Blackbody Radiation And Its Law

The glow of a hot piece of metal, which gives off visible light and whose color varies with the temperature of the metal, goes from red to yellow to white as it becomes hotter and hotter. There are other frequencies also to which our eyes do not respond. At room temperature, most of the radiation is in the infrared part of the spectrum and hence invisible.

“An ideal blackbody is defined as one that absorbs all electromagnetic radiation incident upon it”. Such a body is also a better radiator of energy for all frequencies as compared to other bodies at the same temperature. An ideal blackbody does not exist. “The nearest approximation is a hollow enclosure having a blackened inner wall and a small hole. Any radiation entering the enclosure through the hole will suffer reflection repeatedly and get absorbed inside. If the enclosure is heated to a certain temperature T, it emits radiation. In thermal equilibrium, this radiation depends only on T. A very small fraction of the radiation will pass out through the hole. Since the hole acts as a blackbody, this radiation is called blackbody radiation at temperature T”.

n( ν ) = 8 πν ² / _c 3

U( ν ,T) = 8 πν ² / _c 3kT or

U( λ ,T) = 8 π/ _λ 4kT

This is Rayleigh-Jeans Law.

Planck’s quantum hypothesis:

h = 6.625 10 ^-34 Js

U( ν ,T) = 8 πν ² / _c 3 h ν/ _e h/kT _-1 or

U( λ ,T) = 8 π hc/5 _λ 1/ _e hc/kT _-1

This is Planck’s radiation Law.

• Asλ→0 Planck’s law reduces to Wein’s law

U( λ ,T) ~ 8 π hc/ _λ 5 e ^-hc/kT

• As Planck’s law reduces to Rayleigh-Jeans’ law

U( λ ,T) ~ = 8 π kT/ _λ 4

Wien's Displacement Law

Stefan-Boltzmann law