Question

The Rayleigh-Jeans distribution function (which was based on classical ideas and turned out to be incorrect) is $I(\lambda, T)=2 \pi c k_{\mathrm{B}} T / \lambda^{4} .$ Show that for long wavelengths, this approximates the Planck formula (4.28). (Remember the Taylor series for $e^{x}$.) Sketch the two distribution functions. Can you explain why one might expect the classical result to be better at long wavelengths?

Name: The Rayleigh-Jeans distribution function (which was based on classical ideas and turned out to be incorrect) is I(λ, T)=2 π c kB T / λ^4 . Show that for long wavelengths, this approximates the Planck formula (4.28). (Remember the Taylor series for e^x.) Sketch the two distribution functions. Can you explain why one might expect the classical result to be better at long wavelengths?
Uploaded: 2023-06-20T15:39:13-08:00
Duration: 3 min 46 s
Channel: Adi S
Description: The Rayleigh-Jeans distribution function (which was based on classical ideas and turned out to be incorrect) is I(λ, T)=2 π c kB T / λ^4 . Show that for long wavelengths, this approximates the Planck formula (4.28). (Remember the Taylor series for e^x.) Sketch the two distribution functions. Can you explain why one might expect the classical result to be better at long wavelengths?

          The Rayleigh-Jeans distribution function (which was based on classical ideas and turned out to be incorrect) is $I(\lambda, T)=2 \pi c k_{\mathrm{B}} T / \lambda^{4} .$ Show that for long wavelengths, this approximates the Planck formula (4.28). (Remember the Taylor series for $e^{x}$.) Sketch the two distribution functions. Can you explain why one might expect the classical result to be better at long wavelengths?

Added by Ashley T.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

06/20/2023

Step 1

First, we need to write down the Planck formula. The Planck formula for the spectral radiance of a black body is given by: $$ I(\lambda, T) = \frac{2 \pi h c^2}{\lambda^5} \frac{1}{e^{\frac{hc}{\lambda k_B T}} - 1} $$ Show more…

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The Rayleigh-Jeans distribution function (which was based on classical ideas and turned out to be incorrect) is $I(\lambda, T)=2 \pi c k_{\mathrm{B}} T / \lambda^{4} .$ Show that for long wavelengths, this approximates the Planck formula (4.28). (Remember the Taylor series for $e^{x}$.) Sketch the two distribution functions. Can you explain why one might expect the classical result to be better at long wavelengths?