# What path do electrons actually take in an orbital

1. Jan 4, 2005

### 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.

2. Jan 4, 2005

### dextercioby

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.

3. Jan 4, 2005

### Cheman

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

4. Jan 4, 2005

### fliptomato

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/ .

Best,
Flip

5. Jan 4, 2005

### Staff: Mentor

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.

6. Jan 4, 2005

### DB

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

7. Jan 4, 2005

### dextercioby

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.

8. Dec 17, 2008

### billyell

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

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.

9. Dec 17, 2008

### Staff: Mentor

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

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

10. Dec 18, 2008

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

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 dont 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 ..

11. Dec 18, 2008

### edguy99

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

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?

12. Dec 18, 2008

### mn4j

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

As is usually the case in these discussions, Feynmann 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.

13. Dec 18, 2008

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

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.

14. Dec 18, 2008

### Staff: Mentor

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

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!

15. Dec 18, 2008

### edguy99

Re: What path do electrons actually take in an 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.

16. Dec 18, 2008

### newbee

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

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.

17. Dec 18, 2008

### newbee

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

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.

18. Dec 18, 2008

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

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 lets begin by setting as many variables towards zero as we can ..

1 element .. lets choose the #1 element Hydrogen
1 electron .. the Hydrogen ion .. h+

And lets 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.. lets 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 .

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

Last edited: Dec 18, 2008
19. Dec 19, 2008

### faktor

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

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

20. Dec 19, 2008

### newbee

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

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!