University Physics Notes: Quantum Mechanics – The Stern Gerlach Experiment
An electron, being a particle with an associated magnetic moment, may be pictured as a little spinning top. In the presence of a magnetic field this magnetic moment will align with the field in one of two ways – either spin up or spin down. The quantization of this spin magnetic moment was first observed in 1920 by Otto Stern and Walter Gerlach.
Atoms of silver from the source, a silver furnac shown at the left hand side of the diagram below, emerged, passed through the slits to form a narrow beam and passed through a non uniform magnetic field formed by two specially shaped magnets, onto a photographic plate.
Using classic physical laws we would
expect a single continuous line up the photographic plate, as the
electron spin would classically be oriented in all directions, with
the atom experiencing a force
where
is
the component of the magnetic dipole
oriented
along the
-
axis and
is
the gradient of the magnetic field, which is of course, oriented
along the
–
axis.
In atoms usually the electrons are
located in such way that electrons are paired – spin up paired with
spin down so that there is no net spin, but in the silver atom there
is an electron in the outermost shell will no other electron to pair
with so the silver atom as a whole has a net spin due to this
electron. The atoms are separated into two beams of atoms – one
beam of which has the aforesaid electron with spin oriented up and
one which has spin oriented down.
In 1927 Phipps and Taylor
conducted a similar experiment. This time they used atoms of
hydrogen, not silver. They also observed that the beam of atoms
undergoes splitting into two ones.
Later scientists conducted
experiments using other atoms which have only one electron on the
outer shell (cooper, gold, sodium, potassium). Every time there were
two lines achieved on the photographic plate.
Of course in the atom not only
electrons have spin. The elements of the nucleus also have it. But
protons and neutrons are much more heavier than electrons (about 1836
times), and the magnetic dipole moment is inversely proportional to
the mass. So the proton's and neutron's magnetic dipole momentum is
much smaller than the one of the whole atom. This small magnetic
dipole was later measured by Stern, Frisch and Easterman.