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Unformatted text preview: 1 PHY3101 Detweiler February 2008 Black Body Radiation I. If I get more than two independent requests for more details on the switch from one dimension and waves on a string to three dimensions and electromagnetic waves, then I will provide notes with those details. These notes are a bit advanced for Phy 3101. However, each of you has the ability to wade through the notes and to understand Planck’s derivation of the black body spectrum. It relies upon a few tricky steps in the math and a rather diverse set of basic principles in physics. If you work on these notes until you understand them, then you will be a wiser person for your effort. We are interested in properties of the electromagnetic radiation inside a box, a length L on each side and held at a particular temperature T . Careful observations through a little hole in the side of the box shows that the energy spectrum of the radiation depends only upon the temperature T of the box and not upon its size, shape or the material its made from. Rayleigh and Jeans were the first to come close to figuring out the physics that leads to the energy spectrum. They modeled the electromagnetic waves as a bunch of standing waves inside the box. Each wave acts much like a harmonic oscillator, i.e. a mass on the end of a spring. Boltzmann had already showed that the average energy of a classical harmonic oscillator at temperature T is just kT , where k is Boltzmann’s constant. This is a fundamental result of statistical mechanics. Rayleigh and Jeans then assumed that the energy in the radiation could be determined by adding up the number of “oscillators,” which make up the electromagnetic waves, and multiplying by kT . Determining the number of these oscillators is the first step leading to Planck’s back body spectrum....
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