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The stern and Gerlach experiment basically consisted of emitted a beam of the same element through a magnetic field and rather than all the atoms continuing on a straight path, some of the electrons curved upwards and the others downwards. Because the n,l, and m(l) variables were all the same it meant there was one other variable that also described an atom. This was the spinning characteristic of an electron where some spun up (+ 1/2) and some spun down (- 1/2). I hope that helps/makes sense!
The difference in spin only shows up in the presence of a magnetic field. In the absence of magnetic field, the electron spins have the same energy, however, this is not the case when the atom beam of silver ions passed through a magnetic field in the experiment.
Essentially the experiment proved that there was an intrinsic, binary property of an electron that influenced its behavior in a magnetic field. This property was termed the magnetic spin of the electron, and is the fourth quantum number used to describe the state of an electron in an atom. It can be used to differentiate between electrons in the same orbital: in each orbital there are two electrons, and each of the two electrons must possess opposite spin. If one electron in an orbital has 'down' spin, the other must have 'up' spin. This means that no two electrons in an atom have the exact same quantum number even if they are in the same orbital.
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