How does the Stern Gerlach experiment split a beam of hydrogen atoms?

[Amith2006]

Homework Statement

If a beam of hydrogen atoms in ground state are passed through an inhomogeneous magnetic field, into how many paths will the beam be split? Assume that the beam is moving towards the plane of this page and the magnetic field is directed in the upward direction in the plane of this page.

Homework Equations

The Attempt at a Solution

It is known fact that naturally the beam will be divided into 2. What about the plane in which the 2 split beams exist. When I apply Flemings left hand rule, I find that it is in the horizontal plane. But the answer says, it is in the vertical plane.

 

[jdwood983]

Homework Statement

If a beam of hydrogen atoms in ground state are passed through an inhomogeneous magnetic field, into how many paths will the beam be split? Assume that the beam is moving towards the plane of this page and the magnetic field is directed in the upward direction in the plane of this page.

Homework Equations

The Attempt at a Solution

It is known fact that naturally the beam will be divided into 2. What about the plane in which the 2 split beams exist. When I apply Flemings left hand rule, I find that it is in the horizontal plane. But the answer says, it is in the vertical plane.

I don't know much about Fleming's left hand rule, but the two beams should split along the same plane the magnetic field is in. You can convince yourself of this by looking at the magnetic force and the spin of the particles in terms of vector components.

I'd be careful with using the word 'natural' in anything related to quantum mechanics due to the fact that there are some unnatural features, Stern-Gerlach included. Scientists were shocked when the SG apparatus showed that particles, under the influence of a gradient magnetic field, would have discrete values, rather than a continuous distribution that was actually expected.

 

[jdwood983]

I looked up Fleming's left hand rule real quick online, and it seems that has application for electric motors only, and not magnetic fields.

For Stern-Gerlach, you should be looking at \mathbf{F}=-\nabla\left(-\boldsymbol{\mu}\cdot\mathbf{B}\right) to convince yourself that the particles will separate into the 2 components along the axis of the gradient magnetic field.

 

[Amith2006]

Thanx dude.