# 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.”

“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  Z 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.”

“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.”