Physical Chemistry , 1st ed.

transition to ML1, except it will have the opposite sign. Therefore (and

without the need to do any additional math),

Emag[ML1] 0.9338 cm^1

The transition will turn into a triplet of equally spaced lines. Thus, the

Zeeman spectrum of this transition will resemble Figure 16.6.

The fact that a single line turns into a trio of lines in the above example is

characteristic of a^1 S →^1 P transition. Therefore, the normal Zeeman effect gives

spectroscopists clues about the term symbols of the states involved in atomic

spectra. Each combination of term symbols has, for S0, a certain number of

allowed transitions that is characteristic of the transition, thanks to quantum

numbers. This information is useful for identifying the quantum numbers of

ground and excited states, which is a crucial part of the understanding of atomic

and molecular structure in the quantum-mechanical formalism.

In cases where S0, we do not have a singlet state, and the total angular

momentum quantum number Jmust be considered. (In the previous case,

JL.) In this case, magnetic effects on an electronic spectrum are determined

not only by the orbital angular momentum but by the spin angular momen-

tum as well. The spin of an electron also induces a magnetic dipole, whose

value is similar to equation 16.7, but because spin angular momentum is non-

classical, there is another term in the expression. The spin magnetic dipole m

has a magnitude m(not to be confused with the quantum number for the

zcomponent of orbital angular momentum of

mge



BS (16.10)

where geis a pure number (that is, no units) called the electron g factorand

equals 2.002319304 ...for a free electron.It is slightly different for bound elec-

trons, but not enough for concern at this point. It is almost equal to exactly 2

(and is sometimes approximated as 2), and the reasons it is not exactly 2 are

perhaps worth researching on your own. Regardless, the gfactor is a necessary

addition in order to explain the effects of electron spin and its magnetic dipole.

For nonsinglet states,allof the good quantum numbers—J,S,L, and MJ—

affect the change in energy of the electronic energy levels. However, because

the pattern of the changes is more complicated, the effect of a magnetic field

on nonsinglet electronic states is called the anomalous Zeeman effect.The

change in the electronic energy levels due to the imposition of a magnetic field

of strength Bis given by

EmaggJBMJB (16.11)

where gJis called the Landé g factor.It depends on J,L, and Sand is related to

geby the expression

gJ (^1) (ge1) (16.12)
To a very, very good approximation,ge 1 1, so equation 16.12 is some-
times written as
gJ (^1) J(J^ 1)^ S(S^ 1) L(L^ 1) (16.13)
2 J(J 1)

J(J 1) S(S 1) L(L 1)



2 J(J 1)

566 CHAPTER 16 Introduction to Magnetic Spectroscopy