The Neapolitan Particle

“Welcome back, Jennie.  Why would anyone want to steer an ice cube?

“Thanks, Jeremy, it’s nice to be back..  And the subject’s not an ice cube, it’s IceCube, the big neutrino observatory in the Antarctic.”

“Then I’m with Al’s question.  Observatories have this big dome that rotates and inside there’s a lens or mirror or whatever that goes up and down to sight on the night’s target.  OK, the Hubble doesn’t have a dome and it uses gyros but even there you’ve got to point it.  How does IceCube point?”

“It doesn’t.  The targets point themselves.”

“Huh?”

“Ever relayed a Web-page?”

“Sure.”

“Guess what?  You don’t know where the page came from, you don’t know where it’s going to end up.  But it could carry a tracking bug to tell someone at some call-home server when and where the page had been opened.  IceCube works the same way, sort of.  It has a huge 3D array of detectors to record particles coming in from any direction.  A neutrino can come from above, below, any side, no problem — the detectors it touches will signal its path.”

IceCube architecture

Adapted from a work by Francis Halzen, Department of Physics, University of Wisconsin

“How huge?”

“Vastly huge.  The instrument is basically a cubic kilometer of ultra-clear Antarctic ice that’s ages old.  The equivalent of the tracking bugs is 5000 sensors in a honeycomb array more than a kilometer wide.  Every hexagon vertex marks a vertical string of sensors going down 2½ kilometers into the ice.  Each string has a couple of sensors near the surface but the rest of them are deeper than 1½ kilometers.  The sensors are looking for flashes of light.  Keep track of which sensor registered a flash when and you know the path a particle took through the array.”

icecube event 3“Why should there be flashes? I thought neutrinos didn’t interact with matter.”

“Make that, they rarely interact with matter.  Even that depends on what particle the neutrino encounters and what flavor neutrino it happens to be at the moment.”

That gets both Al and me interested.  His “Neutrinos come in flavors?” overlaps my “At the moment?”

“I thought that would get you into this, Sy.  Early experiments detected only 1/3 of the neutrinos we expected to come from the Sun.  Unwinding all that was worth four Nobel prizes and counting.  The upshot’s that there are three different neutrino flavors and they mutate.  The experiments caught only one.”

Vinnie’s standing behind us.  “You’re going to tell us the flavors, right?”

“Hoy, Vinnie, Jeremy’s question was first, and it bears on the others.  Jeremy, you know that blue glow you see around water-cooled nuclear fuel rods?”

“Yeah, looks spooky.  That’s neutrinos?”

“No, that’s mostly electrons, but it could be other charged particles.  It has to do with exceeding the speed of light in the medium.”

“Hey, me and Sy talked about that.  A lightwave makes local electrons wiggle, and how fast the wiggles move forward can be different from how fast the wave group moves.  Einstein’s speed-of-light thing was about the wave group’s speed, right, Sy?”

“That’s right, Vinnie.”

“So anyhow, Jeremy, a moving charged particle affects the local electromagnetic field.  If the particle moves faster than the surrounding atoms can adjust, that generates light, a conical electromagnetic wave with a continuous spectrum.  The light’s called Cherenkov radiation and it’s mostly in the ultra-violet, but enough leaks down to the visible range that we see it as blue.”

“But you said it takes a charged particle.  Neutrinos aren’t charged.  So how do the flashes happen in IceCube?”

“Suppose an incoming high-energy neutrino transfers some of its momentum to a charged particle in the ice — flash!  Even better, the flash pattern provides information for distinguishing between the neutrino flavors.  Muon neutrinos generate a more sharp-edged Cherenkov cone than electron neutrinos do.  Taus are so short-lived that IceCube doesn’t even see them.”Leptons

“I suppose muon and tau are flavors?”

“Indeed, Vinnie.  Any subatomic reaction that releases an electron also emits an electron-flavored neutrino.  If the reaction releases the electron’s heavier cousin, a muon, then you get a muon-flavored neutrino.  Taus are even heavier  and they’ve got their own associated neutrino.”

