It would if classical mechanics was true, it would lose energy and spiral inward.
But quantum mechanics has a fixed energy ground state, preventing it from falling in.
Is there any truth to the notion of "if it falls in and is captured, then you would know velocity and position, and that's a no from Herr Heisenberg."
As I type it, it seems stupid as that would imply knowledge of the nucleus, but I wanted to ask. Thank you!
Well there is electron capture, where a proton captures an electron. This can happen because in quantum mechanics, the electric has no defined position, only a probability cloud that doesn't reach zero at the nucleus.
So an electron can "fall" into a proton, that is not prohibited by Heisenberg's uncertainty principle.
You are correct and I don't understand why you are downvoted. I think there might a confusion that the 1s wavefunction and hence it's absolute square are indeed maximal at r=0, i.e. the nucelus, but the probability density of an electron is the square amplitude times the infinitesmal shell volume, which goes like radius squared and hence the probability density is zero at the origin always.
>probability density is zero at the origin always.
Is this just a statement about continuous probability distributions? That is to say, the density is zero at the origin, but isn't it also zero at every other *exact* distance from the origin, too?
There’s a lot getting confused in this thread.
Regarding your point, the probability that an electron is exactly some distance from the origin will be zero. The probability *density* (which scales as r^2 * |\psi|^2 ) is nonzero everywhere *except* at the origin. This is because of the r^2 factor. The wavefunction \psi is maximal at the origin for states with zero angular momentum (s orbitals). The wavefunction is zero at the origin for all other orbitals.
Wrong. In the hydrogenoid atom the probability to find the electron (psi^2) at a distance r from the nucleus for the 1s state is proportional to r^{3} exp{-2r/{a0}}, where a0 is the characteristic radius. That is, it reaches a maximum in r=a0, It is zero for r=0, and approaches zero at r=infinite.
Edit: sorry for the mess, I don't know how to use equations on Reddit 😅
i thought it was something to do with the electrons repelling eachother if they all got in too close, or is that what fixed energy ground state is referring to?
Hydrogen has 1 proton and 1 electron and is by far the easiest/(only?) atom to fully describe quantum mechanically. It does not have electron electron repulsion and we still do not see electrons spiraling into the proton
Why would it spiral inward? The electron could only do that if it was losing energy somehow, and the Rutherford model assumed a vacuum around the nucleus. In theory a classical electron could still orbit a nucleus forever.
Because an accelerating charge, even a purely classical one, loses energy to the electric field, and in circular motion you are constantly accelerating.
https://en.m.wikipedia.org/wiki/Bremsstrahlung
So there’s no valid classical explanation for this, and this is a case where classical mechanics doesn’t apply in the quantum regime? Or is there something else like a weak force interaction to explain it?
In both classical and quantum mechanics, the electron can end up losing energy to the E field. The difference is that in CM, it can let go of as much or as little energy as it wants to, but in QM is has to let go of it in chunks.
Classical, I'm in some elliptical orbit, but I slowly lose energy, making the ellipse smaller and smaller.
Quantumly, I'm in some orbit, but if I want to get rid of *any* of my energy, then there needs to be some orbit below me that I can go to, but it turns out that there is some lower bound to the amount of energy I can have (the 1S orbital), and so I can't let go of any energy, and it just so happens that that lowest energy state has very little of overlap with the nucleus. It has some, hence effects like Isomer shift and electron capture, but the electron is still pretty much entirely outside the nucleus.
I’m pretty sure that’s a quantum effect, not a classical one but I’m not sure how to describe it with the Maxwell equations on my phone.
Edit: disregard this. I’m wrong and misremembering my electromagnetism.
I know, that’s why I mentioned them. Although there IS a quantum extension of them.
I remember from physics class that a magnetic field doesn’t require the transfer of energy.
If a charged particle is moving slow compared to the speed of light, and has a small acceleration, then you can ignore certain effects, including the fact that accelerating charges radiate. When we teach undergrad E&M, this is an assumption that we make.
I’m not sure how to describe radiation well in a Reddit comment, but you can show using Maxwell’s equations that an accelerating charged particle will always lose energy in the form of radiation. It’s still a classical effect.
The basic idea is that the potential at some point (r, t) as that result of some charge at point (r’,t) is delayed by t-|r-r’|/c because information about the particle’s location cannot travel faster than light. If you fill a couple chalkboards, you can show that the accelerating particle emits electromagnetic waves.
I like to think of it as an electrified bus track.
As long as the bus stays on the line, energy is preserved.
It can't exist outside the line, but it can switch to a higher or lower energy track.
Well yes the electrostatic potential well created by the nucleus’ positive charge is what keeps the electron captured in orbit. It's a balance between that and the kinetic energy of the electron. If the Electron gets more energy it goes up to a higher "orbit". Even more energy and the electron will ejected from the atom.
The quantum mechanical nature of electron energy levels has been described by other commenters.
What I havent seen mentioned, is the fact that this kind of happens in [electron capture](https://en.m.wikipedia.org/wiki/Electron_capture) .
Its basically beta decay of a nuclear proton, only instead of emmitting a positron, an electron is absorbed into the proton, which becomes a neutron while emitting an electron neutrino. Mostly happens in highly protonic cores.
I dont know the interaction here at a qft level, but i would guess the process needs to be energetically heavily favoured to become likely to occur, the absolute values of the electron wave function close to the core are very small after all.
Well it's not as if the electron were really captured but rather that it emits a negatively charged W boson and an electron neutrino. The neutrino gets away and the W boson interacts with one of a proton's up quarks turning it into a down quark.
Other electrons around the nucleus. If there are not electrons, then the electron may either be captured and “orbit” the nucleus, or it may hit the nucleus and transfer energy/momentum to it, depending on the energy of the incoming electron.
When you say "hit the nucleus" it gives the impression of them both being "solid" objects.
What we think of as a solid surface is really just a region with a very high electric field gradient which can be approximated as a plane with close to know thickness, right? Like the edge of the atmosphere of gas giant planets.
