Two spherical stars A and B emit blackbody radiation. The radius of A is 300 times that of B and A emits 104 times the power emitted from B. The ratio (λAλB) of their wavelengths λA and λB at which the peaks occur in their respective radiation curves is N Then N= ____

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Two spherical stars A and B emit blackbody radiation. The radius of A is 300 times that of B and A emits $10^{4}$ times the power emitted from B. The ratio $(\frac{λ_{A}}{λ_{B}})$ of their wavelengths $λ_{A}$ and $λ_{B}$ at which the peaks occur in their respective radiation curves is $\sqrt{N}$ Then $N =$ ____

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answer is 3.

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Detailed Solution

Radiant power emitted by black body sphere is $P = σ 4 π R^{2} T^{4} a n d λ T = b (c o n s \tan t)$

$P = σ 4 π R^{2} \frac{b^{4}}{λ^{4}}$

$λ \propto {(\frac{R^{2}}{p})}^{\frac{1}{4}}$

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