|MadSci Network: Chemistry|
Greetings, Tom: In one respect, this is an extremely complex subject. Mathematically, Quantum Mechanics is our best description of how electrons behave, but there are limits. The limits are somewhat akin to the "3-body problem" in Gravitational Physics. We know all about how to compute the results of any two objects gravitationally interacting with each other, but if just one more object is added, we have NO generic tool adequate for the task. Instead we make a successive series of approximations, taking two of the 3 objects at a time. It works, but is very tedious. Thus you may understand that just one hydrogen atom (proton interacting with electron) is a 2-body problem, with respect to Quantum Physics. We can indeed describe this pair extremely well, but if we add only one more particle, a mathematical nightmare begins. The simplest possible covalent bond, which exists between two whole hydrogen atoms, is actually a 4-body problem.... In other respects we know in a general way quite a bit about what goes on, and I will attempt to describe it here. There are, of course, various items of background information that must be presented, before a coherent picture can be imagined. The first important thing is the "image" of a lone electron. This is an object smaller than 0.0000000000000001 (or 10E-17) meters. Our best instruments can't measure anything so small as an electron; for all we know, it has the dimensions of a perfect mathematical point -- but we don't know that for sure, either. (The smallest meaningful length in modern Physics is a computed dimension known as the Planck length, which is about 10E-35 meters, while a mathematical point would have a size of exactly zero.) Next, and just as important, the exact location of an average electron is very often quite unknown. We CAN momentarily locate an electron, but in the very next moment, thanks to something known as the Uncertainty Principle, it WILL be located somewhere else, quite probably at some random distance and direction from the previous location. For this reason the electron is often described as a sort of "large and foggy" object: Its most likely location is somewhere in the center of the "fog", but every iota of the "substance" of this "fog" is actually nothing more than another POSSIBLE LOCATION -- a momentary location -- for the tiny tiny electron. It happens that every subatomic particle described by Quantum Mechanics and the Uncertainty Principle can be said to have some of the electron's "foggy" nature. The total amount of a given particle's "fog" is simply and inversely proportional to the mass of the particle: The more mass a particle possesses, the less far it jumps about, and so the smaller is the totality of its possible jump-locations, or "patch of fog". The proton, for example, has more than 1800 times the mass of an electron; its "fog patch" is therefore more than 1800 times smaller than the electron's. This is small enough for the "fog" itself to resemble a particle, but in fact the proton, being roughly 10E-15 meters in diameter, is quite a bit smaller than the "fog" of its random-jump locations. Next, when proton and electron get together to form a hydrogen atom, a peculiar thing happens to the description of the electron's "fogginess". A phenomenon known as the "wave/particle duality" must now be examined closely. This rule states that every solid particle has some wave-like properties, while every wave-like object has some solid-particle properties. The details are quite mathematical, of course, but the consequences are known to be true. Thus THE major reason why the point- like electron jumps all over the place IS the wave-particle duality. Even when supposedly stationary, the wave-like properties of an electron REQUIRE it to be "jumping in place"; it is never really still. And the "fogginess" of an electron's location is the obvious result. However, note that a wave is generally described as a reasonably smooth undulation. Even an electron can do this much, when it is experiencing an overall motion from Point A to a distant Point B. Only when it is supposedly stationary is an electron's wavy nature utterly erratic. So let us now take a proton, and insert it into the middle of an electron's "fog patch": The electron begins to orbit about the proton. Since this is an actual motion of the electron, ordinary wave-like undulations will be a part of that motion. When the electron is in the smallest possible orbit, its motion around the proton may be described like this: One complete orbit is precisely one perfect undulation. (To better visualize this, take a piece of paper and draw one standard sinusoidal waveform. Then roll the paper up, undulation outside, so that the beginning and ending points of the waveform connect. The proton would be located in the center of the paper ring.) Each possible larger orbit for an electron gives it room to undulate exactly twice, or three times, or four, etc. Quantum Mechanics permits two electrons to occupy one orbit. It also defines "shells" about an atomic nucleus, each of which may contain a number of orbits. The innermost shell contains just one orbit for two electrons; the next shell contains a "subshell" with one room for only one orbit, and a second subshell with room for three orbits, for a total of eight electrons in that overall shell. And so on. Standard high- school chemistry classes will offer students the concepts of "shells", "subshells", "orbitals", and the like, so I need not repeat