Monday, May 26, 2008

The Black-Body Spectrum

As Maxwell first described in the nineteenth century, all objects emit radiation at all times because the charged atomic particles of which they are made are constantly in random motion. As these particles move, they generate electromagnetic waves. Heat an object, and its atomic particles will move more rapidly, thereby emitting more radiation. Cool an object, and the particles will slow down, emitting proportionately less electromagnetic radiation. If we can study the spectrum (that is, the intensity of light from a variety of wavelengths) of the electromagnetic radiation emitted by an object, we can understand a lot about the source. One of the most important quantities we can determine is its temperature. Fortunately, we don’t need to stick a thermometer in a star to see how hot it is. All we have to do is look at its light carefully. But how?
All objects emit radiation, but no natural object emits all of its radiation at a single frequency. Typically, the radiation is spread out over a range of frequencies. If we can determine how the intensity (amount or strength) of the radiation emitted by an object is distributed across the spectrum, we can learn a great deal about the object’s properties, including its temperature.
Physicists often refer to a black body, an imaginary object that absorbs all radiation falling upon it and re-emits all the radiation that it absorbs. The way in
which this re-emitted energy is distributed across the range of the spectrum is drawn as a black-body curve. Now, no object in the physical world absorbs and radiates in this ideal fashion, but the black-body curve can be used as a reference index against which the peak intensity of radiation from real objects can be measured. The reason is that the peak of the blackbody curve shifts toward higher frequencies (and shorter wavelengths) as an object’s temperature increases.
Thus, an object or region that is emitting very short wavelength gamma ray photons must be much hotter than one producing longer wavelength radio waves. If we can determine the wavelengths of the peak of an object’s electromagnetic radiation emissions, we can determine its temperature.
Astronomers measure peak intensity with sophisticated scientific instruments, but we all do this intuitively almost every day. You have an electric kitchen range, let’s say. The knob for one of the heating elements is turned to off. The heating element is black in color. This tells you that it may be safe to touch it.
But if you were to turn on the element, and hold your hand above it, you would feel heat rising, and would know that it was starting to get hot. If you had infrared vision, you would see the element “glowing” in the infrared. As the element grows hotter, it will eventually glow red, and you would know that it was absolutely a bad idea to touch it (regardless of where the control knob happened to be pointing). At room temperature, the metal of the heating element is black, but as it heats up, it changes color: from dull red to bright red. If you had a very high-voltage electric range and a sufficiently durable heating element, you could crank up the temperature so that it became even hotter. It would emit most of its electromagnetic radiation at progressively higher frequencies.
Now, an object that omits most of its radiation at optical frequencies would be very hot. And a range will never (we hope) reach temperatures of 6000 K, like the sun. The red color you see from the range is in the “tail” of its black-body spectrum. Even when hot, it is still emitting most of its radiation in the infrared part of the spectrum.

1 comment:

Julio said...

Where's the radiation law?
Don't sell your audience short. And don't stop short of making your web page a useful resource on the web. State the Planck law.
And state it in whatever form is actually relevant to astronomy.
Whatever form, for example, would permit a reader to reproduce the 270K curve that approximates the unattenuated emission spectrum of the Earth (see: ).
I gather that's in frequency-dependent (as opposed to wavelength-dependent) form.