Chapter 13: The Quantum and the Photoelectric Effect

Dr. Einstein is truly the father of Quantum Mechanics, although he was not very happy about the way that his progeny turned out. Kind of like the parents whose beautiful bouncing baby boy turns out to be a tattoo artist with a bleached blond bimbo girlfriend with dark roots who has double’D’ breast implants. One that chews gum with her mouth open.

The basis for Quantum Mechanics was derived by Karl Ernst Ludwig Marx (Max) Plank. Dr. Plank was a very conservative and yet exceptionally bright man who was born just after the middle of the nineteenth century. He could have been a professional musician or a mathematician, but instead he chose physics; because he thought that it would be more exciting. Go figure. Although he enjoyed this field of study, he had trouble finding inspiration for it at the university, and found that his professors were either uninteresting, or lacking dedication to the field. One of them is quoted as saying: “that in this field, almost everything is already discovered, and all that remains is to fill in a few holes.”  You just have to love the foresight expressed in opinions like that, don’t you?

He did manage to find something that piqued his interest though in a series of papers by Dr. Rudolf Clausius that he discovered during his studies. These papers were on the emerging field of Thermodynamics and the mysterious quantity called entropy. It was to this topic that Dr. Planck would devote the next 30 years of his academic life, and would lead to a discovery that neither he, nor even Dr. Einstein, would fully understand the full implications of.

There is a lot of great information about Dr. Planck, and a very famous institute in Germany bears his name. And the author has a great respect for his findings. But it has to be said that, in spite of all of the great insight evidenced in his writings and suppositions, the implications that this discovery had on future thinking (including some of the ideas put forward in this tome) Max had no idea what it was that he had actually discovered.

Let’s set the scene, just a little. This was the post Clerk Maxwell age when everyone fully understood electromagnetism (supposedly) and therefore, radiation (that is, electromagnetic radiation). Max was doing some empirical research on blackbody emission. It was important at the time because there were two leading theories around to describe this phenomenon, each based on different premises. Both had their own shortcomings. Scientists were still working, ‘filling in holes’, you see. One of these theories worked well at high frequencies; the other worked well at low ones. But neither one could explain the absorption and radiation across the full spectrum.

So Max did some testing, and he discovered that, among other things, the energy of the radiation was proportional to its frequency, and furthermore (and this is the part that really changed everything) that the equation he had devised worked only when the constant had an integer multiplier.

Dr. Planck truly believed that this was a mathematical anomaly of his formulation and that he had not discovered anything momentous. He published a paper with his findings, wherein he reduced the relationship to the famous equation:

     E = hν

     Where: E = energy

     ν = frequency of the radiation

     h = (eventually) Planck’s Constant (which, by the way, is a very, very small number; 6.826 * 10-34 Joules * second and is an expression for energy over time. Interestingly enough, these are also the units for angular momentum, which makes sense, since frequency is actually a circular function.)

This expression proved to be exceedingly accurate across the entire spectrum. Max had derived this expression by assuming that matter was composed of harmonic oscillators, and later, again from a momentum equation. He published his findings and this new expression in a paper in 1901, but it was not until four years later when Einstein published his paper on the photoelectric effect, that people really began to take notice.

Dr. Einstein was on a roll. He had just published his striking paper on Special Relativity, and he realized that there was more to Max’s work than met the eye. What caught his attention was a seeming contradiction about the photoelectric effect.

Some materials, you see, will emit an electron when exposed to radiation, especially light (think: solar electric panels). This got him to thinking. How could a mass-less wave knock an electron (a physical ‘thing’) loose from an atom? Furthermore, he discovered that it was not the intensity of the light source that really mattered, but the frequency.

This is essentially why photovoltaic systems cannot convert heat to electricity. Heat radiation has a long wavelength, and therefore, a lower frequency. Therefore, according to Max’s equation, it has less energy. Visible light however, has a much shorter wavelength and a much higher frequency than heat radiation and does have enough energy to kick start an electron flow. You can heat up your photovoltaic panels in the oven as much and long as you want and never generate a current, but if you shine a flashlight on one, you’ll make some current flow.

Dr. Einstein combined this surprising fact with Max’s concepts and proposed that light, and in fact all radiation, was composed of ‘quanta’, that is, little finite packets of energy whose individual energy could be calculated utilizing Max’s equation. It made sense. If a quantum did not contain enough energy to bump an electron hard enough to make it move, it really didn’t matter how many of them there were. But, if it had just the right amount of juice, it could knock one out every time it hit one.

This finding would prove to be the seed of the Quantum Mechanical revolution, and that premise, although valid, has led us down a long path that, while providing a massive quantity of insight into the inner workings of nature, has brought us no closer to a complete understanding.

Both Dr. Einstein and Max got a Nobel Prize for this discovery, and there is every indication that neither one was comfortable with the eventual conclusions that were reached through this line of reasoning. But the validity of the formulation is undeniable. They had established a relationship between energy and matter that Dr. Einstein would later use in his quintessential work, General Relativity, but at a cost to the study of physics that vexes us still.

One thought on “Chapter 13: The Quantum and the Photoelectric Effect

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