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

In summary, the conversation discusses the behavior of a single electron in an l=+1,0,-1 state and how it moves between two regions with equal probability of occupation. The conversation also addresses the misconception of the electron as a point charge and the probability of finding it in certain regions, as well as the shape of the electron cloud. The correct shape is determined by squaring the spherical harmonics, and it is not necessarily a sphere for l=1. It is also clarified that the electron does not pass through the nucleus or get emitted and reabsorbed.
  • #1
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?
 
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  • #2
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
 
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  • #3
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
what_are_electrons said:
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.

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


marlon
 
  • #6
dextercioby said:
WHAT??Speaking without documentation,again,Marlon?

no ellipsoids for l=1

Daniel.

WRONG,...you clearly did not read your own text my boy... :grumpy:

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
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??

READ,Marlon...

Daniel.
 
  • #8
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
what_are_electrons said:
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?

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...

what_are_electrons said:
Does it pass through the nucleus? Is it emitted from one lobe and reabsorbed into the other lobe?

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

READ,Marlon...

Daniel.


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

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

Daniel.
 
  • #12
Go buy Bransden and Joachain "INTRODUCTION TO QM"

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

regards
marlon
 
  • #13
Or check out Zumdahl for that matter and be sure you use the right parameter-representation for them ellpises

marlon
 
  • #14
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
what_are_electrons said:
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?

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 traveling 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
marlon said:
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 traveling 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
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
what_are_electrons said:
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?

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

Daniel.
 
  • #18
dextercioby said:
Are u aware of the concept of SELF-CONTRADICTION?? :wink:

Daniel.

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
what_are_electrons said:
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?


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
marlon said:
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

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?
 
  • #21
what_are_electrons said:
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?

Let me be humble and say I DON'T KNOW. Look, QM does the best job up till now when it comes to explaining all these things. The theory is consistent and it is backed up by many experiments. Also all predictions by QM were sucessfull in this sense that they were all confirmed by experiments. We don't know of any phenomenon (when it comes to atomic scaled phenomena) that is not sucessfully explained and described by QM. It is a matter of regimes really.

regards
marlon
 
  • #22
what_are_electrons said:
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?


That would mean that ALL QUANTUM MECHANICS WOULD BE WRONG!So far,there have passed 80 years over hard-working theorists,and they couldn't come up with a theory FUNDAMENTALLY/CONCEPTUALLY different to replace QM...And QFT as well...

We're "stuck with it"... :tongue2:

Daniel.
 
  • #23
Are we indeed 100% tied to the spherical harmonics?

QED is indeed very well established and has withstood countless tests for the past 80 years, but it seems that there may be a different set of harmonic-like equations that would obey all QM and QED conditions, and yet still generate different charge density regions.

Are we indeed 100% tied to the spherical harmonics?
 
  • #24
Give an example of harmonic-like equations in QM.Not QFT,QM...

Daniel.
 
  • #25
dextercioby said:
Give an example of harmonic-like equations in QM.Not QFT,QM...

Daniel.

Is that a dare or a doubt?
 
  • #26
I had something in mind...But i waited (anxiously :tongue2: ) for your reply with an example that hasn't really come yet...

Daniel.

P.S.A PDE please...From QM & QFT (i've enlargened the "domain"...)
 
  • #27
Please try to pardon my silence, as things are still in the kinematic stage.

Vince
 
  • #28
Then please,try to take into account my advice:
"Don't make affirmations you cannot back up".

Daniel.
 
  • #29
My apologies if I inferred any sort of affirmation. I try hard to avoid misleading anyone. My intent was to review current understanding and knowledge.
 

1. What does it mean for an electron to be in an l=+1,0,-1 state?

When talking about an electron's state, the term "l" refers to its orbital angular momentum. A value of l=+1,0,-1 indicates that the electron is in a p orbital, with the values +1, 0, and -1 corresponding to the p subshells px, py, and pz, respectively.

2. How does an electron hop between different l states?

An electron in an l=+1,0,-1 state can hop to a different l state through a process called electron excitation. This can occur when the electron absorbs energy, causing it to jump to a higher energy level. Alternatively, the electron can lose energy and drop to a lower energy level, resulting in a hop to a different l state.

3. What is the significance of an electron hopping between different l states?

The hopping of electrons between different l states is a crucial process in chemical reactions and materials science. It allows for the formation of new chemical bonds and the transfer of energy within a system. Understanding this process is essential for studying and manipulating the properties of materials and molecules.

4. Is there a specific pattern or frequency to electron hopping between l states?

The frequency of electron hopping between l states depends on the specific energy levels and conditions of the system. However, in general, the rate of electron hopping can be affected by factors such as temperature, pressure, and the presence of other atoms or molecules.

5. Can electron hopping between l states be controlled or manipulated?

Yes, scientists have developed various techniques to control and manipulate the hopping of electrons between l states. This includes using external electric or magnetic fields, as well as engineering materials with specific properties to influence the behavior of electrons. Such control is essential for designing new materials and devices for various applications.

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