Question

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

$\frac{3}{4} \lambda_0$

, the power radiated by it

becomes $nP$. The value of $n$ is

Accepted Answer

$$\lambda_{	ext{max}} T = 	ext{constant} \quad 	ext{(Wien's law)}$$

$$	extbf{So, } \lambda_{	ext{max}_1} T_1 = \lambda_{	ext{max}_2} T_2$$

$$\Rightarrow \lambda_0 T = \frac{3\lambda_0}{4} T'$$

$$\Rightarrow T' = \frac{4}{3}T$$

$$	extbf{So, } \frac{P_2}{P_1} = \left(\frac{T'}{T}ight)^4 = \left(\frac{4}{3}ight)^4 = \frac{256}{81}$$