Archive for February, 2010

Feb 21 2010

Stern-Gerlach Experiment

Published by under Quantum Mechanics

In the Stern-Gerlach experiment, originally performed in 1922, vaporized silver atoms in a high temperature oven are allowed to leave through a small opening, some then passing through a collimating slit so as to travel in a straight line along a horizontal axis.  Next in the path of the silver atoms is created a magnetic field, symmetrical with respect to the yOz plane ([1], Figure 1, pg 388) and having a significant gradient in the z direction which is perpendicular to the surface of the earth.  Beyond the magnetic field in the path of the silver atoms is placed a condensing surface which in the original experiment was a cold metallic plate.  The whole apparatus is placed inside a high vacuum.

The electron configuration of silver is [Kr] 5s1 4d10, with the outer 5s electron giving silver a quantized magnetic moment of one Bohr magneton, μb.  Straight from the periodic table, silver atoms are of neutral charge, so there is no Lorentz force on the atoms passing through the magnetic field.  The only force involved is

Fz = μz ∂Вz/∂z = – ( μb ∂Вz/∂z ) cos θ,

where θ is the angle between the z axis and the magnetic dipole moment of each atom, the group of which, in a time interval, would be expected, according to Quantum Mechanics texts, to race through the magnetic field of the apparatus oriented isotropically, and a continuous vertical pattern to condense on the plate.  Instead, what happens is that half of the atoms condense at the upper bound, and half at the lower bound, with none condensing in between.  Instead of a statistical pattern centered on the y axis, there are two patterns, centered at each of the expected upper and lower bounds, N1 and N2 ([1], Figure 3, pg 391).  The width of each of the two separate spots “corresponds to the effect of the dispersion of the velocities and of the width of the slit F” ([1], A.1.c., pg 391).  Evidently, there are only two discrete forces acting on the atoms as they traverse the magnetic field:

Fz = ± μb ∂Вz/∂z                                       [2], pg 525

Sz “is a quantized physical quantity whose discrete spectrum includes only two eigenvalues. … these eigenvalues are + ћ/2 and – ћ/2” ([1], A.1.c., pg 392).

One thing that puzzles me about what is found in text books is the classically expected pattern of the Stern-Gerlach experiment.  Since silver atoms are paramagnetic, I don’t understand why it would not have its center skewed off the y axis in the z direction.  Nevertheless, it is the quantum result, not the classically expected (which doesn’t happen anyway), that I would like to make an attempt at explaining.

What appears to be happening here is that the nuclei of the free silver atoms make effort to line up with the gravitational field in one of two spin orientations, in order to minimize energy, and to aid in the pass through of the gravitons that are not absorbed, which help pump nuclear spin.  Additionally, the orbiting electrons make effort to get out of the way of the highest flux density of gravitons, making orbital angular momentum also aligned as much as possible with the z axis, and monitored in two patterns, mirror images of each other, each relating to one orientation of the nucleus.


[1] Cohen-Tannoudji, Dui, Laloë, Quantum Mechanics, Hermann, 1977, Paris, France, Chapter IV

[2] Liboff, Richard L., Introductory Quantum Mechanics, Fourth Edition, Addison Wesley, 2003

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