Why do electrons not fall into the nucleus?

https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Quantum_Mechanics/09._The_Hydrogen_Atom/Atomic_Theory/Why_atoms_do_not_Collapse

by thunderbong • 1 year ago

48 50 1 year ago

chem.libretexts.org

senectus1• 1 year ago

Not sure I understand it any better having read this. but I did find it interesting and thought provoking.

aabhay• 1 year ago

I personally think the mere idea that you can map on abstract functions that have infinities and boundary conditions, on to a representation that extremely precisely models our physical world, is more astonishing than having a low level understanding of the equations. The final image of the probability density summed over the region around the nucleus, really drove that home for me

snippy• 1 year ago

However, an electron, unlike a planet or a satellite, is electrically charged, and it has been known since the mid-19th century that an electric charge that undergoes acceleration (changes velocity and direction) will emit electromagnetic radiation, losing energy in the process.

If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?

To me it seems the rest of the article, i.e. probability density, also means that the electrons undergoe acceleration because their location changes.

OgsyedIE• 1 year ago

How do you know that your shaking action in the scenario isn't the input of the same energy that is emitted?

meindnoch3• 1 year ago

If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?

The energy they lose by radiating is exactly balanced by the energy they gain from you by accelerating them.

avian• 1 year ago

If I take a small piece of matter and shake it for a long time, then don't all its electrons and protons emit electromagnetic radiation and lose energy?

Yes, they do. But it's only a very very tiny amount.

You're shaking both the positive (nucleus) and negative (electrons) parts of the atoms. The electromagnetic fields outside of the atom almost perfectly cancel out. This means that the acceleration only affects the very small residual field and there is very little radiation at far distances, unless you shake it really really fast.

Another way to look at it is that atoms are in fact already constantly shaking by themselves because of thermal movement. And this does in fact result in them emitting radiation: objects at room temperature will radiate in the infrared spectrum because of this.

The trick is that thermal movements of atoms are very fast compared to moving something by hand. Room temperature infrared radiation frequencies are on the order of tens of terahertz. Compare this to manually shaking an object at (say) 10 times a second. With some hand waving math this is like giving it an equivalent temperature of around 10^-10 kelvin. It will radiate extremely long wave radio waves, but such a tiny amount that it will be completely unmeasurable.

dave3334• 1 year ago

Mills has developed a better purely classical atomic model where the electrons are concentric spinning fluid spheres with force balance equivalent to 20k atmospheres pressure. The spinning electrons don't radiate because there is no net charge movement over time. See https://brilliantlightpower.com/theory/

tralarpa• 1 year ago

For those who don't know Mills and his company: https://en.wikipedia.org/wiki/Brilliant_Light_Power

dave3334• 1 year ago

That wikipedia page has a strong skeptical bias and is seriously out of date.

meindnoch3• 1 year ago

Crank

t8sr2• 1 year ago

Yes and my yoga teacher has an even better theory where the electrons are stopped from falling in by spirits of their time-traveling ancestors.

ben_w5• 1 year ago

I want to make a joke about Feynman path integrals and the single electron universe etc., but I can't think of an appropriate yoga pun.

terminalbraid2• 1 year ago

They do sometimes.

https://en.wikipedia.org/wiki/Electron_capture

fuzzfactor• 1 year ago

Why do electrons not fall into the nucleus?

It's always possible most of them already have done so :0

Seems to me the positive & negative charges would neutralize, and it would no longer be "matter" as we know it.

Not anti-matter, just not actual matter by any stretch of the imagination.

Which is what most of the universe actually consists of, not actual matter.

Matter itself is extremely rare, few, and far between.

Could be all there is left and can be perceived by those composed of it, are the things that can have a physical nature simply because their electrons haven't collapsed into the nucleii.

Yet.

internet_points• 1 year ago

This was quite interesting, and at a level where I found I understood something new without being overwhelmed – I tried looking around the site for more, but the site itself has me confused as to where to start, is this part of a work in progress book? How do I get to the table of contents or start of the book?

mixmastamyk• 1 year ago

By coincidence I am currently watching this series, which explains this and a lot more:

https://www.thegreatcourses.com/courses/einstein-s-relativit...

