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. `81/256`
B. `3/4`
C. `256/81`
D. `4/3`

Answer

C

Explanation

`P=sigma AT^(4) rArr P prop T^(4)`
According to Wien's law `T prop 1/(lambda_m)`
`rArr P = (1/(lambda_m))^(4) rArr (P_2)/(P_1) = ((lambda_(m_1))/(lambda_(m_2)))^(4)`
`rArr (P_2)/(P_1) = (lambda_(0)/(3/4 lambda_(0)))^(4)`
`rArr (n_P)/(P) = 256/81 rArr n = 256/81`.