The black body spectrum of an object O_1 is s | vedclass

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(D) According to Wien's displacement law,the wavelength $\lambda_{\max}$ at which the radiant intensity is maximum is inversely proportional to the ab

Vedclass · Accepted Answer

$81:1$

Vedclass · Answer

(D) According to Wien's displacement law,the wavelength $\lambda_{\max}$ at which the radiant intensity is maximum is inversely proportional to the absolute temperature $T$ of the black body:$\lambda_{\max} T = b$ (where $b$ is Wien's constant).For object $O_1$: $\lambda_1 = 200\,nm$,so $T_1 = \frac{b}{200}$.For object $O_2$: $\lambda_2 = 600\,nm$,so $T_2 = \frac{b}{600}$.According to the Stefan-Boltzmann law,the power emitted per unit area (emissive power) $E$ is proportional to the fourth power of the absolute temperature:$E \propto T^4$.Therefore,the ratio of power emitted per unit area by $O_1$ to that of $O_2$ is:$\frac{E_1}{E_2} = \left( \frac{T_1}{T_2} \right)^4 = \left( \frac{b/200}{b/600} \right)^4 = \left( \frac{600}{200} \right)^4 = (3)^4 = 81$.Thus,the ratio is $81:1$.

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