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Chapter3_7 - “ultraviolet catastrophe” Classical theory...

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PHY3063 R. D. Field Department of Physics Chapter3_7.doc University of Florida Black-Body Radiation (2) The intensity of the black-body radiation exiting the hole is proportional to the energy density of the electromagnetic fields within the cavity. Let λ ρ d dU V T 1 ) , ( = , where ρ (T, λ )d λ is the energy per unit volume in the cavity at temperature T with wavelength between λ and λ +d λ . Similarly, df dU V f T 1 ) , ( = , where ρ (T,f)df is the energy per unit volume in the cavity at temperature T with frequency between f and f+df . Wien’s Law: It was noticed by Wien that if one plotted ρ (T, λ )/T 5 versus x = λ T that all the data lie on a universal curve . Namely, define 5 ) , ( ) ( T T x Y = , where T x = . Rayleigh-Jeans Theory: The classical prediction for Y(x) is 4 8 ) ( x k x Y classical π = , which becomes infinite as x 0 and disagrees with the data at low x (
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Unformatted text preview: “ultraviolet catastrophe” )! Classical theory predicts an infinite energy when integrated over all wavelengths! The classical prediction for ρ T (f) consists the following two pieces: ( ) > < × = E V df f N df f T ) ( ) , ( . (energy/volume) = (number of states/volume) × (energy/state) Study energy density of EM radiation in thermal equilibrium Spherical Cavity ( i.e. oven) equilibrium Function of x only! ρ is the energy density of E and B fields within the cavity Black Body Radiation: Y(x) versus x 0.002 0.004 0.006 0.008 0.01 x = λΤ (in m K) Y(x) 0.002898 Experimental Data Classical Theory Maxwell-Boltzmann Probability Distribution Number of modes of electromagnetic radiation Energy Density...
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