Lecture 7: Quantized magnetic dipole moments

Prof. Axon's full lecture notes are available in PDF format.

Lecture 7 in PDF (4.4 MB)

The main ideas for today are

the observables by which we can detect and measure angular momemtum within atoms
the connection between angular momentum and magnetic moments
how magnetic moments give rise to torques and potential energies
the Zeeman effect, which demonstrates the splitting of energy levels in an applied magnetic field
the Stern-Gerlach experiment, which demonstrates quantization of angular momenta
electrons (and other particles) have intrinsic spin

We'll also look at the homework assigned for next week.

You can find this material described in your textbook:

Krane: sections 7.5 - 7.7
Thornton and Rex: sections 7.4 - 7.6

Introduction

The goal for today is to make our way through the first half of the following list:

The Zeeman effect: some energy levels split when atoms sit in a magnetic field

Exercise

The torque on a magnetic moment placed in a magnetic field

Review the similarities between linear and rotation quantities:



         Linear                  Rotational
  ----------------------------------------------------------
     m =  mass (kg)        I =  rotational inertia (kg*m^2)

     v =  velocity (m/s)   ω =  angular velocity (rad/s)

     a =  accel (m/s^2)    α = angular accel (rad/s^2)

     F =  force (N)        τ = torque (N*m)

       F = m a                τ = I α

 -----------------------------------------------------------


     Q:  How is force related to momentum?  
         (Hint: consider time derivative)

     Q:  How is torque related to angular momentum?

A slight complication: the "g" factors

Back to the Zeeman effect -- allowed transitions

Electronic spin -- another magnetic moment, another quantum number

We now consider another quantum effect which comes into play when considering magnetic moments.

Let's consider what happens when an object with a magnetic moment is placed into a non-uniform magnetic field.

So, we expect to see a single beam of particles split as it runs through the magnetic field ... but only if the beam contains particles with a magnetic moment.

The Stern-Gerlach experiment

Stern and Gerlach created an experiment in which NOTHING should have happened. They chose a beam of particles which have zero orbital angular momentum and so zero magnetic moment.