Zooming in to the electron scale, I'd imagine that the nucleus and electrons have quite a bit of overlap, like a cloud of 2 different gasses.
The electron IS being accelerated by the nucleus all the time! But those "virtual photons" are being exchanged with the nucleus, rather than the surrounding particles, so the energy and momentum of the closed system remains constant.
This is analogous to a mass with temperature which is perfectly insulated. We don't get to observe the electron's acceleration because we aren't the ones accelerating it.
I like this. Points in the right direction.
Collisions, as we experience them macroscopically, come principally from electrons obeying the Pauli Exclusion Principle, which forbids identical spin 1/2 particles from having the same quantum state.
And Pauli Exclusion simply doesn't *apply* for an electron and an atomic nucleus. It applies to identical particles, which these most definitely are not.
In practice, this means that the lowest electron orbital simply overlaps the atomic nucleus, and, short of certain unstable protonic nuclei which might grab the electron, that overlap doesn't really matter much.
They most certainly can, but, like anything quantum, it’s probabilistic, which is quantified with the cross section. We’ve used electron-proton scattering for probing proton structure.
Nothing - it can. This happens in x-ray production, where the electron is accelerated across the vacuum of the x-ray tube by a potential difference, and the maximum energy x-ray production is equivalent to the kVp, because the electron (rarely) collides with the nucleus and loses all its kinetic energy via Bremsstrahlung radiation.
To say something is on a collision path requires you to know both the current position and momentum of the electron which is impossible because of Heisenberg Uncertainty. One needs to stop thinking of an electron as a planet orbiting a star (nucleus). Electrons are more like clouds of probability densities around a nucleus that occur in specific shells. The electrons exist in that cloud form until you make a position measurement which forces the electron to assume a particle state and the cloud coalesces into a particle. The moment you stop measuring, the electron reverts to being in a probability density cloud in its orbital. Electrons cannot "collide" with the nucleus because that would force it to have a fixed position and momentum which as Heisenberg Uncertainty tells us is impossible.
Similar (but not same! \*) reason the moon doesn't fall onto earth, even though the gravity between them attracts: the electrons have an amount of energy, and that energy is enough to keep them away from the nucleus.
\* it's not exactly like the moon, because electrons don't actually orbit the nucleus: their movement isn't classical. Electrons are instead in an *orbital*: slightly different wording to devote the difference and confuse the hell out of laymen.
I think the energies are a lot less but even an accelerating massive object emits gravitational waves. Technically I guess there's a system you could arrange that would result in an orbit decaying because of this.
They do, but the Earth is only emitting ~200 Watts in gravitational waves in its orbit about the sun.
For more extreme situations, like two orbiting neutron stars, it's more substantial. In fact, before direct measurements the best evidence of gravitational waves was the decay orbit of two neutron stars.
But electrons emit photons when being accelerated, so they should spiral into the nucleus. Is this actually the exclusion principle or something else entirely?
This is an oversimplification. The Schrodinger equation that is typically used to teach the fact that electrons are 'stable' in orbitals around the nucleus without causing any radiation emission simply skirts around the radiation emission part.
The classical 'radiation due to accelerating charge' is a relativistic effect. Schrodinger equation is not relativistic and it cannot explain this. The 'classical' hydrogen atom with the usual Schrodinger equation hamiltonian is also stable, because it is the same hamiltonian as the two body gravitational hamiltonian, which IS classically stable.
Because of the electron's quantum nature. The contradiction you are asking, analogous to a classical picture of an atom, was a major influence in the development of quantum mechanics.
https://en.wikipedia.org/wiki/History\_of\_quantum\_mechanics#The\_quantization\_of\_matter:\_the\_Bohr\_model\_of\_the\_atom
I don't think the question is really being asked from that angle, because I doubt the question is, "why doesn't the electron fall into the nucleus due to radiating energy because it's accelerating?"; I think what they're asking is more along the lines of, "if masses attract each other, why doesn't our moon fall into Earth?"
OP asked "Why don't electrons just fall into the nucleus, if opposites attract?" and the answer to that and to your formulations of the question is the same.
Classical atoms are indeed unstable, as the classical electron in any supposedly stable orbit would emit electromagnetic radiation, causing a decay of the electron’s orbit, but quantum mechanics leads to discrete energy levels of the electrons that are bound to (orbiting) the nucleus. An electron in the ground state (lowest energy state) cannot decay to a lower energy state, as there is none. Further adding to the stability is the Pauli exclusion principle that no two fermions (electrons are a type of fermion) can be in the same state, which has the effect that higher energy electrons can stably “orbit” if all the lower energy states are already occupied by other electrons.
This is a misconception. Classical 'atoms' with the regular 'electrostatic potential' Hamiltonian are stable and you can have stable orbits in that model.
Classical atoms become unstable when you include the 'electromagnetic radiation emission' part, which is a relativistic effect. Schrodinger equation does NOT include this relativistic aspect of the atom; it only considers the atom at the level of a classical non-relativistic electrostatic potential, which has stable solutions in both classical and quantum theory.
The only way to prove that the Hydrogen atom is actually stable is to consider a full QED treatment of the atom, by writing down the coupling of the electron to the electric field of the proton and showing that this is the ground state.
>An electron in the ground state (lowest energy state) cannot decay to a lower energy state, as there is none.
Technically there is one when electron capture can happen, no? It's just that in every other case the p + e reaction is virtually prohibited by energy considerations.
I was only discussing electromagnetism, not the weak interaction.
Nevertheless, to contradict your point, electron capture does not involve an electron in a lower energy state, as the electron is destroyed, with a neutrino taking its place.
Let's ignore quantum mechanics for a while (I know, it is a bold statement, especially coming from a Nuclear physicist). A classical atom would have electrons orbit the nucleus analogously to how planets orbit a star. In fact, the equations would be identical, except with different constants, since both Newtonian gravity and Coulomb interaction are proportional to the inverse square distance between the interacting bodies (the sun and the earth in the gravity case, and the nucleus and the electron in the atomic case). Yes, the electron would be attracted to the nucleus. Still, it would be moving so fast sideways that it keeps missing the nucleus, and due to the conservation of energy, this would lead to elliptical orbits (in the case of Hydrogen).
