Why Does the Electron Not Fall Toward the Nucleus in QM?

[ClubDogo]

Why does in QM the electron does not fall toward the nucleus? After all, the only force between nucleus and electron is attractive (- electron and + nucleus). Is the same reason that justifies the moon does not fall to the earth?

 

[ZapperZ]

Please read our FAQ in the General Physics forum.

Zz.

 

[lalbatros]

ClubDogo,

Electrons do really fall to the nucleus.

They are during sometime in equilibrium on an orbit, exactly like the moon.
In this equilibrium attraction in exactly compensated by inertia (centrifugal force).
However, rotating electrons lose energy because the emit electromagnetic radiations.
Therefore, they actually fall onto the nucleus.

The first strange thing is that they do that suddenly, not continuously.
The second strange thing is that they do not fall little by little but by finite steps to precesely defined orbits.
The last strange thing is that they finally stop falling and do not reach the nucleus.
The last level they reach is called the fundamental level.
This is explained by the wave-like nature of electron and is at the basis and origin of quantum mechanics.
The other level are called excited levels. At low temperatures, most atoms are in the fundamental level where the electron reached the final stable orbit.

In principle the moon could also behave like that because gravitational wave may also dissipate its energy.
However the moon, and the Earth are such big objects that their wave-like behaviour are totally negligible and not observable.

If you want more understanding, you should train and learn in physics and mathematics.

 

[jtbell]

They are during sometime in equilibrium on an orbit, exactly like the moon.
In this equilibrium attraction in exactly compensated by inertia (centrifugal force).

The Bohr-Sommerfeld planetary model of the atom has been dead, dead, dead since the 1920s. Please don't encourage people to think in terms of that model, except as a purely historical exercise.

 

[ClubDogo]

Ok, I'm a physicist.
I know the Bohr-Sommerfeld model.. but it does not explain the atom structure. It states. Nothing else. THAT'S NOT A VALID ANSWER: it's like to say "this is so, because so it is".
And the problem is the same in the planetary motion, gravitational force is only attractive... But why the moon does not fall to the earth? I don't want answers such "there exists strange things, theories that stands tall, etc". Give me the physical reason... I should think that no one knows it?

 

[jtbell]

In the case of the moon (which can be described without QM, of course), it is always falling (accelerating) towards the earth. However, it is also moving sideways because of its orbital motion, so it always misses the earth!

In the case of the atom, the electron does sometimes "hit the nucleus." QM does not allow us to calculate a planet-like trajectory for the electron. All we can calculate (from solving Schrödinger's Equation) is the probability of finding the electron in various locations. It turns out that in general the electron does have a very small probability of being located inside the nucleus, at any instant of time. If it is then possible for the electron to interact with the nucleus, and still satisfy conservation of energy, it can do so. This is called electron capture, and some radioactive nuclei do decay via this process.

 

[lalbatros]

jtbell,

I don't understand the purpose and the utility of this remark:

The Bohr-Sommerfeld planetary model of the atom has been dead, dead, dead since the 1920s. Please don't encourage people to think in terms of that model, except as a purely historical exercise.

To answer the question by ClubDogo, which was in a naïve style, it would have been totally meaningless to come with the Schrödinger equation and wavefunctions.

The main ingredients to answer the question were included in my post, in an "allegorical way" yet useful way.
For students with a 30 hours background in quantum mechanics, the translation to the rigourous language is easy.
However, they usually ignore basic things like radiations by charged particles and of course quantum field theory.
Therefore, it would be an total illusion to think that a more precise language would make a better answer, at this level of a discussion.

Finally, the next question is:

why can't the fundamental level lose anymore energy by radiation​

and to answer this question, the BS model would indeed become insufficient.
Well, I guess so, but I could have fun this evening to think about it.

Michel

Postcriptum:
Electron capture involves the weak interaction.
I think the initial question by ClubDogo was related to the stability of atoms under the electromagnetic interaction only. (- electron and + nucleus). This is indeed an important think to learn and understand in quantum mechanics.
I think it is of no real help to involve the weak interaction in the answer.

 

[lalbatros]

ClubDogo,

You should understand that the BS model gave a first "explanation" of the atomic levels.
The idea was that electrons had a wave-like structure and that stationary states had to be "resonant".

However, this was a naïve theory. Obviously this wave had to be described in 3 spatial dimensions and time. Bohr and Sommerfeld and everybody at that time knew that very well. Many people at that time also had a deep understanding of classical mechanics, like Schrödinger and Dirac. It turned out that Schrödinger was the first to come with a full wave picture for the Hydrogen atom, a result that he based on his knowlegde of CM. Dirac was soon able to go further.

Now, what is the conclusion of this story?
I think that, to some extent, we can not say that the BS theory is dead or that it does not explain the stability of the atoms. We cannot say that it states without explaining. The full consistent quantum theory will not give you any further explanation, altough it will give you more aspects as well as other consequences (vacuum fluctuations for example, ...) The stability of the atom in the BS model or in the full QM theory has the same explanation: the stationary states are a resonant structure.

