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The power radiated by a black body is P and it radiates maximum energy at wavelength, $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4}\lambda_0$, the power radiated by it becomes nP. The value of n is
Explanation
Wien's law gives $T' = 4T/3$; Stefan's law gives $P \propto T^4$.
Detailed Solution
We know, $\lambda_{max}T$ = constant (Wien's law)
So, $\lambda_{max_1}T_1 = \lambda_{max_2}T_2$
$\Rightarrow \lambda_0T = \frac{3\lambda_0}{4}T'$
$\Rightarrow T' = \frac{4}{3}T$
So, $\frac{P_2}{P_1} = \left(\frac{T'}{T}\right)^4 = \left(\frac{4}{3}\right)^4 = \frac{256}{81}$