Solved Problem on Quantum Physics

At what wavelength does a cavity at 6000 K radiate most per unit wavelength?

Problem data:

Temperature of the cavity: T = 6000 K.

Solution

The Wien's Law is given by

\[ \begin{gather} \bbox[#99CCFF,10px] {\lambda_{max}T=2.898\times 10^{-3}} \end{gather} \]

substituting the data

\[ \begin{gather} \lambda _{max}=\frac{2.898\times 10^{-3}}{6000}\\[5pt] \lambda_{max}=\frac{2.898\times 10^{-3}}{6.10^{3}}\\[5pt] \lambda_{max}=\frac{2.898\times 10^{-3}\times 10^{-3}}{6}\\[5pt] \lambda_{max}=0.4981\times 10^{-6}=4981\times 10^{-10} \end{gather} \]

\[ \begin{gather} \bbox[#FFCCCC,10px] {\lambda_{max}=4981\;\overset{\circ}{\mathsf{A}}} \end{gather} \]

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