The thermal emissivitites of two bodies `A` and `B` are in the ratio of `1//e`. The outer surface area of the bodies are same and they radiate the energy at the same rate. Find the ratio of the wavelength corresponding to the maximum spherical radiance in the radiation from `A` to maximum spectral radiance in the radiation from `B`.

Options

A. `e^(1//4)`
B. `(1)/(e^(1//4))`
C. `(1 + e)^(1//4)`
D. `(1)/(1 + e)^(1//4)`

Answer

B

Explanation

`P=1xxA sigma T_(A)^(4) = e A sigmaT_(B)^(4)`
`T_(A)=e^(1//4)T_(B)`
`lambda_(A)T_(A) = lambda_(B)T_(B)`
or `e^(1//4)lambda_(A)T_(B) = lambda_(B)T_(B)`
`lambda_(A)//lambda_(B) = (T_B)/(e^(1//4)T_(B)) = 1/(e^(1//4))`.