Suppose that the channel’s outgoing end is in the hydrogen l=0Stem-Gerlach apparatus of the figure. You place a second such apparatus whose channel is aligned with the first but rotated 90°about the x-axis, so that its B –field lines point roughly in the y-direction instead of the. What would you see emerging at the end of your added apparatus? Consider the behavior of the spin-up and spin-down beams separately. Assume that when these beams are separated in the first apparatus, we can choose to block one or the other for study, but also assume that neither deviates too far from the center of the channel.

Short Answer

Expert verified

The one that emerges at the end of the added apparatus will be a beam with either a left-pointing or right-pointing spin.

Step by step solution

01

Stern-Gerlach experiments.

The Stern-Gerlach experiment provides the demonstration for the quantization of the spatial orientation of the angular momentum, in this experiment a silver atom is used which is made to go through a spatially varying magnetic field.

02

The one that emerges at the end of added apparatus.

In the experiment, each atom is not in a specific dipole up or down until it passes through the magnet that will measure its state with equal probability. Once the state is filtered, either it is dipole upstate or dipole downstate, not in a single left state.

So, when the beam is passed through the second apparatus. It is divided into two beams, depending on whether the second measuring process results in measuring a left-pointing or right-pointing spin.

Conclusion: Therefore, The one that emerges at the end of the added apparatus will be a beam with either a left-pointing or right-pointing spin.

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Here we consider adding two electrons to two "atoms," represented as finite wells. and investigate when the exclusion principle must be taken into account. In the accompanying figure, diagram (a) shows the four lowest-energy wave functions for a double finite well that represents atoms close together. To yield the lowest energy. the first electron added to this system must have wave function Aand is shared equally between the atoms. The second would al so have function Aand be equally shared. but it would have to be opposite spin. A third would have function B. Now consider atoms far a part diagram(b) shows, the bumps do not extend much beyond the atoms - they don't overlap-and functions Aand Bapproach equal energy, as do functions Cand D. Wave functionsAandBin diagram (b) describe essentially identical shapes in the right well. while being opposite in the left well. Because they are of equal energy. sums or differences ofandare now a valid alternative. An electron in a sum or difference would have the same energy as in either alone, so it would be just as "happy" inrole="math" localid="1659956864834" A,B,A+B, orA- B. Argue that in this spread-out situation, electrons can be put in one atom without violating the exclusion principle. no matter what states electrons occupy in the other atom.

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