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Quantum Mechanics for Nanoscience and

By Karl Hess


1.1 Black body radiation and Planck’s hypothesis Black body radiation was the topic of interest in the late 1800’s and early 1900’s. It even captured the interest of the lay people and during tours in the physics institute of the University of Vienna the question often was asked: “where is the famous absolutely black body?”. To their embarrassment the tour guides had to answer “it is this white box in the corner”. The absolutely black body is actually a tiny hole in basically any box, e.g. a cube of side length L. The box is heated to a temperature T and the radiation coming out of the hole is measured to give the energy content U(ν) at frequency ν in the frequency range dν. It has been demonstrated experimentally that in equilibrium U(ν) depends only on the temperature T of the walls and not on the material of which the walls are made. The experimental result for U(ν) follows approximately Wien’s law (later improved by Planck): U(ν) ∼ ν 3 e −hν/kT where T is Boltzmann’s constant. From all the classical knowledge at that time, however, it was found that it should be U(ν) ∼ kT ν

Year: 2008
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