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Author Topic: How does energy level affect the angular momentum of electrons?  (Read 10802 times)

Offline DoctorBeaver

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Ian (and others) talks a lot about angular momentum, and that got me thinking about electrons changing orbits.

I assume that orbiting electrons follow basic rules insofar as those nearer the nucleus travel faster than those at the periphery.

So, what happens to their angular momentum when they jump from 1 energy level to the next?




[MOD: Altered subject to make it a question - CS]
« Last Edit: 27/05/2008 09:16:45 by chris »


 

Offline Soul Surfer

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In a classical sense, a negative charge orbiting around a positive charge would loose angular momentum by emitting electromagnetic radiation until it collapsed on to the positive charge.  That's where quantum mechanics comes in the electron can only lose specific steps of angular momentum.  one way of thinking of it is that an electron in a stable (or metastable) orbit is continually emitting and reabsorbing energy to maintain a constant energy level ans when it changes it emits a quantum of the specific frequency that represents the change in angular momentum and energy.
 

lyner

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If angular momentum is to be conserved (fundamental conservation 'law'), unless a photon can have angular momentum, how can your 'orbiting' electron lose any? Is it transferred to the Nucleus, perhaps?
Does this work for the Hydrogen atom?
« Last Edit: 26/05/2008 11:51:46 by sophiecentaur »
 

Offline DoctorBeaver

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How can a photon have angular momentum if its path is always a geodesic?
 

Offline JP

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This rule that angular momentum must be conserved in a quantum process is part of a more general set of rules called selection rules: http://en.wikipedia.org/wiki/Selection_rule

Whatever process changes the state of the electron must carry away or add appropriate angular momentum so that angular momentum is conserved.
 

Offline JP

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How can a photon have angular momentum if its path is always a geodesic?

The answer is either spin or polarization.  Polarization angular momentum is fairly new, but it appears that light that is appropriately polarized is made up of photons that carry angular momentum: http://www.physics.gla.ac.uk/Optics/play/photonOAM/

The translational path of the photon is still a geodesic, but it's "rotating" as it moves along that path.
 

Offline lightarrow

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If angular momentum is to be conserved (fundamental conservation 'law'), unless a photon can have angular momentum, how can your 'orbiting' electron lose any? Is it transferred to the Nucleus, perhaps?
Does this work for the Hydrogen atom?
A photon can have angular momentum.
 

Offline lightarrow

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How can a photon have angular momentum if its path is always a geodesic?

The translational path of the photon is still a geodesic, but it's "rotating" as it moves along that path.
jpetruccelli, you know physics more than me, but, unless you're talking about "zitterbewegung" or similar peculiar theory, photons don't have a precise trajectory.
 

lyner

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How can a photon have angular momentum if its path is always a geodesic?

The answer is either spin or polarization.  Polarization angular momentum is fairly new, but it appears that light that is appropriately polarized is made up of photons that carry angular momentum: http://www.physics.gla.ac.uk/Optics/play/photonOAM/

The translational path of the photon is still a geodesic, but it's "rotating" as it moves along that path.

But how do you / how does it know which path it is taking at the time it leaves the atom? It could be millions of years before the photon interacts with another system.
What you say implies a directivity in how the photon is emitted. This has been discussed at length, before, without bringing in the angular momentum aspect and this seems to add another headache.
How is the angular momentum of a photon defined? there seems to be a real conflict with the particle / wave models.
 

Offline JP

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Sophiecentaur, I'm not trying to rehash the photon issue again.  I think you can deal with this issue conceptually without needing to deal with the exact nature of photons.  We really only need to know two points of QM:

1) There is a smallest "bit" of light that you can measure (the photon)--we won't dwell on its nature. 

2) The quantum nature of angular momentum is well understood: QM objects (whether you want to call them particles or waves) can certainly carry angular momentum.  For example, electron orbitals have well-defined angular momenta, which is why you can only have transitions that satisfy conservation of angular momentum.

