Speed of Electrons: A Classic View

[jochem]

Hello,
this is my first forum question, so i hope it's at the right place.
My question is about electrons, i know in a QM view electrons don't have a well defined position or speed.
However i am curious, in a classic view of the electron would electrons closer to the nucleus move faster then electron farther away from the nucleus. I tried to reason it with the centripetal force equal to coulombs law. So i came to the conclusion that electrons closer to the nucleus would move faster then electron further a way. Is this reasoning correct or did i made a mistake?P.S. i am sorry for grammar mistakes

 

[RPinPA]

Yes, in the Bohr model (which is what you're talking about) the dynamics are the same as for planets orbiting a sun. The Coulomb force is an inverse square force as Newtonian gravitation is, so you get all very similar equations (with different constants of course).

So for instance in our solar system, Mercury moves at 47 km/s while Earth, farther out, moves at about 30 km/s.

 

[jochem]

Oke thank you!

 

[BPHH85]

Of course this is just a mind game because in such a classical situation, the electron will lose energy by spinning around the nucleus and will collapse in it.

 

[jochem]

i am not sure, why is that? You could reason that the electron, would haven only one force acting on it. This force would be described by coulombs law. However if the electron has a speed around a stable point, the nucleus. Then it will reach a equilibrium where it will circle the nucleus forever.

 

[Nugatory]

i am not sure, why is that?

An accelerating charged particle (and an orbiting particle is accelerating because its direction of travel is constantly changing) emits electromagnetic radiation as it changes speed and/or direction. This causes it to lose energy and slow down.

Thus, an electron orbiting the nucleus won't be in a stable equilibrium; it will continue to lose energy and move closer to the nucleus until its speed is zero and it collides with the nucleus. Thus, the classical model of the orbiting electron predicts that atoms should decay very quickly - but of course they don't. This was a big problem for 19th-century physicists, not resolved until quanum mechanics was discovered early in the 20th century.

 

[RPinPA]

Yeah, that's the well-known difference between the electromagnetic force and the gravitational force which killed the Bohr model. Accelerating electrons radiate energy. That's predicted by Maxwell's Equations, which date to the 19th century.

 

[jochem]

I am sorry but i don't quite get that.
I can understand why you could say a electron is accelerating in different directions. However why does this need to result in a decrease of its energy?
So i think what i don't understand is why would a charged particle that is just moving a round a point, it is accelerating and thus also decreasing, lose energy in this view? (it is also decreasing right? because it speed in one direction changes to a speed in another direction so it must decrease and increase in another direction)

Sub-question: if an electron would hit a proton it would form a neutron right?

 

[jbriggs444]

I am sorry but i don't quite get that.
I can understand why you could say a electron is accelerating in different directions. However why does this need to result in a decrease of its energy?

It is called synchrotron radiation and is emitted by an electron or any other charged particle accelerating radially in a circular path. If it is emitting radiation, it is emitting energy. If it is emitting energy, it is losing energy.

The classical picture is incomplete, of course. An electron in an atom is not actually accelerating radially and does not emit synchrotron radiation.

Sub-question: if an electron would hit a proton it would form a neutron right?

That is a possibility. See https://physics.stackexchange.com/questions/88059/collision-between-electron-and-proton. In order to conserve lepton number, an electron neutrino is produced as well.

 

[RPinPA]

It is also decreasing right? because it speed in one direction changes to a speed in another direction so it must decrease and increase in another direction

Just want to respond to this comment. The answer is no. An object moving in a circle at constant speed is never increasing or decreasing in speed. Yes, the components change, but the magnitude never does.

 

[jochem]

Just want to respond to this comment. The answer is no. An object moving in a circle at constant speed is never increasing or decreasing in speed. Yes, the components change, but the magnitude never does.

But if the components change, the components undergo a acceleration and or a deceleration right?

 

[jochem]

It is called synchrotron radiation and is emitted by an electron or any other charged particle accelerating radially in a circular path. If it is emitting radiation, it is emitting energy. If it is emitting energy, it is losing energy.

I can understand that if, it would emitted radiation it would lose energy. However i can't quite grasp why it would emitted radiation. I read parts of your link and also https://en.wikipedia.org/wiki/Cyclotron_radiation from here. So 2 questions arose, first one: In my mind (i know this is not very scientific) the electron would be in a equilibrium around a nucleus. So why is it unstable.

second question: If its is unstable how exactly would it emitted radiation, i mean not how, but when. We know light is quantised so it must take discreet energy forms, so is the electron emits photons, when its accelerating then it would need to constantly send photons, because in a circle it's constantly accelerating right?

