Biomedical Engineering Reference
In-Depth Information
0.005
0.02
0.009
0.013
0.016
0.02
0.024
0.016
0.013
0.001
80
0.024
0.009
-0.003
-0.003
0.005
-0.006
-0.006
0.001
0.02
0.016
0.013
0.005
0.001
0.009
60
-0.01
-0.01
-0.006
-0.003
-0.006
-0.003
-0.01
-0.01
0.001
40
0.009 0.013
0.016
0.02
0.005
0.001
-0.006
-0.006
0.005
0.024
-0.003
-0.003
0.009
20
0.024
0.001
0.013
0.016
0.009
0.005
0.013 0.016
0.02
0
0
20
40
60
80
Figure 13.7
Hydrogen 3d
zz
orbital
It is easy to demonstrate from classical physics that a particle with mass
M
, charge
Q
and angular momentum
l
is a magnetic dipole:
Q
2
M
l
p
m
=
(13.33)
According to Bohr's model of the hydrogen atom, the allowed electron orbits each had
an angular momentum that was an integral multiple of
h
/2π . Since magnetic dipoles are
linked to angular momentum, the possibility arises that if we could measure the mag-
netic dipole moments of individual atoms we could investigate the quantization of angular
momentum. In the presence of an external magnetic field, the bar magnet will take up one
of its possible alignments with the axis of quantization (the direction of the magnetic field
lines).
Stern and Gerlach (1921) performed the first and most famous experiment designed to
investigate the quantization of angular momentum. Whilst the force on a magnetic dipole is
zero in a uniformmagnetic field, the force is not zero for a
nonuniform
field. It is difficult to
hang a single atom between the poles of a magnet, so a beam of atoms was passed through
such a field and the deflection of the beam measured.
