So what comes to mind when you hear the term catastrophe? It certainly sounds ominous and dreadful. According to merriam-webster.com a catastrophe is: a momentous tragic event ranging from extreme misfortune to utter overthrow or ruin and/or utter failure. It is the “utter failure” description that more accurately describes this particular catastrophe. So just what is the ultraviolet catastrophe and what was its significance to the birth of quantum mechanics? Keep reading to find out.
As the 19th century drew to a close, there was among the scientific community, an belief that most of the physical phenomena could be described and explained through classical physics. Nature, however, had other ideas. A series of discoveries would usher in a new branch of physics that classical or Newtonian physics was not able to describe. The photoelectric effect was one of these discoveries. This phenomena was accurately described by Albert Einstein which demonstrated that light travels as a wave and interacts with matter as particles. This is often described as the dual nature of light. The double slit experiment showed that particles, such as electrons, could produce interference patterns by interfering with themselves as they traveled through a narrow set of slits. This remarkable experiment showed that the behavior of individual particles could travel as particles and still demonstrate wave like behavior. Oddly enough, when scientists attempted to determine which slit the particle traveled through the interference pattern collapsed. The result of this collapse is what would be expected from a series of single particles being fired though one slit or another. Both of these topics have been discussed in earlier blog posts on my site. Feel free to go read those posts if you haven’t already.
So both of the above experiments helped describe discrete amounts of fundamental units. These units were considered to be quantized that is containing the smallest whole number amount of a specific material. For example, a quanta of light is a photon. So let’s see how the ultraviolet catastrophe relates to all this.
Blackbody and Blackbody Radiation
It will be helpful to be familiar with some of the vocabulary associated with this phenomenon. A blackbody is an idealized or theoretical object that absorbs all electromagnetic radiation that falls on it. A blackbody, according to Kirchoff, is a body that is able to “…completely absorb all incident rays, and neither reflects nor transmit any.” A blackbody emits blackbody radiation which is also known as thermal radiation. Many objects such as people, heating elements, flames, and the sun approximate blackbodies.
So you may be wondering how would a person experimentally measure blackbody radiation? You could set up a hollow container with a small hole in it. This cavity allows incident radiation to get in while the design makes it unlikely that much radiation will escape.
A small amount of emitted radiation will pass back out through the cavity opening where it can be measured. Thermal equilibrium occurs when two objects are in direct contact or close contact with each other but no net energy is transferred between them. They may gain energy from one another but no net energy is transferred. The amount of emitted radiation is small enough that it will not disturb the thermal equilibrium inside the cavity. As it turns out, the radiation a blackbody emits depends upon the temperature of the body.
Catastrophe
In science a theory and the mathematical representation of the theory must match the experimental results in order for the theory to be valid. Using classical physics, Lord Rayleigh and Sir James Jeans, working independently developed a law to predict the amount of radiation intensity emitted at a given wavelength. They were trying to come up with a rule that would allow them to accurately predict the color a blackbody would radiate based on temperature. The Rayleigh-Jeans Law predicted that the intensity of radiation was proportional to the wavelength so as the intensity increased the wavelength should decrease.
In the graph above you can see that as the temperature in Kelvin increases the peak of the curve is shifted to the left. At 5000 K the peak of the curve is in the red portion of the spectrum and at 6000 K the peak is in the yellow portion of the spectrum. The catastrophe occurred in the ultraviolet portion of the spectrum and it stated that at low wavelengths the intensity should become infinite. This obviously was a violation of the law of conservation and because this occurred in the ultraviolet portion of the spectrum it was named the ultraviolet catastrophe.
The graph above shows the experimental results versus the classical theory predictions regarding the intensity of radiation versus wavelength. You can see that at higher wavelengths the classical theory closely matches experimental results but at lower wavelengths there is no agreement.
A Quantum Way Out of Catastrophe
Max Planck solved the ultraviolet catastrophe in 1900. Planck developed a model in which the electromagnetic radiation in the cavity is absorbed by simple harmonic oscillators or resonators. These oscillators were merely a description and he didn’t argue that they actually exist in the walls of the cavity. Planck determined that the energy absorbed by these resonators needed to be in discrete packets or quantized. These discrete packets of energy became known as quanta of energy. This idea of quanta of energy was the birth of quantum theory. He developed a formula to relate the energy absorbed to the frequency of oscillation: E = hv where E is the energy absorbed, v is the frequency of oscillation and h is Planck’s constant 6.626 x 10^-34 J s
Max Planck derived his blackbody radiation law working backward from Wein’s distribution law. Planck realized that Wein’s distribution did not agree with experimental data at long wavelengths, that is wavelengths in the infared portion of the spectrum. The results from Planck’s blackbody radiation law are in agreement with experimental data.
The above equation was derived from Wein’s distribution law. Planck’s equation differs in that it allows the units of measure to be derived entirley based on the universal physical constants or the four fundamental constants of nature, Planck’s constant (h), Boltzman’s constant (kB), speed of light (C), and the universal gravitational constant (G).
Max Planck was able to work through the ultraviolet catastrophe and develop an theory that matched the experimental results. His realization that the radiation in the cavity must be absorbed in discrete quantities ushered in a brand new branch of physics called quantum mechanics. Here is a short video describing Planck’s discovery of light being quantized and the birth of quantum mechanis: https://youtu.be/i1TVZIBj7UA Ironically, many physics students probably refer to this as the quantum catastrophe!
Neville’s Phantastic Physics Phun 