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I believe the setup for the experiment was using silver atoms, passed through a magnetic field. These neutral silver atoms have an unpaired electron, in the 5s state I believe. If there was no spin on the electrons to interact with the magnetic field, one would expect a majority of the silver atoms to end up pretty much directly at the end of the path they were shot down, with little deflection. Instead, what was observed was that there were two groups of silver atoms on the detection screen. This indicates some sort of interaction with the magnetic field, which led to the recognition of electrons having spin.
The Stern and Gerlach experiment revealed how electrons don't have the same spin which differed from the classical prediction. Since electrons can be spun up or down, we use a 4th quantum number, ms which is the spin magnetic number.
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