A black body radiates power P and maximum energy is radiated by it at a wavelength `lamda_(0)`. The temperature of the black body is now so changed that it radiates maximum energy at the wavelength `(3lamda_(0))/4`. What is the power radiated by it at the new temperature ?

Options

A. `16/9P`
B. `256/81P`
C. `4/3P`
D. `64/27P`

Answer

B

Explanation

For this equation, we have to use Wien's displacement law and Stefan's law.
According to Wien's law, `lamda_(m)`T = constant
`thereforelamda_(0)xxT=(3lamda_(0))/4T'`
`thereforeT'=(lamda_(0)Txx4)/(3lamda_(0))=(4T)/3`
and according to Stefan's law quantity of heat radiated per sec per unit Area `(Q)propT^(4)`
`therefore(P')/(P)=(T_(2)/T_(1))^(4)=((4T)/(3xxT))^(4)=256/81`
`thereforeP'=256/81P`