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Planck's distribution law

  1. Aug 23, 2012 #1
    1. The problem statement, all variables and given/known data

    Estimate the energy density between 499.5 and 499.6 nm emitted by a blackbody at a temperature of 2000 K. Compare to the classical value predicted by the Rayleigh-Jeans law.

    2. Relevant equations

    http://en.wikipedia.org/wiki/Planck's_law

    3. The attempt at a solution

    now I know how to integrate the indefinite integral of the law by setting x = [itex]\frac{hc}{KλT}[/itex] (K = Boltzmann constant)

    T = 2000K is substituted in and we use the same substitution for λ^5 of the equation.

    However I do not understand how to numerically solve this with λ = 499.5 to 499.6, would we then substitute it to x = [itex]\frac{hc}{KλT}[/itex] and make x the new limits of integration?
     
  2. jcsd
  3. Aug 23, 2012 #2

    Mute

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    Homework Helper

    The fact that the wavelengths you are given are so close together suggests to me you just need to approximate the integral using

    $$\int_{\lambda}^{\lambda+\Delta \lambda} d\lambda'~f(\lambda') \approx \Delta \lambda f(\lambda).$$
     
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