It is on Kanopy now, for “free” (local library pays). I think there’s a subatomic-particle specific course as well that is more focused.

alok-g8• 1 year ago

I have come across the same 'explanation' multiple times but do not find it satisfactory.

> This "battle of the infinities" cannot be won by either side, so a compromise is reached in which theory tells us that the fall in potential energy is just twice the kinetic energy, and the electron dances at an average distance that corresponds to the Bohr radius.

This "cannot be won by either side" isn't a good explanation of the problem. By saying "a compromise is reached in which theory tells us ...", the article seems going around the answer instead of actually telling the answer to the question.

Assuming relativity is not invoked and given a finite size of the nucleus, what is actually bringing this situation of compromise? What is pushing the electron (or its probability cloud) outwards to counter-balance?

rcxdude2• 1 year ago

The opposing effect is the kinetic energy of the electron: as it get squeezed into a smaller area its kinetic energy must go up, assuming energy is constant (a classical system would more or less be the same, think how an elliptical orbit speeds up as it gets closer to the barycenter, but a quantum mechanical system doesn't necessarily have a defined trajectory).

The real sleight of hand in this explanation is it doesn't really explain why the quantum-mechanical electron doesn't radiate energy like the classical electron. That's a bit more subtle, but it's basically due to the fact that the electron is wave-like and confined within the atom (i.e. it does not have enough energy to escape the nucleus). This means that the wave-function has discrete solutions as a series of 'standing waves', which is what causes the quantization in quantum mechanics.

alok-g8• 1 year ago

> The real sleight of hand in this explanation is it doesn't really explain why the quantum-mechanical electron doesn't radiate energy like the classical electron. That's a big more subtle, but it's basically due ...

This subtle part is exactly the piece that I am missing.

So far, we have electron in an orbital. The orbital in itself seems stationary (standing waves), so it may seem nothing is accelerating. I presume that is not it for the answer.

If it is, that still feels like, Oh, I solved Schroginger's equation, and it yields these standing waves for the solution, electron is not really having a certain position and momentum as the wave function hasn't collapsed, and thereby there is no acceleration for the electron to be radiating energy.

Asking a total newbie question. I heard that QM has operators, so momentum also has an operator. Is there one for acceleration? Would it yield a zero?

If so: I see Coulomb's force. Is there another force balancing it? Or is Newton's third law not valid anymore.

Ygg22• 1 year ago

Here is a simple explanation: They can't fall in due to Heisenberg's uncertainty. For that, I'd need you to accept as an axiom[1] (unprovable truth) that the following principle is true: ΔpΔx (uncertainty of momentum times uncertainty of position) is roughly equal (or greater) to some constant, we'll call it H.

Due to this, if one uncertainty grows smaller, the other grows larger.

If the electron is located in the nucleus, its position (Δx) would be much more narrow than if it was around the nucleus. Since the uncertainty of Δx goes down, Δp must go up co compensate. Turns out, this Δp is enough to give it an enough momentum to overcome attractive force.

But then comes a smart observer, and says, but what if an electron managed to lodge itself exactly into the center of a proton. Since Coulomb's law says F= q1q2/r^2, and r is 0[2], that's Infinity! You can't escape infinite charge attractiveness!

To that, you can notice that as r and Δx approaches 0, Δp also approaches infinity, so it will have more chance to escape before that happens. But in some rare cases, it will interact and form a neutron, with some energy being emitted as a neutrino.

[1] It's not an axiom, it's an observation derived from experiments. However, why is the matter behaving like that out of physics wheelhouse. It can tell you a lot about laws, but very little WHY are laws like that. So it might as well be an axiom.

[2] This is, of course, assuming that space is infinitely divisible, which is yet to be confirmed or denied.

alok-g8• 1 year ago

I have heard this too and still feel that there's more to this that is critically missed.

> For that, I'd need you to accept as an axiom (unprovable truth) that the following principle is true: ΔpΔx is roughly equal (or greater) to some constant, we'll call it H.

As far as I know, Heisenberg's principle isn't exactly an axiom. It can largely be derived!

A waveform in time and its Fourier transform have such a relationship, which is entirely mathematical. More confined a time waveform is, more spread out the frequency spectrum is, and vice versa.

