Download The Zeeman Effect

CHEM 342
WINTER 2008-09
The Zeeman Effect
In 1908 P. Zeeman reported his discovery that atomic spectral lines split into multiplets when the atoms
are placed in a magnetic field. A high-resolution spectrometer and/or a very strong magnet are needed
to observe the effect since the splitting is normally only about 0.5 cm-1/T (1 tesla = 104 gauss). Studies
based on the magnetism of electronic and nuclear quantum states are enormously important in modern
chemistry; applications include NMR and ESR spectroscopy.
Quantum theory nicely explains Zeeman's observation. There is an intrinsic magnetism associated with
both the orbital and the spin angular momenta of an electron. The orbital magnetic moment in the zdirection (µz) is directly proportional to the orbital projection quantum number ml:
µz = !
eh
m l = !µB ml
2me
(1),
where the collection of constants denoted µ B and called the Bohr magneton has the value 9.27 x 10-27 J/T.
The corresponding moment due to spin is proportional to ms and has an extra factor of approximately
two due to the theory of relativity:
µ z = !g e µ B m s = !2.002 µ B m s
(2)
The same expressions, but with ml and ms replaced by ML and MS, apply to the combined magnetic
moments of several coupled electrons. When an atom has L≠0 and S≠0, these net magnetic moments are
simply additive. Spin-orbit coupling (itself a magnetic effect) is usually large enough that the total
electronic angular momentum, J, and its projection, MJ, are better overall labels for the atomic states.
In the absence of external fields, MJ states are degenerate. For example, in the first-excited state of atomic
barium, 1P1, the MJ = +1, 0, and -1 states all have the same energy. This means that the J vector has no
preferred orientation in space. If a field (B) is applied along the laboratory-defined +z-direction,
however, the atom's J vector prefers to be oriented in the opposite direction, and the energies of the MJ
states change according to the expression
E M J = !µ z B z = + µB B z (ML + g e M S )
(3).
Now consider the affect of the applied field on the spectrum of atomic barium. Barium exhibits a strong
emission line at 535.5 nm due to the 1P1 → 1S0 transition. Note that the ground state, 1S0, is nondegenerate. Since S = MS = 0, J = L and MJ = ML. The spectral line splits into a triplet as shown in Fig. 10.8
of Silbey, Alberty, and Bawendi.
A further interesting feature of the Zeeman effect is that the light emitted from different M states is
polarized differently. This may be observed simply by viewing the light through a polarizing filter. Leftor right-circular polarization of the light arises because photons, which obey Bose-Einstein quantum
statistics, have angular momentum of ± h, and total angular momentum must be conserved during an
absorption or emission event.