?Wave-Particle DualityShow that Stefan’s law results from Planck’s radiation law. Hint
Chapter 6, Problem 126(choose chapter or problem)
Wave-Particle Duality
Show that Stefan’s law results from Planck’s radiation law. Hint: To compute the total power of blackbody radiation emitted across the entire spectrum of wavelengths at a given temperature, integrate Planck’s law over the entire spectrum
\(P(T)=\int_{0}^{\infty} I(\lambda, T) d \lambda\). Use the substitution \(x=h c / \lambda k T\) and the tabulated value of the integral
\(\int_{0}^{\infty} d x x^{3} /\left(e^{x}-1\right)=\pi^{4} / 15\)
Text Transcription:
P(T)=Int_0^infinity I(lambda, T) d lambda
x=hc/lambda kT
Int_0^infinity dxx^3/(e^x - 1) = pi^4 /15
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