it all here. The next important thing concerns the location of an electron when it is undulating in orbit about a proton. Each moment, it DOES exist at one precise location along that orbit. Our macroscopic view still sees "fogginess", however. We might say, "At this moment, the electron is most probably located about here, but there is a small chance we can find it over here, completely on the other side of the atom." Now think about the electric charge on the proton: The reason the electron is in orbit is because of electrical attraction. From a macroscopic distance, we might see an atom as an electrically neutral object, but if we look closely ... Now at some PARTICULAR moment the proton will be located at Point A, and the electron will be located at Point B, as depicted below: (C) (A)proton (B)electron I wish to bring your attention to Point C, and ask, "Do we detect zero electric charge at that point? The answer is, "No, we can detect some of the positive charge of the proton." And if we next ask, "What if there is an electron, part of another atom, located at Point C?" -- then the answer is, "There will be some electrical attraction between that other atom's electron at Point C and the proton at Point A." This attraction between two hydrogen atoms is a good enough reason why they would tend to join together, to make a hydrogen molecule. The form or arrangement that the four particles take should be relevant to your Question. To approach it, let me begin with just one proton and both electrons: electron proton electron This would be a "negatively charged hydrogen ion". Since the electrons repel each other electrically, they always move such that the proton stays between them. They may most easily be imagined moving, say, clockwise about the proton in the above depiction. HOWEVER, it is more important that you imagine that circle turned on its edge! Visualize the "upper" electron moving downwards, first towards you and then away from you, while the "lower" electron is moving upwards, first away from you and then towards you. Twiddle your thumbs, to keep that in mind as I add the second proton: electron proton proton electron With the electrons still circling in the same kind of orbit as just described above, the only change is the location of that circle relative to the original proton. In this diagram, we can see that each proton gets an equal share of both electrons. Also, the smallest possible orbit for electrons around each proton becomes exactly the SAME orbit, with respect to the two protons. And because there is now only one orbit to talk about, capable of holding exactly two electrons, it is completely filled by one electron from each hydrogen. (Please note that these diagrams are not to scale; an electron's orbit is about 100,000 times larger than a proton.) Now lets move on to a more complex case: a fluorine molecule. A single atom of fluorine has 9 electrons in two "shells", grouped like so: two occupy the innermost electron "shell", two occupy the inner "subshell" of the outer "shell", and five occupy three "orbitals" of the outer "subshell" of the outer "shell". Since each "orbital" can contain only two electrons, there are two full "orbitals" and one half-full "orbital" in that outer "subshell". That half-full "orbital" is the ONLY thing which concerns us here! It is exactly equivalent to the half-full orbit of a lone hydrogen atom: electron (fluorine) (fluorine) electron I am using (fluorine) to indicate the nucleus and 8 electrons; the 9th electron of each is in the same type of shared orbit as previously described for the hydrogen molecule. Next, how about a water molecule? I shall use some abbreviations, to reduce clutter in the following diagram: (H) 2e (O) e e (H) The oxygen nucleus and 6 electrons is (O), a hydrogen nucleus is (H), and an electron is simply e. Depicted are two electrons ON the "plane" of the diagram (at an angle), and a second pair denoted by 2e represents one-in-front and one-behind the "plane" of the diagram. As time passes and the electrons move in their orbits, we might be able to draw this: e (H) (O) e 2e (H) Now the pair of electrons formerly located at an angle is located one-in-front and one-behind the "plane" of the diagram. Remember that electrons repel each other, so they stay as far apart as they can. While the water molecule contains two single covalent bonds, the oxygen molecule contains a double bond, of which I shall sketch two views: e e (O) 2e (O) e 2(O) e e e This may look like four electrons in the same orbit, but more correctly we should treat it as two "orbitals" that just happen to mostly overlap. The double bond between two carbon atoms (or between a carbon and an oxygen) is basically the same. Depicting the triple bond of the nitrogen molecule is similar: e e e 2(N) e e e Of course the 2(N) represents two nitrogen nuclei, each having 4 electrons. One is located in front, and one is located behind the plane of the diagram. The remaining six electrons occupy three overlapping/ shared "orbitals". Notice how closely the electrons are forced to be located near each other. This implies something of a weakness in a triple bond (it is weaker for carbon than for nitrogen, because carbon atoms are smaller, so the electrons are even closer together). It also provides a good reason why carbon is not known to ever form a quadruple bond. Well, I hope the preceding has been appropriatly informative, and hasn't been too far off the mark.
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