Electrons and spin 1/2
Atomic and solid state physics is esentially the physics of electrons, since the small mass of the electron lets its wave function spread out over a much larger distance than the heavier neutron and proton.
One of the amazing properties of the electron is that it has an intrinsic angular momentum. That mean that it is always "spinning" even when it is sitting by itself. This spin cannot have just any value but rather must be either +1/2 or -1/2 when measured in units of h/(2p) . The fact that the angular momentum can only have discrete values can be stated: "The spin (intrinsic angular momentum) of particles is quantized. We will further see that the half-integral vs. integral nature of the spin is of fundamental importance.
We will also see that the orbital states open to an electron in orbit around a nucleus are quantized. This means that only orbits with discrete energies are possible. The combination of the discreteness in the orbits and in the spin gives structure to atomic configurations.