Speed of Electrons: A Classic View

[PeroK]

So what force is preventing the electron to fall on/into the nucleus?

What prevents the electron falling into the nucleus? The Schroedinger equation, of course!

 

[ZapperZ]

I'm not doubting the formalism. I just want to better understand what is going on there. Again: if the electron is "smeared" around the nucleus but not falling into it, a force must keep it from falling. What force is it? And if the "smeared" electron accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule), it emits EM radiation? If not, why not? (for the Bohr model was a big issue, but here is somehow overlooked) If yes, how is this loss of energy affecting the electrons?

But this is exactly the reason why I insisted that you are clinging on to the planetary model, even if you don't realize it!

Let's get this clear first and foremost. If I have a bare nucleus, and then I shoot electrons at the bare nucleus. The electron may hit the nucleus, and a bunch of interesting things may happen. This was a common experiment in the early days of high energy physics. So yes, an electron can definitely reach the nucleus under that situation.

So now, what is the difference with an atom? Why did it take so long, and why did it have to wait until the development of QM to actually be able to account for the most accurate behavior of an atom? Why is the QM description of the atom in terms of the wavefunction so much more accurate than the old Rutherford/Bohr model? What was given up?

Your question has less to do with why an electron doesn't crash into the nucleus, and more to do with why QM is valid and the overall picture of how QM describes our world! This is inescapable once you start with the QM Hamiltonian or the Schrodinger equation. So it isn't the "why", but rather the "how". The issue that you have is bigger than you think.

Until you come to the agreement that that is how we can describe the phenomena at this scale, then the issue here isn't about the electron and the atom, but rather it is about the validity of QM's description.

Period!

Zz.

 

[Nugatory]

Again: if the electron is "smeared" around the nucleus but not falling into it, a force must keep it from falling.

Why must that be so?

This might be a good time to dig into exactly what it means to say "a force must keep it from falling". Force is defined by the equation $F=ma$ and $a$ is defined to be the second derivative of position with respect to time, so any appeal to force as an explanation for electron behavior assumes that the electron has a position. But that assumption is incompatible with the "smeared" model in which the electron has no position. A similar argument applies to the word "falling" which implies that the electron is moving closer to the nucleus - but "closer" only makes sense if the electron has a position so that we can talk about the distance between where it is and the nucleus, and in the "smeared" model there's no position.

Instead, we have to listen to @ZapperZ in post #34 above: Solve Schrodinger's equation for the electron bound to the nucleus. In this solution there are no forces, no positions, no trajectories that seem to fall into the nucleus, no distance from the nucleus... But there is an accurate description of how the electron behaves without any of these misplaced classical notions.

 

[DanMP]

Your question has less to do with why an electron doesn't crash into the nucleus, and more to do with why QM is valid and ...

No, this was your problem all the time: instead of answering my questions, you tried to intimidate me because you thought that I'm against quantum mechanics and "clinging" to Bohr's model. To be clear, I'm not against QM. I'm aware that it is very successful, so I think that its math is OK. Only the interpretation, in my opinion, may be less perfect, so I asked simple, direct, questions, in order to see how this successful theory solved the (apparent?) problems I mentioned.

Nugatory, instead, addressed (one of) my questions and he did it very professionally. Thank you Nugatory!

This might be a good time to dig into exactly what it means to say "a force must keep it from falling". Force is defined by the equation F=maF=maF=ma and aaa is defined to be the second derivative of position with respect to time, so any appeal to force as an explanation for electron behavior assumes that the electron has a position. But that assumption is incompatible with the "smeared" model in which the electron has no position. A similar argument applies to the word "falling" which implies that the electron is moving closer to the nucleus - but "closer" only makes sense if the electron has a position so that we can talk about the distance between where it is and the nucleus, and in the "smeared" model there's no position.

My problem was/is that I thought that the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus means that the electron is somehow "smashed" in little pieces and distributed in a particular geometry around the nucleus (if we do something like that with the Moon, after stopping it, the pieces would fall on the Earth). In such a case, electron "pieces" around the nucleus may have a position and should fall ...

How about my other question?

if the "smeared" electron accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule), it emits EM radiation? If not, why not? (for the Bohr model was a big issue, but here is somehow overlooked)

 

[Nugatory]

How about my other question?

Same issue - no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.

The Bohr model was an effort to reconcile the observed stability of atoms with a classical description of the electrons (small solid object with a definite position) that predicted that atoms would be unstable. The he need for that reconciliation went away when we discovered that the classical description was not right.

 

[DrClaude]

If you accelerate an atom, you are of course accelerating an electron, but you are also accelerating an equal-charge nucleus, and the radiation you would get for each cancel out. You can take the atom as a globally neutral entity, so no emission of radiation due to acceleration.

 

[DanMP]

If you accelerate an atom, you are of course accelerating an electron, but you are also accelerating an equal-charge nucleus, and the radiation you would get for each cancel out.