If you accept these two ideas, it's not far-fetched to conclude that photons (no matter the specifics of the theory) can have angular momentum.  The details of the math are going to be much trickier, but the concepts aren't. 

If you want to talk about photon paths, you need to bring in some heavier machinery.  I was referring to the classical trajectories, which should be the "geodesics" that light rays follow.  The analogy you can draw here is that classical particles traveling along these paths can have separate angular momentum due to rotation in addition to any momentum they have as a result of their path.

I guess the sticking point is whether or not you're willing to accept point (2): that a QM wavefunction can represent a state/particle that has angular momentum.
 

lyner

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I'm fine with most of that BUT, If angular momentum is to be conserved then, as the 'orbit' of an electron around a nucleus changes, the angular momentum will change and that must go somewhere or come from somewhere. The spin of the electron or protons (or the nucleus itself, I suppose) can account for some of this but is it enough to keep the conservation law?
I have a problem with a photon possessing angular momentum. Bringing circular polarisation into it doesn't help because it is a special case and requires specific circumstances. I 'get' circular polarisation in the wave context because I know about RF transmitting antenna theory but to talk of circular polarisation in terms of photons brings on the pains.
 

Offline JP

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Yeah, giving a photon angular momentum is not as simple as just circularly polarizing light.  It apparently depends on how the complex phase of the beam changes as the light propagates.  Thinking back to some talks I heard on this, and looking at the pictures in the link I gave above, you should even be able to throw out all of QM and still see how this is operating:

For beams with no angular momentum, if you draw the rays that correspond to that beam (these are the classical trajectories of the photons), you get straight lines down the beam axis.  The photons traveling along these straight lines don't have angular momentum.

For beams with angular momentum, the rays are going to spiral around the central beam axis as the beam propagates.  (If you look at the picture, imagine the rays are always perpendicular to the phase fronts where they intersect.)  Photons traveling along these rays are going to behave as particles spiraling about the central beam axis, so it makes sense that they would have angular momentum.

But I do think that trying to make this argument rigorous will take quite a lot of mathematics: you need to understand photons well and understand momentum well, and then you have to connect them.
 

Offline Soul Surfer

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Angular momentum is just a form of energy and it can be changed by converting it into a different form of energy during an interaction there is no violation of any conservation law in this.  angular momentum is only strictly conseved in isolated systems with no other sirts of interaction avaiable to them.
 

lyner

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S-S
Quote
Angular momentum is just a form of energy
You can't say that. The units are wrong. Momentum, for an object with mass, is mv whilst the KE is mv2/2.
Angular momentum is Iω and rotational KE is Iω2/2
In collisions, KE may not be conserved but momentum is.

So, are we saying that the direction of the angular momentum vector is somehow related to the direction of its travel? That would imply directivity in the production of a photon by a change of electron energy level.
For a decay which produces a photon with no angular momentum, the changes in spin and orbital momentums must cancel out. Without doing the sums it seems to me that this must be only in a minority of cases as the possible spins are only +/-1/2 but there are many possible orbital changes.
As for spiraling beams; how does that apply to 'one photon at a time' situations?
 

Offline DoctorBeaver

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Now I'm confused (nothing unusual there).

I thought momentum was calculated as mass * velocity. If the mass of a photon is zero, its momentum must also be zero. How can it have momentum of any kind? Or is the momentum in angular momentum different?
 

lyner

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How does energy level affect the angular momentum of electrons?
« Reply #15 on: 27/05/2008 10:07:45 »
I wrote:
Quote
Momentum, for an object with mass, is mv
A photon doesn't have mass but, when it bumps into something, it demonstrates it has momentum. In this case, the momentum is h/λ, where h is the Planck constant and λ is the wavelength.
 

Offline DoctorBeaver

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How does energy level affect the angular momentum of electrons?
« Reply #16 on: 27/05/2008 19:12:06 »
I wrote:
Quote
Momentum, for an object with mass, is mv
A photon doesn't have mass but, when it bumps into something, it demonstrates it has momentum. In this case, the momentum is h/λ, where h is the Planck constant and λ is the wavelength.

