![]() ![]() ![]() The relevant math is detailed in the next section. With the emission now considered per unit frequency, this peak now corresponds to a wavelength about 76% longer than the peak considered per unit wavelength. ![]() ![]() is a constant resulting from the maximization equation, k is the Boltzmann constant, h is the Planck constant, and T is the temperature (in kelvins). However, it had been discovered by Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black-body radiation toward shorter wavelengths as temperature increases.įormally, Wien's displacement law states that the spectral radiance of black-body radiation per unit wavelength, peaks at the wavelength λ peak given by: The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness of black-body radiation as a function of wavelength at any given temperature. Blackbody radiation derivation of Planck s radiation low 1 Classical theories of Lorentz and Debye: Lorentz (oscillator model): Electrons and ions of matter. Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. Each temperature curve peaks at a different wavelength and Wien's law describes the shift of that peak. Black-body radiation as a function of wavelength for various temperatures. ![]()
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