“And they mutate?”

“In a particularly weird way.”

~~ Rich Olcott

Advertisements

Trio for Rubber Ruler

“It’s all about how lightwaves get generated and then what happens.”

Sy and me talked about that, Cathleen.  Lightwaves come from jiggling electrons, right?”

“Any kind of charged particles, Vinnie, but there’s different ways that can happen.  Each leads to its own kind of spectrum.”

“Different kinds of spectrum?  Do you mean like visible versus infrared and ultraviolet, Cathleen?”

“No, I don’t, Sy.  I’m referring to the thing’s overall appearance in every band.  A hundred and fifty years ago Kirchoff pointed out that light from a source can have lines of color, lines without color, or a smooth display without lines.”

“Like that poster that Al put up between the physicist and astronomer corners?”  (We’re still chatting at a table in Al’s coffee shop.  I’m on my fourth scone.)

“Kind of.  That’s based on a famous image created at Kitt Peak Observatory.  In the background there you see a representation of what Kirchoff called a continuous or black-body spectrum, where all the colors fade smoothly into each other in classic rainbow order.  You’re supposed to ignore the horizontal dark lines.”

“And the vertical lines?”

“They form what Kirchoff called an absorption spectrum.  Each dark vertical represents an isolated color that we don’t get from the Sun.”

“You’re saying we get all the other colors but them, right?”

“Exactly, Vinnie.  The Sun’s chromosphere layer filters those specific wavelengths before they get from the deeper photosphere out into space.”

“Complicated filter.”

“Of course.  The Sun contains most of the elements lighter than nickel.  Each kind of atom absorbs its own collection of frequencies.”

“Ah, that’s the quantum thing that Sy and me talked about, right, Sy?”

“Mm-hm.  We only did the hydrogen atom, but the same principles apply.  An electromagnetic wave tickles an atom.  If the wave delivers exactly the right amount of energy, the atom’s chaotic storm of electrons resonates with the energy and goes a different-shaped storm.  But each kind of atom has a limited set of shapes.  If the energy doesn’t match the energy difference between a pair of levels, there’s no absorption and the wave just passes by.”

“But I’ll bet the atom can’t hold that extra energy forever.”

“Good bet, Vinnie.  The flip side of absorption is emission.  I expect that Cathleen has an emission spectrum somewhere on her laptop there.”Emission spectrum“You’re right, Sy.  It’s not a particularly pretty picture, but it shows that nice strong sodium doublet in the yellow and the broad iron and hydrogen lines down in the green and blue.  I’ll admit it, Vinnie, this is a faked image I made to show my students what the solar atmosphere would look like if you could turn off the photosphere’s continuous blast of light.  The point is that the atoms emit exactly the same sets of colors that they absorb.”

“You do what you gotta do, Cathleen.  But tell me, if each kind of atom does only certain colors, where’s that continuous rainbow come from?  Why aren’t we only getting hydrogen colors?”

“Kirchoff didn’t have a clue on that, Vinnie.  It took 50 years and Einstein to solve it.  Not just where the light comes from but also its energy-wavelength profile.”

“So where does the light come from?”

“Pure heat.  You can get a continuous spectrum from a hot wire, molten lava, a hole through the wall of a hot oven, even the primordial chaos of the Big Bang.  It doesn’t matter what kind of matter you’re looking at, the profile just depends on the temperature.  You know that temperature measures the kinetic energy stored in particle random motion, Vinnie?”

“Well, I wouldn’t have put it that way, but yeah.”

“Well, think about the Sun, just a big ball of really hot atoms and electrons and nuclei, all bouncing off each other in frantic motion.  Every time one of those changes direction it affects the electromagnetic field, jiggles it as you say.  The result of all that jiggling is the continuous spectrum.  Absorption and emission lines come from electrons that are confined to an atom, but heat motion is unconfined.”

