The total angular momentum of an atom includes an electron spin component as well as an orbital component.
The orbital motion of each electron of an atom contributes to the angular momentum of the atom, as described earlier. An additional angular momentum contribution comes from the “spin of the electrons.”
The direct experimental demonstration of an electron feature that is described as spin angular momentum was given by the atomic beam studies of O. Stern and W. Gerlach. In the original experiments, a beam of silver atoms was passed through a magnetic field. The result was a splitting of the atom into two components. Thus, when a directional field is composed, two different states of silver atoms can be recognized.
The lowest energy electronic state of silver atoms consists of inner shells of electrons and a single outer shell electron in atom in an s orbital. No additional states should be developed when a directional field is applied to this spherically symmetric, zero angular momentum atom. The Stern-Gerlach results supported the idea that the silver atoms have an angular momentum of ½ h/ (2∏), or 1/2 h, which results from the intrinsic angular momentum of the electron. The magnetic field distinguishes those atoms with a spin angular momentum directed with and opposed to the field. If the electron spins quantum number s has a value of 1/2, jection of the spin angular momentum along an imposed direction is given by m2, h, where m2 = +1/2 or – ½.
In describing the electronic makeup of atoms, we use angular momentum to characterize the atomic states. From the above equations the orbital angular momentum contribution of an electron is √l (l + 1) h, where l = 0, 1, 2 … now there is, in addition, an electronic spin angular momentum contributions are used to describe the states of many electron atoms.