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Phy 361 Modern Physics Fall 2005 Homework Assignment 5 Due 10/4/05 Announcement: The first midterm exam will be on Thursday, October 6. It will be on all the material covered so far in class, i.e., Chapters 2, 3 and 4 of Beiser and all handouts. The exam will be closed book and notes. A page of formula will be provided. Please make sure to bring a calculator. Reading: We now return to Chapter 3 of Beiser. We will cover all of this chapter. Study section 3.1 that introduces the de Broglie wavelength of quantum particle and section 3.2 that discusses the interpretation of the wavelike properties of particles. Study sections 3.3 and 3.4 on the general description of waves (some of this we have already reviewed when discussing diffraction and interference) Now we learn about the superposition of waves of different wavelength or frequency and the notions of phase and group velocity. Study section 3.5 that discusses electron diffraction as a direct experimental evidence of the wave-like properties of electrons. Also review x-ray diffraction from section 2.6 of Beiser, and note the close similarity between the two phenomena. Work through section 3.6 that describes the states of a quantum particle in a box. Study sections 3.7, 3.8 and 3.9 on Heisenberg's uncertainty principles and its consequences. Read Chapter 7 from the book by G. Gamow, Mr. Tompkins in paperback (Cambridge University Press, 1965), that was handed out in class. 1 Problems: 1. (a) Show that the wavelength of a particle of mass m and charge q accelerated from rest through a potential difference V is given by = h . Assume that the potential difference is insufficient to accelerate 2mqV particles to a relativistic speed. (b) If both a proton and an electron are accelerated through potential differences of the same magnitude, which is more like to exhibit a wave nature and why? (c) Now do Exercise 14, Chapter 3, from Beiser. 2. Beiser, Chapter 3, Exercise 8. 3. Beiser, Chapter 3, Exercise 16. 4. Beiser, Chapter 3, Exercise 31. 5. Estimate the minimum kinetic energy an electron would have if it were to be confined to a region of size equal to that of the nucleus, ie., a sphere of radius 5 10-15 m (feel free to use the nonrelativistic expression for the electron's energy, although in this case the electron's momentum is in the relativistic regime). Use this estimate to explain why a stable atom cannot have such a small radius. 2
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