When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum…

When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from $0.26 \mu \mathrm{m}$ to $0.13 \mu \mathrm{m}$. The ratio of the emissive powers of the body at the respective temperature is
  1. $\frac{16}{1}$
  2. $\frac{4}{1}$
  3. $\frac{1}{4}$
  4. $\frac{1}{16}$

Solution

$ \lambda_1=0.26 \mu \mathrm{m}, \lambda_2=0.13 \mu \mathrm{m} $ From Wein's displacement law. $ \begin{aligned} \lambda T & =\text { constant } \\ \lambda_1 T_1 & =\lambda_2 T_2 \\ \frac{T_1}{T_2} & =\frac{\lambda_2}{\lambda_1}=\frac{0.13}{0.26}=\frac{1}{2} \end{aligned} $ Ratio of emissive powers $\frac{E_1}{E_2}=\left(\frac{T_1}{T_2}\right)^4=\left(\frac{1}{2}\right)^4$ $ =1: 16 $

Asked in: AP EAMCET 2002

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