Stern-Gerlach Experiment - I
Stern-Gerlach experiment was designed to study the magnetic properties of electrons. It showed that magnetically, the electrons can have only two orientations.
Visualising the set up
Image Credit: Wikipedia (By Tatoute - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=34095239)
A furnace emits silver atoms which pass through a series collimaters to produce a fine beam. These atoms then pass through a magnetic field created by two magnets whose opposite poles are facing each other. The north magnet has a vee-shaped edge which makes it more powerful than the other. Since silver atoms have act as magnets (more on this later), they are deflected by the magnetic field. After passing through the apparatus, the atoms are collected on a screen.
Experiment with normal magnets (thought experiment)
Stern-Gerlach experiment was carried out with silver atoms. However, to appreciate the significance of the results, we first have carry out the experiment with normal magnets. This, obviously, is a thought experiment.
Imagine that we have managed to create a beam of bar magnets to pass through the magnetic field in the experiment. These are normal bar magnets with which kids love to play. They enter the field in various orientations. Some of them could be perfectly vertical with their south pole closer to the top magnet and north pole closer to the bottom magnet. Some of them might be in opposite orientation with their north poles closer to the top magnet, and south poles closer to the bottom magnet. Some of them could be perfectly horizontal i.e. parallel to the beam. Some of them could be oriented in such a way that they are neither vertical or horizontal. For example, the north pole of a magnet could make an angle of 45 degree with respect to the beam. Figure below shows some of the possible orientations.
When these magnets pass through the magnetic field, they experience a force and get deflected. The magnitude of the force, and hence deflection, depends on the orientation of the magnet. Magnets that vertical to the beam direction experience maximum force, and those that are horizontal experience minimum force (zero). In other words, magnets that are horizontal are not deflected at all, while those that are vertical experience maximum deflection.
Suppose a magnet is aligned vertically with its south pole towards the top magnet. Since opposite poles attract, the magnet is pulled by both the top and bottom magnets. But, our flying magnet is deflected upwards because the magnet at the top is more powerful.
Now, consider a magnet in opposite orientation – its north pole towards the top magnet and south pole towards the bottom magnet. Since like poles repel, our flying magnet is repelled by both the magnets as it passes between them. Eventually, it will be deflected downward as the top magnet exerts larger repulsive force than the bottom one. The vertically oriented magnets also define the boundaries of deflection. Deflection experienced by a magnet in any other orientation will be less than that experienced by a magnet in vertical orientation.
In summary, a large number of bar magnets with random orientations experience different amounts of deflection as they pass through the field. They trace left by these magnets on the screen is a straight vertical line.
Experiments with silver atoms
Before moving onto the actual experiment, we have to learn a bit about the silver atom itself. Silver atom has 47 electrons distributed across five orbits. The first orbit has two electrons, second eight, third and fourth 18 each, and the fifth one. (I should learn why the last electron was moved to the fifth orbit but not accommodated in the fourth orbit itself. Note that the the fourth orbit can accommodate upto 32 electrons.)
Each of these electrons generate magnetic fields as they move around the nucleus. However, for electrons in the first four orbits, the magnetic fields cancel out because each electron has another electron that is rotating in the opposite direction. The lone electron in the fifth orbit is not paired, and hence produces a net magnetic field. Hence, the silver atom is analogous to a little magnet with north and south poles.
It is worth noting that the magnetic field observed in the silver atom is effectively due to the unpaired in the fifth orbit. Therefore, silver atom provides a great opportunity to study the magnetic properties of the electron itself1.
Let’s come back to our experiment now. As usual, we send the silver atoms through the magnetic field which get deflected according to the their orientation. Our intutuion tells us that these atoms leave a continuous trace just like the bigger magnets. However, what we actually see in the experiment is totally different: we see just two groups of traces at the extreme deflection points. This is indeed astonishing because it means that our tiny magnets can have only vertical orientations. If the north pole is up, then the atom is deflected downward, and if the south pole is up, the atom is deflected upward. Nature, clearly has forbidden all other orientations for these tiny magnets.
It is worth stressing again that the actual magnet here is the electron. Therefore, the insights provided by the Stern-Gerlach experiment are about the electron itself even though silver atoms are used in the experiment.
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In fact, the nucleus also contributes to the magnetic field of the silver atom, but its contribution is negligible. ↩