Episode 28 - Why atoms exist

Tomlin Hawthorne

Here's an atom, as it was understood in 1911. A tiny, heavy, positively charged core in the middle. And a negatively charged electron circling round it, like a planet round a sun.

Tomlin Hawthorne

Now, we know from Maxwell that when an electric charge is shaken, or swung round in a circle, it sends out light. That's how a radio mast works. And light carries away energy.

Tomlin Hawthorne

So the electron, as it circles, should be radiating. Losing energy. And as it loses energy, it should spiral inward, toward the core.

Tomlin Hawthorne

How long before it crashes?

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A year? A second?

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About a hundred-billionth of a second.

Tomlin Hawthorne

According to the best physics of 1911, every atom in the universe should have collapsed in a flash of light, long before you finished hearing the word atom. There should be no chairs, no air, no people. Nothing should be solid.

Tomlin Hawthorne

And here we all are. Today's question is why. What does an atom look like inside, and why does it not fall in on itself?

Tomlin Hawthorne

Last time you tried to charge a glow-in-the-dark sticker with red light, and got nothing, and then with a couple of seconds of blue or white, and it lit up. Each speck of that material is a ball in a ditch. Red light taps. Blue light kicks. And from that we got the idea that light arrives in lumps, photons, and that the size of the lump is set by the colour.

Tomlin Hawthorne

Today we take that idea inside the atom. And we start with the most surprising experiment of the twentieth century, which was carried out, for the most part, by a twenty-year-old student.

Tomlin Hawthorne

Ernest Rutherford was born in 1871 on a farm on the South Island of New Zealand, the fourth of twelve children. The story in the family is that he was digging potatoes when the telegram came to say he'd won a scholarship to Cambridge, and that he threw down the spade and said: that's the last potato I'll dig.

Tomlin Hawthorne

He was big, loud, cheerful, and had a voice that could upset delicate apparatus from across the room. His students put up a sign in the laboratory that said: Talk Softly Please. He had no patience with theory for its own sake. He once said that all science is either physics or stamp collecting. He was then given the Nobel Prize in Chemistry, which he thought was very funny.

Tomlin Hawthorne

By 1909 he was professor at Manchester, and he had a new tool. Certain radioactive substances fire out tiny, fast, heavy particles, called alpha particles. Rutherford realised you could use them as bullets. Shoot them at something and see how they bounce, and you can work out the shape of what they hit. It's the method physicists have used ever since. It's how the quark was found, and the Higgs.

Tomlin Hawthorne

So what was an atom thought to be like? The electron had been discovered a dozen years before, and people knew atoms had these tiny negative specks in them. And they knew atoms were electrically neutral overall. So the best guess was that an atom was a soft blob of positive charge, with the electrons dotted through it like raisins in a bun. The English called it the plum pudding model.

Tomlin Hawthorne

Rutherford had a German assistant, Hans Geiger, the one who later invented the counter that clicks. Geiger had been firing alpha particles at a very thin sheet of gold foil and watching where they came out the other side, by the tiny flashes they made on a screen. As expected, they went more or less straight through. A soft pudding couldn't deflect a heavy bullet much.

Tomlin Hawthorne

One day Geiger asked whether a young undergraduate, Ernest Marsden, could be given a small project to get his hand in. And Rutherford said, why not let him see whether any of the alpha particles bounce backwards?

Tomlin Hawthorne

It was a job for a beginner. Nobody expected anything. You had to sit in a completely dark room for half an hour until your eyes adjusted, and then stare through a microscope at a screen placed on the same side of the foil as the source, and count flashes that shouldn't be there.

Tomlin Hawthorne

A few days later Geiger stopped Rutherford on the stairs, very excited. They were there. About one alpha particle in eight thousand was coming straight back.

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Rutherford said later that nothing so unbelievable had ever happened to him. He compared it to firing a naval shell at a sheet of tissue paper and having the shell bounce back and hit you.

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It took him a year and a half to see what it meant. The story is that he walked into Geiger's room one day in 1911, in high spirits, and announced that he now knew what the atom looked like.

Tomlin Hawthorne

Most of the bullets go straight through, so most of the atom must be empty. But a very few bounce right back, so somewhere in there is something very small, very heavy and very strongly charged. Nearly all the mass of the atom is packed into a speck at the centre. He called it the nucleus. And the electrons are somewhere out in the space around it.

Tomlin Hawthorne

How small is the speck? About a hundred-thousandth of the width of the atom. Here's the picture I gave you in episode two. If an atom were the size of a cathedral, the nucleus would be a fly, somewhere near the middle. And all but a tiny fraction of the cathedral's weight would be in the fly.

Tomlin Hawthorne

Because what holds the electrons out there? The nucleus is positive, they're negative, they attract. The obvious answer is that they orbit, the way planets orbit the Sun and don't fall in.

