Readings:
Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics (Dec 2003, Physics Today)
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S-G experiment’s historic importance, not just for spin, but applications extending to probing galaxies and
imaging brains!
Stern was the first pupil of Einstein, interested in light quanta. Did NOT like the Bohr model of spatially
quantized electron orbits (Bohr model, 1913). Later, as assistant to Born, became interested in molecular
beam experiments because they were a simple way to measure atomic properties. Used them to
accurately measure the mean free path of silver atoms in air by looking at the difference in the deflection
of the beam when rotating the beam CW and CCW.
Stern: wanted to do the (now-known as) S-G experiment to test the Bohr model
Gerlach was interested in the photoelectric effect, also conducted beam experiments but wanted to
deflect them in strongly inhomogeneous fields to look for diamagnetism, so set out to create a very high
experimental field gradient.
Gerlach: “No experiment is so dumb that it should not be tried”
Bohr orbits assume discrete spatial orientations with respect to an external field
Pauli appealed to the idea of spatial quantization to make sense of the anomalous Zeeman effect (splitting
of atomic spectral lines in presence of static magnetic field)
Born: “space quantization was a kind of symbolic expression for something which you don’t understand
Debye: “But surely you don’t believe that the spatial orientation of atoms is something physically real”
As of 1922: Bohr model, idea of spatial quantization was out there but questioned, people questioning
Bohr model and spatial quantization not satisfactorily explaining anomalous (newly observed) Zeeman
effect
Stern realized that if the silver atoms had angular momentum (presumed to be +/- h/2pi depending on
orientation) they would be deflected dependent on their orientation, so the S-G experiment would test
Bohr model
Experiment: 0.1 T magnetic field strength with 10 T/cm gradient (huge!), splitting of 0.2 mm, so any
misalignment by more than 0.01mm would ruin the experiment – took well over a year
Did not observe deposits of the silver atoms on the film (so few) until cheep cigar smoke (with lots of
sulfur) got on the plates, turning the silver to more visible silver sulfide
Ran out of funds – Goldman (of Goldman Sachs) sent a check to allow further work
Ran out of ideas – railroad strike delayed Gerlach’s journey giving him a day to re-think the experiment
and make it work successfully
Observed splitting in 1022, sent famous postcard to Bohr telling him his theory is confirmed
Experiment was immediately accepted as among the most compelling evidence for quantum theory
(specifically spatial quantization)
Einstein and Ehrenfest questioned the results – said that they start with random orientations, so the
distribution should be spread out, not split
1925, intrinsic spin was postulated, but not connected to the S-G experiment because people still thought
the S-G results were consistent since they thought silver atoms had non-zero L
1927, found that ground state of silver has L=0, not h/2pi as initially thought!!
Re-interpretation of the S-G results as direct experimental evidence for intrinsic spin
Stern later helped discover the anomalous magnetic moments of proton and deuteron in 1933, leading to
the understanding that they have internal structure
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Gerlach later made the first accurate measurements of radiation pressure showing it is proportional to
light intensity and independent of light wavelength
“spin”: from Wikipedia.org
 spin is a fundamental characteristic property of elementary particles, composite particles (hadrons), and
atomic nuclei.
 The spin of an elementary particle is a truly intrinsic physical property, akin to the particle's electric charge
and rest mass
 results in the Pauli exclusion principle, which in turn grounds the periodic table of chemical elements. The
spin direction (also called spin for short) of a particle is an important intrinsic degree of freedom
(quantum number)
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Wolfgang Pauli was the first to propose the concept of spin, but he did not name it. In 1925, Ralph Kronig,
George Uhlenbeck, and Samuel Goudsmit suggested a physical interpretation of particles spinning around
their own axis. The mathematical theory was worked out in depth by Pauli in 1927.
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spin was originally conceived as the rotation of a particle around some axis. This picture is correct
in so far as spins obey the same mathematical laws as do quantized angular momenta. On the other
hand, spins have some peculiar properties that distinguish them from orbital angular momenta:
Spin quantum numbers may take on half-integer values; The spin of a charged particle is
associated with a magnetic dipole moment with a g-factor differing from 1. This is incompatible
with classical physics, assuming that the charge and mass of the particle are distributed evenly in
spheres of equal radius.
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Particles with spin can possess a magnetic dipole moment, just like a rotating electrically charged body in
classical electrodynamics. These magnetic moments can be experimentally observed in several ways, e.g.
by the deflection of particles by inhomogeneous magnetic fields in a Stern–Gerlach experiment, or by
measuring the magnetic fields generated by the particles themselves.
“g-factor” (gyromagnetic ratio): from Wikipedia.org
 A g-factor (also called g value or dimensionless magnetic moment) is a dimensionless quantity which
characterizes the magnetic moment and gyromagnetic ratio of a particle or nucleus. It is essentially a
proportionality constant that relates the observed magnetic moment μ of a particle to the appropriate
angular momentum quantum number and the appropriate fundamental quantum unit of magnetism,
usually the Bohr magneton or nuclear magneton.
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There are three magnetic moments associated with an electron: One from its spin angular momentum,
one from its orbital angular momentum, and one from its total angular momentum (the quantummechanical sum of those two components).
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The most famous of these is the electron spin g-factor, gS (more often called simply the electron
g-factor, ge), defined by
where μS is the total magnetic moment resulting
from the spin of an electron, S is the magnitude of its spin angular momentum, and μB is the Bohr
magneton.
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The value gS is roughly equal to 2.002319, and is known to extraordinary accuracy.[1][2] The reason it is not
precisely two is explained by quantum electrodynamics.
the electron g-factor is one of the most precisely measured values in physics, with its uncertainty
beginning at the twelfth decimal place. NIST values: Electron ge -2.002 319 304 3622, uncertainty: 0.000
000 000 0015