All macroscopic objects—fires, ice cubes, people, stars—emit radiation at all times. They radiate because the microscopic charged particles in them are in constant 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 2-1). The hotter the object, 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 of its radiation at just one frequency. Instead, the energy is often spread out over a range of frequencies. By studying the way in which the intensity of this radiation is distributed across the electromagnetic spectrum, we can learn much about the object’s properties.

Figure 2.9 illustrates schematically the distribution of radiation emitted by any object. Note that the curve peaks at a single, well-defined frequency and falls off to lesser values above and below that frequency. However, the curve is not symmetrical about the peak—the falloff is more rapid on the high-frequency side of the peak than it is toward lower frequencies. This overall shape is characteristic of the radiation emitted by any object, regardless of its size, shape, composition, or temperature.

 Figure 2.9 Ideal Blackbody Curve The blackbody curve represents the spread of the intensity of the radiation emitted by any object.
The curve drawn in Figure 2.9 refers to a mathematical idealization known as a blackbody—an object that absorbs all radiation falling upon it. In a steady state a blackbody must reemit the same amount of energy as it absorbs. The blackbody curve shown in the figure describes the distribution of that reemitted radiation. No real object absorbs or radiates as a perfect blackbody. However, in many cases the blackbody curve is a very good approximation to reality, and the properties of blackbodies provide important insights into the behavior of real objects, including stars.

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 (see Figure 2.10). This shifting of radiation’s peak frequency with temperature is familiar to us all. Very hot glowing objects, such as lightbulb filaments or stars, emit visible light because their blackbody curves peak in or near the visible range. Cooler objects, such as warm rocks or household radiators, produce invisible radiation—they are warm to the touch but are not glowing hot to the eye. These latter objects emit most of their radiation in the lower-frequency infrared portion of the electromagnetic spectrum.

 Figure 2.10 Blackbody Curves Comparison of blackbody curves for four cosmic objects. (a) A cool, invisible galactic gas cloud called Rho Ophiuchi. At a temperature of 60 K, it emits mostly low-frequency radio radiation. (b) A dim, young star (shown red in the inset photograph) near the center of the Orion Nebula. The star’s atmosphere, at 600 K, radiates primarily in the infrared. (c) The Sun’s surface, at approximately 6000 K, is brightest in the visible region of the electromagnetic spectrum. (d) Some very bright stars in a cluster called Omega Centauri, as observed by a telescope aboard the space shuttle. At a temperature of 60,000 K, these stars radiate strongly in the ultraviolet. (Harvard-Smithsonian Center for Astrophysics; J. Moran; AURA; NASA) The Planck Spectrum This animation shows the growth of the black-body curve and the corresponding shift of peak wavelength with temperature for the spectrum of a heated object. The visible region of the spectrum is indicated. As temperature rises, the "red end" of the spectrum fills up first, so the object would begin to glow red, then orange-red, then yellowish-red. It eventually becomes "white hot" when the entire visible portion of the spectrum is filled in a roughly uniform way. At extremely high temperatures, such as the surface temperatures of very massive young stars, the peak of the spectrum moves beyond the visible range toward higher frequencies, and the resulting tilt in the portion of the spectrum that remains in the visible range causes the object to appear slightly more blue than white.

There is a very simple connection between the frequency or wavelength at which most radiation is emitted and the absolute temperature (that is, temperature measured in kelvins—see More Precisely 2-1) of the emitting object: The peak frequency is directly proportional to the temperature. This relationship is more conventionally stated in terms of wavelength

and is known as Wiens law (after Wilhelm Wien, the German scientist who formulated it in 1897). In essence, it tells us that the hotter the object, the bluer its radiation. For example, an object with a temperature of 6000 K (Figure 2.10) 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 4800 nm, well into the infrared. At a temperature of 60,000 K, the peak would move all the way through the visible range to a wavelength of 48 nm, in the ultraviolet.

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 sharply as the heater warms up and begins to emit visible light. In fact, the total amount of energy radiated per unit time is proportional to the fourth power of an object’s temperature:

This relationship is called Stefans law, after the nineteenth-century Austrian physicist Josef Stefan. It implies that the energy emitted by a body rises dramatically as the body’s temperature increases. Doubling the temperature, for example, causes the total energy radiated to increase by a factor of 16. The radiation laws are presented in more detail in More Precisely 2-2.

Astronomical Applications

Astronomers 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 2.9. 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. Applying Wien’s law to the blackbody curve that best fits the solar spectrum, we find that the temperature of the Sun’s surface is approximately 6000 K. (A more precise measurement 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 2.10). For example, the relatively cool surface of a very young star might 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 would emit 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.

CONCEPT CHECK

Describe, in terms of the radiation laws, how the appearance of an incandescent lightbulb changes as you turn a dimmer switch to increase its brightness from “off” to “maximum.”