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And that's the cold open. A planet can orbit for ever. An electron can't. An electron is a charge, and a charge going in a circle is being accelerated, and by Maxwell's laws an accelerated charge radiates. It has to lose energy. It has to spiral in. The sums are simple and the answer is a hundred-billionth of a second.

Tomlin Hawthorne

So Rutherford's own experiment had shown that atoms have a structure which, according to physics, can't exist for longer than it takes light to cross a room.

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And there was a second mystery sitting beside it. You'll remember it from episode nineteen. Each element, when it's heated, gives out light at certain exact colours and no others. A barcode. Sodium has its two yellow lines. Hydrogen has a red one, a blue-green one, a couple of violets. An electron spiralling inward should give off a smear of every colour as it went. Why the lines?

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There was even a formula for them. In 1885 a Swiss schoolteacher called Johann Balmer, who was sixty and taught at a girls' school in Basel, had been given the wavelengths of the hydrogen lines as a kind of numerical puzzle. And he'd found a simple arithmetical rule, using whole numbers, three, four, five, six, that produced all of them to a fraction of a per cent. It worked beautifully. Nobody had the least idea why. It had sat in the books for nearly thirty years.

Tomlin Hawthorne

Enter a twenty-six-year-old Dane.

Tomlin Hawthorne

Niels Bohr came to Manchester in 1912 to work with Rutherford. They were an odd pair. Rutherford boomed. Bohr mumbled, so softly and with so many hesitations that people leaned forward and still couldn't catch it. He'd been a good footballer, a goalkeeper, though his brother Harald was better and won an Olympic silver medal. He thought by talking, endlessly, going round and round a problem. And Rutherford, who distrusted theorists, made an exception. Bohr's different, he said. He's a football player.

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Bohr took the collapsing atom and did something outrageous. He didn't solve the problem. He simply declared it not to apply. Here's what he said, in 1913.

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One. An electron in an atom can't go round at any distance it likes. Only certain particular orbits are allowed. Think of the rungs of a ladder, or the steps of a staircase. You can stand on this step or that one. You can't stand in between.

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Two. While an electron is on one of its allowed steps, it doesn't radiate. It just doesn't. Maxwell's rule is suspended. And there's a lowest step, and from there, there's nowhere further down to go. That's why the atom doesn't collapse.

Tomlin Hawthorne

Three. An electron can jump from one step to another. And when it drops from a higher step to a lower one, it gives out the difference in energy as a single photon of light. One of Planck's and Einstein's lumps.

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And now, think about that third rule and the barcode.

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The steps are at fixed heights. So the drops between them are fixed sizes. So the photons that come out have fixed energies. And the energy of a photon is its colour. So the atom can only emit certain colours. One for each possible drop.

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The spectral lines are the list of jumps. The barcode is a picture of the staircase.

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Bohr worked out what the steps would have to be for hydrogen. And out of his arithmetic fell Balmer's formula. The schoolteacher's puzzle, exactly, with every number accounted for. Three, four, five, six: those are the numbers of the steps the electron is dropping from.

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Einstein, when he heard that Bohr's theory had also correctly predicted some lines seen in the spectra of stars, said: then it is one of the greatest discoveries.

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So that's the answer to the question from episode nineteen. How could Kirchhoff and Bunsen read the chemistry of the Sun? Because each kind of atom has its own staircase, and announces it in light.

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But you should be dissatisfied. I'd be worried if you weren't.

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Bohr hasn't explained anything. He's replaced two mysteries with three rules, and the rules are just orders. Only these orbits. Why? No radiating. Why not? It works, magnificently, for hydrogen. And it's obviously not the real answer. Bohr knew that better than anyone.

Tomlin Hawthorne

The real answer took ten more years, and it came from an unexpected direction.

Tomlin Hawthorne

Louis de Broglie was a French aristocrat, properly a prince, from one of the grandest families in France. His first degree was in medieval history. Then came the war, which he spent as a radio operator, stationed for much of it at the top of the Eiffel Tower. Afterwards he turned to physics, and in 1924, at thirty-two, he handed in his doctoral thesis.

Tomlin Hawthorne

The idea in it was very short. Einstein had shown that light, which everyone knew was a wave, also behaves as a particle. De Broglie asked: what if it goes both ways? What if the electron, which everyone knew was a particle, also behaves as a wave?

Tomlin Hawthorne

His examiners in Paris didn't know what to make of it. It was either brilliant or absurd. One of them sent a copy to Einstein and asked. Einstein wrote back that de Broglie had lifted a corner of the great veil.

Tomlin Hawthorne

Now. Why does that help with the atom?

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Go back to episode ten. I planted a flag there, and told you to remember it. A guitar string.

Tomlin Hawthorne

A string fixed at both ends can't vibrate any way it likes. It can vibrate as one hump. Or two. Or three. Whole numbers only. Nothing in between, because a pattern with two and a half humps wouldn't be still at the ends. I said: when you confine a wave, it's forced to come in separate, countable steps. Smooth wave in, staircase out.

