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GR9677 #11
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Problem
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Atomic }Stern-Gerlach
Recall the Stern-Gerlach experiment, where (in its original set-up) a beam of neutral silver atoms are sent through an inhomogeneous magnetic field. The beam's split into two---classically, from the Lorentz force, one wouldn't expect anything to happen since all the atoms are neutral, but if one accounts for the Larmor precession, one would expect the beam to be deflected into a smear. Instead, however, the beam deflects into  beams, and thus this supports the idea that electrons are of spin-1/2. (Ag has one unpaired electron in its  orbital.)
With a beam of hydrogen atoms, one should also get a split into two, since  from the electron.
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Comments |
PorcelainMouse
2008-11-07 12:11:16 | http://en.wikipedia.org/wiki/Stern-Gerlach |  | caffeinated
2008-04-09 15:39:26 | So why verticle? Is it because the spin axis aligns up or down with the field?
wakkadojo
2008-09-04 17:58:23 |
The idea is that the vertical  axis is arbitrary. Furthermore,  . Thus the arbitrary magnetic component, in this case it can be observed parallel to the localized magnetic field, either forces the atom up or down. This is where the inhomogeneous magnetic field matters: the different spins will have different magnetic dipoles, thus if the magnetic field is inhomogeneous then the dipole will not experience a symmetric, self-canceling force, causing the beam to split into two dipole classes (i.e.  ).
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wakkadojo
2008-09-04 18:23:23 |
The idea is that the vertical axis is arbitrary. Furthermore, . Thus the arbitrary magnetic component, in this case it can be observed parallel to the localized magnetic field, either forces the atom up or down. This is where the inhomogeneous magnetic field matters: the different spins will have different magnetic dipoles, thus if the magnetic field is inhomogeneous then the dipole will not experience a symmetric, self-canceling force, causing the beam to split into two dipole classes (i.e. ).
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wakkadojo
2008-09-04 18:33:24 |
The idea is that the vertical axis is arbitrary. Furthermore, . Thus the arbitrary magnetic component, in this case it can be observed parallel to the localized magnetic field, either forces the atom up or down. This is where the inhomogeneous magnetic field matters: the different spins will have different magnetic dipoles, thus if the magnetic field is inhomogeneous then the dipole will not experience a symmetric, self-canceling force, causing the beam to split into two dipole classes (i.e. ).
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| | tareq
2007-09-26 06:35:02 | Waht about the spin of the proton ?
kyros
2007-11-02 18:47:02 |
I wondered that too - the reason we don't count it is that it's a small deviation, the gyromagnetic ratio of the proton is much much lower, and hence so is the magnetic moment of the proton, hence the hamiltonian only changes slightly due to proton spin, when compared to the electron.
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