do such people always get the answer: F*ck *ff and read the books?

You are misrepresenting what others are saying, and that (and your language) has just gotten you a warning.

haael said:
If the OP's idea doesn't make sense in quantum physics then please give him the closest idea that makes sense.

What if there isn't one?

haael said:
The "voltage between electron and proton" means change of electron's potential energy in the presence of proton should the electron be pressed into the proton (divided by the unit charge).

You are making the same mistake the OP is making: you are trying to treat the electron and proton as classical point particles. They're not. They're particularly not when they are bound in a hydrogen atom, which was what the OP specified.

Also, there is no experimental procedure by which you can "press" the electron into the proton. (In fact, by the classical logic you are using, you should not have to "press" on the electron at all, it should naturally fall into the proton since they have opposite charges and therefore attract each other. And this process should yield an infinite amount of energy according to the classical physics you are implicitly using.)

haael said:
The energy emitted in a decay of positionium, minus particles kinetic and rest masses could be an analogy to the energy of the classical "voltage" between the electron and positon.

There is no extra energy emitted in decay of positronium, other than the kinetic energies and rest masses of the electron and positron.

haael said:
Keep learning, don't let yourself scared with maths and keep asking questions. And welcome to PF :).

This, at least, is all good advice.

PeterDonis said:
And what "voltage potential" observable will it be an eigenstate of?

Whatever it is, it will commute with r, so an eigenstate of V will be an eigenstate of r. Aned since an eigenstate of r will not be an eigestate of the Hamiltonian, if the voltage is well-defined, the energy will not be. This is true irrespective of the form of the "voltage operator". (I can use scare quotes too! )

Edit: fixed errant not

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haael said:
Are you trying to discourage another guy from learning physics?

I can't speak for others, but I am not trying to discourage him from learning physics. I am, however, trying to discourage him from teaching physics, at least until he has learned it himself.

vanhees71
Whatever it is, it will commute with r, so an eigenstate of V will not be an eigenstate of r.

I assume you mean will be an eigenstate of r?

Thanks. Another wandering "not".

PeterDonis said:
No, it isn't. 13.6 electron volts just means the ionization energy is the same, numerically, as the energy it would take to push one unit of electric charge through a potential change of 13 volts. It does not mean that ionizing a hydrogen atom is the same process, physically, as pushing one unit of electric charge through a potential change of 13 volts.

Also, the energy change of 13.6 electron volts for ionizing a hydrogen atom is the change between the electron being bound in the atom and separated from the atom. It is not the change between the electron being bound in the atom in its normal bound state and the electron being next to the proton, which is what "voltage between the electron and proton" would imply.

Spent another full day on this...

After reading this response again I think my original post was misunderstood since I had a big error in the separation of charges, so it probably didn't make much sense... so I'll try again...

(and moving forward assuming a classic Bohr atom, or point charges, or whatever is needed to humor my pedestrian model...)

Based on this paper and this thread it appears that the inward electrostatic force between the proton and electron is balanced by the outward centrifugal force of the electron. Based on the Coulomb calculation at 53 pm (Bohr radius for hydrogen) the voltage is 27.2 volts between the proton and electron in the ground state. (27.2/2 = 13.6 volts) Makes sense assuming 27.2 volts of tension holding the electron in orbit, minus the outward centrifugal force maintaining a stable orbit, or some geometric wavelength limitation) Either way, it seems good enough to account for the 13.6 eV ionization energy

Then I found that Lyman limit for the hydrogen atom (91.18 nm photon) and found a Rydberg calculator. Assuming I did the calculation right, the Lyman limit is at n-41 on hydrogen, which puts the electron 88.9 nm from the proton. (based on 53pm*n-41 squared) This is why I originally said there would be 13.6 volts at a "certain distance of separation", which produces the 91.18 nm photon. (13.6 eV)

Now, assuming were holding the electron and proton apart by 88.9 nm...

1) The Coulomb calculation tells me that voltage is only 0.016 volts... but I'm expecting to see a voltage of at least 13.6 volts... does the Coulomb calculation not apply here since we have two moving point charges that will be approaching closer and closer?

2) Once the hydrogen is in the ground state, there is no more "potential" since the charges are as close together as they can get. So can we call this 0 volts?

Brain fried... help needed...

thanks,

haael said:
Hello, epotrarz. Keep learning, don't let yourself scared with maths and keep asking questions. And welcome to PF :).

<< Mentor Note -- profanity deleted from this post >>
I've never heard such a bad advice. Of course, we all have to keep learning forever to understand physics. But you should not tell people who want to do so to use the wrong tools. The worst advice you can give is to avoid math and even claiming it would be scaring. Math is the only adequate language to communicate about physics and to think about physics, and it's everything else than scaring. If there is one thing in the world you have the chance to really understand, then it's math, and it's fun to learn and think about math!

epotratz said:
Brain fried... help needed...
You’ve found an example of how thinking about a bound electron as a point particle moving at some distance from the nucleus just does not work. The brain-frying sensations you are experiencing is how reality tells you that you’re on the wrong track here.

epotratz said:
Based on this paper and this thread

The paper looks questionable; we'll have to take a look at it and where it was published. It certainly does not represent standard QM.

The thread is about the Bohr model of the hydrogen atom, which is wrong (and was known to be wrong not long after Bohr first came up with it). It also does not represent standard QM.

epotratz said:
assuming were holding the electron and proton apart by 88.9 nm...

To amplify what @Nugatory said: you can't assume this. In a hydrogen atom, there is no definite value for how far apart the electron and the proton are. The quantum state the atom is in is not an eigenstate of that observable. That makes all of your reasoning invalid.

vanhees71

## 1. What is the voltage between the electron and proton in a ground state hydrogen atom?

The voltage between the electron and proton in a ground state hydrogen atom is zero. This is because the electron and proton are held together by the electromagnetic force, which is a force of attraction between particles with opposite charges. In a ground state hydrogen atom, the electron is in its lowest energy level and is therefore not experiencing any force from the proton.

## 2. How is the voltage between the electron and proton in a ground state hydrogen atom related to the energy of the atom?

The voltage between the electron and proton in a ground state hydrogen atom is directly related to the energy of the atom. This is because the voltage is a measure of the electric potential energy between the two particles. As the energy of the atom increases, the voltage between the electron and proton also increases.

## 3. Can the voltage between the electron and proton in a ground state hydrogen atom be measured?

Yes, the voltage between the electron and proton in a ground state hydrogen atom can be measured. However, it is a very small value (on the order of 10^-18 volts) and requires specialized equipment to accurately measure.

## 4. How does the voltage between the electron and proton change as the electron moves to higher energy levels?

As the electron moves to higher energy levels in a hydrogen atom, the voltage between the electron and proton also increases. This is because the distance between the two particles increases, resulting in a decrease in the attractive force between them. As a result, the voltage between them increases.

## 5. Is the voltage between the electron and proton in a ground state hydrogen atom affected by external electric fields?

Yes, the voltage between the electron and proton in a ground state hydrogen atom can be affected by external electric fields. This is because the electric field can exert a force on the electron, causing it to move and thus altering the voltage between the two particles. However, in a ground state hydrogen atom, the electron is in its lowest energy level and is therefore not easily affected by external electric fields.

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