So radiation/photons is/are emitted both by the nuclei and by the "smeared" electrons, but they "cancel out"?

Nugatory wrote (the underline is mine):

no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.

In Wikipedia I found (again, the underline is mine):

... As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.[1]:67 The charges thus radiate their own electromagnetic wave that is at the same frequency, ...

Who is right then?

And if the electrons in a material can be "shaken" by the EM fields, then they also would be attracted by the nuclei and fall into it ...

 

[DrClaude]

So radiation/photons is/are emitted both by the nuclei and by the "smeared" electrons, but they "cancel out"?

Nugatory wrote (the underline is mine):

no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.

You have to decide what you want to discuss. What Nugatory wrote is correct: no acceleration means no radiation. And by "no acceleration," he is discussing. electrons in atoms.

I was answering you question

How about my other question?

if the "smeared" electron accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule), it emits EM radiation? If not, why not? (for the Bohr model was a big issue, but here is somehow overlooked)

about accelerating atoms, where the electron is accelerating as part of the atom, but not with respect to the nucleus.

And if the electrons in a material can be "shaken" by the EM fields, then they also would be attracted by the nuclei and fall into it ...

I don't know where this Wikipedia quote comes from, but this is pop-sci language. If no lower energy states are accessible to the electron in the atom, it will stay in the same state. If an lower energy state is available, it will eventually decay to it, releasing a photon. This emission as nothing to do with the emission of radiation due to accelerating charges.

 

[DanMP]

I was answering you question
about accelerating atoms, where the electron is accelerating as part of the atom, but not with respect to the nucleus.

Nugatory answered the exact same question, about accelerating atoms ... and his answer was "no radiation" from the electrons, because the "smeared" electron has no position, so it doesn't accelerate when the atom accelerates:

no position means no meaningful notion of acceleration

Again, who is right? And why?

I don't know where this Wikipedia quote comes from ...

Just follow the link ... It's an explanation of how/why light is slowed down in transparent materials and, according to it, the "smeared" electrons can be "shaken" ... so they not only emit EM radiation, but also can be attracted by the nucleus (contrary to what Nugatory said) and fall into it, if no other force prevents it.
Is the Wikipedia explanation wrong? Why? And how is correct?

 

[DrClaude]

Nugatory answered the exact same question, about accelerating atoms ... and his answer was "no radiation" from the electrons, because the "smeared" electron has no position, so it doesn't accelerate when the atom accelerates:

Again, Nugatory is talking about electrons in an atom, not an accelerating atom.

Again, who is right? And why?

Both of us, because we are not talking about the same thing.

Just follow the link ... It's an explanation of how/why light is slowed down in transparent materials and, according to it, the "smeared" electrons can be "shaken" ...

Even in the Wikipedia link, "shaken" is in quotes, because this is simply colloquial language to explain something more complicated. Yes, the electromagnetic radiation will change the wave function of the electrons, and this change will oscillate with the field. This results in an oscillating dipole, and it is this oscillating dipole that will radiate back. Electrons are not really shaken in the classical sense.

so they not only emit EM radiation, but also can be attracted by the nucleus (contrary to what Nugatory said) and fall into it, if no other force prevents it.
Is the Wikipedia explanation wrong? Why? And how is correct?

Nobody said that electrons are not attracted by the nucleus, to the contrary. Thinking of the situation in terms of forces is not the proper approach in quantum mechanics. Have a look at the resource indicated in post #21.

 

[DanMP]

Again, Nugatory is talking about electrons in an atom, not an accelerating atom.

He was talking about electrons in an atom, yes, but the atom was accelerating (due to rotation around the center of the Earth, or due to vibration - if the atom was part of a molecule).

He first said:

... any appeal to force as an explanation for electron behavior assumes that the electron has a position. But that assumption is incompatible with the "smeared" model in which the electron has no position. A similar argument applies to the word "falling" which implies that the electron is moving closer to the nucleus - but "closer" only makes sense if the electron has a position so that we can talk about the distance between where it is and the nucleus, and in the "smeared" model there's no position.

and then, about the "smeared" electron when it accelerates (with our body, around the Earth, or vibrating, with the atom, in a molecule):

Same issue - no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating.

But you said:

If you accelerate an atom, you are of course accelerating an electron, but you are also accelerating an equal-charge nucleus, and the radiation you would get for each cancel out

So you contradicted Nugatory about the "ability" of a "smeared" electron to accelerate (and consequently emit EM radiation). You like it or not, one of you is wrong. Who is wrong? And, more important, how is right/correct?Regarding the microscopic explanation (of how light is slowed down in materials) you wrote:

Even in the Wikipedia link, "shaken" is in quotes, because this is simply colloquial language to explain something more complicated. Yes, the electromagnetic radiation will change the wave function of the electrons, and this change will oscillate with the field. This results in an oscillating dipole, and it is this oscillating dipole that will radiate back.