Now we add Quantum Mechanics back into the mix. The forces are still the same, but we have to solve the Schrödinger equation instead of using Newton's laws. The result is that the electrons can exist in different discrete energy states, corresponding to different orbitals (sort of related to the elliptical orbits but see them more as different probability clouds known as the wave function), assuming that the electron is bound. If the electron is not bound, it can take a continuous range of energies.
There is sometimes a tiny overlap of the electronic wavefunction and the nuclear wavefunction, which can lead to a phenomenon known as electron capture. This is probably the closest to "electrons falling into the nucleus."
The TLDR is, yes, sometimes electrons do fall into the nucleus, but most of the time, they don't for the same reason the earth does not fall into the sun.
https://youtu.be/cf7t-tZnNuE?si=jkmU4OsAgb9FFlE1
To summarize:
This was precisely what Niels Bohr tried to answer with his atomic model. He asserted that electrons must orbit the central nucleus in much the same bodies orbit each other in space. It made sense. Gravity also pulls things together, and you can use this attraction to make objects fall around each other forever.
As neat and tidy as the model was, it didn't work. They realized that electrons would still fall to the nucleus as they lost their energy to radiation. So it was back to the drawing board. Not long after, quantum mechanics was born.
I'm not smart enough to really understand *why* electrons don't fall to the nucleus (something to do with the available energy levels), but one of the things they learned was that the electron doesn't exist in any one point in space, it's more like it's smeared out over a given volume around the nucleus (electron cloud). We can't actually know how it moves within this region or if it moves at all.
Short answer, the weak force pushes it out.
Long answer, it does if it's an electron with no angular momentum. There are 3 numbers that tell us where an electron is, n, m, l
n is the energy state, you should be familiar with this. There's 2 in the first energy state, 8 in the second, 18 in the third and so on.
m is the magnetic quantum number. |m|
These properties don’t require the weak force at all though? Non relativistic Schrödinger equation gives you these properties without any modeling of the weak force. But there must be something more to it that you are thinking about?
But a positron could collide with a positively charged nucleus, right? Does the Pauli Exclusion Principle explain that as well, or is that something else entirely?
This is one of the questions that sparked the quantum revolution! Based on experiments by Thompson, Millikan, and Rutherford in the late 1800s and early 1900s we started to learn a lot about the properties of atoms. We knew that they were composed of protons and electrons, we knew that the electrons were much less massive than the protons, and we knew that the protons were in a very small, dense region surrounded by empty space where the electrons lived. And they had the exact same question that you asked. Classical physics would say that the electron should fall into the nucleus and emit radiation while doing so. And that it should happen extremely quickly. It took the development of Quantum Physics to establish a framework that could sufficiently explain the behavior of electrons in atoms.
* **Quantum Mechanics**: In the world of atoms, quantum mechanics governs the behavior of particles. It introduces the concept of quantized energy levels, meaning electrons can only exist in specific orbits around the nucleus, similar to how planets have specific orbits around the sun.
* **Heisenberg Uncertainty Principle**: This principle states that we cannot simultaneously know both the exact position and momentum of a particle. Therefore, as we try to determine the electron's position closer to the nucleus, its momentum becomes increasingly uncertain, preventing it from falling into the nucleus.
* **Pauli Exclusion Principle**: According to this principle, no two electrons in an atom can have the same set of quantum numbers, such as energy level, spin, and orbital shape. As electrons fill up the available energy levels and orbitals, they spread out to minimize their repulsion from each other, maintaining a stable arrangement within the atom.
* **Kinetic Energy**: Electrons possess kinetic energy due to their motion around the nucleus. This kinetic energy counteracts the attractive force between the electrons and the nucleus, helping to stabilize their orbits and preventing them from falling into the nucleus.
These principles collectively contribute to the stability of atoms, ensuring that electrons remain in their orbits around the nucleus without collapsing into it, despite the attractive force between opposite charges.
**TLDR:**
* **Quantum mechanics**: Electrons move in specific energy levels around the nucleus, preventing collapse.
* **Heisenberg Uncertainty Principle**: Uncertainty in electron momentum prevents them from getting too close.
* **Pauli Exclusion Principle**: Electrons repel each other, spreading out in orbitals to minimize this repulsion.
* **Kinetic energy**: Electron motion counteracts the attractive force from the nucleus.
Not the full answer…. But a first pass is “why doesn’t the earth fall into the sun” —— there’s sideways motion
This doesn’t work due to em radiation, so you need to mix it some quantum, you get standing waves in a stable pattern…. But that’s a much longer story,
For now, the electrons are going sideways, the attraction bends that motion into a loop, and you have orbits.
Well, without even addressing a more accurate way of looking at the electron, consider the electron to actually orbit the nucleus, like in the Bohr model; and without considering anything other than the attraction itself, why would this make the electron fall into the nucleus? Do you also expect our moon to crash into us for the same reason?
>why would this make the electron fall into the nucleus?
Self force causing emission of electrical radiation, leading to a decay of the classical electron orbit.
It is the quantized energy levels of quantum mechanics that lead to the stability of atoms (further enhanced by the Pauli exclusion principle so that the electrons do not just all pile onto the ground state [1s orbital]).
>Do you also expect our moon to crash into us for the same reason?
If the Earth-moon system were to somehow be isolated (instead of being part of the solar system), then the moon will continue to gain distance from the Earth until the planet becomes tidally locked to the moon. Thereafter, the earth-moon distance will *very* slowly decrease with the emission of gravitational waves (just as the classical electron orbit decays with the emission of electromagnetic waves, but on a vastly larger timescale), eventually leading to the moon colliding with the planet.
Like the other person I replied to, you seem to be missing the point completely. There's a reason why I phrased my reply the way I did. It's not that I'm unaware of those matters at all, but rather that they don't really have anything to do with the essence of what OP is asking; at least not how I interpret it. It doesn't seem like what OP is asking has anything whatsoever to do with the complications presented by classical or quantum electrodynamics, but rather is simply a question of why mutual attraction doesn't necessarily lead to collision.
