Any standard model spin doctors here??

[Gian]

Can't get my head around this.
"Spin is the intrinsic angular momentum of particles. Spin is given in units of ħ which is the quantum unit of angular momentum where ħ = h/2π = 6.58x10^-25 GeV s = 1.05x10^-34 J s"

At this stage I just want to know;

1 When it says "spin" is the "angular momentum," does it mean the speed that these particles (Fermions and Bosons?) rotate at, or what?

2. What's the h in the equation h/2π = 6.58x10^-25  ??

3. Is the funny symbol ħ to do with something called the planck constant?

Cheerz

GIAN🙂XXX

science education age about 12½

 

[exchemist]

50 minutes ago, Gian said:

Can't get my head around this.
"Spin is the intrinsic angular momentum of particles. Spin is given in units of ħ which is the quantum unit of angular momentum where ħ = h/2π = 6.58x10^-25 GeV s = 1.05x10^-34 J s"

At this stage I just want to know;

1 When it says "spin" is the "angular momentum," does it mean the speed that these particles (Fermions and Bosons?) rotate at, or what?

2. What's the h in the equation h/2π = 6.58x10^-25  ??

3. Is the funny symbol ħ to do with something called the planck constant?

Cheerz

GIAN🙂XXX

science education age about 12½

 

Yup, h is Planck's constant. The symbol h with a line across, known as "h bar", is h/2π. This quantity appears in a lot of places in QM maths, so it was thought worth giving it its own symbol to simplify algebraic expressions.

When it comes to elementary particles they have angular momentum, just as a spinning top or wheel has. This is often referred to as "spin", but it's  not really like a little ball spinning on its axis. For one thing this "spin" is intrinsic to the particle. An electron has a spin of 1/2 spin units*, always. You can't stop it spinning or make it spin faster. The spin value it has is fundamental to its identity as an electron, just as much as its -ve electric charge is, or its mass.

This so-called spin is a way of saying they have a set amount of angular momentum. That is important because angular momentum is a conserved property, like linear momentum or energy. So in particle interactions, one rule is the total angular momentum of the system, before and after, has to be the same. That has certain consequences in physics.

However, because these elementary particles don't behave like little balls, one can't talk of a speed of rotation or anything like that. They have have a set amount of intrinsic angular momentum and that's that.

 

* I had better add a bit here so I don't get my balls shot off by the real physicists on the forum - always a risk here😁. You don't need really to know this.

"Spin units" is just my lazy shorthand for saying the spin quantum number, s, of electrons is 1/2. The actual magnitude of the angular momentum is given by the angular momentum formula √(s(s+1)). h/2π, which for s=1/2 gives you √3/2. h bar. However the projection of the angular momentum vector along any specified axis is a bit less, 1/2. h bar, basically because of the way Heisenberg's Uncertainty Principle works for angular momentum (There's always a bit of angular momentum left over, that points in an indeterminate direction and which can't be pinned down). So particles like electrons are known as "spin 1/2" particles. The formula you are asking about is the magnitude of this projection - which is what matters in practice, in the lab and so forth. 

 

 

 

 

Edited December 12 by exchemist

[Gian]

2 hours ago, exchemist said:

Yup, h is Planck's constant. The symbol h with a line across, known as "h bar", is h/2π....

 

 

 

 

Thanks Mr Exchemist! I've just printed your reply and I'll get back to you as soon as I've digested it (or not lol)

Cheerz

GIAN🙂XXX

science education age about 12½

[exchemist]

7 minutes ago, Gian said:

Thanks Mr Exchemist! I've just printed your reply and I'll get back to you as soon as I've digested it (or not lol)

Cheerz

GIAN🙂XXX

science education age about 12½

OK. Like a lot of things in quantum theory this is not like the behaviour we are used to at the scale of everyday life, so it may take a few iterations to understand it. 

[studiot]

Remember the spin quantum number is responsible for the magnetic properties of the substance.

[Gian]

15 hours ago, exchemist said:

OK. Like a lot of things in quantum theory this is not like the behaviour we are used to at the scale of everyday life, so it may take a few iterations to understand it. 

 

15 hours ago, studiot said:

Remember the spin quantum number is responsible for the magnetic properties of the substance.

