4 Easy Experiments to Prove Quantum Mechanics to Your Drunk Friend

science_drinking

By Bradley Stockwell

I once had a friend after a long night of drinking consult me on his living room couch, “What does quantum mechanics really mean?” I was taken aback for this particular friend and I had never discussed physics—let alone quantum mechanics—in our entire five year relationship. He was a former UCSB frat boy and he was the friend I turned to when I needed a break from my intellectual studies to indulge in the simpler pleasures of life such as women and beer. He was also so heavily inebriated that I was pretty sure he wasn’t even going to remember asking the question in the morning (which I was indeed later proven right).

I answered casually, “Well, it’s the physics of atoms and atoms make up everything, so I guess it means everything.” Not satisfied with my answer he replied slurredly, “No really, what does it mean? We can’t really see what goes on in an atom so how do we really know? What if it’s just some guys too smart for their own good making it all up? Can we really trust it? From what I know we still don’t completely understand it so how do we know if it’s really real? Maybe there’s just some things as humans were not supposed to understand.”

I’ll be honest I was in shock for I had never heard my friend express this type of existential thinking before. Not to paint him one-sidedly, we had had many intelligent discussions on finances, the economy, politics, but never physics and philosophy. Maybe it had something to do with the marijuana joint I just passed to him. Anyways, after a few moments of contemplation I answered, “Everything from your smartphone to the latest advances in medicine, computer and materials technology, to the fact you’re changing channels on the TV with that remote in your hand is a result of understanding quantum mechanics. But you’re right; we still don’t fully understand it and it’s continually showing us that the universe is probably a place we’ll never fully grasp, but that doesn’t mean we should give up…” I then continued with what might’ve been too highbrow of an explanation of quantum mechanics for an extremely drunk person at 3 a.m. because halfway through he fell asleep.

As my friend snored beside me, I couldn’t help but be bothered that he and so many others still considered quantum mechanics such an abstract thing more than a hundred years after its discovery. I thought if only I could ground it in some way to make people realize that they interact with quantum mechanics every day; that it really was rooted in reality and not a part of some abstract world only understood by physicists. I myself being a layperson with no university-level education in science learned to understand it with nothing more than some old physics books and free online classes. Granted it wasn’t easy and took a lot of work—work I’m still continuing, but it’s an extremely rewarding work because the more I understand, the more exciting and wonderful the world around me becomes.

This was my inspiration behind The Party Trick Physicist blog; to teach others about the extraordinary world of science and physics in a format that drunk people at 3 a.m. might understand. I make no promises and do at times offer more in-depth posts, but I do my best. With this said, as unimaginative as a post about at-home physics experiments felt to me initially, there’s probably no better way to ground quantum mechanics—to even a drunk person at 3 a.m.—than some hands on experience. Below are four simple quantum mechanical experiments that anyone can do at home, or even at a party.

1. See Electron Footprints

For this experiment you’ll be building an easy to make spectroscope/ spectrograph to capture or photograph light spectra. For the step-by-step tutorial on how to build one click here. After following the instructions you should end up with, or see a partial emission spectrum like this one below.

mercury emission spectrum

Now what exactly do these colored lines have to do with electrons? Detailed in a previous post, The Layman’s Guide to Quantum Mechanics- Part 2: Let’s Get Weird, they are electron footprints! You see, electrons can only occupy certain orbital paths within an atom and in order to move up to a higher orbital path, they need energy and they get it by absorbing light—but only the right portions of light. They need specific ranges of energy, or colors, to make these jumps. Then when they jump back down, they emit the light they absorbed and that’s what you’re seeing above; an emission spectrum. An emission spectrum is the specific energies, or colors an electron needs—in this case mercury electrons within the florescent light bulb—to make these orbital, or ‘quantum’ leaps. Every element has a unique emission spectrum and that’s how we identify the chemical composition of something, or know what faraway planets and stars are made of; just by looking at the light they emit.

2. Measure The Speed of Light With a Chocolate Bar

This is probably the easiest experiment as it only requires a chocolate bar, a microwave oven, a ruler and calculator. I’ve actually done this one myself at a party and while you’ll come off as a nerd, you’ll be the coolest one there. Click here for a great step-by-step tutorial and explanation from planet-science.com

3. Prove Light Acts as a Wave

This is how you can replicate Thomas Young’s famous double slit experiment that definitively proved (for about 100 years) that light acts as a wave. All you need is a laser pointer, electrical tape, wire and scissors. Click here for a step-by-step video tutorial.

