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//81`
B. `64//27`
C. `16//9`
D. `(4)/(3)`

Answer

A

Explanation

According to Wien's law, wavelength corresponding to maximum energy decreases. When the temperature of black body increases i.e., `lamda_mT=` constant
`implies=(T_2)/(T_1)=(lamda_1)/(lamda_2)=(lamda_0)/((3lamda_0)/(4))=(4)/(3)`
Now according to Stefan's law
`(E_2)/(E_1)=((T_2)/(T_1))^4=((4)/(3))^4=(256)/(81)`