For an enclosure maintained at $3000 K,$ the maximum radiation occurs at wavelength $λ_{m} .$ If the temperature is raised to $4000 K,$ the peak will shift to $\frac{K}{4} \times λ_{m} .$ Then the value of $K$ is equal to

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answer is 3.

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Detailed Solution

According to Weins displacement law,

$\begin{array}{l} λ_{m} T = constant \\ λ_{1} T_{1} = λ_{2} T_{2} \\ λ_{m} (3000) = (\frac{K}{4} \times λ_{m}) (4000) \\ \Rightarrow K = 3 \end{array}$

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