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Energy spectrum of a body shows a maxima around a wavelength of $λ_{0}$ . Temperature of this body is increased and it is found that energy maxima now occurs around a wavelength $\frac{3 λ_{0}}{4}$ . Power radiated by the black body now increased by a factor of $\frac{256}{k}$ , where $k$ is _____

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answer is 81.

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Detailed Solution

According to Wein’s law

$λ_{m_{1}} T_{1} = λ_{m_{2}} T_{2}$

$\Rightarrow T_{2} = \frac{4}{3} T_{1}$

According to Stefan's law

$\frac{E_{2}}{E_{1}} = {(\frac{T_{2}}{T_{1}})}^{4} = {(\frac{4}{3})}^{4} = \frac{256}{81}$

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