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Planck radiation law problem

  • Thread starter Benzoate
  • Start date
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1. Homework Statement
Deduce an approximation for Planck's radiation law: To what what wavelength does hv/kT=1


2. Homework 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?
 

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