Geometry of Electron Shells

...See, because those standing waves are all the standing waves available, an electron can't occupy any other points- it either is in one of those standing waves, or it's not part of that atom. So if an electron gains some energy, it has to jump to the next standing wave- and that means it can only absorb just enough to jump there, no more, no less. Of course, it could absorb enough to jump two waves, or three, but not two and a half, or a half, or any other fraction. Has to be just precisely one, or two, or three- otherwise, the electron won't stay, and that also would violate conservation laws. Atoms are very constrained little beasties. It's why chemistry works so well, not to mention astrophysics.

A corollary of the fact it can only gain energy in those steps, is that it can only lose energy in those same steps. And only so much; once the lowest energy standing waves are occupied, any more electrons have to occupy the higher ones. From this we get the beauty- and the utility- of spectroscopy. Just precisely these wavelengths right here, these are the wavelengths of this particular element's atoms, no other is precisely like them. No matter where they are, if they absorb energy, or emit energy, we can identify them- like fingerprints. That's how we know what the atmospheres of stars, and the contents of clouds of dust and gas, are made out of, out there.

Okay, I think I grok. Now, I haven't read to the (current) end of the thread yet, so you may have covered this already, but could you give me another analogy for "standing wave"? Is there something to visualize, or would that over-simplify it?
 
...Spin, for a quantum (which an electron is), is a concept that involves phase. ...

...we identify bosons as energy...

...we identify fermions as matter...

Okay, I am totally with you up to this point. I've got no problems visualizing waves, nor with reinforcement or cancellation -- it happens on a big scale so frequently...but up to this point I've been thinking of matter as consisting of atoms -- that is, protons, neutrons, electrons, etc. A fermion, matter, is a quantum (as is an electron). Are electrons fermions, or bosons, or BECs, or can they be either? Are they bosons when not "caught" into an atomic structure, and fermions when they are? Likewise, the bits of stuff that make up protons and neutrons -- also fermions?

Last, but hardly least, the Laws of Spin and Statistics are why Star Wars' "Light Sabers" are so ridiculous. No weapon can be made from bosons; it will merely pass through another such weapon, or even through solid matter, without doing much. If you want to do real damage, you need exclusion; you need fermions. Which means you need matter.

Well, dammit, Schneibster! ; )
 
Okay, I think I grok. Now, I haven't read to the (current) end of the thread yet, so you may have covered this already, but could you give me another analogy for "standing wave"? Is there something to visualize, or would that over-simplify it?
You're quick! I had considered mentioning it, but I only really intended a quick couple paragraphs on spin and statistics, and that grew all out of hand, so standing waves and resonance kind of went by the board.

Those of you who know my writing know that I detest the common misuse of the word "resonance" by woos. I have often said that one can almost always detect the presence of woo by its use. Note well: ALMOST always. There are times and places where it is not woo: the details of design and construction of musical instruments, conversations about mechanical stability, alternating current electronics, and quantum mechanics, for example. By no means a complete list, but relatively comprehensive nevertheless.

When you bow a violin, you are causing the strings to vibrate at their resonant frequency, but in addition, the use of the bow permits accentuation of harmonics of that frequency. This effect is more pronounced in certain techniques of guitar playing, generally called "making harmonics." If you observe the strings' vibrations under a properly designed strobe light, you will observe that there are waves propagating along the string- but that there are places where it moves, and others where it stands still.

You can perform a much lower-frequency (and therefore much more easily visible) form of this trick by tying a rope to a tree, or a post, and setting up waves along it that reflect off the anchor site and set up a standing wave in the rope. Do this properly, and you can see the nodes- places where the rope stands still, while the rest of it is moving violently up and down. You are observing standing waves in the rope. And this only happens when you move your hand at a resonant frequency of the rope. What I am describing is resonance, and resonance always implies the presence of a standing wave. If you were to measure the frequencies at which you can set up standing waves in the rope, you'd find that they were multiples of one another; and there is a fundamental frequency at which the nodes are the ends and the center is moving up and down the most.

Electrons (and all other quanta) have both particle-like and wave-like aspects. It is the wave-like aspects of electrons that form the standing waves around the nuclei of atoms that we call "orbitals." They are still at some points, and violently fluctuating at others. In other words, they are resonating around the nucleus.

So what, you ask, is waving? The answer is where quantum mechanics gets really freaky, from the point of view of ordinary reality. What's waving is the probability of the electron being there. That's what the Schroedinger wave equation describes: the probability that you will find a quantum there. You see, quanta don't have "whereness" the way ordinary physical objects we observe in everyday life do. You can't really say, "Well, it's right there." All you can say is, "Well, it's most likely that if you look right there, you will find the electron." So what you've got is resonant waves around the nucleus of "electron whereness."

At the places where the wave is still, are the least likely places to find the electron; at the places where the wave is fluctuating most violently, the electron is most likely to be found. But you have to understand that if you actually shoot a photon at the atom, you might find the electron anywhere; there is a vanishingly small probability that you just might find it at Alpha Centauri. It's very unlikely; in fact, if you had more atoms than there are in the whole visible universe, most likely not one of them would have an electron at Alpha Centauri unless the nucleus was there too. But any of them just might.

