O Physics: Why doesn’t the electron crash into the proton?

[RandallB]

Why doesn’t the Electron crash into the proton??
We know in an H atom the e- is attracted to the + charge of the proton.
And it wants to get down to the "0 level" orbit.
But what makes that level zero – or why does e- stop going down?
Is there another force that counteracts the force of charge trying to pull them together?

 

[dextercioby]

There are a few things first:a proton and an electron are treated in QM as point particles...Choosing the system of coordinates with the center in the point in which the proton (assumed for simplicity to have an oO mass (if not,the problem doesn't suffer too much)) is found,your situation would require that the electron's position vector/coordinates coincide with the proton's...
QM-al analysis of the H atom proves that the probability density for the electron to be in the origin is ZERO...

A very good (not perfect,however) description is given in "QM" of A.Messiah and an even better in H.A.Bethe and Salpeter:"Quantum Mechanics of One andTwo-electron atoms"​

Daniel.

 

[RandallB]

OK I think I can see how a QM formula can define that an Electron shall never be where a proton is. But is there something in it, or any theory, that tries to explain why it stays away at the distance it does?

How does e- figure out where the zero level is, and stop at that distance from the proton?

 

[dextercioby]

Nope,the electron never stops...He's everywhere.He's not really ubiquous,but the proability of fuinding it in a certain volume everywhere in space is nonzero...As for "zero level",that's linked to the quantization of his energy (bound states-discrete spectrum)...BTW,if the H atom is isolated (doesn't interact with anything),he's in a stationary state,the fundamental one,in which all observables are time independent...Basically,it's a static picture,when it comes to observables,but NOT to states (Schroedinger picture).

QM has answers for all your questions regarding atom world.

Daniel.

P.S.There's a lot more to it,basically a whole book.Things cannot be explained in forum posts in great detail,just generalities,sorry.

 

[RandallB]

Anybody every see any theory other than QM even try to explain this?

 

[dextercioby]

Nope.Reletivistic quantum mechanics (Dirac's theory) makes improvements of the H-atom's model of Schrödinger.That's still QM.Quantum electrodynamics makes improvements to Dirac's theory,but essentially Qed is still built from the framework of QM...

Daniel.

 

[RandallB]

How about any ideas not related to quantum mechanics at all,
Has anybody else ever heard of anyone even caring that this seems like something unaccounted for and unexplained?

 

[dextercioby]

Nope.There are no other fundamental theories.Condensed matter is properly described using QM and QFT.


Daniel.

 

[jtbell]

How about any ideas not related to quantum mechanics at all,

People tried to do this for years (roughly 1900-1925) before quantum mechanics came along, and I'm sure some people continued to try to do it for a while afterwards. Nobody was able to do it adequately, which is why physicists accepted QM when Schrödinger, Heisenberg et al. developed it, even though it has many strange features.

 

[jtbell]

While I'm thinking about this... in heavier atoms, with a nucleus of non-negligible size, there is a small but finite probability for an electron to be inside the nucleus. When this happens, in certain nuclei, the electron can combine with a proton to convert it to a neutron and release a neutrino. This is one of the ways that unstable nuclei decay. Logically enough, it's called electron capture.

This happens only in cases where the new nucleus has a smaller mass than the old nucleus. The mass difference is "converted" into the energy of the neutrino. With hydrogen, it's not possible because the mass of a single neutron is larger than the mass of a single proton.

 

[humanino]

a proton and an electron are treated in QM as point particles

although it is always correct for the electron, let me add that this is not always the case for the proton. The proton is very much like a small ball 1fm diamater. There are ways to take that into account when one probes such distances within the framework of QM. Yet in that case, one is forced to use relativistic QM, because when the point-like approximation fails it implies that the electron has to be ultrarelativistic.

 

[floped perfect]

It's the same kind of thing with the planets, with the centripetal force and all. It's kind of the way you'd think the Earth might crash into the sun because they're attracted towards each other by gravity but they don't because of centripetal force. Maybe the electrons behave like mini-planets?

 

[Norman]

It's the same kind of thing with the planets, with the centripetal force and all. It's kind of the way you'd think the Earth might crash into the sun because they're attracted towards each other by gravity but they don't because of centripetal force. Maybe the electrons behave like mini-planets?

This is not a good way to think about this problem, because the Earth would eventually crash into the sun if the lifetime of the sun weren't so short compared to the time it would take the Earth to loose enough energy to run into it.

 

[floped perfect]

But how can the Earth lose energy if it's in space, There's no friction slowing it down is there?

 

[dextercioby]

It's the same kind of thing with the planets, with the centripetal force and all. It's kind of the way you'd think the Earth might crash into the sun because they're attracted towards each other by gravity but they don't because of centripetal force. Maybe the electrons behave like mini-planets?

For about 92 years it has been scientifically proven that electrons DO NOT behave like (very little) planets.

