Planck's law of blackbody radiation is a general equation for the distribution of the spectral radiative power density of thermal radiation emitted by a blackbody according to wavelength (or frequency) at a given temperature. The mathematical expression for this law is:

M _λ (T)=2πhc² λ ^-5[exp(hc/k λ T)-1]^-1

or abbreviated as

M=c₁ λ ^-5[exp(c₂/ λ T)-1]^-1

Among them, M_入 is the spectral radiation power density of the black body; c is the speed of light in vacuum; k is the Boltzmann constant; T is the absolute temperature; c1 and c2 are the first and second radiation constants, respectively, whose values are determined by the wavelength unit.

 

This law shows that the radiation characteristics of a black body are only related to the radiation temperature; the M_λ ~λ incoming radiation spectrum of a black body at different temperatures varies continuously with wavelength, and there is a maximum radiation value in the middle of each curve, and there is a corresponding peak wavelength (λ_m) ; The higher the spectral radiation temperature, the greater the radiation power density and the shorter the corresponding peak wavelength; the maximum value of the black body spectral radiation density is proportional to the fifth power of its absolute temperature.

Applying Planck's law of blackbody radiation, the energy value of any wavelength radiated by a blackbody from a unit area to a hemispherical space in a unit time can be calculated. This formula is the only radiation law that is accurate over the entire spectrum.