Problem 5.254

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

Reveal Answer

\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}

Thermal Radiation. Quantum Nature of Light.