Three spheres P, Q and R, having radii of 2 m, 3 m and 4 m respectively, are coated with lamp-black on their outer surfaces. The wavelengths corresponding to maximum intensity are 200 nm, 300 nm and 400 nm respectively.

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Correct answer: A. P_P is maximum

Using Wien's displacement law, λ_ T = b T = (b)/(λ_ ) . Using Stefan-Boltzmann law, the power radiated by a black body is P = σ A T^4 = σ (4π r^2) T^4 . Substituting T , we get P = σ (4π r^2) ((b)/(λ_ ))^4 P (r^2)/(λ_ ^4) . For sphere P: P_P (2^2)/((200)^4) (4)/(16 × 10^8) (1)/(4 × 10^8) For sphere Q: P_Q (3^2)/((300)^4) (9)/(81 × 10^8) (1)/(9 × 10^8) For sphere R: P_R (4^2)/((400)^4) (16)/(256 × 10^8) (1)/(16 × 10^8) Comparing the values, P_P > P_Q > P_R . Thus, P_P is maximum. Answer: P_P is maximum

Three spheres P, Q and R, having radii of 2 m, 3 m and 4 m...

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