Another Quantum of Solstice...

Rutherford and Bohr

[this story continues in part from here.]

Ernest Rutherford discovered the atom's very kernel, the nucleus, but his tiny solar system model of the atom failed. It failed because it had a fatal flaw according to classical electromagnetic theory: Viewed side-on in the plane of the ecliptic, the orbiting electron oscillates charge from side to side and should behave like a miniature transmitter, broadcasting electromagnetic energy like a Marconi transmitter. Giving off energy, bit-by-bit, the electron should spiral into the nucleus. Rutherford never explained that away.

The Importance of Being Near Ernest

Luckily, Rutherford confided his 1909 experiments to young Niels Bohr prior to publishing them. Rutherford had invited Bohr to Manchester to study physics after a brief (and apparently unsuccessful) stint at Cambridge. Inspired,* Bohr spent the summer of 1910 and the subsequent spring (taking time off to marry and to honeymoon), devising his own theory which he published in 1913 (two years after Rutherford finally published his planetary model in 1911).

Bohr got around Rutherford's electron death spiral problem by postulating that it didn't happen! That may sound audacious and even glib, but he overcame "illogical leaps" by solving a bigger mystery which had puzzled generations of scientists: he explained the long-known but little-understood signature hydrogen lines observed in the spectra of stars (recall that stars are mostly hydrogen). According to Bohr, the lines represented quantum leaps in units of energy. He did the math for the hydrogen atom to prove it. The simplistic hope that atoms and the universe were fundamentally similar -- the too small to be seen and the too big to be noticed were whirling masses in motion or "turtles all the way down" -- shone briefly.

According to Bohr's new 1913 theory, electrons encircled a nucleus, but only in stable, fixed-distance orbits (shades of Bode's earlier but discredited planetary law?) but without the continuous death spiral energy radiation. Bohr called his quantized orbits "stationary orbits" (whence my title). A quantum of solstice or standing still.

Electrons in Bohr's stationary orbits still gained or lost energy -- but only by jumping from one orbit to a bigger orbit and vice verse. That was revolutionary. Bohr's math worked out too and depended on Planck's constant which was only 13 years old then.

Planck quantized radiation and Bohr quantized matter--viz, electrons. Scientists struggled in subsequent years with the question of whether electrons were waves or particles and whether light rays were waves or particles. They worried about the meanings of such apparent dichotomies until they gradually realized that they were fighting about language and not about science.
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*Inspired is an understatement

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My inspiration for the "Quantum of Solstice" is here at Victoria's old blog, to whom I dedicate this blog post.

Ecce LUMO

Ecce Homo, Caravaggio (1605)

Behold the HOMO (Highest Occupied Molecular Orbital), seeking reception;
Behold the LUMO (Lowest Unoccupied Molecular Orbital), offering reception.

Chemical reactions are electronic transfers. I don't mean electronic transfers like PayPal is (although there are similarities between electricity and money). I mean electronic transfers like oxidations and reductions, substitutions, proton transfers--which all involve electron donors and acceptors.  I still think that BH₃NH₃ best illustrates how chemistry is like sex: link

Presumably, the chemistry of memory has some donor and acceptor aspect at the molecular level. Long term potentiation. Learning is also like transubstantiation--words becoming neuronal flesh and all that. But there is more to learning than replication.  As Plutarch noted, learning is less like bucket filling and more like igniting little fires; Jefferson echoed that same thought: knowledge is contagious.

Here are some mnemonics for today's lesson:

HOMO/LUMO
Donor/Acceptor
Base/Acid
nucleophile/electrophile
Plug/Socket
Hand/Glove
Foot/Shoe

You can guess the rest.

I Must Be Bohred II

There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.  ~Niels Bohr

I suspect the same holds true for elephants and blind men:

More snappy Bohrdom here

I thought this was profoundly cool:

In quantum mechanics one replaces the word 'orbit' with orbital, a word introduced by R.S. Mulliken who defined it in a simple way by saying that an orbital is as much like an orbit as quantum mechanics permits.

You see, Bohr's planetary model of an electron orbiting the nucleus (the iconic "atomic" symbol) was undone by Heisenberg. There can be no precisely defined position and energy for an electron as there is for a planet. It's a blur. So you can't really say that the electron orbits the nucleus even though you want to think that it does.  That's what Mulliken was trying to convey.

