We mentioned that one of the few electromagnetic phenomena that was not nicely explained by Maxwell’s classical equations had to do with heated solid materials. What exactly was the problem, and how serious was it? Let’s return to our humble fireplace poker to see.
First, we need a little bit of terminology. The fancy scientific term for a fireplace-poker-like object is a blackbody. By definition, a true blackbody is an object that absorbs all, and reflects none, of any light that is shined onto it. Blackbodies aren’t always black, though, since they can emit their own “internal” light when heated. Late nineteenth century scientists were having difficulty predicting the emission spectrum of light—the frequency distribution of light emitted over a broad range—from a heated blackbody. Since such spectra are often drawn on a graph that presents the energy of light emitted (y-axis) versus its frequency (x-axis), it is often called a blackbody curve. The graph that we showed you at the end. The emission spectra of a solid object—is a blackbody curve, as are the experimental data points shown in the next two figures.
DEFINITION
A blackbody is any physical object that absorbs all of the radiation falling on it. Such an object reflects no external light, but when heated is capable of emitting thermal radiation from within.
The blackbody curve is a graph that displays the characteristic frequency distribution of emitted radiation; it is also known as the blackbody spectrum.
In the late 1800s, classical physicists were working hard to come up with a theoretical description of the blackbody curve. They began with the hypothesis that there were small, charged particles in the poker that wiggled when heated. This turns out to be correct: the poker is filled with electrons, whose heat-induced vibrations lead to the emission of light. In essence, the electrons absorb the heat and then re-emit it in the form of electromagnetic radiation.
ATOM TRAP
We pretend that our fireplace poker is a true blackbody. In reality, though, even the blackest poker on Earth will reflect some light that shines on it. For this reason, scientists have invented a substitute for the blackbody, formed by a light-tight cavity with only one tiny hole leading in and out. It was through experimental and theoretical studies using such cavities, not actual fireplace pokers, that the protagonists made their important advances.
To make a quantitative prediction of the blackbody curve, classical physicists first assumed that the electrons could move with any possible energy along a continuous range. Then, they assumed that the intensity (or energy) emitted at any particular frequency was given by the product of two things: the number of oscillators at that particular frequency, and average energy of a charge oscillating at that particular frequency.
As you warm the poker to hotter and hotter temperatures, the electrons will oscillate faster and faster and then emit light at higher and higher frequencies. This is in perfect qualitative agreement with what we observe: if a hot poker glows red, a really hot poker will glow yellow, and a really, really hot poker will glow blue. So far, so good.
Finally, they would use equations from classical electromagnetism and thermodynamics to derive a mathematical expression for the blackbody spectrum. The blackbody curve could be illustrated by plotting on a graph the emission energy calculated (along the y-axis) at every possible frequency (along the x-axis).
This was an eminently sensible approach that had proven effective when applied to similar problems countless times before. The only problem was that in this case the predicted result was entirely wrong!
When classical physicists used Maxwell’s theory to predict the blackbody curve, they got catastrophic results.
For starters, it had remarkably little resemblance to what physicists actually observed during laboratory experiments. More gravely, it predicted that the intensity of the light emitted would increase without bound at lower and lower wavelengths—such that in the range of ultraviolet light, the object would emit near infinite amounts of energy! This was so distasteful to physicists at the time that it became known as “the ultraviolet catastrophe.”
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