The energy spectrum of a black body exhibits a maximum around a wavelength ' '. The temperature of the black body is now changed such that the energy is maximum around a wavelength 2 /3 . The power radiated by the black body will now increase by a factor

Step-by-step solution

According to Wien's displacement law: _ m T = b T 1 _ m Given ₁ = and ₂ = 2 3 . T₂ T₁ = ₁ ₂ = 2 3 = 3 2 According to Stefan-Boltzmann law, the power radiated by a black body is given by: P = A T⁴ P T⁴ The ratio of final power to initial power is: P₂ P₁ = ( T₂ T₁ )⁴ = ( 3 2 )⁴ = 81 16 The power radiated increases by a factor of 81 16 . Answer: 81 16