Failed Theories: I Must Be Bohred

A solar system model was applied to the atom in the early 20th century soon after the discovery of the electron. Tiny little electrons were thought to orbit a little sun-like nucleus.  The so-called Bohr model was easy to visualize and actually kinda sorta works for the hydrogen atom (a 1-electron, 1-proton atom) but the theory breaks down for more "complex" atoms like helium. Despite this failure, the planetary model became iconic for anything atomic.

An important outcome of Bohr's planetary model was the notion that electron "orbits" were subject to a discontinuous numerical progression, i.e., the orbits were "digital" not "analog". Go back and look at the planetary model picture here and imagine that like planets, electrons can only exist at certain regular distances. There is an underlying mathematical logic based in whole numbers for electrons (much like the periodic chart itself).  But in fact, some 18th century astronomers proposed such a model for planets more than one hundred years before the Bohr model for atoms.

Johann Daniel Titius was an 18th century German astronomer who first noticed an unusual order to the interplanetary distances between the then known planets (planet discovery had not advanced much since Galileo and astronomers had become obsessed with comets). As early as 1766 Titius had observed that a simple mathematical formulation predicted the planets' relative distances from the Sun.  He even predicted that a small planet would be discovered at 2.8 au where there was no known planet. 

Johann Elert Bode, head of the Berlin Observatory, latched onto Titius's idea and, without crediting Titius, published them. The law become known as the Titius-Bode law.  Here's table showing the actual relative distances of the planets from the Sun and values predicted by the Titius-Bode Law:

                   Relative Distance From Sun in au

Planet                    Actual          T-B Theory
______________________________________
Mercury                 0.39               0.4
Venus                     0.72               0.7
Earth                       1.0                 1.0
Mars                       1.52                1.6
                                   --                   2.8
Jupiter                    5.2                  5.2
Saturn                   9.54                10.0

Except for the lack of a planet at 2.8 au, the fit between theory and actual distances is remarkable. I'm fairly certain that Galileo would have embraced Titius-Bode law too, insofar as it was consistent with empirical data at the time.

Two things happened that catapulted Bode to stardom: first, the planet Uranus was discovered by Herschel in 1781. Uranus is beyond Saturn, but is exactly where the law predicted the next further out planet should be. This exciting discovery (Bode was allowed to name the new planet) led to an all out search to find the "missing" planet at 2.8 au. In the words of Titius:

From Mars there follows a space of 4 + 24 = 28 such parts, but so far no planet was sighted there. But should the Lord Architect have left that space empty?

The search was on. The heavens were divided into observable sectors among the international community of astronomers. Then, in 1801, the Sicilian astronomer Giuseppe Piazze found Ceres, the dwarf planet and largest asteroid in the asteroid belt. The calculated orbit of Ceres put it between Mars and Jupiter at a distance of 2.77 au in astonishing agreement with the Titius-Bode prediction of 2.8 au. Ceres is considered to be the largest chunk of a planet miscarriage. i.e, material which failed to accrete into a fully formed planet.  The new data is shown below in bold. These two discoveries amounted to both an extrapolation and an interpolation of the Titius-Bode law:

                        Relative Distance From Sun in au
Planet               Actual        T-B Theory
__________________________________
Ceres                2.77            2.8
Jupiter                5.2              5.2
Saturn               10.0             9.54
Uranus           19.2             19.6

Few things are as satisfying to a scientist as predicting something which is later backed by experimental data.  The Titius-Bode law was accepted as unexplained fact for a half century.  Its undoing began in 1846 with the discovery of Neptune at a relative distance of 30.06 au~well inside the predicted 38.9 au.  The discovery of Pluto in 1930 did not bode well for the law either. Pluto was found well out there at 77.2 au versus a predicted orbit of 39.44 au.

                         Relative Distance From Sun in au

Planet               Actual        T-B Theory

______________________________________

Uranus              19.2            19.6
Neptune            30.06          38.8
Pluto                   77.2            39.44

I know, I know: eccentric Pluto was downgraded from planetary status in 2006 and deemed extrasolar in origin and so shouldn't count. But that still leaves Ol' Neptune.

Today, Titius-Bode "theory" is regarded as a historical curiosity.