How to understand the periodicity of the moving electron in the hydrogen atom

[Jeremy0922]

For a hydrogen atom at ground state, the electron is moving around the proton (nucleur of H atom). The frequency ν₀ and the energy E₀ of the electron in the H atom at the ground state should consistent with quantum hypothesis, that is :

 

E₀=hν₀

 

Where h is Planck's constant .

 

As we known, the period T and the frequency of the electron must obey the following relationship :

 

T=1/ν

 

Clearly, the electron is moving around the proton with a constant period T₀, and

 

T₀= h /E₀

 

According to the concept of period, the moving electron should be at the same position at the time after a period T₀. That is easy for us to understand by classic concept and theory, but I don't know

 

How to understand the periodicity of the electron in the hydrogen atom by quantum mechanics, would you like tell me ? Thanks !

Edited July 21, 2014 by Jeremy0922

[Strange]

This classical Bhor model of the atom with electrons orbiting the nucleus is not really accurate. It does give correct results for some specific things but is in general not accurate.

 

The quantum mechanical model is that an electrons is not orbiting the nucleus but is "spread out" around the atom with a defined probability if being found in any given position.

http://www.chemguide.co.uk/atoms/properties/orbitsorbitals.html

[Nicholas Kang]

This classical Bhor model of the atom with electrons orbiting the nucleus is not really accurate. It does give correct results for some specific things but is in general not accurate.

 

The quantum mechanical model is that an electrons is not orbiting the nucleus but is "spread out" around the atom with a defined probability if being found in any given position.

http://www.chemguide.co.uk/atoms/properties/orbitsorbitals.html

 

Now I know why I would hate my Chemistry teacher next year. That was a really great scientific website. I learnt a lot of new things and terms. Thanks, Strange.

[Jeremy0922]

This classical Bhor model of the atom with electrons orbiting the nucleus is not really accurate. It does give correct results for some specific things but is in general not accurate.

 

The quantum mechanical model is that an electrons is not orbiting the nucleus but is "spread out" around the atom with a defined probability if being found in any given position.

http://www.chemguide.co.uk/atoms/properties/orbitsorbitals.html

 

Thank you for your answer, but the interpretation by probability wave contradicts to the periodic movement of the electron.

[ajb]

Thank you for your answer, but the interpretation by probability wave contradicts to the periodic movement of the electron.

I am not sure if there is any kind of limit for which the Schrödinger equation for the hydrogen atom reduces to Bohr's model. The only thing I can think of is the classical limit, but that would not give the Bohr quantisation conditions. It maybe possible to use the WKB or something like that to get a hursistic picture of an orbiting electron, but you would have to be very careful with the interpretations here. I don't know if you could recover the quantisation contidtions or something close to them. I expect not as the Bohr model is very huristic and based on an ad-hoc modification of classical mechanics.

 

It sounds like you have some solution here?

[swansont]

 

Thank you for your answer, but the interpretation by probability wave contradicts to the periodic movement of the electron.

 

The conclusion is that there is no periodic motion of the electron, in any meaningful classical sense. The Bohr model is wrong.

[StringJunky]

 

The Bohr model is wrong.

To say I was pissed off when I found this out going into A level chemistry (16-18yrs) would be an understatement. I felt the previous two years was completely wasted on learning inaccurate information. The tutor actually said: "Everything you've learnt so far is wrong"!

[Nicholas Kang]

And what I have learnt in school are all wrong.

[Strange]

 

Thank you for your answer, but the interpretation by probability wave contradicts to the periodic movement of the electron.

 

What periodic movement of the electron are you referring to?

[Jeremy0922]

I am not sure if there is any kind of limit for which the Schrödinger equation for the hydrogen atom reduces to Bohr's model. The only thing I can think of is the classical limit, but that would not give the Bohr quantisation conditions. It maybe possible to use the WKB or something like that to get a hursistic picture of an orbiting electron, but you would have to be very careful with the interpretations here. I don't know if you could recover the quantisation contidtions or something close to them. I expect not as the Bohr model is very huristic and based on an ad-hoc modification of classical mechanics.

 

It sounds like you have some solution here?

 

Hi, ajb, thank you to discuss with you again.

1. The Schrödinger equation can not reduce to trajecctory equation for the moving electron in the center field;

2. Bohr model is the theory closed to sucess for H atom. But we must proof

A) there is a ground orbit (or state) for H atom, and

B) the linear spectrum is caused by resonance of the ground orbit, and

C) the steady state Schrödinger equation of the H atom could be deduced from A) and B)

 

I think the answer or explanation could be found for your questions in my prevous topics and paper:

1. Electromagnetic radiation and steady state of hydrogen atom

 

2. Why don't we build the model of hydrogen atom independently by QM?

 

 

What periodic movement of the electron are you referring to?

 

center of mass coordinate of the H atom

 

The conclusion is that there is no periodic motion of the electron, in any meaningful classical sense. The Bohr model is wrong.

