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(D) According to Wien's displacement law,the product of the wavelength of maximum intensity $(\lambda_m)$ and the absolute temperature $(T)$ of a blac

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(D) According to Wien's displacement law,the product of the wavelength of maximum intensity $(\lambda_m)$ and the absolute temperature $(T)$ of a black body is a constant.$\lambda_m T = b$ (where $b$ is Wien's constant).Therefore,for the sun and the moon,we have:$\lambda_{sun} T_{sun} = \lambda_{moon} T_{moon}$Rearranging to find the ratio of their temperatures $(T_{sun} / T_{moon})$:$\frac{T_{sun}}{T_{moon}} = \frac{\lambda_{moon}}{\lambda_{sun}}$Substituting the given values:$\frac{T_{sun}}{T_{moon}} = \frac{10^{-4} \ m}{0.5 	imes 10^{-6} \ m}$$\frac{T_{sun}}{T_{moon}} = \frac{10^{-4}}{0.5 	imes 10^{-6}} = \frac{10^{-4}}{5 	imes 10^{-7}} = \frac{10^3}{5} = 200$Thus,the ratio of their temperatures is $200$.

If the wavelengths of maximum intensity of radiations emitted by the sun and the moon are $0.5 \times 10^{-6} \ m$ and $10^{-4} \ m$ respectively,the ratio of their temperatures is:

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