 

[jbriggs444]

I can understand that if, it would emitted radiation it would lose energy. However i can't quite grasp why it would emitted radiation. I read parts of your link and also https://en.wikipedia.org/wiki/Cyclotron_radiation from here. So 2 questions arose, first one: In my mind (i know this is not very scientific) the electron would be in a equilibrium around a nucleus. So why is it unstable.

second question: If its is unstable how exactly would it emitted radiation, i mean not how, but when. We know light is quantised so it must take discreet energy forms, so is the electron emits photons, when its accelerating then it would need to constantly send photons, because in a circle it's constantly accelerating right?

In the Bohr model, electrons do orbit the nucleus and do accelerate. Classical electromagnetism (Maxwell's equations) then predicts that they should radiate. If they radiate, they must lose energy. If they lose energy, they must spiral into the nucleus. That is, classical electromagnetism predicts that electrons orbiting atomic nuclei would be unstable.

That answers your first question.

Your second question contains a contradiction. It is only when using the Bohr model of the atom together with the classical model for electromagnetism that we predict the emission of radiation. We know that prediction is incorrect. There is no radiation. You cannot reasonably ask where or how or when the radiation is emitted as photons because

1. Classical electromagnetism does not predict radiated photons because the model is classical and does not include photons.
2. Reality does not include radiated photons because in reality the Bohr model is wrong and there are no accelerating electrons.
3. Photons are not what you think they are.

 

[BPHH85]

Seems that I kicked something off with my remark...

But if the components change, the components undergo a acceleration and or a deceleration right?

This is according to Newtons first law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

 

[jochem]

oke thanks for your quick answer.

Classical electromagnetism (Maxwell's equations) then predicts that they should radiate.

could you say with equations you main?

Reality does not include radiated photons because in reality the Bohr model is wrong and there are no accelerating electrons.

alritght then, what are the electrons then doing around the nucleus i understand that this is not a well defined question because of QM. But are the electron in QM not acceleration around the nucleus?

 

[jochem]

Seems that I kicked something off with my remark...This is according to Newtons first law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

I am sorry what are you trying to say? there is a force acting on the electron right?

 

[jbriggs444]

could you say with equations you main?

https://en.wikipedia.org/wiki/Maxwell's_equations

alritght then, what are the electrons then doing around the nucleus i understand that this is not a well defined question because of QM. But are the electron in QM not acceleration around the nucleus?

It is not a well defined question. Full stop.

 

[jochem]

Why a full stop, i will ask otherwise. Why does the QM view of a electron and its nucleus not result in the radiation Maxwell predicted.

 

[BPHH85]

I am sorry what are you trying to say? there is a force acting on the electron right?

An electron orbiting a nucleus neither remains in rest nor continuous to move at a constant velocity as the direction of the velocity changes ongoing. So the acceleration isn't zero, according to Newtons first law.

 

[BPHH85]

Why a full stop, i will ask otherwise. Why does the QM view of a electron and its nucleus not result in the radiation Maxwell predicted.

To bring together a QM view on light-matter-interaction, you need a deeper understanding in QED (qauntum-electrodynamics). But this is beyond my knowledge. But to point it out...a point mass like electron with charge -e orbiting around a nucleus is a model from the classical physics point of view. As this model will lead to an electron collapsing in the nucleus leading to unstable matter states leading to a world that isn't the world we all are living in can't discribe the way the microscopic world works. Thats why classical phyics failed discribing microscopic behaviour and QM was needed.

 

[ZapperZ]

Why a full stop, i will ask otherwise. Why does the QM view of a electron and its nucleus not result in the radiation Maxwell predicted.

https://www.physicsforums.com/insights/dont-electrons-crash-nucleus-atoms/

Zz.

 

[jochem]

To bring together a QM view on light-matter-interaction, you need a deeper understanding in QED (qauntum-electrodynamics). But this is beyond my knowledge. But to point it out...a point mass like electron with charge -e orbiting around a nucleus is a model from the classical physics point of view. As this model will lead to an electron collapsing in the nucleus leading to unstable matter states leading to a world that isn't the world we all are living in can't discribe the way the microscopic world works. Thats why classical phyics failed discribing microscopic behaviour and QM was needed.

oke thnx!

