Chapter3_15 - PHY3063 R. D. Field Plancks Theory (2) New...

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PHY3063 R. D. Field Department of Physics Chapter3_15.doc University of Florida Planck’s Theory (2) New Partition Function: The classical partition function must now be modified as follows: = = = 0 0 ) ( ) ( n n planck classical E P Z dE E P Z , where P n (E) is the Maxwell-Boltzmann distribution nhf E n Ae Ae E P n β = = ) ( . As before β = kT , but now y A y y A Ay Z n n planck = + + + = = = 1 ) 1 ( 2 0 L , where hf e y = . Thus, hf planck e A Z = 1 New Average Energy: As before ) (log Z d d E >= < , but now kT e x h kT e hc e hf E h x x h a kT hc kT hf planck a a → = = = > < >> 1 ) / ( 1 / 1 / / / λ , where x a = kT λ /c has dimensions of “action” ( i.e. dimensions of h ). Note that the average energy now depends on λ and goes to zero as λ 0 . For
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