# How does the quantum model justify accelerating electrons not losing energy?

A serious flaw in the Planetary model was that it theorized that electrons accelerated around the nucleus which would cause them to continuously lose energy as EMR and crash into the nucleus. The Bohr model also I think, fails to explain WHY the accelerating electrons don't emit EMR . How does the quantum model of the atom justify the electrons not losing energy though? I am aware that electrons act like waves and that the orbitals can only have a circumference that is an integer multiple of the wavelengths; even so, dont accelerating electrons emit EMR?
Thanks! =D

In Quantum Mechanics, you can't take logic or reasoning into your equations.

We have just as barely scratched the surface of QM, so it is still a long way to go to find out exactly why things like this happens, we have theories, but not proof.

Staff Emeritus
2021 Award
I don't think you can always get an answer to "but WHY"? Classical physics has a certain set of behaviors, and quantum physics has a different set - one that more accurately describes observation. That's really all one can expect science to provide.

A serious flaw in the Planetary model was that it theorized that electrons accelerated around the nucleus which would cause them to continuously lose energy as EMR and crash into the nucleus. The Bohr model also I think, fails to explain WHY the accelerating electrons don't emit EMR . How does the quantum model of the atom justify the electrons not losing energy though? I am aware that electrons act like waves and that the orbitals can only have a circumference that is an integer multiple of the wavelengths; even so, dont accelerating electrons emit EMR?
Thanks! =D

There is no acceleration in the ground state: such a state is stationary. The space distribution of the charge is still. And the other (excited) states are nearly stationary.
To make a transition between stationary states, you have to disturb the atomic constituents (push electrons or nucleus).

Bob_for_short.

A The Bohr model also I think, fails to explain WHY the accelerating electrons don't emit EMR . How does the quantum model of the atom justify the electrons not losing energy though? =D

In my personal view, I do not think the Bohr model fails to explain why the accelerating electrons don't emit energy.

In the Bohr model, when the orbital is an interger times the wavelength of an electron,
the motion is stable.

By only the Maxwell's law, the atomic behavior can't be completely explained.
For example, Davisson Germer and two-slit experiments.

There is no acceleration in the ground state: such a state is stationary. The space distribution of the charge is still. And the other (excited) states are nearly stationary.
Bob_for_short.

Your model is granpa's model. If one electron is so big as the electron cloud, the scattering experiment will give different results.

ZapperZ
Staff Emeritus
A serious flaw in the Planetary model was that it theorized that electrons accelerated around the nucleus which would cause them to continuously lose energy as EMR and crash into the nucleus. The Bohr model also I think, fails to explain WHY the accelerating electrons don't emit EMR . How does the quantum model of the atom justify the electrons not losing energy though? I am aware that electrons act like waves and that the orbitals can only have a circumference that is an integer multiple of the wavelengths; even so, dont accelerating electrons emit EMR?
Thanks! =D

You may want to start by reading an entry in our FAQ in the General Physics forum.

Zz.

If one electron is so big as the electron cloud, the scattering experiment will give different results.

Yes, the scattering experiments do give different results. The negative cloud sizes in atoms are described with the elastic atomic form-factors. They depend on the initial and final atomic states <n|, |n>, it is an experimental fact. Moreover, there are positive charge atomic form-factors describing the nucleus de-localisation in atoms (see "Atom as a "dressed" nucleus" by Vladimir Kalitvianski).

Bob.

How does the quantum model of the atom justify the electrons not losing energy though?

The Bohr model is not the same as quantum mechanics. If you treat an atom according to quantum mechanics, you have to take into account the coupling of electrons to the elecromagnetic field. If you atart with an electron in the first excited state and the radiation field in the vacuum state (no photons present), then this state will evolve over time into a superposition of the electron in the initial exicted state and some states with lower energy. Roughly speaking this amounts to the state becoming

A |excited state and no photons> + B|lower energy state plus photon>

The coefficient A will gradually diminish while B will grow over time. In relality, the photons can be in many possible states, of course.