“How about hot metal?”

“The atoms are locked in their lattice, but heat jiggles the whole lattice.”

~~ Rich Olcott

They Went That-away. But Why?

“It’s worse than that, Vinnie.”  I pull out Old Reliable, my math-monster tablet.  “Let me scan in that three-electron drawing of yours.”3 electrons in B-field

“Good enough to keep a record of it?”

“Nope, I want to exercise a new OVR app I just bought.”

“You mean OCR.”

“Uh-uh, this is Original Vector Reconstruction, not Optical Character Recognition.    OCR lets you read a document into a word processor so you can modify it.  OVR does the same thing but with graphics.  Give me a sec … there.  OK, look at this.”3 electrons in B-field revisited

“Cool, you turned my drawing 180°, sort of.  Nice app.  Oh, and you moved the red electron’s path so it’s going opposite to the blue electron instead of parallel to the magnetic field.  Why’d you bother?”

“See the difference between blue and red?”

“Well, yeah, one’s going up, one’s going down.  That’s what I came to you about and you shot down my theory.  Those B-arrows in the magnetic field are going in completely the wrong direction to push things that way.”

“Well, actually, they’re going in exactly the right direction for that, because a magnetic field pushes along perpendiculars.  Ever hear of The Right Hand Rule?”

“You mean like ‘lefty-loosey, righty-tighty’?”

“That works, too, but it’s not the rule I’m talking about.  If you point your thumb in the direction an electron is moving, and your index finger in the direction of the magnetic field, your third finger points in the deflection direction.  Try it.”

“Hurts my wrist when I do it for the blue one, but yeah, the rule works for that.  It’s easier for the red one.  OK, you got this rule, fine, but why does it work?”

“Part of it goes back to the vector math you don’t want me to throw at you.  Let’s just say that there are versions of a Right Hand Rule all over physics.  Many of them are essentially definitions, in the same way that Newton’s Laws of Motion defined force and mass.  Suppose you’re studying the movements directed by some new kind of force.  Typically, you try to define some underlying field in such a way that you can write equations that predict the movement.  You haven’t changed Nature, you’ve just improved our view of how things fit together.”

“So you’re telling me that whoever made that drawing I copied drew the direction those B-arrows pointed just to fit the rule?”

“Almost.  The intensity of the field is whatever it is and the lines minus their pointy parts are wherever they are.  The only thing we can set a rule for is which end of the line gets the arrowhead.  Make sense?”Spiraling electron

“I suppose.  But now I got two questions instead of the one I come in here with.  I can see the deflection twisting that electron’s path into a spiral.  But I don’t see why it spirals upward instead of downward, and I still don’t see how the whole thing works in the first place.”

“I’m afraid you’ve stumbled into a rabbit hole  we don’t generally talk about.  When Newton gave us his Law of Gravity, he didn’t really explain gravity, he just told us how to calculate it.  It took Einstein and General Relativity to get a deeper explanation.  See that really thick book on my shelf over there?  It’s loaded with tables of thermodynamic numbers I can use to calculate chemical reactions, but we didn’t start to understand those numbers until quantum mechanics came along.  Maxwell’s equations let us calculate electricity, magnetism and their interaction — but they don’t tell us why they work.”

“I get the drift.  You’re gonna tell me it goes up because it goes up.”

“That’s pretty much the story.  Electrons are among the simplest particles we know of.  Maxwell and his equations gave us a good handle on how they behave, nothing on why we have a Right Hand Rule instead of a Left Hand Rule.  The parity just falls out of the math.  Left-right asymmetry seems to have something to do with the geometry of the Universe, but we really don’t know.”

“Will string theory help?”

“Physicists have spent 50 years grinding on that without a testable result.  I’m not holding my breath.”

~~ Rich Olcott

Three atop A Crosshatch

“Hey, Sy, what you said back there, ‘three and a fraction‘ ways to link atoms together…”

“Yeah, Vinnie?”

