Magnetism orbital angular momentum

An effect of space quantization of orbital angular momentum may be observed if a magnetic field is introduced along what we now identify as the z axis. The orbital angular momentum vector P, of magnitude Pi, may take up only certain orientations such that the component (Pi) along the z axis is given by... 

For 5 states there is no orbital angular momentum and therefore no resulting magnetic field to couple S to the intemuclear axis. The result is that a 5 state has only one component, whatever the multiplicity. 

The third quantum number m is called the magnetic quantum number for it is only in an applied magnetic field that it is possible to define a direction within the atom with respect to which the orbital can be directed. In general, the magnetic quantum number can take up 2/ + 1 values (i.e. 0, 1,. .., /) thus an s electron (which is spherically symmetrical and has zero orbital angular momentum) can have only one orientation, but a p electron can have three (frequently chosen to be the jc, y, and z directions in Cartesian coordinates). Likewise there are five possibilities for d orbitals and seven for f orbitals. 

The Stern-Gerlach experiment demonstrated that electrons have an intrinsic angular momentum in addition to their orbital angular momentum, and the unfortunate term electron spin was coined to describe this pure quantum-mechanical phenomenon. Many nuclei also possess an internal angular momentum, referred to as nuclear spin. As in classical mechanics, there is a relationship between the angular momentum and the magnetic moment. For electrons, we write... 

Consider the orbital angular momentum of a free-ion term. Here L = 3 and the orbital degeneracy is 7. Application of Van Vleck s formula (5.8) predicts an effective magnetic moment. 

Figure 5.4 The magnetic moment M and the orbital angular momentum L of an electron in a circular orbit.

Figure 5.5 The motion in a magnetic field B of the orbital angular momentum vector L.

Two kinds of environmental interactions are commonly important in the ESR spectrum of a free radical (i) To the extent that the unpaired electron has residual, or unquenched, orbital angular momentum, the total magnetic moment is different from the spin-only moment (either larger or smaller,... 

From the mathematical restrictions on the solution of the equations comes a set of constraints known as quantum numbers. The first of these is n, the principal quantum number, which is restricted to integer values (1, 2, 3,. ..). The second quantum number is 1, the orbital angular momentum quantum number, and it must also be an integer such that it can be at most (n — 1). The third quantum number is m, the magnetic quantum number, which gives the projection of the 1 vector on the z axis as shown in Figure 2.2. 

Orbital angular momentum of an electron in an atom can be measured by the same type of Stern-Gerlach experiment described before for the measurement of electron spin. In this case it will be assumed to use a metal such as magnesium whose atoms have a total electron spin of zero. The magnetic moment... 

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