Danie

 

[Norman]

Now I cannot solve it, but I believe the jury is still out on the gravitational "N-body problem" (I don't know if they include gravitational radiation in these calculations or not). If you include inelastic collisions though energy will slowly leave the system.

But please let us not hijack this thread, if you are interested post in the appropriate forum.

 

[floped perfect]

For about 92 years it has been scientifically proven that electrons DO NOT behave like (very little) planets.

Fair enough, but for them to orbit a nucleus (even in clouds) there must be a force acting on them to keep them in their orbits right? Could it be one of the four fundamental forces?

 

[dextercioby]

It is one of the fundamental forces:electromagnetism.In simple QM,we refer to it as "Coulomb potential".

Daniel.

 

[floped perfect]

But wouldn't that force have the opposite effect since the charges on the electron and proton are different. Would the attraction between positive and negative not just cause the electron to crash into the nucleus? What's keeping the protons and electrons apart?

 

[dextercioby]

In the initial Bohr's model,the quantization of energy levels.In the QM model of the atom,simply the model altogether,as a direct application of the axioms...

Daniel.

 

[Andrew Mason]

But wouldn't that force have the opposite effect since the charges on the electron and proton are different. Would the attraction between positive and negative not just cause the electron to crash into the nucleus? What's keeping the protons and electrons apart?

One could say that the Heisenberg Uncertainty principle keeps them apart.

If they were to fall into the nucleus, we would know where they were and we would know their momentum to a certainty greater than that which is permitted by the Heisenberg Uncertainty Principle. Or you could say that electrons are not really in a particular place at a particular time - so they can't simply fall into the nucleus.

AM

 

[RandallB]

"N-body problem"
But please let us not hijack this thread, if you are interested post in the appropriate forum.

Thanks Norman
At least someone gets it - the intent of this thread is potential descriptions of why the electron does not crash into a proton.
NOT how QM defines it or that QM can claim that no one can describe it.
But how people do try to describe it.
So explaining why an idea doesn't work should also be described in Non-QM terms.
Everybody already knows that uncertainty and the math of QM does work, we do not need to be reminded.

Can you give a reference or start a thread on what the "N-body problem" is?
RB

 

[RandallB]

It's the same kind of thing with the planets, with the centripetal force and all. It's kind of the way you'd think the Earth might crash into the sun because they're attracted towards each other by gravity but they don't because of centripetal force. Maybe the electrons behave like mini-planets?

Don't forget the planets and the sun are made of the same stuff, Electrons and Protons are not.
If planets repelled each other like electrons do orbits would not work.
If you push a plant out of orbit it will fall into the sun.
You cannot get an electron to go inside the "0 level" with applying a lot of extra force.

So I don't think an orbital analogy will hold up.

RB

 

[RandallB]

While I'm thinking about this... in heavier atoms, with a nucleus of non-negligible size, there is a small but finite probability for an electron to be inside the nucleus. When this happens, in certain nuclei, the electron can combine with a proton to convert it to a neutron and release a neutrino. This is one of the ways that unstable nuclei decay. Logically enough, it's called electron capture.

This happens only in cases where the new nucleus has a smaller mass than the old nucleus. The mass difference is "converted" into the energy of the neutrino. With hydrogen, it's not possible because the mass of a single neutron is larger than the mass of a single proton.

Now there's a useful comment!
We have seen an electron come out! But we don't see them go in.
But how to explain both in Non-QM terms? This makes the task even harder I think.

 

[Andrew Mason]

Now there's a useful comment!
We have seen an electron come out! But we don't see them go in.
But how to explain both in Non-QM terms? This makes the task even harder I think.

What makes you think that it can be explained in terms of non-QM terms?

AM

 

[RandallB]

What makes you think that it can be explained in terms of non-QM terms?

I'm not as picky as most - I don't expect a CORRECT explanation, just to hear what attempts have been made to resolve a paradox as if it were real.
I understand how QM explains it as part of the unreal but knowable through it’s math.
Figured folks in the particles forum would know this best – would not expect QM folks to spend much time thinking about it.

RB

 

[Andrew Mason]

I'm not as picky as most - I don't expect a CORRECT explanation, just to hear what attempts have been made to resolve a paradox as if it were real.
I understand how QM explains it as part of the unreal but knowable through it’s math.
Figured folks in the particles forum would know this best – would not expect QM folks to spend much time thinking about it.

I sense that you are skeptical that QM explanations are not 'real'. You do realize that you are communicating that skepticism by way of technology that employs those 'unreal' phenomena several billion times per second.

I also get the sense that you think particle physicists are more in the 'real' world than QM people. Since the Standard Model of particle physics is based entirely on quantum mechanics (quantum electrodynamics, quantum chromodynamics in particular), that seems a rather odd view.

AM

 

[chronon]

1) An attractive force between two particles can result in a circular orbit, with the particles keeping the same distance apart, rather than the particles rushing togther (Newtonian Gravity)

2) If the particles are electromagnetically charged then classical electromagnetism says that they will emit electromagnetic waves, lose energy and hence approach each other until they join.

