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. If the powers radiat

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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. If the powers radiated by them are P_P , P_Q and P_R respectively, then

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Correct answer: A. P_P is maximum

Using Wien's displacement law, _ max T = b T = b _ max . Using Stefan-Boltzmann law, the power radiated by a black body is P = A T^4 = (4 r^2) T^4 . Substituting T , we get P = (4 r^2) ( b _ max )^4 P r^2 _ max ^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 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. If the powers radiated by them are P_P , P_Q and P_R respectively, then

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