Blackbody Radiation

When electromagnetic radiation in an isothermal enclosure, or cavity, is in thermal equilibrium at temperature T , the distribution of radiation density dν, contained in a bandwidth dν, is given by Planck’s law

......(1)

where is the radiation density per unit frequency [J s/cm³], k is Boltzmann’s constant, and c is the velocity of light. The spectral distribution of thermal radiation vanishes at ν = 0 and ν → ∞, and has a peak which depends on the temperature.
The factor

......(2)

in (1) gives the density of radiation modes per unit volume and unit frequency interval. The factor pn can also be interpreted as the number of degrees of freedom associated with a radiation field, per unit volume, per unit frequency interval. The expression for the mode density pn [modes s/cm³] plays an important role in connecting the spontaneous and the induced transition probabilities.
For a uniform, isotropic radiation field, the following relationship is valid

..........(3)

where W is the blackbody radiation [W/cm²] which will be emitted from an opening in the cavity of the blackbody. Many solids radiate like a blackbody. Therefore, the radiation emitted from the surface of a solid can be calculated from (3).
According to the Stefan–Boltzmann equation, the total blackbody radiation is

.......(4)

where σ = 5.68 × 10⁻¹² W/cm² K⁴. The emitted radiation W has a maximum which is obtained from Wien’s displacement law

........(5)

For example, a blackbody at a temperature of 5200 K has its radiation peak at 5564 A° , which is about the center of the visible spectrum.