Question

When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from $0.26\mu \text{m}$ to $0.13\mu \text{m}$ Then ratio of the emissive power of the body at respective temperature is

• A. $16/1$
• B. $4/1$
• C. $1/4$
• D. $1/16$

Answer 1

The correct option is D $1/16$

According to Wein's displacement law
$\frac{({\lambda }_m{)}_1}{({\lambda }_m{)}_2}=\frac{T_2}{T_1}=\frac{0.26}{0.13}=2$
From Stefan's law,
$\therefore \frac{E_1}{E_2}={\left(\frac{T_1}{T_2}\right)}^4={\left(\frac{1}{2}\right)}^4=\frac{1}{16}$