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I just found out Wien's law is only a good approximation at high frequencies/small wavelengths but am not sure why. Does anyone mind explaining?

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2 Answers 2

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Wien's law is indeed an approximation at high frequency that you can obtain from Planck's law. The difference between the two is that Wien's law doesn't take into account the quantum nature of the photons and uses the Boltzmann distribution instead of Bose-Einstein for computing their energy density.

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First it's not talking about $$\lambda_\text{peak}T=\text{a constant}$$

The exact expression for the spectral energy density of the black body given by $$u_\nu=\frac{8\pi h}{c^3}\frac{\nu^3}{e^{\beta h\nu}-1}$$ The crucial insight is that electromagnetic waves in a cavity can be described by simple harmonic oscillators.

For large frequencies $e^{\beta h\nu}-1\rightarrow e^{\beta h\nu}$ $$u_\nu=\frac{8\pi h}{c^3}\nu^3e^{-\beta h\nu}$$

which is what derived by Wien approximation.


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