And remember, until that photon actually hits the electron and is deflected, and that of course assumes it doesn't happen to be the right phase, and the right frequency, just when it goes by the electron, to be absorbed and kick the electron up to a higher standing wave, you haven't "seen" the electron; and even if it does bounce off and you detect it, all you know is where the electron was when the photon hit it, nothing more. Like, how fast it was going; or where it is now.

The "fundamental frequency" of the electron resonance around the nucleus is the lowest orbital. The higher standing waves represent harmonics of that fundamental. But the strength of the electromagnetic field that the nucleus makes isn't constant; it falls off with distance, as the square of distance, as all electromagnetic fields do as they are spread over an ever-increasing area. Because of this, there are many "fundamentals." Each one represents one orbital, and each harmonic of that orbital represents a quantum state, a standing wave, of that orbital. There are more harmonics farther from the nucleus; less closer in. But every electron is in either a fundamental or a harmonic quantum state that represents a resonant standing wave in its probability wave around the nucleus.

And you can't really call them "orbits;" it isn't like you can say the electron is right here in the orbital right now, and at the next point along it at the next instant. It's over on this side at one moment, and over there at the next, and at the next it might be at Alpha Centauri, but most likely, at every instant, it's at one of the maximum probability points along the wave function, which is a resonant standing wave around the nucleus.

Richard Feynman, who was the man who managed to make Dirac's quantum electrodynamics (which Feynman dubbed "QED," in order to tweak the noses of the mathematicians who said he was insane when he talked about eliminating infinities in Dirac's original theory by subtracting slightly smaller infinities from them leaving a residual amount that corresponded so precisely to the observed characteristics of the quanta that it is the most accurate and precise theory in the history of all of science, confirmed experimentally to seventeen significant figures, an achievement for which Feynman was awarded the Nobel prize) yield real results, once said that all of the most important facts about quantum mechanics can be observed in Thomas Young's dual-slit experiment from the nineteenth century. I believe that a great deal of it can be seen as well in the proper description of the orbitals around an atom.
 
He's either a troll, or truely believes this stuff. Sometimes I can't tell which is which...
Nah, he's a troll - trying to get his website posted (in his sig at a minimum) as much as possible.
 
He's either a troll, or truely believes this stuff. Sometimes I can't tell which is which...
Well, those are not mutually exclusive. I think this one believes his stuff, but he is not here to discuss it, he is here to troll about it.

Hans
 
Okay, I am totally with you up to this point. I've got no problems visualizing waves, nor with reinforcement or cancellation -- it happens on a big scale so frequently...but up to this point I've been thinking of matter as consisting of atoms -- that is, protons, neutrons, electrons, etc. A fermion, matter, is a quantum (as is an electron). Are electrons fermions, or bosons, or BECs, or can they be either? Are they bosons when not "caught" into an atomic structure, and fermions when they are? Likewise, the bits of stuff that make up protons and neutrons -- also fermions?
You ask good questions, Jackalgirl. They are a pleasure to answer.

OK, just like you'd think, add a fermion to a fermion and you get a boson. But add three fermions, and you get another fermion. Electrons are individual fermions. As far as we can tell, they are fundamental particles, not made up of other lesser entities added together. They are also very small and light, being the lightest massful member of the lightest class of subatomic particles, the leptons. "Lepton" is derived from a classical Greek word for "light" (as in, "not massive"). (I should mention that the neutrinos are also leptons, and although they were initially thought to be massless, they have recently been shown (albeit somewhat controversially) to have an extremely small, though not zero, mass.)

Neutrons and protons are comparatively massive; 1800-some-odd times the mass of an electron. They are also not fundamental particles; instead, they are composites of fundamental particles called "quarks." And in fact, they are not only "hadrons," which means massive particles made of quarks, they are "baryons," which are the heaviest subatomic particles. The neutron and proton are the lightest baryons. "Baryon" is derived from a Greek word meaning "heavy," and "hadron" is derived from a Greek word meaning, "strong," because the other definition of hadrons besides being made of quarks is that they participate in the strong or color nuclear interaction, which leptons do not. The other hadrons are mesons, from a Greek word meaning "middle," because they are between the baryons and the leptons in mass.

Baryons are made from trios of quarks. Quarks have a special kind of charge that comes in three varieties rather than the one variety of electromagnetism (positive and negative are opposites, but they are the same "kind of thing;" the three "color" charges of quarks each also have a positive and negative). As I parenthetically hinted, these three charges are called "colors," not because they really ARE colors, but because they behave like the three primary colors of paint. When all three colors (or all three anticolors) are combined, they yield white, just as red, blue, and green do, or their opposites cyan, yellow, and magenta. When a color is united with its anticolor, it yields black, or nothing, just as the three primary colors do when united with their opposites. And if two colors (or two anticolors) are combined, they yield an anticolor, the opposite of the color left out of the pair (or the opposite of the anticolor left out of the pair). All of these things are as true of the color charges of the quarks as they are of the primary colors of paint and their complements. With all of these characteristics in mind, you can see why rather whimsical physicists called the phenomenon "color."

