Chapter3_16 - PHY3063 R. D. Field Plancks Theory (3) New...

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PHY3063 R. D. Field Department of Physics Chapter3_16.doc University of Florida Planck’s Theory (3) New Y(x a ) Function: Now, 1 1 8 ) ( ) ( / 5 4 5 5 = = a x h a T a planck e x c hk T x Y π λ ρ where x a = (kT) × ( λ /c) = kx/c , has dimensions of “action” . Y planck agrees perfectly with the data provided s eV s J h × = × = 15 34 10 136 . 4 10 626 . 6 Classical Limit: Note that ) ( 8 1 1 8 ) ( 4 4 5 / 5 4 5 a classical a h x x h a a planck x Y x c k e x c hk x Y a a = → = >> . Calculate z max : It is easier if we define y = 1/z and determine the maximum of Y(y) which occurs when 0 ) ( = dy y dF where 1 ) ( 5 = y e y y F , and y = h/x a . Thus, y max = 1/z max is the solution of the following equation:
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