The power radiated by a black body is P, and it radiates maximum energy around the wavelength `lambda_(0)`. If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength `3lambda_(0)//4`, the power radiated by it will increase by a factor of

Options

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

Answer

C

Explanation

Power radiated (P)=`sigma AT^4`
`implies P prop T^4`
From Wein’s law : `T lambda_(m)=b implies T prop (1)/(lambda_m)`
`P prop ((1)/(lambda_m))^4 implies (P_2)/(P_1)=((lambda_(m_2))/(lambda_(m_1)))^4`
`(P_2)/(P_1)=((lambda_0)/(3/4 lambda_0))^3 implies (nP)/(P)=(256)/(81) implies n = (256)/(81)`