Question

The power radiated by a black body is $P_0$, and the wavelength corresponding to maximum energy is ${\lambda }_0$. On changing the temperature of 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. ${\lambda }_0$
• D. $2{\lambda }_0$

Answer 1

The correct option is A $\frac{{\lambda }_0}{4}$

According to Wien's displacement law,
${\lambda }_0{T}_0=\lambda T$
From Stefan's law, we can say that,
$\frac{P_0}{P}={\left(\frac{T_0}{T}\right)}^4\Rightarrow \frac{P_0}{P}={\left(\frac{\lambda }{{\lambda }_0}\right)}^4$
From the data given in the question,
$\frac{\lambda }{{\lambda }_0}={\left(\frac{81}{256}\right)}^{1/4}=\frac{3}{4}$
$\therefore$ we can say that $\lambda =\frac{3}{4}{\lambda }_0$
Shift in wavelength $|\Delta \lambda |=|\lambda -{\lambda }_0|=|\frac{3{\lambda }_0}{4}-{\lambda }_0|$
or $|\Delta \lambda |=\frac{{\lambda }_0}{4}$
Thus, option (c) is the correct answer.