Instructors_Guide_Ch40

# The classical probability density increases as the

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The classical probability density increases as the particle speed decreases. Thus the wave function amplitude increases as K = E U decreases. The wave function penetrates into classically forbidden regions, where it decreases to zero exponentially. In addition, students should be aware that the Bohr idea of photon emission and absorption via quantum jumps is part of the overall framework of quantum-mechanical thinking. Quantum-mechanical tunneling is an important application that you’ll want to emphasize. All students will have seen images from a scanning tunneling microscope, so this is a good “hook” for showing the relevance of quantum physics. You’ll want to note that the wave-like properties of matter give it “fuzzy edges,” and this is how there can be a finite probability of a “particle” being in a classically-forbidden region. Arguments that tunneling is consistent with the uncertainty principle, as found in more advanced treatments, are too subtle for students at this stage. Using Class Time These last few chapters will be somewhat more lecture oriented. Even so, you should make every opportunity to include reasoning and graph interpretation exercises such as those found in the Student Workbook . It’s important to go slowly enough that students can ask questions and the many new ideas can sink in. Hence three days are recommended. DAY 1: The text “justifies” the Schrödinger equation, so there’s no need to repeat that during class. It’s better to start by reviewing potential energy diagrams and having students do a few Chapter 10 exercises in which they identify turning points, regions where the particle speeds up or slows down, and so on. Students must be fluent at interpreting potential energy diagrams in order for this chapter to make sense. Then consider what kind of potential energies would describe various microscopic situations. For example, Draw the 1/ r potential energy of a hydrogen atom. Note that this is what you mean by the potential-energy function of an atomic particle. Then note that this example is too complex to start with and defer it to the next chapter. Consider the molecular bond of a HBr molecule. In this case, the bromine atom is so massive that you can “model” the molecule as a hydrogen atom on a spring. Then remind students of the potential energy diagram of a spring.

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40-4 Instructor’s Guide Comment that our understanding of the nucleus is that protons and neutrons are more-or-less “free particles” inside the nucleus, but that very strong nuclear forces prevent them from leaving the nucleus. (Rather like the work function for an electron trying to leave a metal.) Walk them through seeing how this can be “modeled” as a finite square-well potential energy.
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