BLACK BODIES

A tuning fork gives out a fairly pure sound, formed by the oscil-lation of air pressure in a very narrow band of frequencies and cor-responding wavelengths. But the sound of a circular saw in operation consists of a broad, continuous spectrum of such fre-quencies and wavelengths.

Quite similarly, the light of a laser is concentrated in a very nar-row band around a single frequency and wavelength, but other light is a combination of electromagnetic oscillations in a con-tinuous band of wavelengths (colors). For example, the "white" light of the sun is emitted at wavelengths ranging from the radio spectrum to infrared, through the visible spectrum from red to violet and then from ultraviolet to X-rays and (oh horrors!) to Chernobyl-like ionizing gamma radiation. The visible colors, in-cidentally, are all jumbled up into "white" sunlight, and prisms (or raindrops under special conditions) have to be used to separate them ("disperse" them, if you want to sound learned) into the individual colors of the rainbow.

What makes a meadow green is a division into absorption and reflection: when this broad spectrum of colors falls onto the meadow, it absorbs the light of all the other colors, but reflects the green that falls into the eye of the beholder.

A perfectly white body would reflect all the wavelengths (colors) of the incident radiation, absorbing nothing; but what we will need to understand a recently revealed process of (hot) fusion is a perfectly black body, which absorbs all of the incident light and reflects nothing.

There is no such thing as perfection, and even a surface black-ened with soot will reflect a little of the incident light. The closest one can get to a perfectly black body is a hole in a cavity, for as shown in the figure, the light entering the hole is reflected all over the place by the inside walls of the cavity and most of it is eventual-ly absorbed by them; only a very tiny fraction of the incident light will find its way out again without being absorbed.

Historically, such a black body formed by a cavity is important,

for it was what led Max Planck in 1900 to discover the quantization of energy. It was known that the total amount of energy radiated by a black body (after it had been pumped full of the incident energy) was dependent only on temperature; but it was not known what law governed the distribution of that energy over the various radiated wavelengths. There was a formula by Lord Rayleigh and Sir James Jeans, which fit the experimentally observed curve well at the end of the short wavelengths, and there was another by Wil-helm Wien which fit the curve well at the other end, but there was no agreement in the middle. Planck used a mathematical artifact to get a formula that united the two laws and fit the curve across the gap and along the entire width of the spectrum. Having thus bridged the gap by what today is known as "Planck's law of black body radiation" (see figure) as the dependence of radiated energy, E, on temperature and wavelength (lambda), he searched for the basic hidden assumption that would give rise to his formula directly, and found it: energy cannot be radiated in arbitrarily small amounts, but only in multiples of a basic energy quantum. To give an analogy with water flow, it is only in the macroscopic world that we per-ceive water to flow in arbitrarily small quantities; in reality amounts of water must be a multiple of a water molecule, counted in integral multiples like eggs, thumbtacks or people.