Question: 4. In class, we expressed the energy density of blackbody radiation in terms of frequency. If the energy density is written in terms of

4. In class, we expressed the energy density of blackbody radiation in

4. In class, we expressed the energy density of blackbody radiation in terms of frequency. If the energy density is written in terms of the wavelengths of radiation emitted, it becomes 8thc p(2,T)= 1 a. The above expression is often used as the basis for estimating the temperature of hot objects by measuring the wavelength distribution of light that is emitted. For light emission in the visible and near infrared regions of the spectrum, eT >>1. Using this assumption, show that the wavelength that maximizes the value of p(2,T) at fixed temperature is given by hc Amax 5k,T %3D b. Although stars are not perfect blackbodies, their emission spectra resemble that of a blackbody. Consequently, the wavelength maximum of a star's emission spectrum can be used to estimate its surface temperature. The red dwarf star Gliese 581 found in the constellation Libra has an emission maximum of -830 nm. Estimate its surface temperature.

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