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A black body emits radiation at the rate P when its temperature is T . At this temperature the wavelength at which the radiation has a maximum intensity is λ 0 . If at another temperature T ' the power radiated is P ' and wavelength at maximum intensity is λ 0 / 2 then

Options

  1. AP ' T ' = 3 2 PT
  2. BP ' T ' = 1 6 PT
  3. CP ' T ' = 8 PT
  4. DP ' T ' = 4 PT

Correct answer

A. P ' T ' = 3 2 PT

Step-by-step solution

For a black body, wavelength for maximum intensity : λ ∝ 1 T and P ∝ T 4   ⇒  P ∝ 1 λ 4 P ' = 1 6 P ∴     P ' T ' = 3 2 PT

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