Question

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

Answer 1

Answer: (C)

$e _ { \lambda } = a _ { \lambda } E _ { \lambda }$

Answer 2

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.,

for a particular wave length

$\left( \frac { e _ { \lambda } } { a _ { \lambda } } \right) _ { \text {body } } = \left( E _ { \lambda } \right) _ { \text {Black body } }$ ⇒ $e _ { \lambda } = a _ { \lambda } E _ { \lambda }$