Angular Momentum: l and m

Back in the 1890's, Dutch physicist Pieter Zeeman

had an idea: was it possible that magnetic fields could affect light?

In consequence of my measurements of Kerr's magneto-optical phenomena, the thought occured to me whether the period of the light emitted by a flame might be altered when the flame was acted upon by magnetic force. It has turned out that such an action really occurs. I introduced into an oxyhydrogen flame placed between the poles of a Ruhmkorff's electromagnet, a filament of asbestos soaked in common salt. The light of the flame was examined with a Rowland's grating. Whenever the circuit was closed both D lines were seen to widen.

spectra of sodium

The photo above shows spectra of the sodium flame: wavelength runs along the X-axis.

What's going on?

Watch the Z-component (shown on the vertical axis) of the probability of the electron's position grow as we increase the m value.

 Q: If the strength of an applied magnetic field is B = 1 Tesla,
    what is the difference in energy between the levels
    m=0 and m=1?

 Q: What is the difference in energy between the n=2 and n=1
    levels of hydrogen?

 Q: How big is the Zeeman effect, compared to ordinary 
    changes in energy levels due to jumps in n?

Just for fun: the radiation emitted by a hydrogen atom in the example above falls within the radio portion of the spectrum. Can you figure out out where -- if anywhere -- that signal would appear on an old-time radio dial?

Image courtesy of Ralph Brandi

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