I am aware that electrons act like waves and that the orbitals can only have a circumference that is an integer multiple of the wavelengths; even so, dont accelerating electrons emit EMR?
Thanks! =D

If the electron loose smoothly its energy radiating, than the orbit is no more with an integer number of wavelength, but this non periodic orbit is not allowed by the Bohr condition. The electron in an atom can only loose energy by discrete amounts equal to the difference between two possible periodic orbitals i.e. the photoelectric effect.

You may want to start by reading an entry in our FAQ in the General Physics forum.

Zz.

woah, didnt see tht XD
thanks!

Yes, the scattering experiments do give different results. The negative cloud sizes in atoms are described with the elastic atomic form-factors. They depend on the initial and final atomic states <n|, |n>, it is an experimental fact. Moreover, there are positive charge atomic form-factors describing the nucleus de-localisation in atoms (see "Atom as a "dressed" nucleus" by Vladimir Kalitvianski).

Bob.

I think in QM, it is difficult to image the atomic behavior.

Are you trying to image the electronic motion concretely?
Do you think one electron can be divided into pieces?
In QM, the electron can change to any form as a magician.

Bohr model, I think, is more natural if we image the electronic motion.

Fredrik
Staff Emeritus
Gold Member
In Quantum Mechanics, you can't take logic or reasoning into your equations.

We have just as barely scratched the surface of QM, so it is still a long way to go to find out exactly why things like this happens, we have theories, but not proof.
That didn't make any sense. Of course you can use logic and reasoning in QM. And proof of what?

I think in QM, it is difficult to image the atomic behavior.

Are you trying to image the electronic motion concretely?
Do you think one electron can be divided into pieces?
In QM, the electron can change to any form as a magician.

Bohr model, I think, is more natural if we image the electronic motion.

The experiments show that the negative charge is smeared in atoms. It is "seen" as smeared.
Division into pieces is possible only in mind. A projectile, as I said, "sees" the negative charge smeared (elastic atomic form-factor). Why then should we appeal to a simpler notion of a point-like and turning around electron? Planetary model is wrong and misleading rather than "natural". It fails theoretically and experimentally.

Bob_for_short.

The experiments show that the negative charge is smeared in atoms. It is "seen" as smeared.
Division into pieces is possible only in mind. A projectile, as I said, "sees" the negative charge smeared (elastic atomic form-factor). Why then should we appeal to a simpler notion of a point-like and turning around electron? Planetary model is wrong and misleading rather than "natural". It fails theoretically and experimentally.

I am sorry that I'm fussing over small details.

OK. I understand you say that the electron is seen as smeared, is not actually smeared
(the electron is not actually divided, enlarged or continuously distributed).

So first you said the below,

There is no acceleration in the ground state: such a state is stationary. The space distribution of the charge is still.

If the electron is not actually smeared (just seen as smeared), how do you explain the constant distribution of the charge of one electron? (which fact is indispensable for justifing that accelerating electrons not losing energy in your first opinion.)

I am sorry that I'm fussing over small details.

OK. I understand you say that the electron is seen as smeared, is not actually smeared
(the electron is not actually divided, enlarged or continuously distributed).

Yes, it is actually smeared, that is why it is seen as smeared. Properly carried out experiments on elastic charge scattering show namely that.

But there is also the so called inclusive picture where all elastic and inelastic cross sections are added. Then the inclusive cross section coincides with the Rutherford cross section as if the target charge were point-like and situated in the center of inertia of a compound system. So the notion of point-like charge is illusory, not true.

Bob_for_short.

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Yes, it is actually smeared, that is why it is seen as smeared. Properly carried out experiments on elastic charge scattering show namely that.
Bob_for_short.

I imagine your model is probably based on the quantum mechanical theory (Is it right?)
In QM there are some incredible problems such as below.

1. In the ground state of hydrogen atom, the orbital angular momentum of the electron is zero, Dose
the electron crush or penetrate into the nucleus?
(If you say the electronic charge is still and moving around the nucleus, that is contrary to the fact that orbital
angular momentum is zero.)

2. In 2P, 3P ,or 3D... , the eddy of the spinning electron is flowing through the static charge.
How can you keep the state of electonic charge still?

3. An electron is too small, so by equating the angular momentum of the spinning electron to 1/2 hbar, the spinning
sphere leads to 100 times the speed of light (In your model,
the size of the electron is variable.)

