If between wavelength `lambda` and`lambda + dlambda`, `e_(lambda)` and `a_(lambda)` be the emissive and absorptive powers of a body and `E_(lambda)` be the emissive power of a perfectly black body, then according to Kirchoff's law, which is true

Options

A. `e_(lamda)=0_(lamda)=E_(lamda)`
B. `e_(lamda)E_(lamda)=a_(lamda)`
C. `e_(lamda)=a_(lamda)E_(lamda)`
D. `e_(lamda)a_(lamda)E_(lamda)=`constant

Answer

C

Explanation

According to Kirchoff's law, the ratio of emissive power of absorptive power is same for all bodies is equal to the emissive power of a perfectly black body i.e.,
`((e)/(a))_(body)=E_("black body")` for a particular wavelength.
`((e_(lamda))/(a_(lamda)))_(body)=(E_(1))_("black body")" "e_(lamda)=a_(lamda)E_(lamda)`.