Question

Upon increasing the temperature of a black body, it is observed that the wavelength corresponding to maximum energy changes from $0.26\mu \text{m}$ to $0.13\mu \text{m}$. The ratio of the emissive powers of the body at the two temperatures is:

• A. $\frac{4}{1}$
• B. $\frac{1}{4}$
• C. $\frac{16}{1}$
• D. $\frac{1}{16}$

Answer 1

The correct option is D $\frac{1}{16}$

According to Wien's displacement law, $\lambda \propto \frac{1}{T}$
Thus, we can write that,
${\lambda }_1{T}_1={\lambda }_2{T}_2\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{T_2}{T_1}=\frac{0.26}{0.13}$
$\Rightarrow T_2=2T_1$
Using Stefan's law, emissive power $E=\sigma T^4$
$\frac{E_1}{E_2}=\frac{\sigma T_1^4}{\sigma T_2^4}=\frac{T_1^4}{(2T_1{)}^4}=\frac{1}{16}$
Thus, option (d) is the correct answer.