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

Since, `lambda_mT`=constant
`implies lambda_(m_1)T_1=lambda_(m_2)T_2`
`implies T_2=(lambda_0)/(3 lambda_0//4)T_1=4/3 T_1`
Now , `P prop T^4`
`(P^2)/(P_1)=((T_2)/(T_1))^4 implies (P_2)/(P_1) =((4/3 T_1)/(T_1))^4 =(256)/(81)`