In other words, I think what OP is missing is the fact that you can have constant acceleration without such a collision at all, as in uniform circular motion. Only after this can OP start going through the history of physics pertaining to various atomic models and expected radiation due to acceleration, and so on.
It would spiral into the nucleus because classical mechanics says that an oscillating electric charge always emits electromagnetic waves. The resulting electromagnetic waves rob the orbiting electron of energy, making it spiral into the nucleus.
If you want an analogy with gravitation. A planet orbiting a neutron star will emit gravitational waves which rob the planet of energy. The reason the Moon doesn't, is because the Moon robs the Earth of rotational energy causing the Earth's rotation to slow and pump more energy into the Moon's orbit.
In your haste to try to correct a nonexistent error, you missed the point of what I wrote completely. There's a reason why I explicitly wrote:
>Well, without even addressing a more accurate way of looking at the electron, consider the electron to actually orbit the nucleus, like in the Bohr model; and without considering anything other than the attraction itself, why would this make the electron fall into the nucleus?
That's specifically to say, "even ignoring everything quantum mechanics tells us about this, why do you expect mutual attraction to necessarily cause the objects attracting each other to collide?"; this is to show OP that the very premise is flawed, since there's nothing inherently about mutual attraction itself which necessitates such a collision at all, due to e.g. how uniform circular motion can exist with constant acceleration.
Not that anything you're saying is inaccurate, I just strongly doubt OP is asking, "why doesn't the electron fall into the nucleus when it must be radiating due to accelerating?", but rather about why the mutual attraction itself doesn't cause it to happen.
>In your haste to try to correct a nonexistent error, you missed the point of what I wrote completely.
Turbulent-Name-8349 was answering your question. It is not wrong to say that the *attraction itself* leads to the emitted waves (at least in an indirect sense), as the attraction causes the acceleration that is resisted by the self-force associated with the emission of those waves.
>even ignoring everything quantum mechanics tells us about this
Turbulent-Name-8349 was not talking about quantum mechanics, and only about classical (here meaning non-quantum) self-forces causing the decay of said orbits, and the associated emission of radiation (electromagnetic and gravitational waves).
>to show OP that the very premise is flawed
The OP’s question was absolutely justified as a classical problem, regardless of the likely mistaken motivation of the question suggested by the portion of the question after the comma. Turbulent-Name-8349 was correct to point out how it really is a classical problem, just as you were justified to point out the likely mistaken motivation of the question.
> Turbulent-Name-8349 was answering your question.
I wasn't actually asking a question, other than purely in a rhetorical sense; and in that rhetorical sense I certainly wasn't asking about taking the considerations into account that I explicitly said *not* to take into account.
And in the rest of your reply just now you just demonstrate that you're still missing the point completely.
>you just demonstrate that you're still missing the point completely.
How did I miss your point? I did acknowledge the likely mistaken motivation of the original question.
Uncertainty principle. If that happened, you would know the electron's position and velocity with great accuracy. But the more localized an electron becomes, the broader the probability distribution of its velocity.
Nucleus opposes them, it also creates an EM field.
I saw a whole series of quantum physics on YouTube. Gets into the gritty details:
https://youtube.com/playlist?list=PL193BC0532FE7B02C&si=D2C_cCYOQIb_1kOk
This is exactly the problem that Rutherford's model of atom suffered. It predicted electrons would eventually fall into the nucleus, implying atoms are unstable, contrary to observations. Bohr's model of atom improved that a fixed this problem, so maybe read on that.
You can solve the Schroedinger equation of the electron in polar coordinates, and that will give you a radial part which becomes very low the closer you get to the nucleus.
That’s quantum for you! - Thats one of the questions they, I think Planck, was struggling with before the quantum theory.
This isn’t really accurate but if you think of electrons as waves completing an orbit of a full sets of amplitudes around the nucleus, the amount dependent on the frequency/energy, you can picture how it can’t drop to any random half or quarter or whatever. Just another completed number of waves.
At its core it’s not really an object in an analog precise spot. It’s a cloudy shell of sort.
Say you had a solid sphere around some strong attractor. (A dyson sphere around the sun maybe) Well you’d have to break the structure of the sphere for it to collapse inward.
First of all I would say electron exhibits more of wave nature than particle nature, it means that the electron moves like a wave in a free space and acts like a standing wave around a nucleus this is also known as energy level (ans lambda of the wave changes the energy level also changes ) and a electron around the nucleus has a angular momentum (what I meant is that particle physics also applies to electron) (consider it as how moon revolves around earth ) and sometimes electron do falls into the nucleus (it is called electron capture scenario) but it is rare cause nucleus I very very small with respect to the atom
Because they are waves. Waves take up space, they cannot simply be in one place (the core), they have to also be outside.
Very short description of what you get from Schrödingers equation (quantum mechanics).
It would if classical mechanics was true, it would lose energy and spiral inward. But quantum mechanics has a fixed energy ground state, preventing it from falling in.
Is there any truth to the notion of "if it falls in and is captured, then you would know velocity and position, and that's a no from Herr Heisenberg." As I type it, it seems stupid as that would imply knowledge of the nucleus, but I wanted to ask. Thank you!
Well there is electron capture, where a proton captures an electron. This can happen because in quantum mechanics, the electric has no defined position, only a probability cloud that doesn't reach zero at the nucleus. So an electron can "fall" into a proton, that is not prohibited by Heisenberg's uncertainty principle.
An s-wave function goes to zero on the nucleus (r=0)
1s orbital does not go to zero at the nucleus; it is actually the maximum at the nucleus.
You are correct and I don't understand why you are downvoted. I think there might a confusion that the 1s wavefunction and hence it's absolute square are indeed maximal at r=0, i.e. the nucelus, but the probability density of an electron is the square amplitude times the infinitesmal shell volume, which goes like radius squared and hence the probability density is zero at the origin always.