 

[jochem]

https://www.physicsforums.com/insights/dont-electrons-crash-nucleus-atoms/

super thank you! I'm gone read it!

 

[DanMP]

An accelerating charged particle (and an orbiting particle is accelerating because its direction of travel is constantly changing) emits electromagnetic radiation as it changes speed and/or direction. This causes it to lose energy and slow down.

Thus, an electron orbiting the nucleus won't be in a stable equilibrium; it will continue to lose energy and move closer to the nucleus until its speed is zero and it collides with the nucleus. Thus, the classical model of the orbiting electron predicts that atoms should decay very quickly - but of course they don't. This was a big problem for 19th-century physicists, not resolved until quanum mechanics was discovered early in the 20th century.

This is very interesting, but the idea that the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus is not only bizarre, but also doesn't seem to solve the whole problem, because the atoms on the Earth are rotating (at least around the Sun), so the "smeared" electron is still accelerating (an orbiting particle is accelerating because its direction of travel is constantly changing) and (supposedly) emitting electromagnetic radiation ...

 

[jbriggs444]

This is very interesting, but the idea that the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus is not only bizarre, but also doesn't seem to solve the whole problem, because the atoms on the Earth are rotating (at least around the Sun), so the "smeared" electron is still accelerating (an orbiting particle is accelerating because its direction of travel is constantly changing) and (supposedly) emitting electromagnetic radiation ...

A particle orbiting in gravitational free fall should not emit. However, if you view it from an accelerating reference frame... https://en.wikipedia.org/wiki/Unruh_effect

In any case, an electron riding on the Earth as the Earth orbits the sun is accelerated much less strongly than a hypothetical classical electron orbiting the nucleus of a hydrogen atom.

 

[ZapperZ]

This is very interesting, but the idea that the “electron” occupies a volume of space simultaneously, so that it is “smeared” in a particular geometry around the nucleus is not only bizarre, but also doesn't seem to solve the whole problem, because the atoms on the Earth are rotating (at least around the Sun), so the "smeared" electron is still accelerating (an orbiting particle is accelerating because its direction of travel is constantly changing) and (supposedly) emitting electromagnetic radiation ...

Electrons in the s-orbital of an atom have angular momentum of ZERO. Now explain that with your "orbit" model.

Zz.

 

[DanMP]

A particle orbiting in gravitational free fall should not emit. However, if you view it from an accelerating reference frame... https://en.wikipedia.org/wiki/Unruh_effect

We are not in free fall while rotating around the center of the Earth ... Are we emitting? And if we do, how is this loss of energy affecting the electrons?From your link I got: "It is currently not clear whether the Unruh effect has actually been observed, since the claimed observations are disputed."

 

[jbriggs444]

We are not in free fall while rotating around the center of the Earth ... Are we emitting?

We are neutrally charged.

From your link I got: "It is currently not clear whether the Unruh effect has actually been observed, since the claimed observations are disputed."

Which is a clue that the magnitude of the expected radiation is small.

 

[DanMP]

We are neutrally charged.

Ok, but the electrons in our body are not neutral. Are they emitting? If not, why not? What prevents them to emit?
If yes, they should lose energy ... Is this allowed by the quantum mechanics? And how would this loss of energy affect the electrons? Is it compensated in any way? How?

On the other hand, what keeps the "smeared electron" from falling into the nucleus? Since there is no rotation (on orbits), there is also no centrifugal force ... So what force is preventing the electron to fall on/into the nucleus?

 

[ZapperZ]

Ok, but the electrons in our body are not neutral. Are they emitting? If not, why not? What prevents them to emit?
If yes, they should lose energy ... Is this allowed by the quantum mechanics? And how would this loss of energy affect the electrons? Is it compensated in any way? How?

On the other hand, what keeps the "smeared electron" from falling into the nucleus? Since there is no rotation (on orbits), there is also no centrifugal force ... So what force is preventing the electron to fall on/into the nucleus?

This is another example of trying to go one step forward, but we end up having to take 2 steps back, because we have to explain the explanation.

Try reading this!

https://www.physicsforums.com/insights/dont-electrons-crash-nucleus-atoms/

In other words, you still lack an understanding of the foundation of your question.

BTW, I can see you in the dark with my IR glasses. What do you think that is?

Zz.