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A Physicist's Guide to Mathematica, 2nd Edition by Patrick T. Tam

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Chapter 6. Quantum Physics

Blackbody Radiation

The Problem

The Planck formula for blackbody radiation is

Equation 6.1.1. 

where u(v, T) is the energy density as a function of frequency v and temperature T, k is Boltzmann’s constant, c is the speed of light, and h is Planck’s constant. Obtain an expression for the energy density as a function of wavelength λ and temperature T. Also, plot this energy density for several temperatures. Then, derive Wien’s displacement law relating T and λmax, the wavelength for which the energy density is maximal. Finally, use 5700 K as an estimate of the Sun’s surface temperature to determine λmax for solar radiation. ...

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