Valency electrons and determining the spin

[shounakbhatta]

Hello,

I need to understand the following:

Considering an element Sulfur - S which has 16 electrons.

How do we calculate the valency electron of S?

Please correct me if I am wrong:2+2+6+2+4=16. So, the valency electron = 4+2=6

Is it that always valency electron is the addition of the last two shells? In that case for Na, sodium, if we take 11 and arrange it as 2+2+6+1, then the valency electron is 1 or 6+1?

Now, considering the fact valency electron is 1, if we go by, up down up down rule, then as it is 1, hence the spin is up?

For 6: is it up(1) down(2) up(3) down(4) up(5) down(6) as it is both up/down hence it would be +-1/2 spin?

For Phosphorous 2,8,5, what would be the valency electron 5 or 13?

If 5 then up down up down up, will it have a up spin?

Is it that for even numbers like 4,6 the spin will be both up/down i.e. +-1/2?

Kindly let me know.

 

[Simon Bridge]

Is it that always valency electron is the addition of the last two shells?

No.
http://en.wikipedia.org/wiki/Valence_electron
In chemistry, a valence electron is an electron that is associated with an atom, and that can participate in the formation of a chemical bond ... For a main group element, a valence electron is defined as an electron that resides in the electronic shell of highest principal quantum number n.

Sulphur is [Ne]3s. 2. 3p. 4. ... the highest principle quantum number is n=3.

Atomic spin, in the ground state, is determined by the unpaired electron.
http://chemwiki.ucdavis.edu/Physica...tomic_Theory/Electrons_in_Atoms/Electron_Spin

 

[shounakbhatta]

Hello,

Thank you very much for the reply. Actually, I later calculated taking some examples of elements and found out exactly what you have pointed. Indeed, I was going through Chemiwiki only.

Well, one question that comes to my mind. Reading over the information, I found that spin of an electron is an intrinsic property. Some say that the electron actually is not spinning, it is the electromagnetic force line that determines the spin, some say it is an angular momentum. Can you please explain me what spin really is?

Thanks.

 

[Simon Bridge]

You know how photons can carry momentum and kinetic energy even though they don't have mass and can only go at one speed? Particles can carry angular momentum the same way.

We don't think of the electron as some object physcally turning on an axis.
The idea comes from noticing that electrons (all kinds of fundamental particles) have an intrinsic magnetic moment, and that magnetic moments are intrinsicaly caught up with angular momentum. See: Einstein deHaas effect.

This question gets asked a lot - these two are from the "related discussions" section (below):
Do electrons actually spin?
do electrons really spin?
... the second is answered by a physical chemist and goes into a lot of detail about common misconceptions.

 

[shounakbhatta]

Hello Simon,

Thank you very much for the answer. Well, I read your link on the Einstein de hass effect. Correct me if I am wrong. The Einstein de hass effect demonstrates, if an electric current is passed through a ferromagnetic materials which is cylindrical shape, the cylinder would rotate, like an angular momentum. It is basically rotation by magnetisation. Now my question is this rotation of the cylinder by passing electric current is it because internally the electrons are rotating? What you are saying is the electric charge causing magnetization have an intrinsic magnetic moment and this moment is similar to the angular momentum in classical/macroscopic scale?

Please let me know.

Thanks

 

[Simon Bridge]

Hello Simon,

Thank you very much for the answer. Well, I read your link on the Einstein de hass effect. Correct me if I am wrong. The Einstein de hass effect demonstrates, if an electric current is passed through a ferromagnetic materials which is cylindrical shape, the cylinder would rotate, like an angular momentum. It is basically rotation by magnetization. Now my question is this rotation of the cylinder by passing electric current is it because internally the electrons are rotating?

No - the rotation of the cylinder is because the electrons carry angular momentum.

What you are saying is the electric charge causing magnetization have an intrinsic magnetic moment and this moment is similar to the angular momentum in classical/macroscopic scale?

That's a lot closer - what the experiment shows is that the magnetic moment of the electrons has an associated angular momentum. [edit] ... <nitpick> and it is not me that's saying that, it's the experiment.

