Question

The power radiated by a black body is $P$ and it radiates maximum energy around wavelength ${\lambda }_{\circ }$. If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength $3{\lambda }_{\circ }/4$, the power radiated by it will increase by a factor of

• A. $\frac{4}{3}$
• B. $\frac{16}{9}$
• C. $\frac{64}{27}$
• D. $\frac{256}{81}$

Answer 1

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

By Wein's Displacement law,
${\lambda }_1{T}_1={\lambda }_2{T}_2$
Let initial temperature be $T$, then the final temperature will be $\frac{4}{3}T$
By Stefan's Law
Power radiated $\propto$ $T^4$
$\frac{P_2}{P_1}=\frac{T_2^4}{T_1^4}=(\frac{4}{3}{)}^4$
$P_2=\frac{256}{81}P$