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

Answer: (C)

We know,
${\lambda }_{\max }$ T = constant (Wien's law)
So, ${\lambda }_{{\max }_1}{T}_1={\lambda }_{{\max }_2}{T}_2$
$\Rightarrow {\lambda }_{0}T=\frac{3{\lambda }_0}{4}{T}^{\prime }$
$\Rightarrow T^{\prime }=\frac{4}{3}T$
So, $\frac{P_2}{P_1}={\left(\frac{T^{\prime }}{T}\right)}^4={\left(\frac{4}{3}\right)}^4=\frac{256}{81}$