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AP Physics 2
15.4 Blackbody Radiation
IntermediateMCQConceptual21.9k
A graph showing spectral radiance on the vertical axis versus wavelength lambda on the horizontal axis. Two curves are drawn. The solid curve representing Planck's law starts at zero at the origin, rises to a single smooth peak at a moderate wavelength, and then gradually decreases toward zero as wavelength increases. A dashed curve representing the classical Rayleigh-Jeans law starts very high near the vertical axis at short wavelengths, decreases steeply, and merges smoothly with the solid Planck curve at long wavelengths on the right side of the graph. No other labels, lines, text, or axes appear.
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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