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JEE Advanced2015PhysicsThermal Properties of MatterActual

Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 10 4 times the power emitted from B . The ratio λ A λ B of their wavelengths λ A and λ B at which the peaks occur in their respective radiation curves is

Correct answer

2

Step-by-step solution

P = e σ A T 4 λ T = constant P A P B = e σ A A T A 4 e σ A B T B 4 = A A A B T A 4 T B 4 = r A 2 r B 2 . λ B 4 λ A 4 10 4 = 400 2 . λ B λ A 4 10 4 16 × 10 4 = λ B λ A 4 λ A λ B = 16 1 1 4 = 2

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