# Some questions about spin in relation to the stern-gerlach experiment

• xortdsc
In summary, the stern-gerlach experiment involves shooting electrically neutral silver atoms through a magnetic field with a gradient along the z-axis. The atoms will be deflected slightly along the z-axis depending on their spin, resulting in two distinct beams. This is also true for other particles such as electrons, but their electric charge causes their beam to spread out. The splitting effect is only seen for moving particles, as a stationary dipole would not feel a force along the z-axis in an inhomogeneous magnetic field. The behavior of the beams for other spins, such as 0, 1, and 3/2, follows the available spin states. The spin of a particle acts like a small magnetic dipole field, creating
xortdsc
Hi,

I have a few questions regarding the experimental outcome of the stern-gerlach experiment.
Let's suppose the following setup: We have a magnetic field whose field-lines point towards the positive z axis and the intensity of that field becomes stronger towards the positive z axis, so there is a gradient in the magnetic field strength with respect to the z-axis.

(1) When shooting a electrically neutral silver atom along the x-axis through this field it will be deflected slightly along the z axis by a specific amount depending on the spin it has. And since it can only have +1/2 or -1/2 spin it follows either one of 2 possible paths.
So a single beam of silver-atoms will split (along the z axis) into 2 sharp beams (assuming it was composed equally of +1/2 and -1/2 spin atoms).
This should be the standard setup of the stern-gerlach experiment. Did I understand that correctly ?

(2) In case the magnetic field would be homogenous no such splitting is seen ?

(3) When performing the original experiment using electrons instead of silver atoms, will the same splitting along the z axis occur ? Is the only difference that the electrons trajectory will additionally bend into a circle in the xy plane because of its electric charge ?

(4) Is the splitting only seen for moving particles ? So an atom at rest within the (inhomogenous) magnetic field will NOT feel any force along the z axis ?

(5) How do the beams behave for other spins like 0, 1 and 3/2 compared to the case of 1/2 ?

(6) How do we know that neutrinos have 1/2 spin ?

I hope somebody can give me some clarity on this. :)
Cheers.

xortdsc said:
Hi,

I have a few questions regarding the experimental outcome of the stern-gerlach experiment.
Let's suppose the following setup: We have a magnetic field whose field-lines point towards the positive z axis and the intensity of that field becomes stronger towards the positive z axis, so there is a gradient in the magnetic field strength with respect to the z-axis.

(1) When shooting a electrically neutral silver atom along the x-axis through this field it will be deflected slightly along the z axis by a specific amount depending on the spin it has. And since it can only have +1/2 or -1/2 spin it follows either one of 2 possible paths.
So a single beam of silver-atoms will split (along the z axis) into 2 sharp beams (assuming it was composed equally of +1/2 and -1/2 spin atoms).
This should be the standard setup of the stern-gerlach experiment. Did I understand that correctly ?
That's good enough - I'd say that the beams are "well defined".

(2) In case the magnetic field would be homogenous no such splitting is seen ?
If the field is uniform then there is no torque on the dipole so yeah - no splitting.

(3) When performing the original experiment using electrons instead of silver atoms, will the same splitting along the z axis occur ? Is the only difference that the electrons trajectory will additionally bend into a circle in the xy plane because of its electric charge ?
The electrons in the beam will also repel each other so the beam spreads out. The effect pretty much wipes out the effect of the electron spins.

You could use very low intensity beams though:
http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1031&context=physicsgay
... suggests that it is a feasible experiment. Don't know if it has been done.

(4) Is the splitting only seen for moving particles ? So an atom at rest within the (inhomogenous) magnetic field will NOT feel any force along the z axis ?
You can check the math for that if you like - does a stationary dipole feel a force in an inhomogeneous B field?

(5) How do the beams behave for other spins like 0, 1 and 3/2 compared to the case of 1/2 ?
... the behavior would be in accordance with the available spin states.

(6) How do we know that neutrinos have 1/2 spin ?
Conservation of angular momentum in neutron experiments?

You could send He3 nuclei through an SG apparatus one at a time.
But why not just do the Stern-Gerlach experiment with neutrons?
http://frhewww.physik.uni-freiburg....genLoesungen/Uebungen_05_SS2011-ExIV-HELM.pdf

Thank you very much.

