12 BlackBodyRadiation corrected 2010

12 BlackBodyRadiation corrected 2010 - Black Body Radiation...

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Black Body Radiation Black body radiation is the electromagnetic radiation given off by a perfect absorber at some temperature, T. For a perfect black body the rate of absorption = rate of emission. Example: When an object is heated the color turns from dull red to yellow to white at the highest temperature. Raleigh Jeans Theory: ρ ν = ρ(ν29 kT = 8 πν 2 Catastrophe! Plank:Energy of each oscillator can appears as multiples of h ν only i.e h ν , 2h ν ,… = 0 ) ( dE E p E E If E is continuous. Use Boltzmann statistics. 1 1 1 qh kT q qh h kT kT q qh e h E e e ν - = - = = = - 0 ( ) E kT E kT e p E e dE - - = If E can assume only discrete values, then Average thermal energy. is the probability a mode has energy E
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Black Body (cont.) 1 ) 1 ( - - kT h e ν Oscillator quantum of energy 1 - = kT h e h E Number of oscillators at h ν . Mode occupation number. Then the energy density in the black body can be written as the product of density of modes, ρ(ν29, times the average energy of the mode <E>, OR This expression describes well the black body spectrum and was one of the great successes of early quantum theory.
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This note was uploaded on 02/23/2011 for the course EE 474 taught by Professor Lingo during the Spring '11 term at USC.

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12 BlackBodyRadiation corrected 2010 - Black Body Radiation...

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