The force that these color charges exert on one another is so much stronger than the electromagnetic force that the latter might as well not exist in the presence of the former. It is therefore often called the "strong nuclear" force. I prefer "color force" because of its origin in the color charge. This is the strongest force of nature, a force so strong that if your body were exposed to it, you'd wind up the size and shape of a grain of sand in an instant. So how is it we never discovered this force until the twentieth century, and why haven't we done anything with it, like we did with electromagnetism? Why aren't there "color radio" or "color motors" or "color computers?"

The first reason is because the color force is confined. We've never seen any phenomenon driven by the color force larger than a nucleus, and it's so tightly confined that it can't even make it all the way across the bigger nuclei; that's why heavy elements are often radioactive. Their nuclei can't really quite be held together by the color force, and they break apart sometimes. And the color force is so strong that when they break apart, they don't just sit there; the broken chunks come flying out. When these broken chunks hit the atoms in your body, they damage them, and eventually enough damage happens that you get something very like a burn from it. We call this a "radiation burn."

So despite the fact that it's so much stronger than electromagnetism, it's very short range, and we don't encounter it in everyday life. It's a good thing, too, if you think about that example I gave above, compressing a human body to the size of a grain of sand; and if you want to know how powerful it is, think about the fact that all the violence and power of a nuclear weapon comes from the action of the strong force in only a few pounds of matter, for a nanosecond or two. Everything that you see as the flash, and the explosion, and the mushroom cloud, and the thunderclap, and all the rest of a nuclear weapon's effects, is just the aftermath of that incredibly violent and powerful interaction over a period of time so short, it is to a second as that second is to your whole life. That's how powerful the color force is. It's the force behind nuclear weapons, and nuclear reactors. And that's the second reason; the fact is, we HAVE done things with the color force, but they're DANGEROUS because it's so powerful.

OK, now we can get down to it. All of the baryons are made from trios of quarks, one of each color. All of the mesons are made from pairs of quarks, actually a quark and an antiquark, of a color and its anticolor. So the baryons have all their strong force cancelled out by the combination of the three colors (and the antibaryons by the combination of the three anticolors), and the mesons have it cancelled out by its negation.

Why, you might ask, don't the quarks just come apart? Well, think how strong the color force binding them together is. What could pull them apart? The answer is, almost nothing. And it's that same force that holds the protons and neutrons (which are baryons) inside the nucleus; scientists knew, because electromagnetism is so strong, and the proton has a positive charge and the neutron no charge, that some really strong force had to be holding nuclei together, and that's how it came to be called the "strong nuclear" force.

It turns out that when hadrons get close enough to one another, they can "see" (by the color force) each others' quarks, and their color charges; and the hadrons interact. In the case of protons and neutrons, they stick together, and form nuclei. These have a strong electric charge, so they attract electrons until there are just enough to balance the charge of the nucleus, and make the atom neutral. And that's where atoms come from, and why they stick together; the protons and neutrons are held in the nucleus by the color force, and the electrons attracted to the nuclei by the electromagnetic force.

So, are the neutrons and protons bosons, or fermions? Well, they're fermions. And since they're made of three quarks, it's obvious that the quarks must be fermions too. And that means that the mesons, which are made of two quarks, must be bosons- and they are. And any nucleus that has an even number of protons and neutrons must be a boson- and any that has an odd number must be a fermion. And those turn out to be true as well. Of course, the fermion qualities of all those electrons, not to mention the protons, neutrons, and the quarks they're made up of, make most atoms behave pretty much as fermions almost all the time; but get bosonic atoms cold enough, and lo and behold, their boson characteristics start to show up, when they're not constantly pinging around all over the place like they do at room temperature. Condensed-matter physicists have dubbed materials made of bosonic atoms at very low temperatures, "Bose-Einstein condensates," or BECs.

The fundamental- that is, non-composite- bosons are all exchange particles of forces. The exchange particle of electromagnetism is the photon. In a manner of speaking, it is correct to state that electromagnetism is the exchange of photons, nothing more. The color force has a collection of different bosons, eight of them in fact, called "gluons," for obvious reasons ("stick together like they were glued"). Unlike photons, gluons can carry color charges themselves- and most of the types of them do. They can exchange color charges between quarks, changing their fundamental charges; something that never happens with electric charges, because there's only one kind of electric charge and no charged bosons associated with it (or perhaps there is only one kind because there are no charged photons- physicists are still considering which). There are two other forces: gravity, which has the graviton, another boson, and the weak force, which is incredibly complicated, related to the other forces, and unlike any other force has massive bosons. The rest of the bosons are all massless. There are some extreme oddities about the weak force, making it not only the most complex force, but the most difficult to understand.

The neutrinos, of course, being leptons, are also fermions. Until recently, physicists thought they were the only massless fermions; now, it appears that they have a very small but non-zero mass.

And there you have it; other than the weak force, I've covered essentially all of nuclear physics and a pretty fair chunk of quantum mechanics for you. See how interesting atoms are? :D
 

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