In other words:

In the simplified BS model as well as in QM, the orbitals are resonnant structures (eigenmodes, eigenvectors).
In the BS model, this structure is oversimplified, but gave the right levels(by chance). It was practically a simple 1D model.
In the QM theory, the structure is almost perfectly described and therefore more predictions are possible.​

 

[ZapperZ]

Ok, I'm a physicist.
I know the Bohr-Sommerfeld model.. but it does not explain the atom structure. It states. Nothing else. THAT'S NOT A VALID ANSWER: it's like to say "this is so, because so it is".
And the problem is the same in the planetary motion, gravitational force is only attractive... But why the moon does not fall to the earth? I don't want answers such "there exists strange things, theories that stands tall, etc". Give me the physical reason... I should think that no one knows it?

This seems to be a common occurrence here lately, and I don't know why.

Can you show something that actually has a "physical reason" so that we can THEN at least understand what you mean by such a thing.

As a "physicist", you of all people should have been aware that at the MOST FUNDAMENTAL LEVEL, all we have for every single phenomenon is a description. Go ahead and pick anything and see if what you think you have "understood" is nothing more than a physical description of that phenomenon.

Zz.

 

[DrChinese]

As a "physicist", you of all people should have been aware that at the MOST FUNDAMENTAL LEVEL, all we have for every single phenomenon is a description. Go ahead and pick anything and see if what you think you have "understood" is nothing more than a physical description of that phenomenon.

Zz.

Echoing what ZapperZ has said: Physics is continuing attempt to answer the "why". That is actually done by way of improved descriptions - usually by way of a theory which has predictive power.

Yet... when you answer one "why" you end up creating another! There are plenty of questions we will likely never be able to answer the "why" about. Why were you born? We might be able to answer the "how" (descriptive) but not the "why".

In sum: It is not a flaw in a theory that it does not "explain" or "describe" in a fashion that answers "why" questions. It is possible that there is no better theory of gravity than General Relativity, for example, and we still do not know "why" we live in 4 spacetime dimensions rather than some other number.

 

[lalbatros]

As I said very often, physics is not about explaining things.
Physics is about describing things of the world and their relations with a minimum amount of information.
We can think that quantum mechanics and electromagnetism explain atomic physics.
It is more correct to think that atomic physics does not need more than these two theories to get a full theoretical description and that moreover, atomic physics shares QM and EM with many other parts of physics.

 

[jtbell]

Electron capture involves the weak interaction.
I think the initial question by ClubDogo was related to the stability of atoms under the electromagnetic interaction only. (- electron and + nucleus). This is indeed an important think to learn and understand in quantum mechanics.
I think it is of no real help to involve the weak interaction in the answer.

I mentioned electron capture because it illustrates that the electron sometimes really does "fall into the nucleus" in some sense, as described by the QM probability distribution. The fact that it proceeds via the weak interaction doesn't matter; the weak interaction doesn't get the electron "into" the nucleus, as far as I know.

 

[lalbatros]

jtbell,

I understood why you mentioned the EC. But an EC depends much more on the state of the nucleus than on the state of the electron.
It was good however to remind ClubDogo of the non-zero probability of presence within the nucleus.
But, I thought ClubDogo was comparing the (apparent) stability of the moon orbit with the stability of atoms.
Therefore, my preffered answer was back to the basics:

without radiative effects, the stability is the consequence of the wave-like nature of the electrons, for any levels
with radiative effects, only the fundamental level is absolutely stable
the next good question is: why does the fundamental level not radiate EM energy?​

 

[reilly]

The Bohr-Sommerfeld theory had lot's of problems; in fact both Bohr and
Sommerfeld beame proponents of the, then new, quantum theory. Among other things, the Bohr-Sommerfeld and Schrödinger/Heisenberg theories were based on very different physical reasoning.

Yet, the fundamental idea of a stationary state, invented by Bohr, became a key ingredient of modern QM. The stability of the hydrogen atom is virtually guaranteed in QM by the stationary states given by the Schrödinger Eq. -- naturally, this assumes that the hydrogen-radiation interaction is small.
Really, we build in atomic stability from the very beginning in QM. And this stability is fundamentally a quantum effect.
Regards,
Reilly Atkinson

 

[lightarrow]

Why does in QM the electron does not fall toward the nucleus? After all, the only force between nucleus and electron is attractive (- electron and + nucleus). Is the same reason that justifies the moon does not fall to the earth?

Maybe your question intended to be: "If a proton and an electron are stationary at some distance and then they are released, if they are point particles, shoudn't there be a non zero probability they don't interact forming the hydrogen atom but, instead, the electron fall directly on the proton?" ?

I personally don't think your is a silly question.
Personal answer: they are not point particles.