What path do electrons actually take in an orbital

[Cheman]

What path do electrons actually take in an orbital...

If electrons are found somewhere within an orbital, what kind of path do they travel within it? ie- is it similar to the orbits of the planets or more random like?

Thanks.

 

[dextercioby]

If electrons are found somewhere within an orbital, what kind of path do they travel within it? ie- is it similar to the orbits of the planets or more random like?

Thanks.

They can be found anywhere in the 'orbital'.Any finite volume of space near the nucleus has a nonzero probability of containing the electron.The answer is:they take all paths,all possible 'trajectories',they move absolutely randomly and that has nothing to do with the "orbits" of Kepler,Rutherford or Bohr.

Daniel.

 

[Cheman]

But surely it cannot be completely random due to the attraction of the nucleus?

 

[fliptomato]

But surely it cannot be completely random due to the attraction of the nucleus?

By solving the Schrodinger equation for a central potential you naturally get the funny shaped "orbitals" that you see in chemistry books. These represent the shape of the probability distribution for the electron--i.e. a given electron has a certain probability for being in one place as opposed to another relative to the nucleus.

As far as nonrelativistic QM is concerned, that's the gist of all there is to know about it. The shapes of these orbitals can be found mathematically, but they say nothing about the dynamical path that an electron takes to get from point a to point b. It's just a probability of finding an electron at a given place.

So in short: yes, you are correct that the nucleus definitely affects the electron in that it provides a potential that affects the probability distrubution of where the electron might be found. However, it's not a physically well posed question to ask about the particular path that an electron takes--this is a question of path integrals.

For some general-public\undergraduate-level insight on that, I highly recommend the Real Media videos at: http://www.vega.org.uk/series/lectures/feynman/ .


Flip

 

[jtbell]

But surely it cannot be completely random due to the attraction of the nucleus?

The position of the electron is random according to the probability distribution given by $$\psi^* \psi$$. Of course, the form of $$\psi$$ is influenced by the presence of the nucleus, and gives larger probabilties in some regions and smaller in others.

I think you're interpreting "completely random" to mean what we usually call "uniformly random", that is, a probability distribution that has the same value everywhere within its domain. I doubt that dextercioby meant that.

 

[DB]

For wavefunctions, what does the star in psi^"star" stand for?

 

[dextercioby]

For wavefunctions, what does the star in psi^"star" stand for?

Complex conjugate.The wave functions are complex functions.Usually (in mathematics especially) u see this complex conjugation marked by a 'bar' over the function complex conjugation.Physics keeps this 'bar' for charge conjugate.

Daniel.

 

[billyell]

uhm, i haven't read all replies to this. But I'm actually reading a book right now that's describing this. It doesn't have to deal with orbit within the orbital but it is the same concept. Feynman's formulation says that the electron will travel EVERY possible trajectory stimulataniously. So, without observing it, we have NO possible way of knowing where it is. On the other hand if we observe it we need to put energy into it... even the smallest amount of energy... photons will cause either the position to change or the velocity to change.

 

[jtbell]

uhm, i haven't read all replies to this.

I guess you didn't notice the dates on the posts either. The last post was close to four years ago.

 

[thaddeus]

another nice question tho ..

This example demonstrates why the collapsing wave packet analogy is valuable .

Given that the electron is simultaneously to be found in any of the 'possible' locations it then somehow collapses that distributed probability cloud density into a more defined location .. and the probabilities associated with it collapse also .. its a great analogy . I don't see why it gets some bad press -- worded with proper reverence it is a beautiful and greatly useful metaphor .

As far as where the "electron" is in its living orbital environment .. the answer may be that it is not in any single location .. this is not to say it is nowhere but that it is strongly spread over a larger area .

So look at the orbital again in terms of a standing wave .. consider that the Orbital zone around a oppositely charged nucleus works to compress the electron Wave form .. perhaps wrapping the electrons freeform wave packet around the nucleus like a blanket .

Given that such a representation is usefully correct .. we can then imagine quite easily that the orbital Zone itself would likely be able to be described as something of a gradient .. the electrical/ionic attraction will be stronger closer , and the probability densities should simply mirror this relationship .