“What’s that about?  How do fractions come in when you’re counting?”

“Well, I was thinking about how atoms in separate molecules can interact short of reacting and forming new molecular orbitals.  I figure that as a fraction.”

Charge sharing ain’t the whole story?”

“It would be except that sharing usually isn’t equal.  It depends on where the atoms are in the Periodic Table.”

“What’s it got to do with the Periodic Table?”

“The Table’s structure reflects atom structures — how many shells are active in a base-state atom of each element and how many units of charge are in its outermost shell.  Hydrogen and Helium are in Row 1 because the 1-node shell is the only active one in those atoms.  The atoms from Lithium to Neon in Row 2 have charge activating both the 1-node shell and the 2-node shell, and so on.”

“What’s that get us?”

“It gets us a feel for how the atoms behave.  You know I’m all about dimensions, right?”

“Ohhh, yeah.”

“OK, we’ve got a two-dimensional table here.  Going across, each atom’s nucleus has one more proton than its buddy to the left.  What’s that going to do to the electronic charge?”

“Gonna pull it in closer.”

“Wait, Vinnie, there’s an extra electron in there, too.  Won’t that cancel out the proton, Sy?”

“Good thinking, Eddie.  Yes, it does, but only partially.  The atoms do get smaller as you go across, but it’s irregular because negative-negative repulsion within a shell works to expand it almost as much as negative-positive attraction contracts it.”

“Bet things get bigger as you go down the Table, though.”

“Mostly, Vinnie, because each row down adds a shell that’s bigger than the shrinking inner shells.”

“Mostly?”

“The bigger shells with more nodes have more complex charge patterns than just balls and dumbbells.  Those two rows below the main table actually squinch into the lowest two boxes in the third column.  In those elements, some of the activated patterns barely shield the nucleus.  The atoms to their right in the main table are almost identical in size to the elements above them.”

“So I can guess an atom’s size.  So what?”

“So that and the charge give you a handle on the element’s properties and chemistry.  Up there in the top right corner you’ve got the atoms with the highest ratio of nuclear charge to size.  If given the opportunity to pull charge from atoms to their left and below them, what do you suppose happens?”

“You get lop-sided bonds, I guess.”

“Exactly.  In water, for instance, the Oxygen pulls charge towards itself and away from the Hydrogen atoms.  That makes each O-H bond a little dipole, positive-ish at the hydrogen end and negative-ish at the oxygen end.”

“Won’t the positive-ish ends pull on the negative-ish parts of next-door molecules?”

“You’ve just invented hydrogen bonding, Eddie.  That’s exactly what happens in liquid water.  Each molecule can link up like that with many adjacent ones and build a huge but floppy structure.  It’s floppy because hydrogen bonds are nowhere near as strong as orbital-sharing bonds.  Even so, the energy required to move through liquid H2O or to vaporize it is much greater than for liquid methane (CH4), ammonia (NH3) or any similar molecule.”

“Can that pull-away action go all the way?”

“You’ve just invented ionic bonding, Vinnie.  The elements in the Oxygen and Fluorine columns can extract charge completely away from many of those far to the left and below them.  Fluorine steals charge from Lithium, for instance.  Fluoride ions are net negative, lithium ions are net positive.  Opposites attract, same as always, but now it’s  entire ions that attract each other and you get crystals.”

“That’s your and-a-fraction?”

“Not quite, Vinnie.  There’s one more, Van der Waals forces.  They come from momentary polarizations as electron chaos sloshes back and forth in neighboring molecules.  They’re why solids are solid even without ionic or hydrogen bonding.”

“Geez, look at the time.  Rosalie’s got my dinner waiting.  Bye, guys, everybody out!”

~~ Rich Olcott

The Mastery of The Pyramids

“Hard to believe, Sy.”

“What’s hard to believe, Vinnie?”

“What you said back there, about all molecules being tetrahedron-shaped.”

