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Planck's distribution law

  • Thread starter johnnyies
  • Start date
  • #1
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Homework Statement



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.

Homework Equations



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

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?
 

Answers and Replies

  • #2
Mute
Homework Helper
1,388
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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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