Two spherical stars A and B emit blackbody ra | vedclass

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(B) According to the Stefan-Boltzmann law,the power radiated by a blackbody is given by $P = \sigma A T^4 = \sigma (4\pi R^2) T^4$.Given that $R_A = 4

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$2$

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(B) According to the Stefan-Boltzmann law,the power radiated by a blackbody is given by $P = \sigma A T^4 = \sigma (4\pi R^2) T^4$.Given that $R_A = 400 R_B$ and $P_A = 10^4 P_B$.Substituting these into the power ratio equation: $\frac{P_A}{P_B} = \left(\frac{R_A}{R_B}ight)^2 \left(\frac{T_A}{T_B}ight)^4$.$10^4 = (400)^2 \left(\frac{T_A}{T_B}ight)^4$.$10^4 = 160000 \left(\frac{T_A}{T_B}ight)^4 = 1.6 	imes 10^5 \left(\frac{T_A}{T_B}ight)^4$.$\left(\frac{T_A}{T_B}ight)^4 = \frac{10^4}{1.6 	imes 10^5} = \frac{1}{16}$.Taking the fourth root,$\frac{T_A}{T_B} = \frac{1}{2}$,which implies $T_B = 2 T_A$.According to Wien's displacement law,$\lambda T = 	ext{constant}$,so $\lambda_A T_A = \lambda_B T_B$.Therefore,$\frac{\lambda_A}{\lambda_B} = \frac{T_B}{T_A} = 2$.

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