Using a waveform metaphor .. the waves might be drawn closer together for being stronger .

thus we get something akin to the type of imagery depicted as follows ..

http://webapps.lsa.umich.edu/physics/demolab/controls/imagedemosm.aspx?picid=759

 

[edguy99]

I agree, nice question. Is there a distance scale in the image you have posted? Is this image meant to represent that there is an x% chance that an electron will be found within a y distance from the center?

I assume this is a 1s orbital?

 

[mn4j]

Feynman's formulation says that the electron will travel EVERY possible trajectory stimulataniously. So, without observing it, we have NO possible way of knowing where it is.

As is usually the case in these discussions, Feynman apparently had a different meaning for the words, trajectory and position.

There is one definition of position used by everyone else, and a completely different one used by QM people. Just as there is one definition of trajectory used by everyone else and another used by QM people. For the statement that "an electron travels every possible trajectory simultaneously" to make sense, you have to redefine trajectory and possibly also position.

It is mind boggling how QM people have been 'raping' language for almost a century without outcry.

 

[thaddeus]

hey Ed ,

Its actually an image of an electron diffraction pattern .. but it has a graphic content that conveys well the animus of a living orbital zone .. so the scalar is not specifically accurate ..

Here by way of contrast is a plot of electron S1 positions ..
http://www.jce.divched.org/JCEDLib/LivTexts/pChem/JCE2005p1880_2LTXT/QuantumStates/Bookfolder/L25OrbitalShapes_files/eq0002M.gif

http://www.jce.divched.org/JCEDLib/LivTexts/pChem/JCE2005p1880_2LTXT/QuantumStates/Bookfolder/L25OrbitalShapes_files/image004.jpgFigure L25.2
Cloud plot of the 1s orbital.

 

[jtbell]

Feynman's formulation says that the electron will travel EVERY possible trajectory stimulataniously.

Given that the electron is simultaneously to be found in any of the 'possible' locations [...]

As far as where the "electron" is in its living orbital environment .. the answer may be that it is not in any single location .. this is not to say it is nowhere but that it is strongly spread over a larger area.

These are interpretations of QM.

QM itself (the mathematical formalism that we use for calculating predicted results of experiments) does not contain the notion of a detailed trajectory for the electron, or a definite position (or any other quantity if the system isn't in an eigenstate of the operator corresponding to that quantity), before a measurement is made. It doesn't forbid these things, it simply doesn't say anything about them.

Various interpretations of what is "really happening" have been proposed, and there is no general agreement on which one is "best" or "most correct," because there is no way to distinguish between them experimentally, as long as they make the same predictions for the results of experiments.

So the best answer that we can give to the original question of this thead is: We don't know!

 

[edguy99]

hey Ed ,

Its actually an image of an electron diffraction pattern .. but it has a graphic content that conveys well the animus of a living orbital zone .. so the scalar is not specifically accurate ..

Here by way of contrast is a plot of electron S1 positions ..
...

Figure L25.2
Cloud plot of the 1s orbital.

Thank you for the link. Its JMO maybe, but a group of orbitals like the attached would produce a pretty neat diffraction pattern and corresponding electron positions.

 

[newbee]

... they move absolutely randomly ...
Daniel.

This is an incorrect statement in the context of QM. The dynamics of a QM system is deterministic. The measurement problem is where the "randomness" enters.

 

[newbee]

So the best answer that we can give to the original question of this thead is: We don't know!

I think the best answer to the OP is not an answer at all but rather a response. That response should be: In the context of QM your question makes no sense.

 

[thaddeus]

Re: What path do electrons actually take in an orbital...
Originally Posted by jtbell View Post

So the best answer that we can give to the original question of this thead is: We don't know!

I think the best answer to the OP is not an answer at all but rather a response. That response should be: In the context of QM your question makes no sense.

The question may not be perfect .. but show me a question that is ..

