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Thermal Radiation. Quantum Nature of Light.

Problem 5.254

Assuming the spectral distribution of thermal radiation energy to obey Wien's formula u(ω,T)=Aω3exp(aω/T),u(\omega, T)=A \omega^{3} \exp (-a \omega / T), where a=7.64a=7.64 ps. K, find for a temperature T=2000 KT=2000 \mathrm{~K} the most probable (a) radiation frequency; (b) radiation wavelength.

Reveal Answer
5.254.(a)ωpr=3T/a=7.851014 s1;(b).λpr=2πca/5T==1.44μ m.\begin{aligned} & 5.254 .(\mathrm{a}) \omega_{p r}=3 T / a=7.85 \cdot 10^{14} \mathrm{~s}^{-1} ;(\mathrm{b}) . \lambda_{p r}=2 \pi c a / 5 T=\\ =& 1.44 \mu \mathrm{~m} . \end{aligned}