4. Prove Light Also Acts as a Particle 

This experiment is probably only for the most ambitious at-home physicists because it is the most labor and materials extensive. However this was the experiment that started it all; the one that gave birth to quantum mechanics and eventually led to our modern view of the subatomic world; that particles, whether they be of light or matter, act as both a wave and a particle. Explained in detail in my previous post The Layman’s Guide to Quantum Mechanics- Part I: The Beginning, this was the experiment that proved Einstein’s photoelectric effect theory, for which he won his only Nobel Prize. Click here to learn how to make your own photoelectric effect experiment.

Good luck my fellow party trick physicists and until next time, stay curious.

The Layman’s Guide to Quantum Mechanics- Part I: The Beginning

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By Bradley Stockwell

My next blog topic was scheduled to be a crash course in String Theory as it seemed like a logical follow-up to a previous post, A Crash Course in Relativity and Quantum Mechanics. However as I was trying to put together this crash course on String Theory, I realized that while my previous post did an excellent job of explaining the basics of relativity, it was far too brief on the basics of quantum mechanics (so much so that you should just regard it as a crash course on relativity). It could also be that I’m just procrastinating in writing a blog post on String Theory because, as you can probably assume, it’s not exactly the simplest of tasks. So in the name of procrastination I’ve decided to write a comprehensive overview on something much easier (in comparison): quantum mechanics. I not only want to explain it, but to also tell the dramatic story behind its development and how it has not only revolutionized all of physics, but made the modern world possible. While you may think of quantum mechanics as an abstract concept unrelated to your life, without it there would be no computers, smartphones, or any of the modern electronic devices the world has become so dependent on today. Before we begin, unless you’re already familiar with the electromagnetic spectrum, I recommend reading my post, Why We Are Tone Deaf to the Music of Light before reading this. While it’s not necessary, if you begin to feel lost while reading, it will make this post much easier to swallow.

In 1900 the physicist Lord Kelvin (who is so famous there’s a unit of measurement for temperature named after him) stated, “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” As history now tells he couldn’t have been any more wrong. But this sentiment was not one he shared alone; the physics community as a whole agreed. The incredible leaps we (the human race) made in science during the 19th century had us feeling pretty cocky in thinking we had Mother Nature pretty much figured out. There were a few little discrepancies, but they were sure to smooth out with just some ‘more precise measurement’. To paraphrase Richard Feynman (as I so often do), Mother Nature’s imagination is much greater than our own; she’s never going to let us relax.

The shortest summary I can give of quantum mechanics is that all matter exhibits properties of a particle and a wave on a subatomic scale. To find out how we came to such a silly conclusion, let’s begin with one of the above referenced discrepancies which was later called the ultraviolet catastrophe. The UV catastrophe is associated with something called black body radiation. A black body is an ‘ideal’ body that has a constant temperature, or is in what is called thermal equilibrium and radiates light according to that body’s temperature. An example of a body in thermal equilibrium would be a pot of cold water mixed into a pot of hot water and after some time it settles down into a pot with room temperature water. On the atomic level, the emission of electron energy is matched by the absorption of electron energy. The hot, high energy water molecules emit energy to cold ones making the hot ones cool down and the cold ones warm up. This happens until all the molecules reach a consistent temperature throughout the body. Another easily relatable example of a black body is us, as in humans. We and all other warm-blooded mammals radiate light in the infrared spectrum; which is why we glow when we are viewed through an infrared camera.

As you are aware, we cannot see the infrared light we emit with the naked eye because the frequency is too low for our eyes to detect. But what if we were to raise our body’s temperature to far higher than the 98.6 degrees F we’re familiar with? Won’t those emitted light waves eventually have a high enough frequency to become visible? The answer is yes, but unfortunately you’d kill yourself in the process. Let’s use a more sustainable example such as a kiln used for hardening clay pottery. If you were to peer through a small hole into the inside of the kiln, you’ll notice that when it’s not running it is completely black. Light waves are being emitted by the walls of the kiln but they are far too low in frequency for you to see them. As the kiln heats up you notice the walls are turning red. This is because they are now emitting light waves with a high enough frequency for your eyes to detect. As the temperature continues to rise the colors emitted move up the color spectrum as the light wave frequency continues to increase: red, orange, yellow, white (a combination of red, orange, yellow, green and blue produces white), blue and maybe some purple.