“Whoa, that’s not what I said.  What I did say was that the tetrahedron is the fundamental structural building block for most of the Universe’s molecules. To put a finer point on it, it’s the building block for most kinds of molecules.”

“What kinds are you leaving out?”

“Molecular hydrogen, for instance.  It’s probably the most common molecule in the Universe but it’s got only two atoms and two electrons and it doesn’t do tetrahedra.  I was talking about almost all the other flavors.  Molecules can have all kinds of shapes, from spherical to long and skinny.  Say, Eddie, do your kids play with Legos?”

“Geez, yes.  My feet find blocks all over the house.  Only thing worse is glitter.”

“You can build just about any shape from those rectangular blocks, right?  Pegs on one block plug into holes on other blocks and pretty soon you’ve got a rocket ship or something.  Atoms can work the same way.  Four bonding orbitals pointing out to those pyramid corners, ready to share with whatever comes along.”

“Not just with hydrogen like with that CH4 stuff?”

“Depends on the atom, but in general, yeah.  Except for the outermost columns of the Periodic Table, most of the elements in the upper rows can be persuaded to share at least one bond with most of the others.  Carbon’s the champ that links with practically everything.”Tetrahedral bonding

“Even carbon?”

“Especially carbon, Vinnie.  Linking to carbon is carbon’s best thing.  It’s even got three and a fraction different ways to do it.  Here’s a sketch.  It boils down to the different ways you can have two tetrahedra match up points.”

“Lemme look at this for a minute… OK, that point-to-point one at the top —”

“It’s called a single bond.”

“Whatever, you’re saying that could be like two –CH3 pieces tied together.”

“Mm-hm.  The –CH3‘s are methyl groups, and with two of them you’ve got ethane.  Or link a methyl to a –CH2CH3 and you’ve got propane, or link it to an –OH to get methyl alcohol.  At least in principle you can pop a methyl onto any other atom or molecule that started off with only one unit of charge in an unshared orbital.”

“So it’s like my daughter’s bead necklace where she can pop it apart and add all different kinds of beads.”

“Exactly, Eddie, except her beads probably have their two links in a straight line.  These atoms support four links at 109° angles to each other.”

“That picture reminds me of one of my kids’ toys that’s like a top spinning on top of another top.  Is there anything that locks the two sides together so they can’t do that?”

“One way is if the two sides are each linked to bulky groups that get in each other’s way.  Hydrogens don’t much.  Scientists have measured methyl group rotation rates above 10 million cycles per second.”

“Hey, I’m still looking over here.  These other diagrams say that the tetrahedron things can link along an edge —”

“That’d be a double bond, Vinnie.”

“Looks to me like those double-bond shapes are locked in.  No rotation there, right?”

“Right.  In fact, rotational stability across a double bond is so strong that different arrangements operate like different compounds.  Switching A\B:C\D to A\B:D\C can be the difference between a useful med and something that’s inert or even toxic.”

“And I suppose when they match up whole triangles that’s a triple bond?”

“You got it.”

“Well, that can’t spin, for sure.”

“Nah, Vinnie, that’s like the atom-in-a-field thing, no difference between x- and y- axes.  Spinning like crazy except you can’t see it.”

“Eddie’s right, Vinnie.  The four atoms in a triple-bond structure are in a line.  The charge of three electron pairs mushes into a barrel-shaped region between the two carbons.”

“All that pent-up charge, I bet it’s reactive as hell.”

“Uh-huh.  With hydrogen atoms at both ends that’s acetylene gas.  Let that stuff touch copper and you get explosive decomposition.”

“So that’s why they say don’t run acetylene through copper tubing or brass fittings.”

“Believe it, Vinnie.  Believe it.”

~~ Rich Olcott

The Shape of Water

Amazing what you can do with mozzarella drips and crumbled pizza edges.  Vinnie’s rolling his crumbs into decent-sized marbles.  (Pizza-maker Eddie’s giving him a look.)  He adds a fourth ball to his triangle to make a square.  “So anyway, what you’re telling us is that Bohr’s 8-electron shell isn’t that far off.”

