Page 37 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

28 The wave function

silver atom is found only in one of two orientations, either parallel or
antiparallel to the magnetic ®eld gradient, even though the magnetic moments
of the atoms are randomly oriented when they emerge from the oven. Thus, the
possible orientations of the atomic magnetic moment are quantized, i.e., only
certain discrete values are observed. Since the direction of the quantization is
determined by the direction of the magnetic ®eld gradient, the experimental
process itself in¯uences the result of the measurement. This feature occurs in
other experiments as well and is characteristic of quantum behavior.
If the beam of silver atoms is allowed to pass sequentially between the poles
of two or three magnets, additional interesting phenomena are observed. We
describe here three such related experimental arrangements. In the ®rst
arrangement the collimated beam passes through a magnetic ®eld gradient
pointing in the positive x-direction. One of the two exiting beams is blocked
(say the one with antiparallel orientation), while the other (with parallel
orientation) passes through a second magnetic ®eld gradient which is parallel
to the ®rst. The atoms exiting the second magnet are deposited on a detection
plate. In this case only one spot is observed, because the magnetic moments of
the atoms entering the second magnetic ®eld are all oriented parallel to the
gradient and remain parallel until they strike the detection plate.
The second arrangement is the same as the ®rst except that the gradient of
the second magnetic ®eld is along the positive y-axis, i.e., it is perpendicular to
the gradient of the ®rst magnetic ®eld. For this arrangement, two spots of silver
atoms appear on the detection plate, one to the left and one to the right of the
vertical x-axis. The beam leaving the ®rst magnet with all the atomic magnetic
moments oriented in the positive x-direction is now split into two equal beams
with the magnetic moments oriented parallel and antiparallel to the second
magnetic ®eld gradient.
The third arrangement adds yet another vertical inhomogeneous magnetic
®eld to the setup of the second arrangement. In this new arrangement the
collimated beam of silver atoms coming from the oven ®rst encounters a
magnetic ®eld gradient in the positive x-direction, which splits the beam
vertically into two parts. The lower beam is blocked and the upper beam passes
through a magnetic ®eld gradient in the positive y-direction. This beam is split
horizontally into two parts. The left beam is blocked and the right beam is now
directed through a magnetic ®eld gradient parallel to the ®rst one, i.e., oriented
in the positive x-direction. The resulting pattern on the detection plate might be
expected to be a single spot, corresponding to the magnetic moments of all
atoms being aligned in the positive x-direction. What is observed in this case,
however, are two spots situated on a vertical axis and corresponding to atomic
magnetic moments aligned in equal numbers in both the positive and negative