Now according to this logic of thinking, and classical physics of the time, if we were to continue to increase the temperature we should be able to push the emitted light from the visible spectrum into the ultraviolet spectrum and beyond. However this would also mean the total energy carried by the electromagnetic radiation inside the kiln would be infinite for any chosen temperature. So what happens in real life when you try to heat this hypothetical kiln to emit light waves beyond the visible spectrum? It stops emitting any light at all, visible or not.

bbrgraph

The infinitely increasing dotted represents what the accepted classical theory of the time said should happen in regards to black body radiation. The solid line represents experimental results. Reference these graphed lines from right to left since I refered to light waves increasing in frequency not length. 

This was our first glimpse into the strange order of the subatomic world. The person who was able to solve this problem was a physicist by the name of Max Planck who had to ‘tweak’ the rules of classical wave mechanics in order to explain the phenomenon. What he said, put simply, is that the atoms which make up the black body, or in our case the kiln, oscillate to absorb and emit energy. Think of the atoms as tiny springs that stretch and contract to absorb and emit energy. The more energy they absorb (stretch) the more energy they emit (contract). The reason no light is emitted at high energies is that these atoms (springs) have a limit to the energy they can absorb (stretch) and consequently emit. Once that limit is reached they can no longer absorb or emit energies of higher frequencies. However what this implied is that energy cannot be any arbitrary value, as a wave would suggest, when it is absorbed and emitted; it must be absorbed and emitted in distinct whole number values (or in Latin quanta) for each color. Why whole number values? Because each absorption and emission (stretch and contraction) by an atom can only be counted in whole number values. There could be no such thing as a half or a quarter of an emission. It would sort of be like asking to push someone on swing a half or a quarter of the way but no farther. Planck was fervent in stating though that energy only became ‘quantized’, or came in chunks, when it was being absorbed and emitted but still acted like a wave otherwise. The notion of energy as a wave was long established experimentally and was something no one would question—unless you’re Einstein as we’ll see later. How did Planck come to this conclusion? Through exhausting trial and error calculating, he found that when the number 6.63 ×10−34  (that’s point 33 zeros then 663) was multiplied against the frequency of the wave, it could determine the individual amounts of energy that were absorbed and emitted by the black body on each oscillation. When calculated this way, it matched the experimental results beautifully. Whether he truly believed that energy came in quantifiable chunks, even temporary ones, is left to question. He was quoted as stating his magical number (later to become Planck’s constant) was nothing more than a ‘mathematical trick’.

If you’re a little lost, that’s okay. The second discrepancy I’ll address will make sense of it all called the photoelectric effect. To summarize plainly, when light is casted upon many metals they emit electrons. The energy from the light is transferred to the electron until it becomes so energetic that it is ejected from the metal. At high rates, this is seen to the naked eye as sparks. According to the classical view of light as a wave, changing the amplitude (the brightness) should change the speed in which these electrons are ejected. Think of the light as a bat and the electron as a baseball on a tee. The harder you whack the metal with light the faster those electrons are going to speed away. However the experimental results done by Heinrich Hertz in 1887 showed nature didn’t actually work the way classical physics said it should.

At higher frequencies (higher temperatures) of light, electrons were emitted at the same speed from the metal no matter how bright or how dim the light was. This would be like whacking the baseball off the tee and seeing it fly away at the same speed whether you took a full swing or gently tapped it. However as the intensity (brightness) of the light increased, so did the amount of electrons ejected. On the other hand, at lower frequencies, regardless of how intense the light was, no electrons were ejected. This would be like taking a full swing and not even dislodging the baseball from the tee. While it was expected that lower frequency light waves should take longer to eject electrons because they carry less energy, to not eject any electrons at all regardless of the intensity seemed to laugh in the face of well-established and experimentally proven light wave mechanics. Think of it this way, if you were to have a vertical cylindrical tube with an opening at the top end and a water spigot at the bottom end then placed a ping pong ball inside (representative of an electron lodged in metal), no matter how quickly or slowing the tube filled with water (low or high frequency light waves), eventually the ball will come shooting out of the top—obviously with varying velocities according to how fast the tube was filled. If energy is a continuous wave, or stream, ejecting electrons with light should follow the same principles.

