What Are the Essential Concepts for Teaching Zeeman Splitting?

[brian0918]

Besides the following, what other content needs to be covered in order to teach Zeeman splitting to someone who has only had a basic introductory E&M course (course description below).

• Energy level transitions
• • Selection rules
• Orbital magnetic moment
• • Magnetic moments
• • Magnetic dipoles
• Orbital angular momentum
• • Quantum numbers

Intro E&M course description: E&M emphasizing the basic laws of Ampere, Faraday, and Gauss. Maxwell's equations, electromagnetic waves, interference, diffraction.

 

[Gokul43201]

I think it's important to make it clear that Zeeman splitting is a Quantum effect, and so a classical treatment of it is only for descriptive puropses.

Also, it might be useful to spend 5 minutes deriving the potential energy of an electric dipole in an applied electric field ($\Delta U = - \vec{p} \cdot \vec{E}$); then draw the parallel to a magnetic dipole in a B-field (ie : $\Delta U = - \vec{\mu} \cdot \vec{H}$). That will give you something purely classical to compare with.

 

[brian0918]

So do I have to cover the Schrödinger equation and QM as well?

 

[daba]

you don't need to cover the Schrödinger eq,if you only use the rydberg energy levels(which are the same,but so you don't need to go into solving the schrodiger.eq);and then go on with the additional potential energy if a magnetic field is added(because of the angular&spin momentum...),which leads to the zeeman splitting

 

[marlon]

It is also important to realize that the Zeeman effect gave a clear demonstration of the existence of what we call the intrinsic spin angular momentum. Beware of that you know what intrinsic really means and that you realize what spin actually is about. It is NOT about electrons spinning around some axis, ok. It has to do with symmetry of the equations that describe the invariance of the 'physics' under coordinate transformations. I know the last sentence may sound general and vague but check out my journal for more indept info. Also, realize that this Zeeman thing is not inherent to electrons but it arises thanks to the interaction between an electron and an atomic nucleus, just like the spin orbit coupling. Thus all these electronic energy levels we like to talk about in the Aufbau principle all arise because the electrons are feeling an atomic nucleus in their vicinity.

Also, do not think that electrons orbit the nucleus in circles. QM tells us clearly that we can only talk about regions where we have a certain probability of finding an electron: ie the orbitals. For example, the lowest energy orbital (the s-orbital) is spherical around the nucleus, so you can say that an electron in this orbital really is everywhere around the nucleus at the same time...You can only speak about the probability that you will find such an electron in this specific spatial region around the atomic nucleus.

regards
marlon

 

[brian0918]

I'm not really trying to explain everything about the Zeeman effect, just the necessary physics up to it, and its relation to observations of cosmic magnetic fields.

 

[Gokul43201]

To completely understand the Zeeman Effect you need to first have at least a couple of months of QM under your belt. Since that is not an option here, I repeat my suggestion of throwing in the disclaimer (and no, do not do a half-hearted job of "teaching" QM for the sake of explaining why the Zeeman effect happens) before getting into some of the details. What's important for a quick semi-classical route is understanding that there is an interaction between a magnetic moment and a magnetic field, and where these magnetic moments come from. All the rest is really just details, at this level.

If you wan't to be able to field questions from the more well-prepared students, you must make sure you are clear about the concepts that marlon mentioned in #5.

As for the outline you have proposed in the OP - I do not like how it is structured (talking about selection rules before mentioning quantum numbers ??).

Here's how I'd do it :

1. The Bohr picture and the "Principal Quantum Number" - electronic transitions in the Bohr Model ("all transitions allowed" in the Bohr picture)

2. The advent of QM - Quantum Numbers (perhaps a very brief statement that they pop out of the SE for the H-atom) and what they represent

3. Selection rules for "allowed transitions" (this might need a few words about the properties of a photon, but that can be skipped)

3. Orbital and Spin angular momenta and the associated magnetic moments

4. The interaction of a magnetic moment with an applied field (perhaps using the classical picture - the QM calculation is hardly trivial, and meaningless to someone that has little background in QM) - "the Zeeman Effect" (and please, do not mispronounce Zeeman )

5. What the Zeeman Effect does to the emission/absorption spectrum (keeping close tabs on the selection rules)


Note : This material can be taught over a single class, or over an entire semester. Depending on the time-frame you have, make a determination of the rigor and detail you wish to use.

PS : I'd wait for more suggestions on the outline from others here .

 

[brian0918]

I didn't say that was an order, just a list of things that need to be covered. Thanks for the helpful reply!

 

[marlon]

PS : I'd wait for more suggestions on the outline from others here .

You gave a good general outline so i have nothing to add there. However i do think it is important that you stress the point i tried to make in my previous post, just to avoid some of the most popular misconceptions in QM. It is also very necessary that students keep in touch with the actual physical nature they are describing, nomatter how counter-intuitive that may be.

regards
marlon