Biomedical Engineering Reference
In-Depth Information
A schematic diagram of the Stern-Gerlach equipment is shown in Figure 13.10. A beam
of atoms is produced in an oven, and they pass through a collimating slit and often a
velocity selector in order to form a mono-energetic beam. They then travel in the
x
direction
through a long, powerful electromagnet whose pole pieces are deliberately shaped to give a
nonuniform magnetic field in the
z
direction. Detailed analysis shows that the force on the
magnetic dipoles in the
z
direction is given by a force proportional to the
z
component of the
magnetic dipole moment (and hence the
z
component of the angular momentum vector):
p
m,
z
∂
B
z
∂
z
F
z
=
(13.34)
It is a difficult experiment to perform satisfactorily, for the atoms collide with each other
in the beam and so distort the result. An essential part of such an
atomic beam
apparatus
is that there should be a good vacuum system, and very low beam intensities have to be
used. Despite the experimental difficulties, the findings were positive; the atom beam was
shown to split on passage through the magnetic field and this confirmed the quantization
of angular momentum.
Slit
N
beam
Oven
S
Detector
z
x
Figure 13.10
Stern-Gerlach experiment
13.9 Electron Spin
The first experiments were made with silver atoms. The surprising result of the Stern-
Gerlach experiment was not that the beam split, but that it split into two components, with
a different separation than that expected. Similar results were obtained for copper and gold,
and in later work for the alkali metals and for hydrogen atoms. The point is that an atomic
dipole moment characterized by quantum number
l
should show 2
l
1 orientations with
the magnetic field. Since the quantum number takes values 0, 1, 2, ...there should always
be an odd number of orientations and hence the atom beam should split into an odd number
of components.
The explanation came in 1925, when Goudsmit and Uhlenbeck (1925) analysed the
splittings of spectral lines occurringwhen atoms are subject to an externalmagnetic field (the
Zeeman effect
). They showed that the measured splittings could be explained if electrons
were postulated to have an intrinsic magnetic moment, in addition to the one they acquired
by motion about the atomic nucleus. In order to explain the experimental results, they
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