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 at wavelength $\frac{3}{4} \lambda_0$ , the power radiated by it becomes $nP$. The value of $n$ is

• A. $\frac{81}{256}$
• B. $\frac{3}{4}$
• C. $\frac{256}{81}$
• D. $\frac{4}{3}$

Answer 1

The Correct Option is C

We know,
$\lambda_{\max} $ T = constant (Wien's law)
So, $\lambda_{\max_1} T_{1} = \lambda_{\max_2 } T_{2}$
$ \Rightarrow \lambda_{0} T = \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} $