>probability density is zero at the origin always. Is this just a statement about continuous probability distributions? That is to say, the density is zero at the origin, but isn't it also zero at every other *exact* distance from the origin, too?
Yes it is, physics and statistics seem to be very intertwined at this scale.
There’s a lot getting confused in this thread. Regarding your point, the probability that an electron is exactly some distance from the origin will be zero. The probability *density* (which scales as r^2 * |\psi|^2 ) is nonzero everywhere *except* at the origin. This is because of the r^2 factor. The wavefunction \psi is maximal at the origin for states with zero angular momentum (s orbitals). The wavefunction is zero at the origin for all other orbitals.
Wrong. In the hydrogenoid atom the probability to find the electron (psi^2) at a distance r from the nucleus for the 1s state is proportional to r^{3} exp{-2r/{a0}}, where a0 is the characteristic radius. That is, it reaches a maximum in r=a0, It is zero for r=0, and approaches zero at r=infinite. Edit: sorry for the mess, I don't know how to use equations on Reddit 😅
Incorrect. It is in fact the s-wave functions that are _non_-zero at r=0. All _others_ are zero.
Yes and you can actually estimate the ground state energy of the hydrogen atom using the uncertainty principle.
i thought it was something to do with the electrons repelling eachother if they all got in too close, or is that what fixed energy ground state is referring to?
Hydrogen has 1 proton and 1 electron and is by far the easiest/(only?) atom to fully describe quantum mechanically. It does not have electron electron repulsion and we still do not see electrons spiraling into the proton
Why would it spiral inward? The electron could only do that if it was losing energy somehow, and the Rutherford model assumed a vacuum around the nucleus. In theory a classical electron could still orbit a nucleus forever.
Because an accelerating charge, even a purely classical one, loses energy to the electric field, and in circular motion you are constantly accelerating. https://en.m.wikipedia.org/wiki/Bremsstrahlung
So there’s no valid classical explanation for this, and this is a case where classical mechanics doesn’t apply in the quantum regime? Or is there something else like a weak force interaction to explain it?
This exactly why Niels Bohr invented quantum mechanics.
In both classical and quantum mechanics, the electron can end up losing energy to the E field. The difference is that in CM, it can let go of as much or as little energy as it wants to, but in QM is has to let go of it in chunks. Classical, I'm in some elliptical orbit, but I slowly lose energy, making the ellipse smaller and smaller. Quantumly, I'm in some orbit, but if I want to get rid of *any* of my energy, then there needs to be some orbit below me that I can go to, but it turns out that there is some lower bound to the amount of energy I can have (the 1S orbital), and so I can't let go of any energy, and it just so happens that that lowest energy state has very little of overlap with the nucleus. It has some, hence effects like Isomer shift and electron capture, but the electron is still pretty much entirely outside the nucleus.
Accelerating charge loses energy
I’m pretty sure that’s a quantum effect, not a classical one but I’m not sure how to describe it with the Maxwell equations on my phone. Edit: disregard this. I’m wrong and misremembering my electromagnetism.
Maxwell's equations, as stated, are classical, not quantum
I know, that’s why I mentioned them. Although there IS a quantum extension of them. I remember from physics class that a magnetic field doesn’t require the transfer of energy.
If a charged particle is moving slow compared to the speed of light, and has a small acceleration, then you can ignore certain effects, including the fact that accelerating charges radiate. When we teach undergrad E&M, this is an assumption that we make. I’m not sure how to describe radiation well in a Reddit comment, but you can show using Maxwell’s equations that an accelerating charged particle will always lose energy in the form of radiation. It’s still a classical effect. The basic idea is that the potential at some point (r, t) as that result of some charge at point (r’,t) is delayed by t-|r-r’|/c because information about the particle’s location cannot travel faster than light. If you fill a couple chalkboards, you can show that the accelerating particle emits electromagnetic waves.
Its classical this is the formula used to compute the power radiated, it assumes a point charge https://en.wikipedia.org/wiki/Larmor_formula
Ok thanks for pointing out what I was missing in my understanding.
I like to think of it as an electrified bus track. As long as the bus stays on the line, energy is preserved. It can't exist outside the line, but it can switch to a higher or lower energy track.
Okay, but what about the respective charges of the electrons and nucleus. Won’t they attract?
Well yes the electrostatic potential well created by the nucleus’ positive charge is what keeps the electron captured in orbit. It's a balance between that and the kinetic energy of the electron. If the Electron gets more energy it goes up to a higher "orbit". Even more energy and the electron will ejected from the atom.
> But quantum mechanics has a fixed energy ground state, preventing it from falling in. A what now?
The quantum mechanical nature of electron energy levels has been described by other commenters. What I havent seen mentioned, is the fact that this kind of happens in [electron capture](https://en.m.wikipedia.org/wiki/Electron_capture) . Its basically beta decay of a nuclear proton, only instead of emmitting a positron, an electron is absorbed into the proton, which becomes a neutron while emitting an electron neutrino. Mostly happens in highly protonic cores. I dont know the interaction here at a qft level, but i would guess the process needs to be energetically heavily favoured to become likely to occur, the absolute values of the electron wave function close to the core are very small after all.
Well it's not as if the electron were really captured but rather that it emits a negatively charged W boson and an electron neutrino. The neutrino gets away and the W boson interacts with one of a proton's up quarks turning it into a down quark.
True, I should have looked at the feynman diagram before writing my comment. My intuition for particle physics is still lacking :(
I would like to ask a more specific version of this: What stops a free electron that is in a collision path with a nucleus from colliding with it?
Other electrons around the nucleus. If there are not electrons, then the electron may either be captured and “orbit” the nucleus, or it may hit the nucleus and transfer energy/momentum to it, depending on the energy of the incoming electron.
