2 - The de Broglie Hypothesis
Abstract (TL;DR):
Planck, Bohr, Einstein, de Broglie. Four of the most important figures in atomic theory, beginning the Quantum Revolution.
Planck discovered energy quanta, overwriting past physical law. Bohr discovered that light, a form of energy, emanated from atoms whose electrons were dropping from a higher energy state to a lower one, only at distinct levels. Einstein, who had discovered the “photon” around the same time, explained that the connection between the electrons and light was that both existed at distinct states. De Broglie put it all together, saying that electrons, like light, had the behavior of waveforms and particles. This hypothesis, coined the “Matter Wave” hypothesis, has such strong evidence that it is still one of the most accepted atomic theories in existence today.
Circle Wave by Dave Whyte
It’s interesting how the deeper you dive into the atom, the more you find. There really is a whole universe in these atoms. As such, I recommend that you take a look at the previous lesson in the Elemental Flow series in order to really understand where I will be going in this one.
Before I jump right in, I recommend that you actively participate in this lesson. Grab a notepad and pen or use your word processor of choice and take notes. This one is very involved and you may have questions that I encourage you to answer. They will help not only you, but me as well, and you might even inspire another chapter of the storyline.
Without further ado, enjoy…and keep an extra box of tissues nearby; this one’s is a tear-jerker.
What Are Electrons?
Imagine, for a moment, a situation where there are many electrons surrounding a nucleus. As we previously discussed, Schrödinger created a model where electrons are a certain length and orientation away from the nucleus, yet close enough to experience its attractive force while maintaining a respectable distance away from other electrons – a tough balancing act for sure. With respect to this model, you might expect them orient themselves around a nucleus in any way that reduces their energy.
But why do they move at all? Why would they not just orient themselves in the spots that satisfy those three conditions and then simply vibrate in place to get rid of any excess energy that enters their system? On a macroscopic scale, magnets do this: they don’t bounce around – they either snap in place or repel each other.
The reason that electrons can’t just settle is because these, like other microscopic particles, have a hidden second nature that they must abide by.
I imagine that this is an area where most college chemistry professors avoided, much to all of our dismay, because it explains quite a bit about why electrons do what they do. They must have thought that everyone understood beginner level Quantum Mechanics. Common mistake, I suppose (sarcasm). If you’re a part of the 99% that doesn’t know what I’m talking about, strap in. This will probably be a bumpy ride.
Niels Bohr’s Atomic Light Discovery
Quantum Mechanics has the capacity to either make you worry about how difficult it is, excite you over its mythos and the scientists responsible for its inception or terrify you about the microscopic world that composed everything you know and love. Or a combination of the three.
In the quest for the “hidden nature”, I say we dive into a few of the key figures that wanted to model the electron. Let’s begin with Niels Bohr and his model of the electron.
Image via Universe Today
Shortly after Rutherford’s model, which you saw in the last lesson, Bohr edited the model to be more consistent with his findings.
He noticed that, during the reduction of energy in the electrons, they would release light.
But, alone, that is not such a big deal – light is a form of energy and electrons want to reduce their energy. The problem was the strange way that light was coming from the atoms. Let’s take a brief divergence into the physics of light to figure the phenomenon out.
From Light Comes Color
Light, as we can see it, is the mixture of energies on the visible spectrum. That might sound complex, but it’s actually quite simple to understand, given that you see it in effect after the sun comes out after a nice rainstorm.
Image via Clipart Library
White light, when refracted, or bended, through a substance (water in the case of a rainbow) splits into seven memorable colors: red, orange, yellow, green, blue, indigo and violet. They are split according to the size of their wave, or wavelength, with red light having the highest wavelength (around 700 nanometers) and violet having the lowest (around 400 nanometers).These wavelengths are inversely-proportional to the amount of energy, meaning as wavelength grows, energy drops.
Image via Lumen Learning
Image via Astronomy Online
You can see that if you put in bigger and bigger numbers in the wavelength symbol, lambda, energy gets smaller and smaller. And there’s another constant! Don’t worry, we’ll get to Planck when we talk about quantum mechanics. He is the founder of the field, after all.
There’s even a nice formula for this, created by the Father of Quantum Mechanics, Max Planck. I’ll show it below, but don’t worry about this for now. It won’t be on the test.
Discrete Discovery
So, what was the strange discovery Bohr made?
He noticed specific colors coming from the electrons when he measured the system. If the electrons could truly be anywhere around the nucleus, Bohr would have seen the full visible spectrum of colors like what you see in a rainbow. In quantum mechanical terms, this electron is quantized, meaning that it only releases discrete, or distinct, energy levels, not continuous ones, like that of a rainbow.
Image by Dmitry Karpenko & Vahe Ganapetyan via Reef Leo Lab
Continuous on the top, discrete on the bottom.
This led Bohr to think that the electrons must be an exact distance away from the nucleus and each other. When higher-energy electrons decrease in energy level, they go to another exact distance from the nucleus that is lower than the one they were. The transition to lower orbits creates a specific color of light, caused by the energy that they give off.
As reasonable as these discoveries seem, science isn’t always so easy to get right the first time, no matter how many years one has spent on the topic. Important lesson.
First, electrons do not just infinitely continue to expand outward from the nucleus according to their energy state. You might imagine that if it gets too far away, it would just break free of the attractive electric force of the nucleus. That is absolutely true, and there is such a concept called a “free electron”, which is defined as just that.
Secondly, Bohr seems to think here that electrons are traveling on an orbit like planets around a star, making the model completely two-dimensional. Think about that for a moment. Are school buses in children’s drawings really as flat as they look on a piece of paper? Realistically, they’re three-dimensional; school buses carry rows and rows of children. This limits the electrons in his model to only expand outward, overlapping with the first problem.
