Q. If between wavelength $\lambda$ and $\lambda + d\lambda,\ e_{\lambda}$ 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
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
Explanation
(c) According to Kirchoff’s law, the ratio of emissive power to absorptive power is same for all bodies is equal to the emissive power of a perfectly black body $i.e.,$
$\left( \frac{e}{a} \right)_{body} = E_{black\ body}$ for a particular wave length
$\left( \frac{e_{\lambda}}{a_{\lambda}} \right)_{body} = \left( E_{\lambda} \right)_{black\ body} \Rightarrow e_{\lambda} = a_{\lambda}E_{\lambda}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.