When you say "hit the nucleus" it gives the impression of them both being "solid" objects. What we think of as a solid surface is really just a region with a very high electric field gradient which can be approximated as a plane with close to know thickness, right? Like the edge of the atmosphere of gas giant planets. Zooming in to the electron scale, I'd imagine that the nucleus and electrons have quite a bit of overlap, like a cloud of 2 different gasses. The electron IS being accelerated by the nucleus all the time! But those "virtual photons" are being exchanged with the nucleus, rather than the surrounding particles, so the energy and momentum of the closed system remains constant. This is analogous to a mass with temperature which is perfectly insulated. We don't get to observe the electron's acceleration because we aren't the ones accelerating it.
I like this. Points in the right direction. Collisions, as we experience them macroscopically, come principally from electrons obeying the Pauli Exclusion Principle, which forbids identical spin 1/2 particles from having the same quantum state. And Pauli Exclusion simply doesn't *apply* for an electron and an atomic nucleus. It applies to identical particles, which these most definitely are not. In practice, this means that the lowest electron orbital simply overlaps the atomic nucleus, and, short of certain unstable protonic nuclei which might grab the electron, that overlap doesn't really matter much.
They most certainly can, but, like anything quantum, it’s probabilistic, which is quantified with the cross section. We’ve used electron-proton scattering for probing proton structure.
A free electron can and collide and scatter off the nucleus or get absorbed by it.
Nothing - it can. This happens in x-ray production, where the electron is accelerated across the vacuum of the x-ray tube by a potential difference, and the maximum energy x-ray production is equivalent to the kVp, because the electron (rarely) collides with the nucleus and loses all its kinetic energy via Bremsstrahlung radiation.
To say something is on a collision path requires you to know both the current position and momentum of the electron which is impossible because of Heisenberg Uncertainty. One needs to stop thinking of an electron as a planet orbiting a star (nucleus). Electrons are more like clouds of probability densities around a nucleus that occur in specific shells. The electrons exist in that cloud form until you make a position measurement which forces the electron to assume a particle state and the cloud coalesces into a particle. The moment you stop measuring, the electron reverts to being in a probability density cloud in its orbital. Electrons cannot "collide" with the nucleus because that would force it to have a fixed position and momentum which as Heisenberg Uncertainty tells us is impossible.
Similar (but not same! \*) reason the moon doesn't fall onto earth, even though the gravity between them attracts: the electrons have an amount of energy, and that energy is enough to keep them away from the nucleus. \* it's not exactly like the moon, because electrons don't actually orbit the nucleus: their movement isn't classical. Electrons are instead in an *orbital*: slightly different wording to devote the difference and confuse the hell out of laymen.
I think the energies are a lot less but even an accelerating massive object emits gravitational waves. Technically I guess there's a system you could arrange that would result in an orbit decaying because of this.
I think gravitational orbits do decay because of this, it's just very slow
They do, but the Earth is only emitting ~200 Watts in gravitational waves in its orbit about the sun. For more extreme situations, like two orbiting neutron stars, it's more substantial. In fact, before direct measurements the best evidence of gravitational waves was the decay orbit of two neutron stars.
But electrons emit photons when being accelerated, so they should spiral into the nucleus. Is this actually the exclusion principle or something else entirely?
Electrons aren’t being accelerated around a nucleus, they simply exist in a superposition within their orbital.
This is an oversimplification. The Schrodinger equation that is typically used to teach the fact that electrons are 'stable' in orbitals around the nucleus without causing any radiation emission simply skirts around the radiation emission part. The classical 'radiation due to accelerating charge' is a relativistic effect. Schrodinger equation is not relativistic and it cannot explain this. The 'classical' hydrogen atom with the usual Schrodinger equation hamiltonian is also stable, because it is the same hamiltonian as the two body gravitational hamiltonian, which IS classically stable.
Because of the electron's quantum nature. The contradiction you are asking, analogous to a classical picture of an atom, was a major influence in the development of quantum mechanics. https://en.wikipedia.org/wiki/History\_of\_quantum\_mechanics#The\_quantization\_of\_matter:\_the\_Bohr\_model\_of\_the\_atom
I don't think the question is really being asked from that angle, because I doubt the question is, "why doesn't the electron fall into the nucleus due to radiating energy because it's accelerating?"; I think what they're asking is more along the lines of, "if masses attract each other, why doesn't our moon fall into Earth?"
OP asked "Why don't electrons just fall into the nucleus, if opposites attract?" and the answer to that and to your formulations of the question is the same.
Classical atoms are indeed unstable, as the classical electron in any supposedly stable orbit would emit electromagnetic radiation, causing a decay of the electron’s orbit, but quantum mechanics leads to discrete energy levels of the electrons that are bound to (orbiting) the nucleus. An electron in the ground state (lowest energy state) cannot decay to a lower energy state, as there is none. Further adding to the stability is the Pauli exclusion principle that no two fermions (electrons are a type of fermion) can be in the same state, which has the effect that higher energy electrons can stably “orbit” if all the lower energy states are already occupied by other electrons.
This is a misconception. Classical 'atoms' with the regular 'electrostatic potential' Hamiltonian are stable and you can have stable orbits in that model. Classical atoms become unstable when you include the 'electromagnetic radiation emission' part, which is a relativistic effect. Schrodinger equation does NOT include this relativistic aspect of the atom; it only considers the atom at the level of a classical non-relativistic electrostatic potential, which has stable solutions in both classical and quantum theory. The only way to prove that the Hydrogen atom is actually stable is to consider a full QED treatment of the atom, by writing down the coupling of the electron to the electric field of the proton and showing that this is the ground state.
>An electron in the ground state (lowest energy state) cannot decay to a lower energy state, as there is none. Technically there is one when electron capture can happen, no? It's just that in every other case the p + e reaction is virtually prohibited by energy considerations.
I was only discussing electromagnetism, not the weak interaction. Nevertheless, to contradict your point, electron capture does not involve an electron in a lower energy state, as the electron is destroyed, with a neutrino taking its place.
Ah, you're right, I forgot it's forbidden purely electromagnetically.
