The power radiated by a black body is P and it radiates maximum energy at wavelength, λ 0 . If the temperature of the black body is now changed so that it radiates maximum energy at wavelength 3 4 λ 0 , the power radiated by it becomes nP. The value of n is

Step-by-step solution

By Stefan's law, P = σ A T 4 ⇒ P ∝ T 4 According to Wien's law T ∝ 1 λ m ⇒     P ∝ 1 λ m 4 ⇒ P 2 P 1 = λ m 1 λ m 2 4 ⇒     P 2 P 1 = λ 0 3 4 λ 0 4 ⇒ n P P = 256 81 ⇒ n = 256 81