It is as if the electrons were little balls of spinning charge.
It is possible to work out how fast an electron would have to spin to get the observed magnetic moment - using the maximum classical electron size (a huge over-estimate) you still get a surface rotation speed faster than light. re:
http://scienceblogs.com/principles/2010/07/26/electron-spin-for-toddlers/

You could probably be a bit more careful and use the known charge, magnetic moment, and angular momentum, assume a sphere, and work out the required radius. Compare with experiment.

The gripping hand is: electrons cannot be spinning balls of charge in that sense.
They just act like it.

 

[shounakbhatta]

Hello Simon,

Thank you very much for your wonderful. I have earlier read Chad Orzel's Electron spin for toddlers. It is really wonderfully ! Truly it is unique and lucid explanation. The comparison with turntable, related to the angular momentum is definitely wonderful. So, the magnetic moment of the electron has an angular momentum, which is analogous to the classical concept of 'spinning', through in true sense it is not actually spinning, right? Now one more question - what about the particles, baryons, who have +1/2 spin but no electric charge? Like nucleon/neutron? Does that mean that angular momentum for particles is gained only due to magnetic moment?

Thanks.

 

[Simon Bridge]

what about the particles, baryons, who have +1/2 spin but no electric charge? Like nucleon/neutron?

Even classically, it is possible for neutral objects to have a non-zero magnetic moment ... consider neutral atoms.

Does that mean that angular momentum for particles is gained only due to magnetic moment?

There is no reason to infer a cause-and-effect about it - you can equally say that the magnetic moment for particles is is gained only due to angular momentum. Experimentally we usually infer the angular momentum from the magnetic moment but we could, in principle, do it directly by one of those torque experiments.

Angular momentum and magnetic moment go together.

 

[shounakbhatta]

Hello Simon,

Thank you once more for your answer. As per the first question, you said that for neutral objects can have a magnetic moment, like neutral atoms can have a spin. One question. Photon which has no charge yet has a spin 1, a positive integer, definitely not following Pauli exclusion principle. So a photon, where electric charge=0, mediates through electromagnetism, hence have a magnetic moment, hence have a spin 1 and as it is unlike fermions so have a full spin instead of half. Am I right saying that? So, it is not necessary to have a electric charge for a subatomic particle to have a spin, but should mediate either through a magnetic moment or electromagnetism or through some force. Right?

 

[Simon Bridge]

Hello Simon,

Thank you once more for your answer. As per the first question, you said that for neutral objects can have a magnetic moment, like neutral atoms can have a spin. One question. Photon which has no charge yet has a spin 1,

Photon has no charge nor anything that can be said to be composite of charges. It is electromagnetism. I you google about the photon spin, though, you'll see that it is the Electric and Magnetic field vectors that are modeled as rotating, to get a magnetic moment. But I think this example, more than any other, illuminates that the QM "spin" does not conform to classical ideas.

So, it is not necessary to have a electric charge for a subatomic particle to have a spin,

No. i.e. the neutron.

but should mediate either through a magnetic moment or electromagnetism or through some force. Right?

That would be correct - the neutron magnetic moment allows it to interact electromagnetically ... like magnets do.

http://neutrons.phy.bnl.gov/presentations/MagneticNeutronScattering_proofed_indexed_unlinked.pdf
http://prola.aps.org/abstract/PR/v136/i6B/pB1678_1

But try not to mix up the models ... the "magnetic moment", and "electromagnetism", are the same thing. And "some force" is a bit vague.

In the particle model - there are no "forces" as such, just interactions between fundamental particles.
The photon is the force-carrier for electromagnetism. i.e. "photon interactions" is electromagnetism.

Newtonian forces are considered to be the emergent behavior resulting from these interactions.

 

[shounakbhatta]

Thank you Simon, once again for your response. So the general norm for particle physics is that there is interaction, no force. Now, may I ask you one more question, which might not be relevant especially in this thread? A conceptual one. Light, composed of photons don't have a mass, how gravity bends light? I mean to ask you that something which don't have a mass how can it bend?

Thanks.

 

[Simon Bridge]

You are right - it is off-topic for this post.
Simply put - gravity does not depend solely on mass, but on energy-density. Mass just has a very high energy density. But photons have energy too, therefore they can be affected by gravity.
More generally, gravitation is understood in term of the geometry of space-time. Light-rays are bent by massive bodies because these bodies curve the space-time that the light moves through.