Stern-Gerlach experiment ↩

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created: 2022-01-06 08:22:04
modified: 2022-01-10 04:13:04

In the experiment, an atomic beam traverses an inhomogeneous magnetic field. In the normal Zeeman effect, we saw that the interaction term of the Hamiltonian operator is:

Where is the angular momentum operator and is the magnetic moment:

Based on this, since the Hamiltonian gives the energy, the force acting on the atom is:

Here we assumed that the magnetic field is approximately parallel to the direction.

From the preceding, one would expect a splitting into an odd number of beams . The experiment was carried out by O. Stern and W. Gerlach in 1922 with silver atoms. Silver has a spherically symmetric charge distribution plus one -electron. This, the total angular momentum of silver is zero, i.e., ; no splitting should occur. If the electron from the fifth shell were in a -state, one would expect a splitting into three beams . The experiment gives a splitting into two beams. Consequently, the electron must possess an internal angular magnetic momentum (spin) with corresponding gyromagnetic ratio .