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The Stern-Gerlach experiment

The Stern Gerlach Experiment
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The experiment carried out by Otto Stern and Walther Gerlach was originally designed to test the “space quantization” theory of Niels Bohr, which got replaced with quantum mechanics soon afterwards. The experiment supported the predictions of the Bohr model of the atom, but really it demonstrated the quantization of angular momentum, and remains an important demonstration of some interesting ideas in quantum mechanics.

The experiment was surprisingly simple (and under funded, but more on that later). It consisted of heating up silver atoms, and firing them between two magnets towards a screen where they could be observed. As we understand now, a silver atom has a magnetic moment, and so for this discussion, it can be thought of as a tiny magnetic marble. Since the silver atoms came flying from a hot oven, they had all sorts of speeds and their magnetic poles (north and south) pointed in random directions. One can imagine, that when such a tiny magnet flies between the larger magnets of the experimental apparatus (in red and blue in the figure above), its path would be deflected. For example, if the silver atom’s north pole points up in the z direction (towards the north pole of the top magnet), It will be repelled downwards. If its pole points downwards, -z direction, it should be deflected downwards. And if its pole points somewhere in between, it should be deflected somewhere in between. And hence, since all the atoms point in random directions, one could have expected to see silver atoms on the screen forming a kind of smear, since clearly, all atoms would be deflected in different directions. However, this was not observed. To the disappointment of Stern, the atoms formed two distinct smears, one above and one below the center line. No atoms were observed to fly out undisturbed by the magnets! Moreover, it was as though the atoms had only two possible magnetic orientations; they could point upwards in the z direction, or point downwards in the -z direction. Instead of observing the magnetic moment taking a value form a smooth distribution, it was quantized, and the atoms split evenly between the two quantized values.

This gets weirder still. Let us draw the experiment schematically, as below, so we could complicate it without burdening my drawing skills.

The oven and experimental magnets are represented by boxes, and the letter in the magnet box (z in this case) tells which way the North pole of the magnets points. The two outgoing lines form the z magnet represent the upwards deflected atoms and downwards deflected atoms. We can now consider putting a second set of magnets, still pointing in the same direction, so that they capture the beam that moved upwards only. Unsurprisingly, it does not split again.

But we are not restricted to orienting the magnets in the z direction. Consider discarding one of the two beams after each split (represented by the red stop sign below). Now what if another set of magnets in the x direction was put following the z magnet, capturing all upwards moving atoms? The atoms split again; one beam is deflected in the x direction (out of the page), the other in the opposite -x direction. And again about half of the atoms take each path.

And let us split the beam once again, this time in the z direction as before. What do you think happens? Does it split, or not?

Let us recap. Silver atoms, behaving like tiny magnets, are fired from an oven towards sets of magnets designed to split them according to their magnetic moment:

  1. First the beam is split along the z axis, remarkably, half the atoms are deflected upwards, the other half deflected downwards. The down moving atoms are blocked.
  2. The up-moving beam has another set of magnets put in its path, splitting along the x axis. Two beams emerge, half deflected into the page, the other half out of the page. Those moving out of the page are blocked.
  3. The remaining beam (atoms that deflected upwards, then into the page) has another set of magnets put in its path, again pointing in the z direction.

And the beam splits again, half deflected upwards, the other half deflected downwards. As though it was a freshly heated beam from the oven. Somehow, measuring the magnetic moment of the atoms in the x direction has destroyed information about the magnetic moment originally measured in the z direction.

Closing remarks:

Being under funded, Gerlach could only afford cheap cigars, the type that contain a lot of sulfur. When examining glass slides on which the silver atoms should have been deposited, the experimenters originally could not see the very thinly deposited silver atoms. But as Gerlach breathed his sulfur filled breath on the glass slides, the pattern of the silver atoms began to emerge in black! The silver reacted with the sulfur to form black silver sulfide. To read more about this, take a look at “Stern and Gerlach; how a bad cigar helped reorient atomic physics” by B. Friedrich and D. Herschbach. For a more detailed and careful treatment of the experiment, check out “Modern quatum mechanics” by J. J. Sakurai.

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