3.4 The Distribution of Radiation

The Distribution of Radiation

All macroscopic objects—fires, ice cubes, people, stars—emit radiation at all times, regardless of their size, shape, or chemical composition. They radiate mainly because the microscopic charged particles they are made up of are in constantly varying random motion, and whenever charges change their state of motion, electromagnetic radiation is emitted. The temperature of an object is a direct measure of the amount of microscopic motion within it (see More Precisely 3-1). The hotter the object—that is, the higher its temperature—the faster its constituent particles move and the more energy they radiate.

THE BLACKBODY SPECTRUM

Intensity is a term often used to specify the amount or strength of radiation at any point in space. Like frequency and wavelength, intensity is a basic property of radiation. No natural object emits all its radiation at just one frequency. Instead, the energy is generally spread out over a range of frequencies. By studying how the intensity of this radiation is distributed across the electromagnetic spectrum, we can learn much about the object's properties.

	Figure 3.10 Ideal Blackbody Curve The blackbody, or Planck curve, represents the distribution of the intensity of radiation emitted by any object.

Figure 3.10 illustrates schematically the distribution of radiation emitted by any object. The curve peaks at a single, well-defined frequency and falls off to lesser values above and below that frequency. Note that the curve is not shaped like a symmetrical bell that declines evenly on either side of the peak. The intensity falls off more slowly from the peak to lower frequencies than it does on the high-frequency side. This overall shape is characteristic of the radiation emitted by any object, regardless of its size, shape, composition, or temperature.

The curve drawn in Figure 3.10 is the radiation-distribution curve for a mathematical idealization known as a blackbody—an object that absorbs all radiation falling on it. In a steady state, a blackbody must reemit the same amount of energy it absorbs. The blackbody curve shown in the figure describes the distribution of that reemitted radiation. (The curve is also known as the Planck curve, after Max Planck, whose mathematical analysis of such thermal emission in 1900 played a key role in modern physics.) No real object absorbs and radiates as a perfect blackbody. However, in many cases, the blackbody curve is a good approximation to reality, and the properties of blackbodies provide important insights into the behavior of real objects.

THE RADIATION LAWS

The blackbody curve shifts toward higher frequencies (shorter wavelengths) and greater intensities as an object's temperature increases. Even so, the shape of the curve remains the same. This shifting of radiation's peak frequency with temperature is familiar to us all: Very hot glowing objects, such as toaster filaments or stars, emit visible light. Cooler objects, such as warm rocks or household radiators, produce invisible radiation—warm to the touch but not glowing hot to the eye. These latter objects emit most of their radiation in the lower-frequency infrared part of the electromagnetic spectrum (Figure 3.9).

	Figure 3.11 Blackbody Curves As an object is heated, the radiation it emits peaks at higher and higher frequencies. Shown here are curves corresponding to temperatures of 300 K (room temperature), 1000 K (beginning to glow dull red), 4000 K (red hot), and 7000 K (white hot).

Imagine a piece of metal placed in a hot furnace. At first, the metal becomes warm, although its visual appearance doesn't change. As it heats up, it begins to glow dull red, then orange, brilliant yellow, and finally white. How do we explain this? As illustrated in Figure 3.11, when the metal is at room temperature (300 K—see More Precisely 3-1 for a discussion of the Kelvin temperature scale), it emits only invisible infrared radiation. As the metal becomes hotter, the peak of its blackbody curve shifts toward higher frequencies. At 1000 K, for instance, most of the emitted radiation is still infrared, but now there is also a small amount of visible (dull red) radiation being emitted (note in Figure 3.11 that the high-frequency portion of the 1000 K curve just overlaps the visible region of the graph).

As the temperature continues to rise, the peak of the metal's blackbody curve moves through the visible spectrum, from red (the 4000 K curve) through yellow. The metal eventually becomes white hot because, when its blackbody curve peaks in the blue or violet part of the spectrum (the 7000 K curve), the low-frequency tail of the curve extends through the entire visible spectrum (to the left in Figure 3.11), meaning that substantial amounts of green, yellow, orange, and red light are also emitted. Together, all these colors combine to produce white.

