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_(lambda) = a_(lambda) = E_(lambda)`
B. `e_(lambda)E_(lambda) = a_(lambda)`
C. `e_(lambda) = a_(lambda)E_(lambda)`
D. `e_(lambda)a_(lambda)E_(lambda)`=constant

Answer

C

Explanation

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