Definitively clear evidence for the quantization of angular momentum. In the original experiment, silver atoms are shot through an inhomogeneous magnetic field. The inhomogeneous magnetic field spreads the silver atoms along one axis in a plane perpendicular to the inhomogeneous field, and onto a screen where they are detected.

The classical prediction is related to our intuition from a spinning top -- we would expect that the angular momentum vector could point in any direction just like a top (or a gyroscope if you like) can point in any direction. Thus the silver atoms should be smeared out continuously on the screen.

In fact, they can only assume discrete values -- there are a bunch of lines rather than a continuous smear on the screen -- which are determined in part by angular momentum that the silver atoms possess when they are entirely still. This kind of "intrinsic" angular momentum is referred to as spin. Electrons, which are as far as modern science is concerned structureless particles (they are like geometric points) are spin 1/2 particles, or fermions.