In the Stern Gerlach experiment, the silver atoms is passing through the inhomogeneous magnetic field. Initially the detector showed a single hump since the magnetic field isn't strong enough to exert a force to realign the atoms, but when the magnetic field strength is increased the detector immediately showed 2 wings. Initially the detector measured high intensity in the center area and now it dropped suddenly when magnetic field is increased. Increasing the magnetic field strength further only adds to the separation of the wings, my question is why the atoms all experienced the same torque? If all the atoms had the same energy when passing through the inhomogeneous magnetic field what would I see then?
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2$\begingroup$ You are very wrong in the interpretation of basically everything in the experiment. The magnetic field is usually presented as fixed in time. The atoms are not experiencing torque. $\endgroup$– naturallyInconsistentCommented Dec 21, 2023 at 8:19
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$\begingroup$ OP, here is a useful description of the SG apparatus: feynmanlectures.caltech.edu/III_05.html#Ch5-S1 $\endgroup$– hftCommented Jan 12 at 0:34
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1 Answer
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I believe OP watched the video The Stern-Gerlach Experiment with MIT Prof. Jerrold R. Zacharias: https://youtu.be/AcTqcyv-V1I?t=834. The magnetic field dependency OP describes is seen there.
I think OP's mistake is to use the word torque. Perhaps OP thinks that the atoms experience the same force. The exact apparatus in the video is explained in Ch. 9 (Angular Momentum) of Introduction to Quantum Physics by French and Taylor. It is very accessible introduction for a beginner or any physicist. I have not encountered any other text that explains the experimental minutiae so well.
OP's second question is
If all the atoms had the same energy when passing through the inhomogeneous magnetic field what would I see then?
From French and Taylor the deflection $z_1$ due to the field is dependant on the speed $v$ of the atoms and the field gradient $\frac{\partial B}{\partial x}$: \begin{equation}z_1 \propto \frac{\partial B}{\partial x}\frac{1}{v^2}.\end{equation} The full equation can be found in Eq. 9-2.
The distribution of speeds causes the breadth and shape of the humps in the plots. A beam of atoms all with the same KE will have the same speeds, and thus the same deflection. To first order, it is the idealized Stern-Gerlach experiment seen in textbooks. The magnetic field plots would have two very narrow spikes that move outward with increasing field gradient. The height of the peaks would be much higher because the area under the graph must be the same because the number of atoms hitting the detector is the same.
To second order, the apparatus will affect things. I guess the collimating slit might produce a single-slit diffraction. It would depend on dimensions and details of the apparatus. The later beam stop might interfere with this or might make single-slit diffraction of its own, but the schematic makes it out to be very wide so that would be weak.
All in all, my guess is that you would see a single slit diffraction pattern centred on each of the locations of the humps.
