When the temperature of a black body increases, it is observed that the wavelenght corresponding to maximum energy changes from `0.26` `mum` to `0.13 mum`. The ration of the emissive power of the body at the respective temperature is

Options

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

Answer

D

Explanation

According to weins displacement law, `gamma_(m)T = Constant`
`gamma_(1)/(gamma_(2))=T_(2)/T_(1)`
`implies T_(1)/T_(2)=(0.13)/(0.26)=(1)/(2)`
Stefan's law, `E alpha T^(4)`
`E_(1)/E_(2)=(T_(1)/T_(2))^(4)`
`E_(1)/E_(2)=((1)/(2))^(4)`
`E_(1):E_(2)=1:16`