“Oh, it is far off.  Bohr put his electrons in a plane like your square there.  Try putting that fourth ball on top of the others to make a triangular pyramid.  See that?  Counting the bottom it’s a four-sided figure called a tetrahedron.  It’s the fundamental structural building block for most of the Universe’s molecules.”Water molecule“Hey, that’s the alpha-particle shape that the protons and neutrons get themselves into.”

“Good point, Vinnie.  Mind you, though, an alpha particle doesn’t have a central attractor, and it’s a quarter-million times smaller than an atom’s electron cloud.  Got that pyramid shape in mind?”

“Sure.”

“OK, put those balls back in your square. … Put a finger on the north ball and another on the south one.  Now roll them both up into contact on top of the line between the east and west ones.”

“Hey, it’s that tetra-thing again.”

“Right, Eddie.  Any time you have four objects each the same distance from all the others, you’ve got a tetrahedron.  If the ‘objects’ are clouds of electron charge all attracted to the nucleus and all repelled by the other clouds, that’s the shape they’ll take.  It’s no accident that an equal mix of an atom’s spherical and three dumbbell orbitals in a shell makes four equivalent orbitals pointing to the corners of a tetrahedron.”

“Cute, but what’s it get us?”

“It gets us to the chemists’ trick for thinking about molecular structures without doing all the quantum mechanics.  The key is that 8-electron shell.  Forget electrons racing in a ring or electron pairs in a square.  When you see a chemical diagram with four lines coming out of a central atom, think of them in a tetrahedron.  Here’s an example.  Guess what’s the commonest atom in the Universe.”

“Helium.”

“Hydrogen.”

“Eddie’s win with hydrogen — 923,000 atoms out of a million.  Carbon’s the fourth most common, 480 atoms per million.  Think of a carbon atom, floating around in space with four of its six units of electronic charge in its 2-shell.  And it’s surrounded by hydrogen atoms with electrons just begging to pair up with something.  No surprise, there’s suddenly a lot of electron pairing and you’ve got a molecule of methane, CH4.  What’s its shape?  Any hydrogen-hydrogen chains in there?”

“With this build-up, I gotta guess they’re all on the carbon and that they’re splayed out tetrahedron-like, hydrogen centers trying to get away from the other ones and shared charge clouds trying to get away from each other, too.”

“Couldn’t put it better myself, Vinnie.”

“Hey, water’s H2O, right?  You can’t make a tetrahedron from only three atoms.”

“True, Eddie, but an oxygen atom comes with two more electrons than carbon has.  We’ve still got a tetrahedron, but only two of its corners carry a hydrogen.  The other two orbitals stick out their own directions, each loaded with negative charge.  The chemists call that unshared kind of orbital a lone pair.  They often show it as a double-dot on the structure diagram. That’s basically just a bookkeeping device to keep track of electron counts.  All the charge is really spread around throughout all the molecular orbitals just like with atomic orbitals, only it’s not spread evenly.”

“Why do they bother to keep track like that?”

“Lone pairs affect the molecule’s structure.  If it weren’t for them, the water molecule would be a straight line.  In fact, a lone pair orbital crowds the space a bit more than a bonding pair — the H–O–H angle is about 5º smaller than a perfect tetrahedron.”

“Makes sense when you think about it, like you can wave a stick all over the place unless someone grabs the other end.”

“Mm-hm.  The big reason chemists care, though, is that lone pairs can be active centers during a chemical reaction.  All that negative charge just waiting for something positive-ish to come along.”

“Like a really good tip,” grumbles Eddie.

~~ Rich Olcott

 

To Bond Or Not To Bond, That Is The Question

Vinnie’s pushing pizza crumbs around his plate, watching them clump together.  “These molecular orbitals gotta be pretty complicated.  How do you even write them down?”