Tomlin Hawthorne

Now take an electron, and say it's a wave. And wrap that wave round a nucleus, in a circle.

Tomlin Hawthorne

As the wave goes round, it has to meet up with itself. It has to join smoothly where it started. And that only works if a whole number of waves fits exactly round the circle. One wave. Two. Three. If you try to fit two and a half, the wave arrives back out of step with itself and cancels out.

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So only certain circles are possible. The ones where the wave fits.

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Those are Bohr's allowed orbits. That's where the staircase comes from. Not a decree. A wave, confined, has to fit.

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An atom is a musical instrument. Its energy levels are its harmonics. The periodic table is a set of chords. I mean that almost literally.

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And the collapse? There's a lowest note on a guitar string. One hump. You can't have half a hump. In the same way, there's a lowest pattern for the electron wave, and nothing below it. The electron can't spiral in, because there's no wave pattern for it to spiral into.

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It sounded like a metaphor. It was tested, almost by accident.

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In 1925, at Bell Laboratories in New York, two physicists, Davisson and Germer, were bouncing electrons off a piece of nickel. A bottle of liquid air exploded in the lab and ruined their sample. To clean it up they baked it at high temperature, which, without their knowing, turned the nickel into a few large crystals. And when they went back to bouncing electrons, the electrons came off in a pattern. Strong in some directions, absent in others.

Tomlin Hawthorne

That's interference. That's the two loudspeakers, the bright and dark stripes. Electrons were doing what only waves can do.

Tomlin Hawthorne

And there's a nice family footnote. The electron was discovered, as a particle, in 1897, by J. J. Thomson, who got a Nobel Prize for it. In 1927 his son, George Thomson, independently showed that the electron is a wave, and got a Nobel Prize for that. The father for proving it's a particle. The son for proving it isn't. One hopes Christmas was civil.

Tomlin Hawthorne

The finishing touch came from Erwin Schrödinger, the Austrian we met in episode fifteen giving lectures on life. Over Christmas 1925 he went off to a villa in the Swiss Alps, with, biographers agree, a companion who was not his wife and has never been identified. He came back with the equation that describes how de Broglie's waves behave. It's the central equation of quantum mechanics. Whatever was going on at that villa, it was productive.

Tomlin Hawthorne

And Schrödinger's equation gives us the modern picture of the atom. Forget the little solar system. There are no tracks. There's no tiny ball going round. The electron in an atom is a standing wave in three dimensions: a kind of cloud around the nucleus, with a definite shape, humming at a definite frequency, and not moving at all. The lowest state of hydrogen is a round ball of fog. The higher ones have lobes, and rings, and dumbbells.

Tomlin Hawthorne

What that fog is a fog of is a question I'm going to hold back. It's the subject of the next episode, and it's where the trouble really starts.

Tomlin Hawthorne

The myth of the week is on every logo for anything to do with science. The atom as a miniature solar system. A dot in the middle, and three little balls whizzing round on crossed ovals.

Tomlin Hawthorne

That was Rutherford's picture in 1911, patched by Bohr in 1913, and abandoned by 1926. It's been wrong for a century. It survives because it's easy to draw, and because the truth, a motionless three-dimensional standing wave of something we haven't defined yet, is not.

Tomlin Hawthorne

And the question to take away.

Tomlin Hawthorne

Bohr's model was wrong. There are no little orbits. And it was one of the most fruitful ideas in the history of physics. It explained the spectrum, it pointed straight at the right answer, it trained a generation.

Tomlin Hawthorne

That's the second time in this series. Carnot got the right law from the wrong theory of heat. And you could say Newton's gravity is a third: wrong about what gravity is, and good enough to land a spacecraft on a comet.

Tomlin Hawthorne

So what's a model for? If a false picture can lead you to the truth, is truth the right standard for judging pictures? And if not truth, then what? Fruitfulness? How would you know in advance?

Tomlin Hawthorne

Your challenge. You need a guitar, or any stringed instrument. If you don't have one, a stretched rubber band will do in a pinch, but find a guitar if you can.

Tomlin Hawthorne

Pluck an open string and listen. Now touch the string very lightly, don't press it down, exactly at its midpoint, above the twelfth fret, and pluck again. You'll get a clear, bell-like note an octave higher. That's the two-hump pattern. Now touch it lightly a third of the way along, above the seventh fret. Higher again. Three humps.

Tomlin Hawthorne

Try touching it at some random place in between. You get a dull thud. That's a pattern that doesn't fit.

Tomlin Hawthorne

You've just found the energy levels of a guitar string. The allowed notes, and nothing between them. And that's what an atom is doing, with an electron wave where the string is, and the pull of the nucleus where the two fixed ends are.

Tomlin Hawthorne

Next time. I've told you that light is a wave and a particle. And now I've told you an electron is a particle and a wave. In the next episode we stop being polite about that. We take single electrons, one at a time, and send them toward a wall with two slits in it. Richard Feynman said this one experiment contains the only mystery in quantum mechanics. I think he was right.