Now de Broglie principle linked momentum of a particle to its frequency! That makes the trick. So far, in Newtonian mechanics, momentum just related to position via derivative of position, i.e., velocity. Both were time waveforms.

But with de Broglie principal, momentum (also?) links to frequency domain, while the position remains in time domain. Now the Schrodinger's equation yields the said relation between position and momentum.

What I'll write next fits better in another comment box, so will do that.

(Edit:) Wrote here: https://news.ycombinator.com/item?id=43819506

elashri• 1 year ago

How can something be an axiom and at the same time has a mathematical derivation well understood from Quantum Mechanics [1] and are supported by experimental observations ?

[1] https://courses.physics.illinois.edu/phys580/fa2013/uncertai...

mr_mitm4• 1 year ago

The way I see it is that it could only actually collapse if the electron was headed precisely at the nucleus (the nucleus has diameter zero in this simplified model). Even in classical physics, the electron would move on an ellipsis around the nucleus in almost all cases, so the average distance would be non-zero.

Being pointed exactly at the nucleus is not possible in quantum mechanics, because that would require infinite precision, which is precisely what we give up in this model, so the average distance is yet again non-zero.

alok-g8• 1 year ago

This explanation is not correct. Here, the electron is again accelerating, will lose energy, and ultimately spiral into the nucleus. This does not require it to be pointing exactly into the nucleus.

t8sr2• 1 year ago

I don't like mechanistic explanations of particle physics - they're an attempt to relate what's going on to our macroscopic experience, but they usually fall apart when you look too closely.

I find it much easier to understand the stability of hydrogen by thinking about ground states. If the electron in H could merge with the proton, they'd make a neutron. But a free neutron is not stable and decays in a few minutes back into a proton, electron and an antineutrino.

With very large, proton-rich nuclei, eventually you get to the opposite situation where the ground state is one less proton, one less electron and one more neutron and the atom decays into that state by, you guessed it, an electron "falling into" the nucleus.

d--b• 1 year ago

To me the article says: the electron doesn't fall into the nucleus because we found an equation that says it doesn't.

vkazanov• 1 year ago

Yup. Half of physics is written just like this.

mr_mitm4• 1 year ago

In the end, that's true for all why questions in physics. In the end, things don't have a reason for how they behave, they just do.

The question of why only makes sense in a framework. Classical EM theory says electrons should fall into the nucleus, but they clearly don't. Asking why they don't is one step towards finding out about quantum mechanics, so it's a really important question to ask.

Yes, at the end of the day, the answer is "because classical EM is wrong and quantum mechanics is right (or at least less wrong)". But there is a lot to learn along the way.

fithisux2• 1 year ago

Second law of thermodynamics? The electron and the environment have the same temperature. If it falls, it emits energy warming the environment without consumption of energy. But this is impossible.

mr_mitm4• 1 year ago

Single particles do not have a temperature. It's an emergent property of many-particle systems.

fithisux2• 1 year ago

you forget the thermal bath

gus_massa• 1 year ago

Good question, but no.

For example you can make a very similar system with a positron and an electron https://en.wikipedia.org/wiki/Positronium . It's stable for a while, and it has very similar properties and levels like an Hydrogen atom. So the "second law" should apply too. But it has a mean lifetime of only 0.12 ns (1.2E-10s).

The second law consider also the properties of the materials. For example there are small bags with sodium acetate that are used as hand heaters https://en.wikipedia.org/wiki/Sodium_acetate#Heating_pad https://www.youtube.com/watch?v=Oj0plwm_NMs You put them in hot water, the content dissolves, and you let them cold to room temperature. When you click the metallic part, they crystallize and release heat.

Another example is connecting a small lamp to a battery. It release light and heat, specially if you can get an old incandescent light bulb.

rolph• 1 year ago

ELI5 version, why doesnt an elephant fall into a mouse? because the elephant wavelength is too long to fit inside the mouse, so it nestles around the mouse at S1 orbit.

so, why doesnt an electron fall into a nucleus?

because the nucleus is too small to encompass an electron wave.

Why do electrons not fall into the nucleus?

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