# Electron in an l=+1,0,-1 state hopping

1. Jan 24, 2005

### what_are_electrons

Electron in an l=+1,0,-1 state "hopping"

If a single electron is a point-like particle as needed by the Dirac Equation, and it is occupying an l=+1 state, how does the point like particle get from the charge density region above the nucleus down (over) to the lower charge density region?

Both regions are occupied with equal probability, but a point charge is a point charge and to equally occupy the other region a point charge has to move (hop) very quickly to the opposing region and then back again. How does a point charge do that? Most importantly what PATH in space does it take? Does it physically hop back and forth between the upper density region to the lower density region? Does it pass through the nucleus? Does it avoid the nucleus and hop around the nucleus?

2. Jan 25, 2005

### marlon

You are looking at this in the wrong way. Each l-value denotes a different energy-level of an electron. The reason this energy-level exists is indeed because the electron interacts with the atomic nucleus. However you are looking at this with "classical" eyes. All the possible l-states are put into the wavefunction as a superposition, so they denote all possible electron configurations in this case. To exemplify : each atoms has a certain amount of surrounding electrons. The number of l-values really is determined by QM for each atom but what happens is that all electrons are placed on all available l-levels. There is no jumping from one level to another (if there is no excitation ofcourse). On each l level you can place 2(2l+1) electrons.

Again it is important to realize that these l-energy-levels all arise because the electron interacts with some nucleus or some kind of extern magnetic field. They are not inherent to the electron itself, viewed as a single entity.

But what you say about these regions above or below the nucleus is wrong...you cannot be talking about above and below the nucleus...

marlon

Last edited: Jan 25, 2005
3. Jan 25, 2005

### what_are_electrons

Various texts have used dumbell-like shapes to represent cloud density of electrons wih l=+1,0-1. Please describe the most probable shape of the electron cloud for a single electron with l=+1.

4. Jan 26, 2005

### marlon

answer is easy, just square the pherical harmonics. The answer is ellipsoidal

marlon

5. Jan 26, 2005

### dextercioby

WHAT??Speaking without documentation,again,Marlon???

no ellipsoids for l=1

Daniel.

6. Jan 26, 2005

### marlon

marlon

besides you misinterpreted my answer...i never stated that the actual orbitals have a definite shape because they DON'T. I am afraid that with your post you (once again) convert this discussion into a discussion on personal interpretations. THIS IS NOT HOW SCIENCE WORKS. Please, stick to the facts...

7. Jan 26, 2005

### dextercioby

What do you mean "my text"...?Shouldn't have i read YOUR TEXT,which was wrong...???

You said square the spherical harmonics.I did.Chose l=1 (the OP's question),i did and DIDN'T WIND UP WITH ELLIPSOIDS...

How would i wind up with ELLIPSOID BY SQUARING SPHERICAL HARMONICS??

Daniel.

8. Jan 26, 2005

### what_are_electrons

Now that we have established that the "l" quantum numbers do indeed produce dumbell like clouds, my question is:

If an electron is a true "point charge" or a very small charge (say 10(-11) to 10(-13) cm) that runs around inside the lobe obeying the HUP, then how does that point charge (or very small charge) manage to move from one of the lobes over to the other lobe? Does it pass through the nucleus? Is it emitted from one lobe and reabsorbed into the other lobe?

9. Jan 26, 2005

### dextercioby

Let's establish some things.Those "lobes" represent the angular distribution of the probability density of localization for the electron.However,those "lobes" do not tell us anything about the RADIAL DISTRIBUTION of probability density.Only after taking the latter into account we can say some things about the probabilities of finding the electron in some nonzero space volumes...

To the second question the answer is definitely NO.As for the first part,the answer is NO.The probability density is zero for the electron to be in/on the nucleus...

Daniel.

P.S.Compute the probability of finding the electron in one ball of radius 10^{-15}m centred on the origin (where we assume to find the pointlike nucleus)...

10. Jan 26, 2005

### marlon

Sorry but you are wrong again. Just because they are called spherical harmonics does not mean an ellipsiodal structure is not possible

And for l = 1 NOT all harmonics are spheres. This counts only for the one corresponding to l = 0 and m (magnetic quantumnumber) equal to ZERO. For l =1, they are NOT spheres

Read the text you referred to in your first erronous post...Please, try to be more reasonable when correcting others...

marlon

11. Jan 26, 2005

### dextercioby

Please indicate me to a link where i can find ellipsoides constructed from squaring spherical harmonics...

BTW,which erroneous post?? :uhh: In this thread??

Daniel.

12. Jan 26, 2005

### marlon

Go buy Bransden and Joachain "INTRODUCTION TO QM"

It is litteraly in there...or any GOOD book on introductory QM will do fine

regards
marlon

13. Jan 26, 2005

### marlon

Or check out Zumdahl for that matter and be sure you use the right parameter-representation for them ellpises

marlon

14. Jan 26, 2005

### what_are_electrons

Yes, the cloud has a radial function and the surface of the lobe does not represent a limiting radius. Yes the electron has a probability of being located anywhere within the radial function that the lobe very crudely represents.

I understand that the electron (pt size or sm size) does not pass through the nucleus. I understand that the electron in probably not emitted and reabsorbed (recaptured).

Just now it does not matter if the surface of the cloud or the bulk density forms an ellipsoidal or a nearly spherical surface.

The question at hand is: What is the most probable 3D spatial path that the electron moves over as it physically moves from one radial-based charge density cloud to the other opposing radial-based charge density cloud within an atom that has "l" = +1 or -1?

15. Jan 27, 2005

### marlon

Like i explained before excitation of atoms is not described in terms of the trajectories that electrons follow when they go from one energy-level to another. Just like in the double slit experiment, one cannot tell what happens when the particles are travelling the trajectory between the emitting-source and the two openings. This is just the same here. The only thing that counts is once you know the energy-levels and the excitation energy, you can calculate the probabilities of the possible electron-transitions yielding the excited-state. However : NO trajectories.

regards
marlon

16. Jan 27, 2005

### what_are_electrons

Am NOT talking about higher energy levels. Am talking ONLY about different charge density regions for the same energy state. These regions are equally distributed around the core and appear as lobes. For l=+1 (p-orbitals), there are two lobes. For l=+2 (d-orbitals) there are basically 4 lobes. For l=+3 (f-orbitals) there are basically 8 lobes.

The question remains: How does a point charge or sm charge move from one lobe to another in any of these different angular momentum states that are all in a ground state configuration?

17. Jan 27, 2005

### dextercioby

Are u aware of the concept of SELF-CONTRADICTION??

Daniel.

18. Jan 27, 2005

### what_are_electrons

I understand that what I ask seems contradictory to you, but please try to take a different viewpoint. A picture would be great just about now.

19. Jan 28, 2005

### marlon

Yes i understand your question very well: how to go from one lobe to another, which trajectory. Again i can only refer to my previous post and especially the analogy with the double slit experiment. try not to think in terms of trajectory but only in terms of "the probability that an electron will go from one lobe to another". The trajectory is irrelevant and cannot be studied if you make the analogy with the double slit experiment.

regards
marlon

20. Jan 28, 2005

### what_are_electrons

Let me ask this: Is it possible that the spherical harmonics that are currently used are wrong? Is it possible that other equations would reveal other charge density clouds that would not indicate a node at the nucleus for any of the different "l" states?