Finally in 1905 somebody, that somebody being Albert Einstein, was able to make sense of all this wackiness and consequently opened Pandora’s box on wackiness which would later be called quantum mechanics. In his ‘miracle year’ which included papers on special relativity and the size and proof of atoms (yes the existence of the atom was still debatable at the time), Einstein stated that quantization of light waves (dividing light into chunks) was not a mechanic of energy absorption and emission like Planck said in regards to black body radiation, but a characteristic of light, or energy, itself—and the photoelectric effect proved it! Einstein realized that Planck’s magical number (Planck’s constant) wasn’t just a ‘mathematical trick’ to solve the UV catastrophe, it in fact determined the energy capacity (the size) of these individual light quanta. It was for this he’d later earn his only Nobel Prize.

So how did Einstein conclude this? Well let’s imagine a ball in a ditch. This will represent our electron lodged in metal. We want to get this ball out of the ditch but the only way to do it is by throwing another ball at it. This other ball will represent a quantum of light (later known as a photon). In order to do this you must exert a certain amount of force (energy) to give the ball a high enough velocity to knock the ball in the ditch out. So you call upon your friend to help you who happens to be an MLB pitcher. He’ll represent our high frequency (high energy) light source. Let’s say he can ‘consistently’ throw the ball with 10 units of energy (the units are called electron volts calculated by Planck’s constant times the frequency) and it takes 2 units of this energy just to dislodge the ball from the pit. 2 represents something called the work function in physics. Since it takes 2 units of energy to dislodge the ball, when the ball comes flying out of the ditch it will do so with 8 units of energy (10 – 2 = 8). This energy is called kinetic energy. Now let’s imagine there is ten balls in the pit so we clone our friend ten times (anything is possible in thought experiments). This is representative of turning up the light’s intensity. No matter how many balls are ejected from the pit they all leave with 8 units of energy. This is how we get a result of seeing an electron fly away from the metal at the same speed whether we smacked it or gently tapped it with high frequency light. Seeing your dilemma, your sweet grandmother also wants to help you dislodge balls from this pit. She’ll represent our low frequency light source. Unfortunately she can only throw with a force of 2 units of energy and while she may get the balls to roll a little bit, there isn’t enough kinetic energy left to dislodge them from the pit, no matter how many times we clone her (2 – 2 = 0). This is how we get the result of smacking the metal with a full swing of low frequency light and not see any electrons become ejected.

At the time, Einstein was still nothing more than a struggling physicist working at a patent office and his paper on the photoelectric effect took a while to get traction. However in 1914 his solution was experimentally tested and it matched the results to a tee. Proof that light had properties of a particle was hard to swallow because it had been so definitively proven as a wave during the previous two hundred plus years or so (something we’ll discuss more in part two of this series). In fact many of the forefathers of quantum mechanics, including Einstein and Planck, would spend the rest of their careers trying to disprove what they started. Truthfully, compared to our perception of reality, quantum mechanics is outrageous, but it is an undeniable proven feature of our world. How we figured this out is something we’ll continue with in the next part of this series. Until then, stay curious my friends.

Flight of the Timeless Photon

sunshinelove

By Bradley Stockwell

One of my favorite stories in all of physics is the story of sunlight because it touches on such a wide range of concepts. I apologize for the length of this post, but I guarantee you’ll be enlightened on many terms you probably hear thrown around a lot, but not a lot of people understand. Also, we learned in my previous post some of the important uses of light, but didn’t address the most important use of all, life!

Sunlight’s story, along with almost everything in the universe (we’ll ignore something called dark matter for now), begins with a hydrogen atom. Hydrogen is the most elementary and abundant element in the universe, hence the reason it is element one on the periodic table. Also because it’s comprised of one positively charged particle called a proton, which makes up its nucleus, and one negatively charged particle called an electron, which orbits around that single-proton nucleus. Within the sun, or any star, there is a process called nuclear fusion which transforms hydrogen into all 92 elements found in nature. Every grain of matter that makes up our physical world is forged in the heart of stars and is released when they begin to die. Not all stars produce all 92 elements however, like our sun will never get hot enough to fuse enough atoms together to produce heavy metals like gold. When I say heavy, what I am referring to is the element’s mass. The more sub-atomic particles shoved into an element’s nucleus, the heavier it is. Stars of different sizes produce different elements, but all stars begin with fusing hydrogen into helium as our sun is currently doing.

