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

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Prelude to A Shell Game

Big Vinnie barrels into the office.  “Hey, Sy, word is that you’ve been trash-talking Niels Bohr.  What’s the story?”

“Nothing against Bohr, Vinnie, he was a smart guy who ran a numbers game out of C-town —”

“Which C-town, Cincy or Cleveland?”

“Copenhagen.  But he got caught short at payoff time.  Trouble is, some people still think the game’s good which it’s not.”

Hydrogen spectrum

Hydrogen spectrum, adapted from work by Caitlin Jo Ramsey
(CC BY-SA 3.0)
via Wikimedia Commons

“Which numbers game was this — policy, mutuale, bolita?”

“Rydberg.”

“Never heard of that one.”

“Rydberg was a Swedish physicist in the late 1800s.  He systemized a pile of lab and astronomy data about how hydrogen gas interacts with light.  Physicists like Lyman and Balmer showed how hydrogen’s complicated pattern (the white lines on black on this diagram) could be broken down to subsets that all have a similar shape (the colored lines).  Rydberg found a remarkably simple formula that worked for all the subsets.  Pick a line, measure its waves per meter. There’ll be a pair of numbers n1 and n2 such that the wave count is given by  Rydberg equationZ is the nuclear charge, which they’d just figured out how to measure, and R is a constant.  Funny how it just happens to be Rydberg’s initial.”

“Any numbers?”

“Small whole numbers, like 1, 2, up to 20 or so.  Each subset has the same n1 and a range of values for n2. The Lyman series, for instance, is based on n1=1, so you’ve got 1/1–1/4=3/4, 1/1–1/9=8/9, 15/16, 24/25, and so on. See how the fractions get closer together just like those lines do?”

“Nice, but why does it work out that way?”

“Excellent question, but no-one had an answer to that for 25 years until Bohr came up with his model.  Which on the one hand was genius and on the other was so bogus I can’t believe it’s still taught in schools.”

“So what did he say?”

“He suggested that an atom is structured like a solar system, planar, with electrons circling a central nucleus like little planets in their orbits. Unlike our Solar System, multiple electrons could share an orbit, chasing each other around a ring.  The 1/n² numbers are the energies of the different orbits, from n=1 outwards.  An electron in a close-in orbit would be tightly held by the nuclear electrical field; not so much for electrons further out.”

“Yeah, that sounds like what they taught us, alright.”

“Bohr then proposed that an incoming lightwave (he didn’t believe in photons) energizes an electron, moves it to a further-out orbit.  Conversely, a far-away electron can fall inward, emitting energy in the form of a lightwave.  Either way, the amount of energy in the lightwave depends only on the (1/n1²–1/n2²) energy difference between the two orbits.  The lightwave’s energy shows up in that wave number — more energy means more waves per meter and bluer light.”

“Ah, so that Ly series with n1=1 is from electrons falling all the way to the lowest-energy orbit and that’s why it’s all up in the … is that ultra-violet?”

“Yup, and you got it.  The Balmer series is the one with four lines in the visible.”

“Uhh… why wouldn’t everything just fall into the middle?”

“Bohr said each orbit would have a capacity limit, beyond which the ring would crinkle and eject surplus electrons.  He worked out limits for the first half-dozen elements but then things get fuzzy, with rings maybe colliding and swapping places.  Not satisfactory for predictions.  Worse, the physics just doesn’t work for his basic model.”No Bohr

“Really?  Bohr was a world-class physicist.”

“This was early days for atomic physics and people were still learning what to think about.  The Solar System is flat, more or less, so Bohr came up with a flat model.  But electrons repel each other.  They wouldn’t stay in a ring, they’d pop out to the corners of a regular figure like a tetrahedron or a cube.  That’d blow all his numbers.  The breaker payout, though, is his orbiting electrons must continually radiate lightwaves but don’t have an energy source for that.”

“Was he right about anything?”

“The model’s only correct notion was that lightwaves participate in shell transitions.  Schools should teach shells, not orbits.”

~~ Rich Olcott