He continues to falter in a more serious way. He explains that the electrons exist at discrete levels due to quantization of the electromagnetic field that these electrons reside within (theorized by James Clerk Maxwell, who we will discuss in time). But this is incomplete. He failed to dig deeper. Why is the electromagnetic field quantized? The electrons are certainly not doing it themselves.
In actuality, an electromagnetic field can only be quantized with the inclusion of discrete energy. That makes sense, right? If quantization is existence at specific energy levels, then there must be something putting the electromagnetic field at those specific energy levels. Energy must be conserved. Electrons can't just generate that energy on their own.
Unfortunately, Bohr didn't agree with the person with the right answer - the famed Albert Einstein.
Albert Einstein’s Quantum Theory of Light
Einstein made a name for himself by publishing a set of papers that included a discovery of the photon. The photon is defined as light’s quantum, or the discrete and fundamental unit of energy of light. Einstein found that the quantum had no rest mass, meaning that, when the photon is not in motion (at rest), it has no mass. That mind-blowing discovery revolutionized physics for good.
It is the existence of these discrete energy packets interacting with the electrons, which generate an electromagnetic field, that creates discrete electromagnetic fields. Whenever an electron moves to a lower energy level, as previously stated, it gives off these photons and you see the light energy that represents one discrete level subtracted by the lower one.
To be more specific, if an electron exists at energy level 5, and it wishes to move down, it must move to 4, as 4 is a specific value. When it does move to 4, it gives off the color of light equivalent to an energy level of 1, which is why you see only one color. If the electron was moving to level 3, the photon would have an energy level of 2, and you would see a different color, and so on. It's too bad that Bohr didn't believe in the existence of photons, isn't it?
Nevertheless, it was odd that an electron mirrored the photon in that it behaved as though it was quantized. Why would an electron, a particle with mass, share qualities with a photon, a particle without mass? Perhaps there were more similarities between these particles than just this?
Electromagnetic Forces of Nature
Image drawn by John Adam Houston
Light has been debated long before Einstein and Bohr, at least since the times of the legendary Sir Isaac Newton. Despite his own experiment of splitting light into its seven colors with a prism (yes, that was him), Newton believed that it was a particle because of how light created clear shadows.
See? Even great scientists can miss things. You’ll remember that the only reason that we get the rainbow of colors is due to refraction.
The kicker is that particles do not refract. Only waves do.
Experiments done over hundreds of years following Newton have yielded similar results. The most notable experiments were done by James Clerk Maxwell in the 1800s, who developed a set of equations for electromagnetic waves that we still use to this day. They influenced Bohr's explanation for his model. Of course, Einstein would rebel in the early 1900s and move on to experimentally prove that light was not only a wave, but also a particle.
So light is massless, and behaves like waves and particles. It’s crazy to insist that an electron could be similar, right?
Louis de Broglie’s Wave Hypothesis
Louis de Broglie, a scientist of France, didn’t think so. He saw where Bohr’s experiments left him and, unsatisfied with his model, tried to take it a step further theorizing that microscopic particles with mass also behaved like waves.
Using the aforementioned equations of Maxwell and Einstein’s discovery of the dual nature of light, de Broglie was set to make history. He knew that, as a charged particle, an electron would likely be under the influence of both an electric field and a magnetic field making their wave pattern electromagnetic. Electromagnetic waves, are defined as oscillations, or regular movements back and forth (like a pendulum), that are caused by both electric and magnetic fields.
Remember that equation we talked about in the last part – Coulomb’s Law? It defined the electrostatic “power” of charged particles. The relationship between particles, whether they were attracted to or repulsed by each other, would create an electric field!
Image via Splung
The strength of the field from any individual charge is determined by the strength of that charge.
Magnetic fields are created, simply, whenever charges move.
Image via School Physics
Beautiful Curves
With this knowledge, de Broglie only needed to validate his theory by comparing it to Bohr’s findings while improving upon them to eliminate the previously-mentioned shortcomings in Bohr’s model.
Fortunately, it is theoretically easy to do all three. Bohr found that the electrons must be in defined orbits – otherwise they would not be exhibiting discrete energy in the form of photons when they went from a higher to a lower energy state. That means electrons must exist such that their orbits are uninterrupted and stable. We define waves that are constant and not under any interference standing waves. The electrons must also be in phase with their orbits, meaning that they stay on a consistent path over time.
This is what that looks like:
Image via HyperPhysics
The frequency of the waves, or how many humps there are, is purely determined by how much energy the electrons have. In fact, the only possible way that one can have an exact orbit as more and more electrons are added is if the electrons are at an energy level that allows them to be a standing wave. If electrons were to become excited and the energy used to excite them was not enough to bring them to a standing wave, it would not move to a higher energy state.
Also, notice that n = 1 looks exactly like Bohr’s model, a simple circular orbit. Bohr’s model was only correct for the case where there is only one electron present – the hydrogen atom!
Lastly, wrapping it up nicely, the waves from this model move into three dimensions, supplanting the limited 2D model of Bohr.
Image by Andrew D. Hwang via StackExchange
This is how electrons move, creating the wave-particle duality of all things composed of microscopic particles. We know that electrons are absurdly fast, as well, so, by observation, we can never know where on the path electrons are at any time. This is what ultimately inspired Schrödinger to create the electron cloud model that we use today. Despite the messiness of that model, electrons on it are moving in these same wave-like patterns. Schrödinger’s concern, unlike de Broglie’s, was to create a mathematical model to figure out the probability of finding an electron in a certain position, which he was successful in doing, beginning orbital theory.
Image via Pinterest
At an atomic level, your body is behaving like both a wave and a particle. I hope that doesn’t keep you up at night. If it does, just stare at this image that is strikingly similar to the above model. It might just calm you down.