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Planck radiation law problem

  1. Sep 17, 2007 #1
    1. The problem statement, all variables and given/known data
    Deduce an approximation for Planck's radiation law: To what what wavelength does hv/kT=1


    2. Relevant equations
    Wien Distribution equation
    B(lambda)= 2hc^2/lambda^5*exp(-hc/kT(lambda))
    Rayleigh-jeans approximation
    B(lambda)=2ckT/lambda^4
    3. The attempt at a solution
    My main concern is with the latter part of the question: To what wavelength does hv/kT=1?

    My first attempt at finding a wavelength was to equate Rayleigh-jeans approximation equations and the Wien Distribution equations to each other.

    (2hc^2/lambda^5)*exp(1/lambda) = 2ckT/lambda^4 . Then to eliminate T from the equation , I would set T= hv/k. Therefore 2ck(hv/k)/(lambda)^4 = 2hc^2/(lambda)^5*(exp(-1/lambda) => lambda=c/2/v. The only problem is , I still have an unwanted unknown, which is the frequency. Do you need the frequency in order to determine the wavelength?
     
  2. jcsd
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