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AP Physics 2
15.4 Blackbody Radiation
IntermediateMCQConceptual21.9k
Spectral radiance versus wavelength for blackbody radiation at a fixed temperature.
Spectral radiance versus wavelength for blackbody radiation at a fixed temperature.
According to Planck's quantum hypothesis, the average energy of an atomic oscillator emitting radiation of frequency \(f\) in a blackbody cavity at absolute temperature \(T\) is given by \(\langle E \rangle = \dfrac{hf}{e^{hf/(k_B T)} - 1}\), where \(h\) is Planck's constant and \(k_B\) is the Boltzmann constant. As shown in the graph, Planck's quantum distribution matches the classical Rayleigh-Jeans prediction \(\langle E \rangle = k_B T\) at long wavelengths, but deviates significantly at short wavelengths. Which of the following statements correctly explains why Planck's quantum model reduces to the classical prediction in the long-wavelength limit?

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