The power radiated by a black body is P and it radiates maximum energy at wavelength, \(\lambda_o\). If the temperature of the black body is now changed so that it radiates maximum energy at wavelength \(\frac{3}{4} \lambda_o\) the power radiated by it becomes nP. The value of n is :

\(\frac{256}{81}\)

\(\lambda_{max} T = constant \)  [ Wien's Law ]

\(\lambda_{max_1} T_1 = \lambda_{max_2} T_2 \)

\(\lambda_o T_1 = \frac{3}{4} \lambda_o T'\)

T' = \(\frac{4}{3}T\)

\(\frac{P_2}{P_1} = (\frac{T'}{T})^4 = \frac{256}{81} \)