Simon Bridge said:
You can check the math for that if you like - does a stationary dipole feel a force in an inhomogeneous B field?

I'd think the dipole should accelerate along (or against, depeding on spin) the gradient of the B field, is that right ?

Simon Bridge said:
... the behavior would be in accordance with the available spin states.

So that means that a beam of 0-spin particles will not split and a beam of 1-spin particles will split in two just like the 1/2-spin do, but with double the magnitude ?

Simon Bridge said:
does a stationary dipole feel a force in an inhomogeneous B field?

xortdsc said:
I'd think the dipole should accelerate along (or against, depeding on spin) the gradient of the B field, is that right ?

The usual gradient vector applies to a scalar field, but ##\vec B## is a vector field. There is a force, but it's not a simple "gradient of ##\vec B##":

http://en.wikipedia.org/wiki/Magnet..._external_magnetic_field_on_a_magnetic_moment

ah okay. thank you :)

I'd think the dipole should accelerate along (or against, depeding on spin) the gradient of the B field, is that right ?
...
It sounds like you are guessing.

The answer requires doing some maths - as suggested.
You will only get suggestions like that if I think the answer is within your ability.

You can always look up the answers:
http://www.physicsinsights.org/force_on_dipole_1.html

Simon Bridge said:
It sounds like you are guessing.

The answer requires doing some maths - as suggested.
You will only get suggestions like that if I think the answer is within your ability.

I wasn't sure what math to apply, so yes, I was just guessing.
However the link provided by jtbell made it clear what the math is.

Thanks both of you :)

Simon Bridge said:
You can always look up the answers:
http://www.physicsinsights.org/force_on_dipole_1.html

That link is very nice, too.

So finally it can be said that the spin of a particle acts like there would be some current running in a infinitesimal loop and therefore creating a small magnetic dipole field with all the effects that follow from that (such as interaction with other magnetic fields) ? Or does it behave different from that in some situations ?

No worries.

Usually when a student learns about S-G we start them off by deriving the expression for the deflection angle, which means they have the math already. You can't get very far from qualitative descriptions but fortunately the extra stuff is easy to look up.
Enjoy.

The spin is so-named exactly because particles behave like they have some sort of current loop - which you'd expect from a spacially distributed charge that is rotating.

A real current would have a thickness, so the field close to it would depart from the field of an intrinsic dipole.
Also: given the charge and the magnetic moment of, say, an electron, you can work out what radius the "current loop" would have to be and compare with the measured particle size. (Similarly you could work out the smallest spatial distribution of charge that would give rise to that magnetic moment to compare.)

So there are differences - what the links are using is a mathematical model.
WE can also do the calculations from the intrinsic moment without pretending there is a current loop.

## 1. What is the Stern-Gerlach experiment?

The Stern-Gerlach experiment is a physics experiment that was first performed in 1922 by Otto Stern and Walther Gerlach. It involves passing a beam of atoms through an inhomogeneous magnetic field, which causes the atoms to split into multiple beams. This experiment was significant in the development of quantum mechanics and helped to confirm the existence of electron spin.

## 2. How does spin relate to the Stern-Gerlach experiment?

Spin refers to an intrinsic property of particles, such as electrons, that causes them to act like tiny magnets. In the Stern-Gerlach experiment, the inhomogeneous magnetic field causes the particles' spins to align in different directions, resulting in the splitting of the beam. This splitting is a direct result of the particles' spin orientations.

## 3. What is the significance of the Stern-Gerlach experiment?

The Stern-Gerlach experiment was significant in providing evidence for the quantization of angular momentum and the existence of electron spin. It also helped to confirm the principles of quantum mechanics, which revolutionized our understanding of the behavior of subatomic particles.

## 4. Are there any limitations to the Stern-Gerlach experiment?

Yes, there are some limitations to the Stern-Gerlach experiment. For example, the experiment can only measure the spin of particles in one direction at a time. It also does not take into account the wave-like nature of particles, and therefore, cannot fully explain all quantum phenomena.

## 5. How is the Stern-Gerlach experiment used in modern research?

The Stern-Gerlach experiment is still used in modern research to study the properties of subatomic particles, such as electrons. It has also been adapted for use in other fields, such as materials science and biology, to study the magnetic properties of different materials and biological molecules.

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