4. The spinning electron must be rotated by an angle of 4π in order to return to their original configuration. It is
ridiculous!

In Bohr model, All these problems do not occur.

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Hootenanny
Staff Emeritus
Gold Member
I haven't read the majority of this thread or any of your posts in their entirety. However, this comment just jumped out at me:
3. An electron is too small, so by equating the angular momentum of the spinning electron to 1/2 hbar, the spinning
sphere leads to 100 times the speed of light (In your model,
the size of the electron is variable.)
What is the size of an electron?

I have also noticed that all of your points hinge on the notion that the QM orbital angular momentum corresponds to the classical concept of angular momentum.

I imagine your model is probably based on the quantum mechanical theory (Is it right?) In QM there are some incredible problems such as below.

Yes, that is right, it is based on QM, it is a QM result.

The problems your are mentioning are not problems in QM. They are failures of classical picture applied to the quantum world. The smearing is quantum mechanical, not classical mechanical. In CM the charge smearing is described with charge density. In QM it is probability which is smeared.

I cannot give here lessons of QM. For that there are textbooks.

Regards,

Bob.

You may want to start by reading an entry in our FAQ in the General Physics forum.

WHY DON’T ELECTRONS CRASH INTO THE NUCLEUS IN ATOMS?

Contributed by Marlon and edited by ZapperZ

If one describes atoms using only the Coulomb forces, the electron and the nucleus will attract each other and no stable atoms could exist. Obviously this is not the case. Niels Bohr was the first (1913) to propose a better model, which consisted of electrons moving around the nucleus in circular orbits. Each orbit corresponds to a certain discrete energy level. This model is based upon the quantisation of the angular momentum.

Unfortunately, electrons moving in a circular orbit have an acceleration due to the centripetal force. In classical electromagnetic theory, an accelerated charged particle must emit EM-radiation due to energy conservation. Hence, the electron would lose energy and spiral down towards the nucleus. Again stable atoms could not exist. What is wrong now?

It turns out that the picture of electrons moving in circular orbits around the nucleus isn’t correct either(*). The solution here is the implementation of Quantum Mechanics via the Schrödinger Equation and the concept of wavefunction. By applying such formalism, the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus. While there are no more “orbits”, we do use the term “orbitals” to indicate the shape of such geometry. However, this term should not be confused to mean an orbiting electron similar to our planets in the solar system. By describing the system in terms of the QM wavefunction, it creates stable states for the nucleus+electrons system that matches very well with experimental observation of standard atomic spectra.

Since there are no more “orbits” in the conventional sense, the problem of electrons radiating due to an accelerated motion is no longer meaningful. It explains why we have stable atoms. Zz.

But it does not really explain the question: "WHY DON’T ELECTRONS CRASH INTO THE NUCLEUS IN ATOMS". It only points out what's wrong with classical and Bohr's models. The only explanation is that the electron is "smeared" in the atom. But it fails to explain why "smeared" electron won't crash into the nucleus and why the problem of electrons radiating due to an accelerated motion is no longer meaningful, just because no more “orbits” in the conventional sense and "smeared" electrons. In quantum mechanics, what is "smeared" is the "wavefunction" of electron, not electron itself. Since electron is a particle and can't have fractional charge when measured

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https://www.physicsforums.com/showpost.php?p=1287217&postcount=8

Ok. But what if we considered the electron not as point-like but instead smeared out in the orbit? In this case there shouldn't be any resultant radiation.
Jackson-Classical Electrodynamics-exercise 14.12 asks to prove that the resultant radiation emitted by N charges moving in a circular path at constant distances goes to zero when N goes to infinity.
So, if we could think of the electron in the H atom as a continuous distribution of charge, it shouldn't radiate.

