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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.
 Spring '14
 Physics

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