The energy spectrum f a black body exhibits a maximum around a wavelength `lamda_0`. The temperature of the black body is now changed such that the energy is maximum around a wavelength `3 lamda_0//4`. The power radiated by the black body will now increase by a factor of

Options

A. `(256)/(1)`
B. `(81)/(256)`
C. `(4)/(3)`
D. `(3)/(4)`

Answer

A

Explanation

From Wien's law, `lambda_(0) T_(1) = (3 lambda_(0))/(4) T_(2) implies (T_(2))/(T_(1)) = (4)/(3)`
Using Stefan's law,
`(nP)/(P) = ((T_(2))/(T_(1)))^(4) = ((4)/(3))^(4)`
`n = (256)/(81)`