Given that the "electron" exists in the orbital shell in a standing wave form , much akin to the ripples from throwing a pebble into a lake - except these ripples do not spread , but are bound .
Lets do it in the time honored proven ancient Greek (et al et al) manner and derive a-priori from known principles ..
A classical method to distill certainty - to separate what changes from what is consistent .So let's begin by setting as many variables towards zero as we can .. 1 element .. let's choose the #1 element Hydrogen
1 electron .. the Hydrogen ion .. h+

And let's get pristine by isolating the h+ ion from the ionic environment ..
This Electron probability-density with fidelity .. i.e. just the Nucleus-Electron relationship and no external influences So what remains .. how does the Probability density look under this pristine condition ?Well , it would at this stage be something of a perfect probability curve .. an Orbital shell whose density gradient is mathematically exemplar .. All about the spherical orbital shell the radial density gradient would be similar .. symmetrical and spherical ..

This is the bench mark .. the unaffected hydrogen ion .. Now.. let's simply introduce some variables Spherical EPD Symmetry should vary according to the nucleus charge density ..

The abundant earthly form of the Hydrogen Ion has 1 proton , 0 neutron .. If the proton has a natural phase of any degree this would be expected to influence the electron probability density , EPD .

If the proton has a charge phase bias at all , then the EPD should demonstrate bias towards this .
Similarly , if the Proton should be observed to exhibit a dual phase charge density profile (a dipole) then the EPD should have a observable phase dipole .

https://www.physicsforums.com/attachment.php?attachmentid=16893&stc=1&d=1229639263
The image above shows the first few hydrogen atom orbitals (energy eigenfunctions). These are cross-sections of the probability density for the electron at different quantum numbers (l) .. Other forms of the Hydrogen Ion (isotopes of h+) such as deuterium (1Proton,1Neutron) and tritium (1proton,2Neutrons) etc would be expected to create variations of dipole moments in nucleus charge density because of the specific interactions of these nucleic structures .And there are types of environmental variables we can consider also

A nearby positive charge beyond the Electrons orbital shell , should exhibit a pull on the EPD .. the probability of 'finding' the orbital electron should be higher closer to the external positive charge .

A nearby negative charge external to the orbital shell should exhibit a push on the EPD .. the probability of finding the orbital electron should be lower proximate to the external negative charge .

In the classic Hydrogen Ion [h+,(s1)] a approaching electron would push the resident s1 EPD away from its direct line path towards the Proton phase charge . This path would also represent the initial phase position whereby a second electron concentrates its initial EPD .. That is a second electron will bond preferentially (perhaps only) in the region where the s1 EPD is lowest .

A great deal of flux in environmental variables is possible .. the sum of all influences shaping the orbital EPD and determining with very significant certainty the position an electron may be found .

The line path connecting all these space-time points of highest electron probability density is the orbital path of the Electron .

Sum(EPD)/(space-time) = orbital path of the electron

 

[faktor]

As is usually the case in these discussions, Feynman apparently had a different meaning for the words, trajectory and position.

There is one definition of position used by everyone else, and a completely different one used by QM people. Just as there is one definition of trajectory used by everyone else and another used by QM people. For the statement that "an electron travels every possible trajectory simultaneously" to make sense, you have to redefine trajectory and possibly also position.

It is mind boggling how QM people have been 'raping' language for almost a century without outcry.

I think that missing TRUE physical model and not appropriate math is real problem with explanation of micro-world by QM…

 

[newbee]

The question may not be perfect .. but show me a question that is ..

You are grossly missing the point. The type of questions that make sense in the context of QM are different from those that make sense in the context of CM. Pointing this out isn't nitpicking. It is of the essence of QM.

And what significance did the rest of your last post have in relation to the OP. Whew!

 

[newbee]

As is usually the case in these discussions, Feynman apparently had a different meaning for the words, trajectory and position.

There is one definition of position used by everyone else, and a completely different one used by QM people. Just as there is one definition of trajectory used by everyone else and another used by QM people. For the statement that "an electron travels every possible trajectory simultaneously" to make sense, you have to redefine trajectory and possibly also position.

