Question

When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from 0.26 $\mu$ m to 0.13$\mu$m. The ratio of the emissive powers of the body at the respective temperature is :

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

According to Wein’s displacement law, $\lambda$T = constant, ie.,

${\lambda }_1{T}_1={\lambda }_2{T}_{2}or\frac{{\lambda }_1}{{\lambda }_2}=\frac{T_2}{T_1}=\frac{0.26}{0.13}=2or{T}_2=2T_1$

According to Stefan’s law, $E_1=\sigma T_1^{4}and{E}_2\sigma T_2^4$

$Hence\frac{E_1}{E_2}=\frac{\sigma T_1^4}{\sigma T_2^4}={\left(\frac{T_1}{T_2}\right)}^4={\left(\frac{1}{2}\right)}^4=\frac{1}{16}(\because T_2=2T_1)$