Question

When the temperature of 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 temperatures is:

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

Answer 1

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

From Wien's displacement law,
${\lambda }_{max}\propto \frac{1}{T}$
Let initial and final temperature $T_1$ and $T_2$ , and corresponding powers $P_1$ and $P_2$ respectively.
From Stefan's law,
$\frac{P_1}{P_2}=(\frac{T_1}{T_2}{)}^4=(\frac{1}{2}{)}^4=\frac{1}{16}$