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CHEM 322 - 01

Chapter 13

Spin-Orbit Coupling

I. Spin-Orbit Coupling in Hydrogenic Atoms

a. Because an electron has spin angular momentum, and because a moving charge generates a magnetic field, an electron has a magnetic moment that arises from its spin. Also, that same electron has an orbital angular momentum and possesses a magnetic moment that arises from its orbital angular momentum. The interaction of the spin magnetic moment and the magnetic field arising from the orbital angular momentum is known as spin-orbit coupling.

b. The extent of the spin-orbit coupling depends on the relative orientation of the spin and orbital magnetic moments, and therefore on the relative orientation of the spin and orbital angular momenta.

c. The total angular momentum of an electron is described by the quantum numbers l and . s

jls=+

When the two angular momenta are in the same direction, 12jl=+, and when they are in the opposite direction, 12=−jl. The different values of that can arise for a given value of l label levels of a term. j

d. The dependence of the spin-orbit interaction on the value of is expressed in terms of the spin-orbit coupling constant, . The energies of the levels with quantum numbers l, , and jAsj are given by the equation:

()()(),,1112lsjEhcAjjllss=+−+−−1

e. The strength of the spin-orbit coupling increases sharply with atomic number ( as 4Z). So there is less spin-orbit coupling in hydrogen than in lead.

f. Observed transitions in the electronic spectrum of atoms arising from levels of different values of j are known as fine structure of the spectrum.

II. Term Symbols of Multi-Electron Atoms

a. A term symbol is a label used to indicate the values of the orbital, spin, and total angular momentum of an electronic state, and since the energy of that state depends on the values of these angular momenta, the term symbol becomes a useful way to label an electronic state. The general form of a term symbol is:

21SJL+

is the quantum number...

Chapter 13

Spin-Orbit Coupling

I. Spin-Orbit Coupling in Hydrogenic Atoms

a. Because an electron has spin angular momentum, and because a moving charge generates a magnetic field, an electron has a magnetic moment that arises from its spin. Also, that same electron has an orbital angular momentum and possesses a magnetic moment that arises from its orbital angular momentum. The interaction of the spin magnetic moment and the magnetic field arising from the orbital angular momentum is known as spin-orbit coupling.

b. The extent of the spin-orbit coupling depends on the relative orientation of the spin and orbital magnetic moments, and therefore on the relative orientation of the spin and orbital angular momenta.

c. The total angular momentum of an electron is described by the quantum numbers l and . s

jls=+

When the two angular momenta are in the same direction, 12jl=+, and when they are in the opposite direction, 12=−jl. The different values of that can arise for a given value of l label levels of a term. j

d. The dependence of the spin-orbit interaction on the value of is expressed in terms of the spin-orbit coupling constant, . The energies of the levels with quantum numbers l, , and jAsj are given by the equation:

()()(),,1112lsjEhcAjjllss=+−+−−1

e. The strength of the spin-orbit coupling increases sharply with atomic number ( as 4Z). So there is less spin-orbit coupling in hydrogen than in lead.

f. Observed transitions in the electronic spectrum of atoms arising from levels of different values of j are known as fine structure of the spectrum.

II. Term Symbols of Multi-Electron Atoms

a. A term symbol is a label used to indicate the values of the orbital, spin, and total angular momentum of an electronic state, and since the energy of that state depends on the values of these angular momenta, the term symbol becomes a useful way to label an electronic state. The general form of a term symbol is:

21SJL+

is the quantum number...

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