By "radiate back" you imply that photons are emitted, right? So photons are produced apparently without incident photons being absorbed. This sounds like producing photons/energy without consuming energy. How is this possible? What am I missing?

 

[Nugatory]

Again, Nugatory is talking about electrons in an atom, not an accelerating atom.

There's an easy way to analyze the radiation produced by accelerating an atom and a hard way.

The easy way: The atom as a whole is neutral. Accelerating a neutral object produces no radiation. Done.

The hard way: Treat the atom as a complicated distribution of positive and negative electrical charges (the mathematical representation of the "smeared" mental model that you're using - did I not say something about solving Schrödinger's equation somewhere above?), shift to a classical model to calculate what happens when we accelerate it, note that all the effects cancel so that no radiation is emitted. (Or if you can't make them cancel go back through calculations to find your error).

 

[DrClaude]

So you contradicted Nugatory about the "ability" of a "smeared" electron to accelerate (and consequently emit EM radiation). You like it or not, one of you is wrong. Who is wrong? And, more important, how is right/correct?

@Nugatory and I are not contradicting each other. There are two situations: the electron with respect to the nucleus, and the electron as part of the atom as a whole. The electron does not orbit around the nucleus, but is in a "smeared" stationary state (wave function), and therefore does not accelerate, so no emission of radiation and no loss of energy. If the atom as a whole is accelerated, then the electron, as part of that atom, is also accelerated, but the change in the electric field created by that is exactly canceled by the acceleration of the nucleus, so again no emission. The fact that the electron is "smeared" plays no role in this latter case.

By "radiate back" you imply that photons are emitted, right? So photons are produced apparently without incident photons being absorbed. This sounds like producing photons/energy without consuming energy. How is this possible? What am I missing?

The energy can come from any source: thermal, collisions, etc.

 

[DanMP]

The energy can come from any source: thermal, collisions, etc.

Really? So, if we "send" a single photon through an ordinary glass window, we will observe/measure at the other end countless similar photons? And the "amplification" would increase with the width of the glass, because there are more atoms ready to "produce" new photons? In what world/reality is this true?

The hard way: Treat the atom as a complicated distribution of positive and negative electrical charges (the mathematical representation of the "smeared" mental model that you're using - did I not say something about solving Schrödinger's equation somewhere above?), shift to a classical model to calculate what happens when we accelerate it, note that all the effects cancel so that no radiation is emitted. (Or if you can't make them cancel go back through calculations to find your error).

So, you (kind off) admit that DrClaude was right: radiation is (or may be) emitted by the "positive and negative electrical charges", but "all the effects cancel".

For me, the apparent absence of radiation is not the main issue. The idea that the "smeared" electron can/may emit is the problem. You previously said that "no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating", and now you seem to forget/dismiss it ... This raises again the issue about falling towards the nucleus, as long as there is no force in this "smeared" electron interpretation to prevent it. Again, a "complicated distribution" of a static Moon around the Earth, would result in pieces of the Moon falling to the ground. Why is this not happening with the "smeared" electron? Maybe because the electron still rotates, but it's much more convenient to work with wave functions instead of particles?

And if the "smeared" electron does emit when the atom accelerates (rotates or vibrates), how is the electron energy "replenished"? This was a big issue for the orbiting electron ...

 

[A.T.]

Again, a "complicated distribution" of a static Moon around the Earth, would result in pieces of the Moon falling to the ground. Why is this not happening with the "smeared" electron?

Because this analogy is flawed?

 

[DrClaude]

Time to close this thread. @DanMP, you have been incredibly stubborn in this thread, not showing any desire to learn.

Really? So, if we "send" a single photon through an ordinary glass window, we will observe/measure at the other end countless similar photons? And the "amplification" would increase with the width of the glass, because there are more atoms ready to "produce" new photons? In what world/reality is this true?

Only in bad faith can you infer that this is what I was saying. As light goes through a piece of glass, that piece of glass will heat up and emit photons of lower frequency. Amplification only takes place if you manage to make a laser out of it.

For me, the apparent absence of radiation is not the main issue. The idea that the "smeared" electron can/may emit is the problem. You previously said that "no position means no meaningful notion of acceleration, no acceleration means no radiation from accelerating", and now you seem to forget/dismiss it ...
This raises again the issue about falling towards the nucleus, as long as there is no force in this "smeared" electron interpretation to prevent it. Again, a "complicated distribution" of a static Moon around the Earth, would result in pieces of the Moon falling to the ground. Why is this not happening with the "smeared" electron? Maybe because the electron still rotates, but it's much more convenient to work with wave functions instead of particles?

You are the one who refuses to understand that @Nugatory was discussing stationary states of the electron in atoms. There is no state of the electron where it can fall into the nucleus.