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 temperatures is:

• A. 16 : 1
• B. 4 : 1
• C. 1 : 4
• D. 1 : 16

Answer 1

Answer: (D)

1 : 16

By Kirchoff's law, energy is proportional to the fourth power of temperature.

By Wien's law, the peak wavelength is inversely proportional to temperature.

Combining the above 2, we get that the energy is inversely proportional to the fourth power of peak wavelength

So, $\frac{E_1}{E_2}={\left(\frac{{\lambda }_2}{{\lambda }_1}\right)}^4$ $={\left(\frac{0.13}{0.26}\right)}^4$ $=1:16$