Question

The power radiated by a black body is $P$, and it radiates maximum energy around wavelength ${\lambda }_B$. If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength $3{\lambda }_0/4$, 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 $Wei{n}^{\prime }s$ $Displacement$ 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 $Stepha{n}^{\prime }s$ Law

Power radiated $\alpha$ $T^4$

$\frac{P_2}{P_1}=\frac{T_2^4}{T_1^4}=(\frac{{\lambda }_1}{{\lambda }_2}{)}^4=(\frac{4}{3}{)}^4$

$P_2=\frac{256}{81}P$