Figure 3.12 The Sun at Many Wavelengths Three images of the Sun, made using (a) radio waves, (b) infrared radiation, and (c) visible light, are shown here in false color. By studying the similarities and differences among these views of the same object, acquired on the same day, astronomers can find important clues to its structure, composition, and surface activity. Although most sunlight is emitted in the form of infrared and visible radiation, a wealth of information about our parent star can be obtained by studying it in other regions of the electromagnetic spectrum. (NRAO; AURA)

From studies of the precise form of the blackbody curve we obtain a very simple connection between the wavelength at which most radiation is emitted and the absolute temperature (that is, the temperature measured in kelvins) of the emitting object:

This relationship, called Wien's law, is discussed in more detail in More Precisely 3-2.

Simply put, Wien's law tells us that the hotter the object, the bluer its radiation. For example (see Figure 3.13), an object with a temperature of 6000 K emits most of its energy in the visible part of the spectrum, with a peak wavelength of 480 nm. At 600 K, the object's emission would peak at a wavelength of 4800 nm, well into the infrared portion of the spectrum. At a temperature of 60,000 K, the peak would move all the way through the visible spectrum to a wavelength of 48 nm, in the ultraviolet range.

It is also a matter of everyday experience that, as the temperature of an object increases, the total amount of energy it radiates (summed over all frequencies) increases rapidly. For example, the heat given off by an electric heater increases very sharply as it warms up and begins to emit visible light. Careful experimentation leads to the conclusion that the total amount of energy radiated per unit time is actually proportional to the fourth power of the object's temperature:

total energy emission  temperature⁴.

This relation is called Stefan's law. This is discussed further inMore Precisely 3-2. From the form of Stefan's law we can see that the energy emitted by a body rises dramatically as its temperature increases. Doubling the temperature causes the total energy radiated to increase by a factor of

2⁴ = 16; tripling the temperature increases the emission by 3⁴= 81, and
so on.


ASTRONOMICAL APPLICATIONS

No known natural terrestrial objects reach temperatures high enough to emit very-high-frequency radiation. Only human-made thermonuclear explosions are hot enough for their spectra to peak in the X-ray or gamma-ray range. (Most human inventions that produce short-wavelength, high-frequency radiation, such as X-ray machines, are designed to emit only a specific range of wavelengths and do not operate at high temperatures. They are said to produce a nonthermal spectrum of radiation.) Many extraterrestrial objects, however, do emit copious quantities of ultraviolet, X-ray, and even gamma-ray radiation. Figure 3.12 shows a familiar object—our Sun—as it appears when viewed using radiation from different parts of the electromagnetic spectrum.

Astronomers often use blackbody curves as thermometers to determine the temperatures of distant objects. For example, study of the solar spectrum makes it possible to measure the temperature of the Sun's surface. Observations of the radiation from the Sun at many frequencies yield a curve shaped somewhat like that shown in Figure 3.10. The Sun's curve peaks in the visible part of the electromagnetic spectrum; the Sun also emits a lot of infrared and a little ultraviolet radiation. Using Wien's law, we find that the temperature of the Sun's surface is approximately 6000 K. (A more precise measurement, applying Wien's law to the blackbody curve that best fits the solar spectrum, yields a temperature of 5800 K.)

Other cosmic objects have surfaces very much cooler or hotter than the Sun's, emitting most of their radiation in invisible parts of the spectrum (Figure 3.13). For example, the relatively cool surface of a very young star may measure 600 K and emit mostly infrared radiation. Cooler still is the interstellar gas cloud from which the star formed; at a temperature of 60 K, such a cloud emits mainly long-wavelength radiation in the radio and infrared parts of the spectrum. The brightest stars, by contrast, have surface temperatures as high as 60,000 K and hence emit mostly ultraviolet radiation.

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