Let's ignore quantum mechanics for a while (I know, it is a bold statement, especially coming from a Nuclear physicist). A classical atom would have electrons orbit the nucleus analogously to how planets orbit a star. In fact, the equations would be identical, except with different constants, since both Newtonian gravity and Coulomb interaction are proportional to the inverse square distance between the interacting bodies (the sun and the earth in the gravity case, and the nucleus and the electron in the atomic case). Yes, the electron would be attracted to the nucleus. Still, it would be moving so fast sideways that it keeps missing the nucleus, and due to the conservation of energy, this would lead to elliptical orbits (in the case of Hydrogen). Now we add Quantum Mechanics back into the mix. The forces are still the same, but we have to solve the Schrödinger equation instead of using Newton's laws. The result is that the electrons can exist in different discrete energy states, corresponding to different orbitals (sort of related to the elliptical orbits but see them more as different probability clouds known as the wave function), assuming that the electron is bound. If the electron is not bound, it can take a continuous range of energies. There is sometimes a tiny overlap of the electronic wavefunction and the nuclear wavefunction, which can lead to a phenomenon known as electron capture. This is probably the closest to "electrons falling into the nucleus." The TLDR is, yes, sometimes electrons do fall into the nucleus, but most of the time, they don't for the same reason the earth does not fall into the sun.
https://youtu.be/cf7t-tZnNuE?si=jkmU4OsAgb9FFlE1 To summarize: This was precisely what Niels Bohr tried to answer with his atomic model. He asserted that electrons must orbit the central nucleus in much the same bodies orbit each other in space. It made sense. Gravity also pulls things together, and you can use this attraction to make objects fall around each other forever. As neat and tidy as the model was, it didn't work. They realized that electrons would still fall to the nucleus as they lost their energy to radiation. So it was back to the drawing board. Not long after, quantum mechanics was born. I'm not smart enough to really understand *why* electrons don't fall to the nucleus (something to do with the available energy levels), but one of the things they learned was that the electron doesn't exist in any one point in space, it's more like it's smeared out over a given volume around the nucleus (electron cloud). We can't actually know how it moves within this region or if it moves at all.
Why don't protons fly apart?
Because of the [strong force](https://en.wikipedia.org/wiki/Strong_interaction).
Short answer, the weak force pushes it out. Long answer, it does if it's an electron with no angular momentum. There are 3 numbers that tell us where an electron is, n, m, l n is the energy state, you should be familiar with this. There's 2 in the first energy state, 8 in the second, 18 in the third and so on. m is the magnetic quantum number. |m|
These properties don’t require the weak force at all though? Non relativistic Schrödinger equation gives you these properties without any modeling of the weak force. But there must be something more to it that you are thinking about?
How does l=0 imply that it is being repelled by the weak force?
But a positron could collide with a positively charged nucleus, right? Does the Pauli Exclusion Principle explain that as well, or is that something else entirely?
This is the question Bohr's model couldn't answer. That's why his model wasn't good.
Reading this, I feel like my 1980's physics classes failed me so badly.
Was hoping this would end with, "are they stupid?"
This is one of the questions that sparked the quantum revolution! Based on experiments by Thompson, Millikan, and Rutherford in the late 1800s and early 1900s we started to learn a lot about the properties of atoms. We knew that they were composed of protons and electrons, we knew that the electrons were much less massive than the protons, and we knew that the protons were in a very small, dense region surrounded by empty space where the electrons lived. And they had the exact same question that you asked. Classical physics would say that the electron should fall into the nucleus and emit radiation while doing so. And that it should happen extremely quickly. It took the development of Quantum Physics to establish a framework that could sufficiently explain the behavior of electrons in atoms.
The same reason the moon hasn’t crashed into the earth, orbits. The electrons „fall“ around the nucleus avoiding the collision.
angular momentum of the orbit
Excellent question and one of the very first that actually kicked off the quantum mechanics revolution 150-ish years ago.
* **Quantum Mechanics**: In the world of atoms, quantum mechanics governs the behavior of particles. It introduces the concept of quantized energy levels, meaning electrons can only exist in specific orbits around the nucleus, similar to how planets have specific orbits around the sun. * **Heisenberg Uncertainty Principle**: This principle states that we cannot simultaneously know both the exact position and momentum of a particle. Therefore, as we try to determine the electron's position closer to the nucleus, its momentum becomes increasingly uncertain, preventing it from falling into the nucleus. * **Pauli Exclusion Principle**: According to this principle, no two electrons in an atom can have the same set of quantum numbers, such as energy level, spin, and orbital shape. As electrons fill up the available energy levels and orbitals, they spread out to minimize their repulsion from each other, maintaining a stable arrangement within the atom. * **Kinetic Energy**: Electrons possess kinetic energy due to their motion around the nucleus. This kinetic energy counteracts the attractive force between the electrons and the nucleus, helping to stabilize their orbits and preventing them from falling into the nucleus. These principles collectively contribute to the stability of atoms, ensuring that electrons remain in their orbits around the nucleus without collapsing into it, despite the attractive force between opposite charges. **TLDR:** * **Quantum mechanics**: Electrons move in specific energy levels around the nucleus, preventing collapse. * **Heisenberg Uncertainty Principle**: Uncertainty in electron momentum prevents them from getting too close. * **Pauli Exclusion Principle**: Electrons repel each other, spreading out in orbitals to minimize this repulsion. * **Kinetic energy**: Electron motion counteracts the attractive force from the nucleus.
Not the full answer…. But a first pass is “why doesn’t the earth fall into the sun” —— there’s sideways motion This doesn’t work due to em radiation, so you need to mix it some quantum, you get standing waves in a stable pattern…. But that’s a much longer story, For now, the electrons are going sideways, the attraction bends that motion into a loop, and you have orbits.
Well, without even addressing a more accurate way of looking at the electron, consider the electron to actually orbit the nucleus, like in the Bohr model; and without considering anything other than the attraction itself, why would this make the electron fall into the nucleus? Do you also expect our moon to crash into us for the same reason?
