Question

Power radiated by a black body is $P_0$ and the wavelength corresponding to maximum energy is around ${\lambda }_0$ . On changing the temperature of the black body, it was observed that the power radiated becomes $\frac{256}{81}{P}_0$ . The shift in wavelength corresponding to the maximum energy will be

• A. $+\frac{{\lambda }_0}{4}$
• B. $+\frac{{\lambda }_0}{2}$
• C. $-\frac{{\lambda }_0}{4}$
• D. $-\frac{{\lambda }_0}{2}$

Answer 1

Answer: (C)

According to Wien's law ${\lambda }_0{T}_0=\lambda T$
According to Stefan's law $\frac{(P{)}_0}{P}={\left(\frac{(T{)}_0}{T}\right)}^4$
As $P=\frac{256}{81}{P}_0\Rightarrow \lambda =\frac{3}{4}{\lambda }_0$
$\therefore$ Wavelength shift $D\lambda =\lambda -{\lambda }_0=-\frac{{\lambda }_0}{4}$