“Combinations.  There’s a bunch of different strategies, but they all go back to Laplace’s spherical harmonics.  Remember, he showed that every possible distribution around a central attractor could be described as a combination of his patterns.  Turn on a field, like from another atom, and you just change what combination is active.  Here’s a sketch of the simplest case, two hydrogen atoms — see how the charge on each one bulges toward the other?  The bulge is a combination of a spherical orbital and a dumbbell one.  The molecular orbitals are combinations of orbitals from both atoms, describing how the charges overlap, or not.”Hydrogen molecule

“What’s that blue in the other direction?”

“Another possible combination.  You can combine atomic orbitals with pluses or minuses.  The difference is that the minus combination will always have an additional node in between.  Extra nodes mean higher energy, harder to activate. When the molecule’s in the lowest energy state, charge will be between the atoms where that extra node isn’t.”

“So the overlapped charge here is negative, right, and it pulls the two positive nucleusses —”

“Nuclei”

“Whatever, it pulls ’em together.  Why don’t they just merge?”

“Positive-positive repulsion counts, too.  At the equilibrium bond distance, the nuclei repel each other exactly as much as the shared charge pulls them together.”

Eddie’s still hovering by our table.  “You said that there’s this huge number of possible atomic orbitals.  Wouldn’t there be an even huger number of molecular orbitals?”

“Sure.  The trick is in figuring out which of them are lowest-energy and activated and how that relates to the molecule’s configuration.  Keep track of your model’s total energy as you move the atoms about, for instance, and you can predict the equilibrium distance where the energy is a minimum.  In principle you can calculate configuration changes as two molecules approach each other and react.”

“Looks like a lot of work.”

“For sure, Eddie.  Even a handful of atoms has lots of atomic orbitals to keep track of.  That can burn up acres of compute time.”

Vinnie pushes three crumbs into a triangle.  “You got three distances, you can figure their angles.  So you got the whole shape of the thing.”

“Right, but like Eddie said, that’s a lot of computer work.  Chemists had to come up with shortcuts.  As a matter of fact, they had the shortcuts way before the computers came along.”

“They used, like, abacuses?”

“Funny, Vinnie.  No, no math at all.  And it’s why they still show school-kids those Bohr diagrams.”

“Crazy Eights.”

“Eddie, you got games on the brain.  But yeah, eights.  Or better, quartets of pairs.  One thing I’ve not mentioned yet is that even though they’ve got the same charge, electrons are willing to pair up.”

“How come?”

“That’s the thing of it, Vinnie.  There’s a story about Richard Feynman, probably the foremost physicist of the mid-20th Century.  Someone asked him to explain the pairing-up without using math.  Feynman went into his office for a week, came back out and said he couldn’t do it.  The math demands pairing-up, but outside of the math all we can say is experiments show that’s how it works.”

“HAH, that’s the reason for the ‘two charge units per orbital’ rule!”

“Exactly, Eddie.  It’s how charge can collect in that bonding molecular orbital in the first place.  It’s also the reason that helium doesn’t form molecules at all.  Imagine two helium atoms, each with two units of charge.  Suppose they come close to each other like those hydrogens did.  Where would the charge go?”

“OK, you got two units going into that in-between space, ahh, and the other two activating that blue orbital and pulling the two atoms apart.  So that adds up to zero?”

“Uh-huh.  They just bounce off and away.”

“Cool.”

“Hey, I got a question.  Your sketch has a ball orbital combining with a dumbbell.  But they’ve got different node counts, one and two.  Can you mix things from different shells?”

“Sure, Vinnie, if there’s enough energy.  The electron pair-up can release that much.”

“Cool.”

~~ Rich Olcott

  • A friend pointed out that I’m doing my best to avoid saying the word “electron.” He’s absolutely right.  At least in this series I’m taking Bohr’s side in his debate with Einstein — electrons in atoms don’t act like little billiard balls, they act like statistical averages, smeared-out ones at that.  It’s closer to reality to talk about where the charge is so that’s how I’m writing it.