Understanding The Experiment That Introduced The Concept Of Spin In Quantum Mechanics. 3

Understanding The Experiment That Introduced The Concept Of Spin In Quantum Mechanics.

This article on the Stern-Gerlach Experiment is a guest article by Rishabh Sharma, a third-year integrated Ph.D. student from the Indian Institute of Science Education and Research (IISER) Tirupati, pursuing a Ph.D. in experimental High Energy Physics. 

In the 1920s, Neils Bohr propounded an interpretation of quantum mechanics where the properties of any physical system were probabilistic and non-deterministic until they are measured. The idea was so perplexing that Einstein was dismayed by the mere thought of it. Einstein believed in a deterministic universe where there is always a reason for certain behavior of any system. “Moon simply does not disappear when we are not looking at it”, he said later. 

Understanding The Experiment That Introduced The Concept Of Spin In Quantum Mechanics. 5

One of Einstein’s first pupils, Otto Stern was influenced by Einstein’s deterministic universe. Stern got interested in light quanta and statistical physics from his discussions with Einstein in a cafe. He was quite shocked by Bohr’s interpretation of quantum mechanics and vowed that if this ‘nonsense’ of Bohr were to be true, he would leave physics! 

Stern with Walther Gerlach, later, designed an experiment that would only go on to prove Bohr’s nonsense to be true. Though  Stern did not leave physics, he did go on to receive the Nobel prize in physics in 1944,  “for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton”.

The Experiment

Spin and Stern-Gerlach Experiment

To explain the discrete atomic spectra, the Bohr model predicted that a hydrogen atom can only have two orientations of orbital angular momentum in an external magnetic field- it can either be in the direction of the magnetic field or opposite to it. This is known as space quantization. The concept of space quantization is not there in the classical description of the atom. The classical theory of Larmor held the point of view that the atom can have any arbitrary orientation of its orbital angular momentum in an external magnetic field.

The idea of space quantization had not been tested and it inspired Stern to have a closer look at it. One morning when “it was really cold to get out of the bed”, Stern laid on his bed and imagined the idea of the experiment that would test space quantization. He imagined a beam of hydrogen atoms passing through a strong non-uniform magnetic field. If the quantum theory of Bohr were to be true, hydrogen atoms can only have two orientations of their orbital angular momentum and the beam would split into two components depending on the orientation.

On the other hand, no such splitting will be visible if the classical theory was to be believed. Therefore, Stern’s imaginary experiment put quantum mechanics and classical mechanics against each other to describe nature. 

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Stern discussed this idea with Max Born who did not take it seriously.  Stern later found an acquaintance in Gerlach and with his expertise in molecular beams, it took them over a year to design the final apparatus of the experiment in which, instead of hydrogen atoms, they used silver atoms.

Setup of the Stern Gerlach Experiment

When they ran the experiment, due to some misalignment in the apparatus they could only manage to get a very thin silver film on the observational screen, too thin to be visible to the naked eye. Gerlach passed this blank screen to Stern, on which, to his surprise, the black slitting pattern started to emerge gradually.

Later they figured that the gradual appearance of the pattern was due to the smoke of the cheap cigar (containing sulfur) Stern was smoking. Stern was an assistant professor with a salary too low to afford good cigars. The sulfur from the smoke reacted with the traces of silver on the screen forming a jet black layer of silver sulfide. This made the splitting quite evident on the observational screen.

Gerlach later sent a postcard to Bohr congratulating him with a picture of the screen on which splitting was visible.

Stern Gerlach Experiment Observations
(Postcard showing the splitting of silver beam sent to Bohr by Gerlach. Courtesy AIP Emilio Segrè Visual Archives)

Happy ending as it may seem, it quite wasn’t! Bohr’s quantum theory, in the years to come, faced many blows. The main problem with the model was its inability to explain the properties of many-electron atoms.

Stern and Gerlach interpreted the results that they obtained from their experiment as a victory of old quantum theory over the classical theory but in reality, they only proved the classical theory incapable of explaining the results they got from the experiment. Nothing conclusive about the old quantum theory could be said because it might have got the predictions of this particular experiment correct but was failing when it came to explaining other phenomena like fine structure, Zeeman effect, etc.

Did the new quantum theory explain the results of the experiment?

The sun was about to set on the old quantum theory of Bohr, et al. and a new wave mechanics would replace as new quantum theory developed by Heisenberg, Schrödinger, et al., but even this new formulation could not do quite the job to explain the observations of the experiment.

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According to the new quantum theory, the silver atoms could have three orientations of orbital angular momentum when placed in an external magnetic field. This means that instead of two components, Stern and Gerlach should have observed three components of the beam on the screen! That’s even worse! Therefore, the Stern-Gerlach experiment poised a problem for the new quantum theory as well.

The Solution?

The solution to the problem came from a completely different observation. Wolfgang Pauli, while studying the atomic structure, realized that he required an extra property attributed to the atom to make sense of various atomic spectra but he could not find any physical significance of this property.

The solution came from Dutch physicists, Uhlenbeck, and Goudsmit in 1925. They were studying spectral lines from the Zeeman effect and soon realized that Pauli’s extra property was the spin of the electron. They assumed that the electron had an intrinsic spin angular momentum along with an orbital angular momentum, which was not considered in any of the earlier theories- classical, old, and even new quantum theory. Much like the earth is both revolving around the sun and rotating along its own axis, the electron also has both orbital and spin angular momentum.

The Correct Explanation

The silver atom, as predicted by modern quantum mechanics, has zero orbital angular momentum. This would have given no splitting of the beam at all. The splitting of the beam came from the spin angular momentum of the valence unpaired electron of the silver atom and not from the orbital angular momentum.

Spin of an electron

An electron can have two spin orientations, they are called spin-up and spin-down. They act like tiny magnets in an external magnetic field. When the silver beam passed through the nonuniform magnetic field in the experiment, the field separated spin-up and spin-down valence electrons in different silver atoms and guided them through different trajectories- causing the beam to split.

Therefore, Stern and Gerlach, unknowingly, were the first to observe the quantization of electron spin. While Uhlenbeck and Goudsmit used the concept of spin to solve many problems in atomic spectra they never cited the Stern-Gerlach experiment as a possible demonstration of spin quantization. The Stern-Gerlach experiment is, therefore, one instance in the history of physics that forms a nice case study of the relation between theory and experiment.

Previous guest article by Rishabh Sharma:
The journey to the LHC and beyond

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2 thoughts on “Understanding The Experiment That Introduced The Concept Of Spin In Quantum Mechanics.”

  1. It is quite amazing that great minds contradict yet science always comes out victorious and with harmony even though theories are proved wrong and ideas clash a beautiful solution awaits.

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