DIRECT  EVIDENCE  OF MOMENTUM:  THE  STERN  GERLACH EXP ERIMENT

One of the great experiments in quantum physics, the Stern Gerlach experiment, showed that angular momentum was indeed quantized and could be described by an integer quantity (i.e., it could only assume certain, allowed, values).  That energy levels are quantized (in the Franck Hertz experiment), but the properties of angular momentum are also important to understand. This is certainly an important feature since our application of angular momentum to electron energy levels requires this to be a quantized quantity.

Figure 1.1. Stern Gerlach experiment.

      The original experiment, depicted in Figure 1.1, involved the deflection of a beam of neutral silver atoms emerging from a hot oven via a magnetic field and onto the target of a photographic plate. Silver atoms were used since the outer electron, like that of a hydrogen atom, has no angular momentum (an S orbital with l = 0), so no interaction with an external magnetic field would be expected. The beam of atoms was directed through an inhomogeneous magnetic field whose field could be varied and directed toward a photographic plate, where it could be detected. When no magnetic field is applied, the beam appears as a line on the plate. Thinking classically, one would expect that the spinning outer electron (spinning like an orbiting satellite) acts as a dipole that has a magnetic moment.

      When a magnetic field is applied to the beam, the expectation is that this dipole can have any orientation, and hence the deflection of these atoms by the applied magnetic field will be in all orientations, producing a continuous range of deflections. The results of the actual experiment show that the beam was deflected into two discrete areas with no regard to the intensity of the magnetic field applied. If the magnetic field was above a certain threshold, it caused the deflection to occur in these two discrete areas; magnetic fields below this threshold value caused no deflection to occur.

      At the time it was a startling fact that the electron interacted with the magnetic field at all. This outer electron has no angular momentum and so does not possess a magnetic moment (caused by a current loop in classical analogy). The implication is that the electron has an intrinsic momentum (as opposed to an orbital momentum). This new type of angular momentum, called spin, is so named because an electron spinning on its axis would create a magnetic moment for which there would be two natural values for clockwise and counterclockwise rotation. Further evidence of spin is provided by the fact that the deflection occurred in only two areas. Orbital angular momentum occurs in integrals of 2l+ 1 states (since there are that many states of m_l for each value of l). One would then expect to see 2l+1 discrete areas in the pattern, not two. It appeared that this new type of angular momentum, spin, occurred in quantized units of ½.