Electron spin and the magnetic properties of atoms

The quantity is the spin quantum number it may have only the values or —j. The Schrodinger equation in its usual form gives no indication of the existence of the electron spin. However, Dirac has shown that if the Schrodinger equation is cast into a form that satisfies certain requirements of relativity theory, then four quantum numbers, the fourth being the electron spin quantum number, appear in the solution for the hydrogen atom. Thus the spin is a coherent part of the fundamental theory and is not tacked on just to patch things up. 

Two electrons in an atom that differ only in the value of the spin quantum number are called paired electrons. The z component of spin angular momentum of the second electron is equal and opposite in sign to that of the first electron. The net z component of spin angular momentum of the electron pair is the sum, jh + = 0 thus the pair 

Similarly, the net orbital angular momentum of any filled subshell is zero. First of all, the orbital angular momentum in an s level is zero by definition. In a group of p levels, the possible values of m are — 1, 0, -I-1. If we place a pair of electrons in each of these p levels, then two electrons have m = — I, two have m = -1-1, two have m = 0. The net z component for all of these is zero since 2( — 1) -I- 2(0) -I- 2( -I-1) = 0. A filled subshell has no net component of orbital angular momentum around any specified axis, and so it contributes no magnetic moment due to orbital motion. 

The magnetic moment of an atom is due entirely to partially filled subshells and unpaired spins. The completed subshells do not contribute to the permanent magnetic moment of an atom. In this connection we might remark that most molecules have an even number of electrons whose spins in the ground state are all paired. Also the subshells are usually complete so that there is no contribution to the magnetic moment from the orbital motion. It is unusual for a molecule to have a permanent magnetic moment the possession of a permanent magnetic moment is an important key to the electronic structure of the molecule. 

---