Within the sun’s core, hydrogen atoms are sped up from high amounts of energy, or heat, created by the force of the star’s mass on itself and collide at very high speeds, fusing them together to make helium. The sun has to smash four hydrogen atoms together to make one helium atom. The radioactive elements created in the steps in between are called hydrogen isotopes. Two hydrogen atoms make the stable isotope deuterium, three, the unstable isotope tritium, and four a helium atom. The difference between a stable and an unstable isotope is the even pairing of protons and neutrons (we’ll get to what a neutron is soon) in the nucleus. An even pairing, like one proton and one neutron (deuterium), is stable, but an uneven pairing, like one proton and two neutrons (tritium) is not and eventually falls apart into stable isotopes because it is too energetic to stay together. This ‘falling apart’ is known as radioactive decay.

 

NuclearFusion

 

Two hydrogen atoms make the stable isotope deuterium, three, the unstable isotope tritium, and four a helium atom.

If you’re a fan of The Simpsons, you may remember the Springfield baseball team was called The Isotopes. This was in reference to the town’s nuclear power plant, in which a forced and more violent version of this process occurs called nuclear fission. Typically uranium nuclei are loaded up with extra neutrons until it reaches what is called critical mass. Once critical mass is reached, the nuclei split and large amounts of energy are released because they can’t hold this new influx of neutrons. It’s kind of like your friend who drinks too much at a bar then spews all over the place. This neutron ‘spewing’ is what provides us with electrical power. While the process releases energy, it also leaves varying forms of unstable uranium isotopes that decay naturally into stable isotopes over sometimes hundreds of years. This is because uranium is such a heavier element in comparison to hydrogen, which its isotopes decay rather quickly. These radioactive leftovers are still highly energetic and emit damaging gamma and x-ray waves (we learned what these were in my previous post) and that is why containment is so crucial. My apologies for this nuclear fission tangent, but one should know the difference between fusion and fission. Fusion brings atoms together, fission rips them apart.

So back to the story of sunlight. When the sun does finally manage to smash four hydrogen atoms together, two of the hydrogen’s protons lose mass in the process and become neutrally charged particles called neutrons, making a total of two protons and two neutrons in the new helium nucleus with two orbiting electrons, one for each proton. The expelled proton mass, which eventually will become our beloved sunlight, is given off as energy in the form of highly energetic electromagnetic radiation (a.k.a. light) known as gamma rays. This is an excellent example of Einstein’s famous equation for energy, E=mc2, at work. What this equation says is mass (m) can be converted to energy (E). If you’ve ever tried to lose weight, the same concept applies. You’re trying to convert your mass into energy to lose it. However things on a quantum level work in funny ways. The neutron instead of being less massive actually becomes more massive than it was when it was a proton. This can be blamed on particles within protons and neutrons called quarks and how they behave; something I’ll leave for another post. The ‘C’ part of the equation stands for the speed of light constant which is just something that needs to be added formulaically in order to receive a correct calculation and we’ll get to why later.

We learned in my previous post that electromagnetic radiation is made of particles called photons. These newly created gamma ray photons are at first far too dangerous for earthly consumption. However after tens of thousands of years of being passed around between densely packed atoms within the sun, the photons tire out a bit until they become less energetic visible light photons, or what we call sunshine. Even traveling at the speed of light, photons can take up to a million years to escape the sun; a distance of 432,000 miles from core to surface. While this may seem like a long distance, compare it to the 93 million miles photons travel in only 8 minutes and it becomes apparent how abated those photons are by being continually absorbed and emitted by the soup of atoms within the sun. However once they hit the empty vacuum of space, they have a straight shot to Earth.

When photons finally enter Earth’s atmosphere, some of them are absorbed by tiny pores on plants’ leaves called stomata that convert those photons into chemical energy. This is done by the synthesizing of hydrogen atoms from water in the plant with carbon dioxide in the air to create sugars. This process, I’m sure you’re familiar with, is called photosynthesis. Since plants only use the hydrogen from water, they emit the remaining oxygen as a waste product and we literally breathe their shit. The sugar is stored and later converted into kinetic energy to allow the plant to function. This sugar however can be transferred to a creature that eats the plant and a creature that eats that creature and so forth. Animals (including us) extract energy from these sugars by reacting them with the oxygen they breathe and exhale the remaining carbon dioxide from the sugars so that another plant can use it to create more sugar and oxygen for them to consume.

