QM1 - 1 PARTICLES AND WAVES THE ATOMIC MODEL 1 Particles...

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Unformatted text preview: 1. PARTICLES AND WAVES. THE ATOMIC MODEL 1. Particles and Waves: Neutrons and Light 2. The Bohr Hydrogen Atom: Quantized Energies and Spectra Problems It will be assumed that the reader has some background in “modern physics.” This chapter is not meant to be a review of that subject. At the heart of quantum mechanics is the bizarre matter of wave-particle du- ality. (Webster’s: “bizarre ... involving sensational contrasts or incongruities.”) After a very brief sketch of early developments, two modern examples are given: The interference and diffraction of neutrons by a double slit and by a sharp edge; and the interference of photons, one at a time, in an interferometer. The discus- sion includes “interaction-free measurements,” a quantum-mechanical way to see in the dark. From Rutherford came the picture of the atom as roughly like a little solar system, with electrons orbiting a tiny nuclear sun that contains all the positive charge and nearly all the mass. However, on classical principles Rutherford’s atom seemed to be completely unstable; yet the world is made of extremely stable atoms. Said Bohr, so much the worse for classical principles. He postulated that the single electron bound in the simplest atom, hydrogen, could only exist in certain discrete stable orbits; and he derived the properties of these orbits using the few hydrogen spectral lines then known and assuming that in the limit of large orbits the electron would radiate like a classical antenna. Although Bohr’s planetary orbits have been replaced by the nebulous states of quantum mechanics, his model was a giant step forward. In the following, there are occasional historical notes and quotes. In any physics text, such notes give an extremely superficial idea of the messiness of what actually happened. For a proper history, see M. Jammer, The Conceptual De- velopment of Quantum Mechanics (McGraw-Hill, New York, 1966) or A. Pais, Inward Bound (Clarendon Press, Oxford, 1986). Much of these are difficult read- ing because they require an understanding of the physics of the times, but they are full of interesting and accessible passages. c ⃝ 2011, Charles G. Wohl, work in progress. 1 1 · 1. PARTICLES AND WAVES: NEUTRONS AND LIGHT Planck, Einstein, Compton, de Broglie —A cavity in a block of material contains electromagnetic radiation. The energy density of the radiation depends sharply on the absolute temperature T of the walls of the cavity. The energy distribution of the radiation as a function of frequency and T is found by measuring the radiation that emerges from a small hole from the cavity to the outside; if the block is heated to incandescence, the brightest spot is the hole from the cavity. Such measurements, which require instruments that see at frequencies at which our eyes cannot, were quite good by the end of the nineteenth century. However, no one could derive the experimental results from theory....
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This note was uploaded on 01/28/2011 for the course PHY 137b taught by Professor Lee during the Spring '09 term at Berkeley.

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QM1 - 1 PARTICLES AND WAVES THE ATOMIC MODEL 1 Particles...

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