Thanks guys, well I don't think I'm going to get it this time, other than it sounds like it's like potential energy, wrapped up in the electron. 
I'm still at GCSE level maths and physics and quantum theory doesn't seem to come into it at this stage. Maybe it will become clearer when I've done a lot more stuff first. 
cheerz

 

GIAN🙂XXX

science education age about 12½

 

[exchemist]

22 minutes ago, Gian said:

 

Thanks guys, well I don't think I'm going to get it this time, other than it sounds like it's like potential energy, wrapped up in the electron. 
I'm still at GCSE level maths and physics and quantum theory doesn't seem to come into it at this stage. Maybe it will become clearer when I've done a lot more stuff first. 
cheerz

 

GIAN🙂XXX

science education age about 12½

 

Hmm, whether this intrinsic angular momentum also represents energy or not is a bit of a moot point, since you can't stop the spin, i.e. you could never get any such energy out of the particle. These particles certainly do have energy associated with their mass, according to E=mc², but I don't think it's a good idea to think they have a kind of kinetic energy due to their "spin".  

Anyway, for GCSE, all you need to know is you can put a maximum of 2 electrons into each atomic orbital, which is allowed so long as one has spin "up" and the other has spin "down".  

 

[swansont]

Spin with a charged particle gives them a magnetic moment, so “spin up” and “spin down” (the two possible values of the spin orientation) will have a different energy in a magnetic field, which you have in an atom.

[Gian]

54 minutes ago, swansont said:

Spin with a charged particle gives them a magnetic moment, so “spin up” and “spin down” (the two possible values of the spin orientation) will have a different energy in a magnetic field, which you have in an atom.

So what is a "magnetic moment?" 
 

cheerz

GIAN🙂XXX

science education age about 12½

[swansont]

44 minutes ago, Gian said:

So what is a "magnetic moment?" 

It’s a measure of how strong a magnet is.

[exchemist]

49 minutes ago, Gian said:

So what is a "magnetic moment?" 
 

cheerz

GIAN🙂XXX

science education age about 12½

It means the particle behaves like a tiny bar magnet, with a North and South pole. Like a magnetised compass needle, it will tend to line up with any external magnetic field. Conversely, if you can get a lot of these particles, in practice electrons,  to line up in a block of material, that will make the bulk material magnetic - which is what happens in a permanent magnet. You have a lot of atoms each with an electron that can be made to line up in the same direction,  adding their effects together to make a stronger field.  So permanent magnets are magnetic because - or mostly because -  of the “spin” of electrons.

Edited December 13 by exchemist

[swansont]

5 minutes ago, exchemist said:

It means the particle behaves like a tiny bar magnet

In this case, yes, but you can have quadrupole moments, sextupole and octupole moments (and so on for any multipole, but always an even number) for more complex systems. 

[studiot]

Just now, Gian said:

So what is a "magnetic moment?" 
 

cheerz

GIAN🙂XXX

science education age about 12½

Magnetic Moment is not on the GCSE syllabus.

However this american MaGrawHill introduction includes it simply, rather as swansont has said.

https://www.accessscience.com/content/article/a223000

 

Ask again when you have read it.

[exchemist]

3 hours ago, swansont said:

In this case, yes, but you can have quadrupole moments, sextupole and octupole moments (and so on for any multipole, but always an even number) for more complex systems. 

Fair enough, but this guy is at GCSE level. No point in blowing up his brain with all that 😄

[swansont]

1 hour ago, studiot said:

Magnetic Moment is not on the GCSE syllabus.

And neither is quantum physics, apparently (“I'm still at GCSE level maths and physics and quantum theory doesn't seem to come into it at this stage.”) so it appears this isn’t about GCSE exams

[studiot]

Just now, swansont said:

And neither is quantum physics, apparently (“I'm still at GCSE level maths and physics and quantum theory doesn't seem to come into it at this stage.”) so it appears this isn’t about GCSE exams

I seem to remember that Gian is reading a bit ahead of the syllabus, which is designed to lay the groundwork to introduce such things at the next level.
Since I endorse that good attitude, I try to help with this so long as I am circumspect in what I offer before time.
Basically GCSE magnetism tells students that magnetic fields are directional and have a North and South.
They use Flemings rule to indicate a force on charged material crossing the magnetic lines to demonstrate the principle of how that induces a turning moment on a bar magnet in an electric motor.
The work is all qualititative.