State and prove Kirchhoff’s law.

Kirchoff's law states that the ratio of the emissive power to absorptive power for the radiation of a given wavelength is constant for all substances, at the same temperature. This constant is equal to the emissive power of a perfectly black body at the same temperature and corresponding to the same wavelength. 

Proof:
Let e_λ and a_λ be the monochromatic emittance and absorptance of the body for wavelength at temperature T.
Let Q be the amount of radiation incident per unit area on the body in the wavelength range (λ–1/2) to (λ + 1/2 ).

Therefore,
Amount of radiation absorbed by body per second per unit area = a_λ Q.
The body is in thermal equilibrium with the enclosure.
Therefore, the amount of radiations absorbed by body per sec per unit area in unit wavelength region is equal to the amount of radiations emitted by body per sec per unit area in the same unit wavelength region.
 
Therefore, for black body

where,
 is the emissive power of  black body. 
From (1) and (2), we have,

 , which is Kirchhoff's law.
Also from (3), we have,
              
i.e. good absorbers of radiation are also good emitters of radiation.