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

Answer 1

The correct option is A $\frac{256}{81}$

${\lambda }_o\to P$

$E=\frac{hc}{\lambda }$

$\Rightarrow \frac{1}{\lambda }\propto T$ & $T^4\propto P$

$\Rightarrow {\left(\frac{1}{{\lambda }_o}\right)}^4\propto P$

$\Rightarrow \frac{P}{nP}={\left(\frac{3{\lambda }_{o_{/4}}}{{\lambda }_o}\right)}^4=\frac{81{\lambda }_o}{256{\lambda }_o}$

$\Rightarrow n=\frac{256}{81}$

Option 1.