Gustav Robert Kirchhoff's contribution to our understanding of how light and matter interact is his set of three laws of radiation. They predict what sort of spectrum an object will emit based upon the physical properties of the object. Kirchhoff devised these laws in the latter half of the nineteenth century, prior to our understanding of atomic physics and quantum mechanics, but on a macroscopic level they describe the interaction of matter and radiation quite well. The laws are as follows:

  1. Any hot, dense object will emit a continuous spectrum -- a black body spectrum.

  2. A hot, thin gas will emit light only at specific wavelengths according to the electron configuration of the atoms in the gas -- an emission line spectrum.

  3. A continuous spectrum passed through a cool, thin gas will result in a continuum spectrum with breaks at the same wavelengths as the emission lines described in the Second Law -- an absorption line spectrum.

These three laws embody much of the fundamental physics of radiation and radiative transfer. The first is a simplified explanation of black body radiation, namely that any dense object will emit a characteristic, continuous spectrum. It was later determined that the shape and intensity of this spectrum is only a function of the object's temperature, and nothing else, but from a purely phenomenological standpoint, the first law is a good descriptor of black bodies. In particular, it makes no qualifications as to the properties of the object -- it could be a metal rod in a fire, it could be a jar full of mercury, or an incredibly dense sphere of gas. All that matters is that it is dense. More accurately, we now say it is "optically thick"(*) rather than dense, but Kirchhoff's description is good enough.

The second and third laws also cover a large swath of physics, that of emission and absorption processes by atoms in a gas or plasma. The second law says that a thin ("optically thin"), hot gas will have an emission line spectrum; the third law states that a cool gas will behave the opposite way, and exhibit absorption lines. As the theory behind atomic structure and quantum mechanics grew during the late nineteenth century, Kirchhoff and others (notably Robert Bunsen) realized that each element has its own unique signature of emission and absorption lines, governed by its electron configuration. The lines are generated by electrons emitting and absorbing energy by shifting their position within the electronic structure of a given atom.

All atoms of a given element exhibit the same set of lines. This is important, because it means that hydrogen atoms (and all other elements) behave the same way on the Sun as they do here on Earth. In this way, we can apply our knowledge of gases here on Earth to what we see elsewhere in the universe, and use light as a way to study the physical properties of distant objects. This is precisely what Kirchhoff and others did in their studies of the Sun -- by comparing the absorption lines in the solar spectrum to those of gases here on Earth, they found the Sun's photosphere is composed of elements like hydrogen, helium, calcium, iron, and nearly every other element we see here on Earth.

(*) The optical depth of a material is defined as the ability a photon to pass through it without being scattered or absorbed. A material with an optical depth τ of exactly one is one in which the intensity of light passing through it will be reduced by a factor of e. Mathematically, this is

I = I0 e

Thus, when the optical depth becomes large, the amount of light which passes through is very small. Physically, it indicates that the mean free path of a photon is shorter than the thickness of the material itself.

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