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 become $\left(\frac{256}{81}\right)$$P_0$. The shift in wavelength corresponding to the maximum energy will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is 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 $\Delta \lambda$ = $\lambda -{\lambda }_0$ = $-\frac{{\lambda }_0}{4}$