Methinks I shall have to ponder on that for a wee while.
 

Offline JP

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How does energy level affect the angular momentum of electrons?
« Reply #17 on: 27/05/2008 19:24:42 »
So, are we saying that the direction of the angular momentum vector is somehow related to the direction of its travel? That would imply directivity in the production of a photon by a change of electron energy level.
For a decay which produces a photon with no angular momentum, the changes in spin and orbital momentums must cancel out. Without doing the sums it seems to me that this must be only in a minority of cases as the possible spins are only +/-1/2 but there are many possible orbital changes.
As for spiraling beams; how does that apply to 'one photon at a time' situations?

I spent some time looking at the articles published on measuring orbital angular momentum (OAM is their acronym, to distinguish it from spin).  I take back my earlier comment on this relating to polarization of the light.  It depends rather on the phase-fronts of the beam (spin is what gets correlated to polarization).  Phase-fronts are what correspond to the direction of the light "rays," and OAM corresponds to rays that spiral along the beam, which is what I was getting at before.

They get the angular momentum of a light beam by looking at different possible structures of the beam.  Since a beam has a "beam direction" down the axis, the orbital angular momentum will always be parallel or antiparallel to that axis (angular momentum is always perpendicular to the direction of "rotation", and the beam "rotates" around the axis).  So yes, from what I understand, the angular momentum has a definite direction.  This seems reasonable to me, since the photons in a beam are going to have a directionality associated with them as well (they travel down the beam).  If you're looking at a non-beam light source, you'll probably end up with a mash of all sorts of photons, and probably all sorts of angular momenta.  However, it may also be the case that nature doesn't generate these creatures normally and you have to set up crazy beams in the lab to actually make them.

One-photon-at-a-time works for these spiral beams.  All they did to test this was to set up a system that would detect the angular momentum of the light passing through and decrease the light levels until they expected <1 photon at a time hitting their detector.  They still saw that they were getting results that showed the appropriate orbital angular momenta (associated with the higher-intensity spiraling beams). 

Now I'm going to speculate a bit, so don't hold me to any of this:
As for directionality of photons emitted from atoms, I don't see that being a problem in itself.  Stimulated emission (what they use to make lasers) is an example where the photons being emitted by the atoms have a direction of propagation.  I don't know the details of trying to work out the relationship between orbital angular momentum/spin and the direction of photon emission, but I think you're right: there has to be some sort of connection.  I think what will end up saving the day in this situation is that the electron orbitals are symmetric enough that the direction of the angular momentum of the incoming photon doesn't matter in terms of kicking the electron up or knocking it down energy levels.  It's only the total angular momentum given or taken away that matters.  Now if the photon's going to energy level "2" for example, it might have 5 possible states to choose from.  The particular one it chooses will probably depend on the direction of angular momentum of the incident photon, but getting to level "2" probably won't.
 

Offline DoctorBeaver

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How does energy level affect the angular momentum of electrons?
« Reply #18 on: 27/05/2008 20:14:29 »
Here's a little spanner to throw in the works...

What happens if 2 photons with different angular momentum simultaneously hit the electron? Would the electron "choose" 1 or the other, or would both have an effect?
 

Offline Soul Surfer

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How does energy level affect the angular momentum of electrons?
« Reply #19 on: 28/05/2008 08:47:23 »
It is a quantum effect so you strictly cannot talk about individual particles and photons like that.  To perform the experiment you have to direct beams of photons with various energies at a comllection of atoms (usually with several electrons at different energy levels) and look at the statistics of what happens.  The answer is a statistical mix of all the things that are allowed to happen which could be resolved if you can identify the individual photons that come out of the interaction.
 

Offline DoctorBeaver

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How does energy level affect the angular momentum of electrons?
« Reply #20 on: 28/05/2008 09:08:56 »
Ah yes - probabilities again. I think I understand now. Sort of. Kinda. Ish.
 

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How does energy level affect the angular momentum of electrons?
« Reply #20 on: 28/05/2008 09:08:56 »

 

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