Stern-Gerlach Experiment Animation

Introduction

            The Stern-Gerlach experiment (1922) clearly showed that the magnetic moment of the silver atoms used could have only two orientations-either parallel or anti-parallel to the average magnetic field through which the atoms passed.  The atoms were sent through a magnetic field Bz whose average value was in the z direction but varied along the z direction so that dBz/dz was not equal to zero.  Probably the most mysterious thing about the experiment is that the atoms’ magnetic moments seemed to attain perfect alignment with the z direction as soon as they passed into the field region.  In concept that would require an infinite instantaneous torque to rotate the spinning mass from its initial random orientation to being aligned with the z axis.  If the electron were a classical current loop, it would start precessing about the magnetic field lines when it entered the magnetic field.  But the component of its magnetic moment along the magnetic field lines wouldn’t change.

 

Calculations

            Putting the mystery aside for a moment, let’s just compute the deflection of an electron that passes through a spatially varying magnetic field where the average field is 1 Tesla and the field variation in the z direction is 10% cm-1.  First we compute the energy difference between aligned and anti-aligned spins.  This is

                                                                                                                        (1)

where mB=9.28x10-24 Joules Tesla-1, g=2.002 and B is in units of Tesla.

To compute the force, F, exerted on the particle with the magnetic moment, we use the equation:

                                                                (2)

The acceleration of the particle is by Newton’s laws of motion

                                                                                              (3)

The z velocity attained due to this acceleration is

                                                                                                   (4)

where Ly is the length of the magnet and v=vy is the initial speed of the particle along the y direction. 

Since the display screen is usually placed at a distance much greater than Ly, we are usually interested in the final angle of flight of the particle.  Since the magnetic field can’t change the speed of the particle,

                                                              

so that the angle of the velocity of the particle with respect to the initial y direction is

 

  

                                                                                             (5)

Discussion

            The Stern-Gerlach experiment proves absolutely nothing about the angular momentum of the particles.  It simply shows that measured components of the magnetic moments of the particles parallel to the average applied magnetic field are all approximately equal and that these measured components can be either positive or negative with respect to the applied magnet field.  It does not prove that the magnetic moments are associated with any angular momentum. So how is it that these magnetic moment components, which are totally random prior to arriving at the applied magnetic field can suddenly become either parallel of anti-parallel to this field?  Since it occurs instantaneously, I would have to say that it has nothing to do with the angular momentum.