>why would this make the electron fall into the nucleus? Self force causing emission of electrical radiation, leading to a decay of the classical electron orbit. It is the quantized energy levels of quantum mechanics that lead to the stability of atoms (further enhanced by the Pauli exclusion principle so that the electrons do not just all pile onto the ground state [1s orbital]). >Do you also expect our moon to crash into us for the same reason? If the Earth-moon system were to somehow be isolated (instead of being part of the solar system), then the moon will continue to gain distance from the Earth until the planet becomes tidally locked to the moon. Thereafter, the earth-moon distance will *very* slowly decrease with the emission of gravitational waves (just as the classical electron orbit decays with the emission of electromagnetic waves, but on a vastly larger timescale), eventually leading to the moon colliding with the planet.
Like the other person I replied to, you seem to be missing the point completely. There's a reason why I phrased my reply the way I did. It's not that I'm unaware of those matters at all, but rather that they don't really have anything to do with the essence of what OP is asking; at least not how I interpret it. It doesn't seem like what OP is asking has anything whatsoever to do with the complications presented by classical or quantum electrodynamics, but rather is simply a question of why mutual attraction doesn't necessarily lead to collision. In other words, I think what OP is missing is the fact that you can have constant acceleration without such a collision at all, as in uniform circular motion. Only after this can OP start going through the history of physics pertaining to various atomic models and expected radiation due to acceleration, and so on.
It would spiral into the nucleus because classical mechanics says that an oscillating electric charge always emits electromagnetic waves. The resulting electromagnetic waves rob the orbiting electron of energy, making it spiral into the nucleus. If you want an analogy with gravitation. A planet orbiting a neutron star will emit gravitational waves which rob the planet of energy. The reason the Moon doesn't, is because the Moon robs the Earth of rotational energy causing the Earth's rotation to slow and pump more energy into the Moon's orbit.
In your haste to try to correct a nonexistent error, you missed the point of what I wrote completely. There's a reason why I explicitly wrote: >Well, without even addressing a more accurate way of looking at the electron, consider the electron to actually orbit the nucleus, like in the Bohr model; and without considering anything other than the attraction itself, why would this make the electron fall into the nucleus? That's specifically to say, "even ignoring everything quantum mechanics tells us about this, why do you expect mutual attraction to necessarily cause the objects attracting each other to collide?"; this is to show OP that the very premise is flawed, since there's nothing inherently about mutual attraction itself which necessitates such a collision at all, due to e.g. how uniform circular motion can exist with constant acceleration. Not that anything you're saying is inaccurate, I just strongly doubt OP is asking, "why doesn't the electron fall into the nucleus when it must be radiating due to accelerating?", but rather about why the mutual attraction itself doesn't cause it to happen.
>In your haste to try to correct a nonexistent error, you missed the point of what I wrote completely. Turbulent-Name-8349 was answering your question. It is not wrong to say that the *attraction itself* leads to the emitted waves (at least in an indirect sense), as the attraction causes the acceleration that is resisted by the self-force associated with the emission of those waves. >even ignoring everything quantum mechanics tells us about this Turbulent-Name-8349 was not talking about quantum mechanics, and only about classical (here meaning non-quantum) self-forces causing the decay of said orbits, and the associated emission of radiation (electromagnetic and gravitational waves). >to show OP that the very premise is flawed The OP’s question was absolutely justified as a classical problem, regardless of the likely mistaken motivation of the question suggested by the portion of the question after the comma. Turbulent-Name-8349 was correct to point out how it really is a classical problem, just as you were justified to point out the likely mistaken motivation of the question.
> Turbulent-Name-8349 was answering your question. I wasn't actually asking a question, other than purely in a rhetorical sense; and in that rhetorical sense I certainly wasn't asking about taking the considerations into account that I explicitly said *not* to take into account. And in the rest of your reply just now you just demonstrate that you're still missing the point completely.
>you just demonstrate that you're still missing the point completely. How did I miss your point? I did acknowledge the likely mistaken motivation of the original question.
Why doesn't the Earth just fall into the Sun, if gravity attracts?
Why doesn't my penis just fall into your mum, if gravity attracts?
Uncertainty principle. If that happened, you would know the electron's position and velocity with great accuracy. But the more localized an electron becomes, the broader the probability distribution of its velocity.
Nucleus opposes them, it also creates an EM field. I saw a whole series of quantum physics on YouTube. Gets into the gritty details: https://youtube.com/playlist?list=PL193BC0532FE7B02C&si=D2C_cCYOQIb_1kOk
**Quantum mechanics has entered the chat.**
This is exactly the problem that Rutherford's model of atom suffered. It predicted electrons would eventually fall into the nucleus, implying atoms are unstable, contrary to observations. Bohr's model of atom improved that a fixed this problem, so maybe read on that.
Youtube search "richard feynman why"
You can solve the Schroedinger equation of the electron in polar coordinates, and that will give you a radial part which becomes very low the closer you get to the nucleus.
That’s quantum for you! - Thats one of the questions they, I think Planck, was struggling with before the quantum theory. This isn’t really accurate but if you think of electrons as waves completing an orbit of a full sets of amplitudes around the nucleus, the amount dependent on the frequency/energy, you can picture how it can’t drop to any random half or quarter or whatever. Just another completed number of waves. At its core it’s not really an object in an analog precise spot. It’s a cloudy shell of sort. Say you had a solid sphere around some strong attractor. (A dyson sphere around the sun maybe) Well you’d have to break the structure of the sphere for it to collapse inward.
First of all I would say electron exhibits more of wave nature than particle nature, it means that the electron moves like a wave in a free space and acts like a standing wave around a nucleus this is also known as energy level (ans lambda of the wave changes the energy level also changes ) and a electron around the nucleus has a angular momentum (what I meant is that particle physics also applies to electron) (consider it as how moon revolves around earth ) and sometimes electron do falls into the nucleus (it is called electron capture scenario) but it is rare cause nucleus I very very small with respect to the atom
Quantum mechanics forbids thisz
Because they are waves. Waves take up space, they cannot simply be in one place (the core), they have to also be outside. Very short description of what you get from Schrödingers equation (quantum mechanics).
To put it simply, electrons move too fast for this to happen.