The phrase "an electron travels every possible trajectory simultaneously" is a phrase that people sometimes use to help the layman, in the absence of sufficient mathematical background or the understanding of the concept of the superposition of states, to develop a feel for QM. It usually fails and spawns ignorant comments like

It is mind boggling how QM people have been 'raping' language for almost a century without outcry.

Its not a problem with language. It's that you simply do not understand the theory of QM.

 

[thaddeus]

You are grossly missing the point. The type of questions that make sense in the context of QM are different from those that make sense in the context of CM. Pointing this out isn't nitpicking. It is of the essence of QM.

And what significance did the rest of your last post have in relation to the OP. Whew!

newbee : What exactly do you want to know , that you don't ?

 

[mn4j]

Its not a problem with language. It's that you simply do not understand the theory of QM.

Oh, is that the case. Why don't you help me understand the following statement:

JR Oppenheimer: "Consider an electron in the ground state of the hydrogen atom. If you ask, `Is it moving?' the answer is `no.' If you ask, `Is it standing still?' the answer is `no'."

Or is this just another statement meant for laymen? I see it as just another abuse of logic and language which in the end does nothing to help laymen understand better.

Mind you that sometimes claiming ignorance is the intellectually honest thing to do? Had Oppy said ...

"Consider an electron in the ground state of the hydrogen atom. If you ask, `Is it moving?' the answer is `I don't know.' If you ask, `Is it standing still?' the answer is `I don't know'."

... he would have been okay, language wise, and logically and laymen like us will understand him better.

The openning post has been answered accurately in the context of QM by jtbell:
What path do electrons actually take in an orbital ? We don't know.

 

[Dmitry67]

No, WE KNOW - WE DO KNOW that an ORBITAL does not make any sense

'We don't know' - we have no information about something that exists, I believe it is not applicable here.

 

[mn4j]

No, WE KNOW - WE DO KNOW that an ORBITAL does not make any sense

'We don't know' - we have no information about something that exists, I believe it is not applicable here.

So then maybe you can answer the question:
Consider an electron in the ground state of the hydrogen atom. `Is it moving?'

 

[Nick89]

So then maybe you can answer the question:
Consider an electron in the ground state of the hydrogen atom. `Is it moving?'

I am certainly no expert on the matter but I thought I would say this: if we measure the position of the electron several times, we expect to find it at several different places (otherwise the wavefunction of the electron in the ground state would not make sense as it would be a point somewhere around the nucleus). So if we find the electron at several different places, then it has moved. Whether it is moving at the time of the measurement is irrelevant (well that depends on how you mean the question) but as far as I see it, if the electron is at different places in different measurements, it has moved (unless you don't count "warping" from one place to another moving)

 

[edguy99]

So then maybe you can answer the question:
Consider an electron in the ground state of the hydrogen atom. `Is it moving?'

It depends how much energy the electron has. If less then the "escape energy" needed to get out of an orbital (or energy level), then the electron could move around inside the orbital depending on other forces.

Lots of energy levels specify a fairly wide area (hydrogen proton) where the electron can move around. Other energy levels can specify a fairly precise spot in space where you can expect to find the electron (crystals/semiconductors).

 

[Dmitry67]

So then maybe you can answer the question:
Consider an electron in the ground state of the hydrogen atom. `Is it moving?'

It ispossible to answer your question only if you define 'IS MOVING'
Depending on how you define it the answer can be different

 

[mn4j]

It ispossible to answer your question only if you define 'IS MOVING'
Depending on how you define it the answer can be different

An object is moving if it's position is not a static space-time from a reference frame which itself is a static space-time.

 

[Dmitry67]

An object is moving if it's position is not a static space-time from a reference frame which itself is a static space-time.

Ok, so 'particles' do not have a 'position' in a classical sense

I can explain why I don't like the answer 'we don't know'. Because it is confusing: it sounds like 'there is some path but we just don't know it/can not measure'. I sounds exactly like a theory with the hidden variables which is proven to be wrong (Bell's theorem)

 

[mn4j]

Ok, so 'particles' do not have a 'position' in a classical sense

I can explain why I don't like the answer 'we don't know'. Because it is confusing: it sounds like 'there is some path but we just don't know it/can not measure'. I sounds exactly like a theory with the hidden variables which is proven to be wrong (Bell's theorem)

1. 'We don't know' is a claim of ignorance. It does not exclude any of the three logical possibilities. (a) That particles do not move at all, (b) that particles move but are stationary in this case, (c) that particles move and are in motion in this case.

