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 $\frac{2 5 6}{8 1}P_{0}$ . 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 $D \lambda=\lambda-\lambda_{0}=-\frac{\lambda_{0}}{4}$