Black Body Radiation

When a body is heated, it seen to radiate; in equilibrium the light emitted ranges over the whole spectrum of frequencies v, with a spectral distribution that depend on the frequency or equivalently on the wavelength of light λ and on the temperature.

Gustav Kirchhoff proved a theorem when he showed by arguments based on thermodynamics that for any body in thermal equilibrium with radiation, the emitted power is proportional to the power absorbed, that is:

    e_f =  J(f, T)A_f

Where e_f is the power emitted per unit area per unit frequency by a particular heated object. A_f is the absorption power (fraction of the incident power absorbed per unit area per unit frequency by the heated object), and J(f, T) is a universal function (the same for all bodies) that depends only on f, the light frequency and T, the absolute temperature of the body. Therefore, we can define a blackbody as an object that absorbs all the electromagnetic radiation falling on it and as a result appears black. It has Af = 1 for all frequencies and hence Kirchhoff’s theorem for a blackbody becomes:

e_f =  J(f, T)                             

Kirchhoff showed that for a given λ, the ratio of the emissive power E to the absorptivity A, defined as the fraction of incident radiation of wavelength λ that is absorbed by the body, is the same for all the bodies.

Related: Basic Facts about Photons

Recommended Resource: A Student’s Guide to the Schrodinger’s Equation