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

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$5000$

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(A) 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 constant.$\lambda_m T = b$Given for the celestial body:$\lambda_1 = 12 \; \mu m = 12 	imes 10^{-6} \; m$$T_1 = 200 \; K$Given for the star:$\lambda_2 = 4800 \; \mathring A = 4800 	imes 10^{-10} \; m$Using the relation $\lambda_1 T_1 = \lambda_2 T_2$:$12 	imes 10^{-6} 	imes 200 = 4800 	imes 10^{-10} 	imes T_2$$T_2 = \frac{12 	imes 10^{-6} 	imes 200}{4800 	imes 10^{-10}}$$T_2 = \frac{2400 	imes 10^{-6}}{4800 	imes 10^{-10}} = 0.5 	imes 10^4 = 5000 \; K$

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