Physical Chemistry , 1st ed.

For atoms, four quantum numbers describe the energy of an electron:n,,

m, and ms. (All electrons have s^12 .) For multielectronic atoms, however,

there are more accurate quantum numbers, as explained in the last chapter:J,

L,ML, and MS. The type and magnitude of Zeeman splitting depends on the

possible values of certain of these quantum numbers.

If the electronic transitions involved in an allowed transition are singlet

states(remember that for allowed transitions, S0), then magnetic effects

on electronic spectra are determined exclusively by the orbital angular mo-

mentum, not the spin angular momentum. What is observed is the normal

Zeeman effect:transitions are split as each Lstate separates into its 2L 1 pos-

sible different MLvalues. This is illustrated for a^1 S →^1 P transition in Figure

16.6. The single transition that occurs without a magnetic field is split into a

triplet of lines when a magnetic field is turned on. The selection rules are the

same as for electronic transitions in multielectron atoms:

L0, 

1

S 0

J0, 

1

ML0, 1(but ML 0 →ML0 if J0) (16.8)

The final exception (ML0 does not change to a different state where MLalso

equals 0 if J0) derives from the exact symmetry properties of the wave-

functions (as do all selection rules). Figure 16.6 is relatively simple, since only

one of the states, the excited state, is splitting. The amount of the splitting—

that is, the change in the energy of the state upon turning on the magnetic

field—depends on the strength of the magnetic field Band the value of the

z-component quantum number MLand is given by

EmagBMLB (16.9)

Since MLcan have positive or negative values or even be 0, the change in the

energy can be positive, negative, or even zero.

Example 16.4

Calculate the splitting due to a magnetic field of 2.0 T on a^1 S →^1 P transi-

tion. Assume that only the^1 P state will split. (Why?)

Solution

The^1 S state will not split because it has L0 and so only ML0. However,

the^1 P state will split due to the presence of degenerate ML1, 0, and 1

states. According to equation 16.9,

Emag[ML1] (1)(9.274  10 ^24 J/T)(2.0 T) 1.855  10 ^24 J

The Evalue in this case is negative.Convert this into units of cm^1 (using

units of cm/s for the speed of light):

0.9338 cm^1

The energy of the transition decreases by just under one wavenumber due

to the presence of the magnetic field. Emag[ML0] will be zero because

ML0. The Emag[ML1] will have the same magnitude as the

1.855  10 ^24 J



(6.626  10 ^34 Js)(2.9979  1010 cm/s)

16.3 Zeeman Spectroscopy 565

ML   1

ML   1

ML  0

B  0



Spectrum:

Energy

(^1) P
(^1) S
B  0

Spectrum:
Energy
(^1) P
(^1) S
Figure 16.6 An example of the normal
Zeeman effect. The^1 S →^1 P electronic transition
is split into a triplet as a magnetic field separates
the individual MLlevels in the^1 P excited state.