So next time you look up at the sun (not directly!), think about what’s going on inside there. Think about everything nuclear fusion gives you; air, food— the very matter you’re made of, and say thanks. And as the sunlight warms your skin, think about the tens of thousands of years it took for those photons to reach it. And here’s another interesting fact to blow your mind on; for those photons, you are their entire existence! Well at least within our idea of existence. This is where the ‘C’ (the speed of light constant) in E=mc2 comes into play. The photon, which is energy, travels at the speed of light and that is why that speed needs to be figured into every calculation for energy. It is ‘constant’. And according to Einstein’s theory of relativity, time slows down the faster you move relative to another object until it completely stops at the speed of light. The photon’s time, relative to ours, doesn’t exist. The photon is considered timeless . . . well at least until it’s brought into our reality when you absorbed it as heat. I’ll segue this into my next post which will be on the theory of relativity and quantum mechanics. Until then, stay curious my friends!

Why We Are Tone Deaf to the Music of Light

the-art-of-sound

By Bradley Stockwell

When I sit down at a piano I see a lot more than keys; I see an immense sonic spectrum ranging from sound frequencies of 27 hertz to over 4,000. A hertz, if you’re unaware, is one cycle of a wave per second, in this case a sound wave. When I press a C4 key, a vibrating string is displacing waves of air molecules at 260 times per second against my eardrum and my brain interprets those fluctuations as a middle C. And our amazing brain can do that with a range of frequencies about five times the size of a piano’s. It’s too bad our eyes are so limited in comparison.

While a human eye is an incredibly complex organ, it is severely tone deaf when it comes to the music of light. To understand what I mean by this, we must first change how you view light. On a sub-atomic level, light is made up of little spiraling packets of energy called photons. When these twisted little guys interact with one another they dance in a synchronized wave pattern and form light waves. This is how particles behave on a quantum-scale; they exhibit features both of a particle and of a wave. The varying energies of these photons, or how fast the little guys are spinning, produce differing light wave frequencies that our eyes detect as colors. For example the light waves that make up the color red cycle slower than the light waves that make up the color blue.

Just like there are sounds we can’t hear, either the sound waves are too fast or too slow for our brain to detect, there are also colors, or light waves, we can’t see. Of course just because we can’t see them doesn’t mean they don’t exist. In fact we interact with these colors all the time. When you tune into a radio station, you’re tuning into a signal being transmitted over a light wave called a radio wave. A radio station such as 95.5 KLOS is broadcasting their signal over a light wave with a frequency of roughly 95.5 megahertz; that’s 95.5 million oscillations per second, which is actually quite low. The lower the frequency, the longer the wavelength. That is how radio signals travel over long distances. Infrared light waves, just outside the lower end of visible light, is what your body emits as heat and changes the channel on your television when they are transmitted from your remote. If you’ve ever had a sunburn, that is the result of light waves just outside the higher end of visible light, called ultraviolet waves, overexciting the DNA that creates your skin tissue. If you’ve ever had an x-ray image taken, that is an inverted visual display of the high frequency waves, known as x-rays, which were shot through your body that weren’t absorbed by dense objects like your bones. A low energy wave called a microwave excites molecules of water inside your food to produce heat when you zap your leftovers. These are all things you’re familiar with and they all involve light, or in the language of physics, electromagnetic radiation.

Now just to give you a perspective of how limited our eyes are at detecting light I’m going to transpose the electromagnetic spectrum, the known frequencies of light from 1,000 hertz to one zettahertz (that’s 1 with 21 zeros after it), onto the sound frequencies found on an 88-key piano (this sounds more impressive than it actually is—only simple algebra involved). Radio waves, like the ones radio and TV stations use, take up the lowest 26 keys from A0 to A#2. Microwaves take up the next 16, B2 to D4. Infrared waves the next 14, D#4 to E5. Then visible light, which makes up our entire visual reality, takes up only one key, F5. The next eleven keys, F#5 to E6 are ultraviolet waves. The following ten, F6 to D7 are x-ray waves and the remaining ten are called gamma waves; D#7 to C8.*

 

electromagnetic_spectrum_piano*These proportions aren’t exact because where one type of wave begins and ends is debatable and I had to approximate for demonstration purposes. But it does accurately show the limited perspective of our vision.