 

Nice to meet you again, Swansont.

please see my quote above to answer ajb.

Edited July 21, 2014 by Jeremy0922

[Strange]

center of mass coordinate of the H atom

 

Does the center of mass move?

[Jeremy0922]

 

Does the center of mass move?

Yes, it is moving refere to Lab

[Strange]

Yes, it is moving refere to Lab

 

I wasn't aware of that. Can you provide a reference describing it?

[swansont]

Yes, it is moving refere to Lab

 

 

In the center of mass coordinates, the center of mass is stationary, by definition.

1. The Schrödinger equation can not reduce to trajecctory equation for the moving electron in the center field;

 

No. That's one of the big differences when compared to classical physics, and one of the central ideas of QM.

 

2. Bohr model is the theory closed to sucess for H atom.

 

The Bohr model explains a few things properly, but where it fails it fails spectacularly. In a seemingly unrecoverable way.

[Jeremy0922]

 

I wasn't aware of that. Can you provide a reference describing it?

 

You can find the answer in a text book about classical mechanics or wiki, for two-bodies system.

http://en.wikipedia.org/w/index.php?title=Center-of-mass_frame&redirect=no

 

 

In the center of mass coordinates, the center of mass is stationary, by definition.

 

 

The atom is moving to Lab., so, it's center of mass (coordinates) is also moving.

[swansont]

 

You can find the answer in a text book about classical mechanics or wiki, for two-bodies system.

http://en.wikipedia.org/w/index.php?title=Center-of-mass_frame&redirect=no

 

The atom is moving to Lab., so, it's center of mass (coordinates) is also moving.

 

Moving relative to the lab. But the center of mass is not moving with respect to its own coordinate system.

 

From the Wikipedia page

 

"In all COM frames, the center of mass is at rest"

[Strange]

 

You can find the answer in a text book about classical mechanics or wiki, for two-bodies system.

http://en.wikipedia.org/w/index.php?title=Center-of-mass_frame&redirect=no

 

That doesn't say anything about hydrogen atoms.

 

Do hydrogen atoms really move due to the movement of the electron?

[ajb]

1. The Schrödinger equation can not reduce to trajecctory equation for the moving electron in the center field;

You mean that the WKB approximation is not sutiable for what you want to do? I have not looked into this at all. Do you have a reference here? (or is it something I would have to workout myself, null results don't get published!)

[swansont]

You mean that the WKB approximation is not sutiable for what you want to do? I have not looked into this at all. Do you have a reference here? (or is it something I would have to workout myself, null results don't get published!)

 

I took this to mean that you don't get classical equations of motion from the Schrödinger equation.

[Jeremy0922]

You mean that the WKB approximation is not sutiable for what you want to do? I have not looked into this at all. Do you have a reference here? (or is it something I would have to workout myself, null results don't get published!)

 

WKB approximation is only a mathematical method or semiclassical calcultion for finding approximate solutions for the quantum sysytem, the reliability of results depends on whether the Schrödinger equation of the quantum system is correct.

 

By my opnion, Schrödinger equation could be used to describe the resonance of the orbit in atom, eigenvalues of energy from the equation's solutions decide the eigenvalues of orbit radius. For the H atom, we can get eigenvalues of orbit radius of the ground and resonate states by solution of Schrödinger equation, and the elelctron moves along one of the eigen-orbits which obey the control of the Lorentz force.

 

In addition, H atom is only at the ground orbit for the isolated state, and could be at high eigen-orbit by outer resonate field.

Edited July 22, 2014 by Jeremy0922

[hoola]

I liked strange's question....do hydrogen atoms really move due to the movement of the electron...? I would presume that movement is due to electron repulsion from adjacent atoms...

[Jeremy0922]

I liked strange's question....do hydrogen atoms really move due to the movement of the electron...? I would presume that movement is due to electron repulsion from adjacent atoms...

 

For an isolated hydrogen atom, there is no adjacent atom.

[Strange]

 

For an isolated hydrogen atom, there is no adjacent atom.

 

But, again, you haven't answered the question!

[Jeremy0922]

 

But, again, you haven't answered the question!

 

In the hygrogen atom, there is an electron and a proton. As a clsssical mechanical system, that is a two-body system. About the treatment for two-body system, you could find the answer from text book of physics about mechanics and movement.

[Strange]

 

In the hygrogen atom, there is an electron and a proton. As a clsssical mechanical system, that is a two-body system. About the treatment for two-body system, you could find the answer from text book of physics about mechanics and movement.

 

You still haven't answered the question. The question is: do hydrogen atoms move because of the movement of the electrons?

 

I am not asking about classical mechanics, two body systems, or text books. After all, the hydrogen atom is not a classical system so all of that is irrelevant. I am asking about what actually happens.

 

So, again, can you provide a reference that shows experimental measurements of a hydrogen atom oscillating due to the movement of the electron?