2. If particles do not have a position, then they do not have a velocity either which means particle accelerators are fiction, etc. Which is more confusing, just admitting that you do not know the position or going down this slippery slope. Remember that the wavefunction only makes sense in the space-time coordinate system. If particles do not have a position, then quantum mechanics breaks down. Or maybe you can define 'position' in the quantum sense.

3. Bell's theorem does not disprove hidden variable theorems. Tons of articles have been written about it. In fact computer simulations have been done which reproduce the quantum result and violate bells inequalities without making use of quantum mechanics. But that is a whole 'nother topic.

 

[Dmitry67]

1. Again, the classical definition of 'movement' is not applicable here. Option (b) is a closest to the reality.

2. Not correct. Read about the uncertenity principle

3. Please provide at least one article.

 

[mn4j]

1. Again, the classical definition of 'movement' is not applicable here. Option (b) is a closest to the reality.

2. Not correct. Read about the uncertenity principle

3. Please provide at least one article.

1- What definition of movement/position apply. Or do you claim there is no concept of movement or position at all.
2- Please read about the meaning of the word "uncertainty".
3- Event-by-Event Simulation of Einstein-Podolsky-Rosen-Bohm Experiments:

http://www.springerlink.com/content/p28v88867w7213mu/ Open Access
http://arxiv.org/pdf/0712.3693

Abstract We construct an event-based computer simulation model of the Einstein-Podolsky-Rosen-Bohm experiments with photons. The algorithm is a one-to-one copy of the data gathering and analysis procedures used in real laboratory experiments. We consider two types of experiments, those with a source emitting photons with opposite but otherwise unpredictable polarization and those with a source emitting photons with fixed polarization. In the simulation, the choice of the direction of polarization measurement for each detection event is arbitrary. We use three different procedures to identify pairs of photons and compute the frequency of coincidences by analyzing experimental data and simulation data. The model strictly satisfies Einstein’s criteria of local causality, does not rely on any concept of quantum theory and reproduces the results of quantum theory for both types of experiments. We give a rigorous proof that the probabilistic description of the simulation model yields the quantum theoretical expressions for the single- and two-particle expectation values.​

 

[Dmitry67]

1. I don't suggest anything new except what already exists in QM. And you are trying to take back from the grave the theory of the hidden parameters. In fact, even in QM people use words 'position of a particle', 'moving', etc.
2. See 1.
3. Ha ha ha!
People who believe in hidden variables write *computer program* to make their own version of reality, and then use it to 'prove' something :)

 

[tim_lou]

I am surprised that nobody bought up the idea that the funny orbitals you get from chemistry books are only stationary solutions. In general, you can visualize an electron as a wave packet traveling in space. You can even think about the electron as like a cloud (a probability cloud), whose shape changes and it moves around according to Schrodinger's eq. The mean of the position will actually move like in classical mechanics (elliptical orbits).The "orbit" that you speak of depends on the initial shape of wave. I haven't seen any program around that shows you this... However, you can search around google for quantum harmonic oscillator applet to get a feeling of what I am talking about.

In my personal opinion, I feel that many people really make quantum mechanics a lot more abstract than it really is. To me, quantum mechanics is nothing but adding an additional structure to the concept of particle. In CM, you get a point moving around, whereas in QM, you get a cloud moving around while the shape of the cloud changes from time to time.edit: of course, the picture of electron moving around is neglecting things like photoemissions, but this phenomenon comes from QFT and not ordinary QM. A electron will radiate in addition to moving around and will likely end up in the (stationary) ground state after ~10^-9 seconds. Hey, this should be expected classically, since accelerated charges are suppose to radiate (and collapse to nothing) so their orbits aren't really elliptical.