8 quantum mechanical emission of light emission of

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Unformatted text preview: 4 x3 U (T ) = 3 4 $ ex " 1 dx c h0 U (T ) = ( 7.52 ! 10 "16 J/m 3 K 4 )T 4 Which is the empirical Stefan ­Boltzmann law So two empirical laws governing the energy distribuEon of a photon gas at temperature T were completely explained by 1) photons are bosons and 2) energy is quanEzed. 8 Quantum mechanical emission of light Emission of light occurs when an energeEc transiEon from an excited state to a lower state E E2 !! = E2 " E1 E1 Quantum mechanics tells us about the energeEcs, but not about the dynamics How fast does the transiEon occur? 9 TransiEon rates Suppose have a populaEon of excited quantum emikers (atoms for instance) N2 = populaEon of excited state N1 = populaEon of ground state Rate at which the excited state decays to the ground state is proporEonal to the number of excited atoms. dN 2 = ! RN 2 (t ) dt N 2 (t ) = N 0 e! Rt 10 ExponenEal decay of excited states N 1.0 0.8 0.6 N/N0=1/e 0.4 =.368 0.2 1 t1/2=ln(2)/R “half ­life” 2 3 4 5 Rt t=1/R decay Eme 11 Classical radiaEon Classically, the source of all radiaEon is the non ­uniform mo...
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This document was uploaded on 02/04/2014.

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