When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from `0.26 mu m`. The ratio of the emissive powers of the body at the respective temperature is:

Options

A. `16/1`
B. `4/1`
C. `1/4`
D. `1/16`

Answer

D

Explanation

`lambda_(1)T_(1) = lambda_(2)T_(2)`
`:. (lambda_1)/(lambda_2) = (T_2)/(T_1) = (0.26)/(0.15) = 2`
`:. T_(2) = 2T_(1)`
By Stefan's law, emissive power `E = sigma T^(4)`
`E_(1) = sigmaT_(1)^(4) , E_(2) = sigma T_(2)^(4)`
`:. (E_1)/(E_2) = (sigmaT_(1)^(4))/(sigmaT_(2)^(4)) = (T_(1)^(4))/((2T_(1))^(4)) = 1/16`.