3)Quantum theory says that energy can only be lost in discrete amounts, and in particular there is a minimum energy a system can have, so that electrons do not fall into the nucleus as predicted by 2)

4) General relativity says that a body orbiting a star will lose energy by gravitational radiation, and so suffer the same fate as in (2). However, for the earth-sun system this effect is too slow to be of importance

 

[RandallB]

I sense that you are skeptical that QM explanations are not 'real'.

Even as QM provides a foundation for defining the "weird" as real, it does call it "Weird"!

I also get the sense that you think particle physicists are more in the 'real' world than QM people.

No just that they may know more about this paradox and some of the failed “Classical” attempts to explain it. Obviously I like looking at potential classical explanations.

Since the Standard Model of particle physics is based entirely on quantum mechanics (quantum electrodynamics, quantum chromodynamics in particular)...

A good point and good advice. QM would know about the paradoxes that QM resolves.
Thx RB

 

[gnome]

This happens only in cases where the new nucleus has a smaller mass than the old nucleus. The mass difference is "converted" into the energy of the neutrino. With hydrogen, it's not possible because the mass of a single neutron is larger than the mass of a single proton.

Please explain this statement. I know very little about quantum mechanics but this sounded intriguing so I googled around & found that one example of electron capture is potassium-argon decay in which an atom of $_{19}^{40} \text{K}$ decays into an atom of $_{18}^{40} \text{Ar}$. It appears that the resulting Argon nucleus is heavier than the original Potassium nucleus.

But anyway, even if that's a different phenomenon, how in general would a nucleus have a smaller mass after transforming a proton into a neutron, unless it then loses a neutron?

 

[jtbell]

I googled around & found that one example of electron capture is potassium-argon decay in which an atom of $_{19}^{40} \text{K}$ decays into an atom of $_{18}^{40} \text{Ar}$. It appears that the resulting Argon nucleus is heavier than the original Potassium nucleus.

You mean "lighter" not "heavier", right? My table of atomic masses lists $_{18}^{40} \text{Ar}$ as 39.962384 u and $_{19}^{40} \text{K}$ as 39.963999 u. To get the nuclear masses, we have to subtract 18 and 19 orbital electrons, respectively, but then on the K side we have to add the mass of the electron that it captures, so the net mass difference is the same as you get from the masses listed above.

how in general would a nucleus have a smaller mass after transforming a proton into a neutron, unless it then loses a neutron?

By having a larger binding energy. The mass of a nucleus is the sum of the masses of its protons and neutrons, minus the mass-equivalent of their total binding energy. In this case, changing a proton into a neutron increases the binding energy because 19 protons and 21 neutrons interact differently, as a group, than 18 protons and 22 neutrons.

 

[hexhunter]

?
well I'm lost

i presume the the Earth doesn't crash into the sun because of the speed at which it orbits, is the reason that it orbits the convection currents on the sun?

so simply, does or doesn't the electron orbiting the proton act like the Earth orbiting the sun?

as an awnser to the guy saying about Earth not being able to lose energy because of the lack of atmosphere in space, well what about reflecting light and heat...

finally, if the sun gives off light and heat energy to earth, then would Earth never lose enough energy to lose orbit and crush into the sun, atleast before the sun loses all H anyway

 

[RandallB]

?
well I'm lost - - i presume the the Earth doesn't crash into the sun because of the speed at which it orbits,

But the point is the sun is made of lots of matter that could have been planets but DID crash into the area that became the sun!
Atoms don't work that way, they don't use gravity the use, and here we are 'giving' that + charges are being held together by 'color'.
We just looking at why a - charge dosn't ever just go right in, with noted execptions on "capture"

 

[gnome]

The mass of a nucleus is the sum of the masses of its protons and neutrons, minus the mass-equivalent of their total binding energy. In this case, changing a proton into a neutron increases the binding energy because 19 protons and 21 neutrons interact differently, as a group, than 18 protons and 22 neutrons.

Thanks! You just showed me something new (new to me, anyway). I thought I could just look at the numbers of protons & neutrons & multiply by their respective weights.

Now, I think I see the light.

Does this mean that when a proton and a neutron bind together as a nucleus, that leaves them in a lower energy state, so energy is released and the result is that the nucleus has less mass than the proton and neutron? And is that the source of the energy that is released in fusion?

I see, if I add up the masses of 1 tritium atom at 3.016 u plus 1 hydrogen atom at 1.008 (total 4.024); or 2 deuterium atoms (total 4.028 u) whereas the mass of a helium atom is 4.003 u.

Is that difference of about 0.02 u per atom of helium where the energy released by a hydrogen bomb comes from?

 

[elas]

Anybody every see any theory other than QM even try to explain this?

Try

Are All Particles Identical?
Sheldon Goldstein, James Taylor,
Roderich Tumulka, and Nino Zangh
September 28, 2004