ZapperZ
Staff Emeritus
But it does not really explain the question: "WHY DON’T ELECTRONS CRASH INTO THE NUCLEUS IN ATOMS". It only points out what's wrong with classical and Bohr's models. The only explanation is that the electron is "smeared" in the atom. But it fails to explain why "smeared" electron won't crash into the nucleus and why the problem of electrons radiating due to an accelerated motion is no longer meaningful, just because no more “orbits” in the conventional sense and "smeared" electrons. In quantum mechanics, what is "smeared" is the "wavefunction" of electron, not electron itself. Since electron is a particle and can't have fractional charge when measured

But it points out to the fallacy of the question, i.e. the question is contextually invalid. One can't answer such a thing. That's like asking what is the color of an electron! You are trying to force a square object through a round hole, and then when it can't get through, you're asking why that hole is round.

BTW, do a search on fractional charge and fractional quantum hall effect.

Zz.

But it does not really explain the question: "WHY DON’T ELECTRONS CRASH INTO THE NUCLEUS IN ATOMS".

Only one thing is missing from the explanation: That the set of all possible "orbits" form a complete set, i.e., any possible physical state is a linear combination of these orbits. Also, one has to consider free states, i.e. states corresponding to the electron not being bound to the nucleus.

Then, you can write down a state corresponding to an electron being located to within a very short distance of the nucleus, but then such a state contains many free states with positive energy. Indeed, if you want to probe the nucleus with electrons at short range, you need to fire a high energy electron beam into the nucleus.

Electrons --- Coulomb Force and stuff

Hi,

Why doesn't the electron fall into nucleus? The Coulomb force should attract it into more dense nucleus where proton resides I would think.

Is the electron a wave? I am use to solar system analogy when describing orbits but I know this is wrong. Therefore, if it is not billard ball type object is it wave and how is a wave bound? How does a wave carry a charge?

Cyosis
Homework Helper

Using the planetary model for the atom, there is no real difference between the orbiting electron and an orbiting planet. Gravity attracts a planet so by your reasoning the earth should crash into the sun as well. Do you understand why this doesn't happen in the case of the earth?

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I would venture to guess angular velocity of earth. But electron is in reality a wave. Can waves have angular velocity?

Cyosis
Homework Helper
Yes conservation of momentum and gravity, being the centripetal force in this case, keep the earth in orbit. Or as you will freely falling to the earth but always missing it.

When using a planetary model for atoms you can use this same argument with the Coulomb force generating the centripetal force.

Your question was why doesn't it fall to the nucleus using the planetary model. Therefore you can't treat the electron as a wave.

As you already pointed out this model is wrong of course. Electrons have this particle/wave duality and in quantum mechanics they are described by a wave function. In quantum mechanics electrons can still have orbital angular momentum and spin angular momentum. It describes the electrons to be smeared out like a cloud around the nucleus.

1) How does a wave(electron) spin?
2) why is the term 'particle' still used when referring to electrons? Is it because the waves that we call electrons are composed of 'leptonic particles' which, as name implies, true particles?

Cyosis
Homework Helper
Why do you insist on calling an electron a wave. You suggest it is more wavelike than particle like. Explain the photo electric effect, or any other collision with the wave model, you can't. Explain diffraction with the particle model, you can't. Quantum mechanics brought forth the particle-wave duality description. In certain cases it acts like a particle in others it acts like a wave.

It seems you want to have some kind of classical image of the electron. I am afraid that is going to be impossible.

alxm
1. In the ground state of hydrogen atom, the orbital angular momentum of the electron is zero, Dose
the electron crush or penetrate into the nucleus?

The 1s electron does[/I_ spend a small amount of its time 'inside' the nucleus. The problem of "why the electron doesn't fall into the nucleus" is not a problem in quantum theory, because it does not have an exact position.

2. In 2P, 3P ,or 3D... , the eddy of the spinning electron is flowing through the static charge.
How can you keep the state of electonic charge still?

The states you're talking about are stationary solutions to the wave equation. I don't need to 'keep the state still'.

3. An electron is too small, so by equating the angular momentum of the spinning electron to 1/2 hbar, the spinning sphere leads to 100 times the speed of light (In your model, the size of the electron is variable.)

Electrons aren't spinning spheres.

4. The spinning electron must be rotated by an angle of 4π in order to return to their original configuration. It is ridiculous!

A spinor describing an electron needs to be spatially rotated by 4 Pi. So? They're not three-dimensional objects.

In short: You don't understand quantum mechanics.

alxm