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The power radiated by a black-body is P 0 and it radiates maximum energy around the wavelength λ 0 . If the temperature of the black-body is now changed so that it radiates maximum energy around a wavelength 3 λ 0 4 , then the power radiated by it will be

Options

  1. A4 3 P 0
  2. B16 9 P 0
  3. C64 27 P 0
  4. D256 81 P 0

Correct answer

D. 256 81 P 0

Step-by-step solution

Let T 0 be the initial temperature of the black body ∴   λ 0 T 0 = b   (Wien's law) Power radiated, P 0 = C T 0 4 ,   where, C is constant. If T is new temperature of black body, then 3 λ 0 4 T = b = λ 0 T 0     o r     T = 4 3   T 0 Power radiated, P = C T 4 = C T 0 4 4 3 4 P = 256 81 P 0

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