Instructors_Guide_Ch40

# The particle in a capacitor can be left for reading

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The particle in a capacitor can be left for reading, but it’s worthwhile to spend a few minutes on the simple model of a covalent bond. Chemistry classes always describe bonding as the “sharing” of electrons, but this doesn’t make much sense when thinking of electrons as classical particles. Now, by doing elementary but “real” quantum mechanics, we can put forward a simple explanation of bonding. The second half of day 3 can be spent on tunneling. Students find this mysterious but very interesting—like something from Star Trek! End-of-chapter Problem 44 on the scanning tunneling microscope could be worked as an in-class example if you’re not going to assign it. Comment that

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40-6 Instructor’s Guide tunneling can be important even if the tunneling probability per electron is extremely small. This is due, of course, to the very large number of electrons. Alternatively, you could use a simple model of alpha decay as an example of tunneling. This can be motivated by noting the number of times the text has referred to experiments that use alpha particles. After reminding them of the potential energy diagram for a neutron, from day 2, note that two protons and two neutrons often clump together as a “single particle” because they form such a stable structure. This particle has a relatively constant potential energy while inside the nucleus and a positive 1/ r Coulomb potential energy outside. You can sketch the correct potential energy, and then propose a model potential energy shown below for which they can do the tunneling calculation. A 10 MeV alpha in the model potential well shown below has a tunneling probability P 5 × 10 20 , so it can be expected to tunnel, on average, after 2 × 10 19 collisions with the wall. The 60 MeV kinetic energy inside the nucleus gives a transit time across the nucleus of 1.5 × 10 22 s, leading to an estimated decay time of 3 ms. x 8 fm 8 fm 8 fm 10 MeV 50 MeV 0 MeV 50 MeV Coulomb barrier Nucleus A simple model of alpha decay Sample Reading Quiz Questions 1. What is the correspondence principle? 2. A quantum particle can pass through a region of space that would be forbidden to a classical particle. What is the name of this process? 3. A particle in the ground state of a potential energy well a. is at rest. b. has a zero-point motion. c. is equally probable to be found at any point inside the well. d. has a wave function that is zero at all points. e. has zero energy. 4. Which of these was not analyzed in this chapter? a. A particle in a capacitor. d. An electron in an atom. b. A particle in a finite potential well. e. An electron in a quantum-well device. c. A neutron in a nucleus. f. A quantum harmonic oscillator.
Chapter 40: One-Dimensional Quantum Mechanics 40-7 Sample Exam Questions These questions cover the material of Chapters 39–40.

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• Spring '10
• kant

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