by Harry Cliff
But the pollen particles do move! In other words, Einstein had shown that you could only explain Brownian motion if atoms were real. Not only that, but he had provided a new way to calculate the number of water molecules in a drop of water based on how far a pollen particle wanders in a given amount of time.
Now this all sounds very neat and tidy, but unfortunately the history of science is never quite as straightforward as that. Einstein didn’t actually set out to explain Brownian motion. His aim was to find a way to prove atoms existed, and it seems that it was only after he’d done his calculations that he realized there might be a link with Brown’s jiggling pollen particles. To seal the deal, Einstein needed experimental proof that the way small particles wander about in the water corresponds precisely to his equation. At the end of his paper he threw down the gauntlet to his experimental colleagues: “It is to be hoped that some enquirer may succeed shortly in solving the problem suggested here, which is so important in connection with the theory of Heat [kinetic theory].”
It was the French physicist Jean Baptiste Perrin who eventually took up Einstein’s challenge. Between 1908 and 1911 he and his team of research students performed a series of tour-de-force experiments that verified Einstein’s predictions in every way. Einstein’s theoretical brilliance and Perrin’s experimental guile had finally proven old John Dalton right. The age-old debate was finally settled. Matter is made of atoms.
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At last we can answer Carl Sagan’s original question: How many times do you need to cut an apple pie in half until you get down to an individual atom? Along with verifying Einstein’s equation, Perrin also measured Avogadro’s number, which allows you to figure out the number of atoms or molecules in a given mass of a substance, including, for instance, an apple pie. Popping one of Mr. Kipling’s finest on my kitchen weighing scales and doing a quick calculation reveals that a single apple pie contains roughly four trillion trillion atoms!
How many times would we need to cut the pie in half to get down to one of these atoms? Well, in Cosmos Sagan tells us that the answer is twenty-nine. His apple pie was a bit bigger than mine, though, so I thought I’d better check this for myself. After running the numbers, I was appalled to find that the great Carl Sagan had got it wrong! His calculation assumes only cutting the pie in one dimension, which would give you a slice one atom thick but as high and deep as the original pie. The correct approach is to ask how many cuts do we need to make until the last two pieces are each a one-quarter of a trillionth of a trillionth share of the initial apple pie? In other words, one atom. This gives you the correct answer of eighty-two cuts. There’s a letter of correction winging its way to the producers at PBS as we speak. Sorry, Carl.
Anyway, a good scientist should test their theoretical predictions, so I grabbed my best kitchen knife and had a go. After about fourteen cuts I was left with a crumbly mess and, I confess, none the wiser about the atomic structure of apple pie. The problem is that atoms are just too fantastically small: a single carbon atom is around a tenth of a billionth of a meter across. If you struggle to imagine something that tiny, then an analogy from the great theoretical physicist Richard Feynman may help. If you took an ordinary apple and blew it up to the size of the Earth, then one of its atoms would end up around the same size as the original apple. No knife made by humans is capable of slicing an apple pie finely enough to get down to something that small. How then could I check if the apple pie really is made of atoms? Actually, all you need is a pestle and mortar and a microscope.
First off, I ground up some of the black apple pie charcoal that we’d made in the first experiment. Unfortunately, it turned out that my charcoal wasn’t as pure as I’d thought; it must have still contained quite a lot of oils and moisture and formed a paste instead of the fine dust I was after. After some vigorous heating to drive off the last impurities I managed to get the dry powder I wanted. I proceeded to place a small drop of the yellowish apple pie liquid onto a microscope slide, dusted it with a tiny amount of the charcoal, slid the slide onto the microscope’s stage, and peered downward.
At four-hundred-times magnification the powder particles were huge, filling almost the entire field of view. I was worried that I’d not ground the charcoal up finely enough and was about to remove the slide when I noticed a group of much smaller black particles in the bottom left. Letting my eye adjust and keeping as still as possible, I suddenly saw it. They were moving. Not in a gentle flowing way that might have suggested currents in the liquid, but with an agitated jittering. I could see immediately why Brown had initially thought he’d discovered living molecules; they really did look as though they were dancing about. I was genuinely delighted, a similar feeling to when I first looked through a telescope at a yellowish dot in the sky to see a perfect little image of Saturn, complete with rings and pinprick moons, hanging in the blackness of space. It may sound silly, but on seeing Saturn my instant reaction had been “Oh my god, it’s real!” Images in books or on TV are one thing, but seeing it with my own eyes made it real to me in a way it had never been before.
Those dancing black specks of incinerated apple pie had a similar, and completely unexpected, effect on me. To think that each wiggle, zig, and zag was caused by untold numbers of unseen blows from indescribably small and yet (suddenly) undeniably physical atoms was strangely affecting. As a physicist, the concept of atoms is so familiar it can breed a kind of unthinking complacency, and I realized that this was one of the few times I had really seen evidence of their existence with my own eyes, proof positive that at least some of this particular apple pie really was made of atoms.*4
Of course, atoms are not the end of the story. Paradoxically, signs that they were made of even smaller things had been being uncovered in the labs of Europe for at least a decade by the time Perrin’s experiments sealed the deal for their existence. The consequences of these discoveries were to prove profound, triggering a revolution in our understanding of matter and the laws of nature, while unleashing forces that had been hitherto unimaginable.
Skip Notes
*1 Dalton was having none of it and rejected Davy’s advances out of hand. This proud northern radical had little time for the Royal Society, which he regarded as part of the corrupt political establishment. Its president, Joseph Banks, had stuffed the society full of his mates, and at the time the society was criticized as little more than a glorified gentlemen’s club for dilettante aristocrats who dabbled in science. He only eventually joined in 1822 when some of his friends put his name forward without his knowledge.
*2 Among other successes, kinetic theory provides a sound theoretical basis for the well-known rule that “the one who smelt it dealt it.”
*3 Its greatest triumph was the completely counterintuitive prediction that the viscosity or “stickiness” of a gas doesn’t increase as you increase the density of the gas, which was soon confirmed by experiment. This is really weird if you think about it; it implies that a pendulum swinging in ordinary air experiences no more resistance than a pendulum swinging in an airtight container with half the air pumped out.
*4 Strictly speaking, it proves that the acrid yellow liquid that came off the apple pie is made of molecules, since it’s the molecules in the liquid that continually hammer against the black particles and cause the jittering motion.
CHAPTER 3
The Ingredients of Atoms
Atoms are small. Stupendously, indescribably, unimaginably small. How small? Well, you could line up around 5 million carbon atoms across the period at the end of this sentence. That probably doesn’t really help, to be honest. It’s a pretty hard ask to picture something that’s less than a millionth of a millimeter across. After all, what’s the smallest thing you’ve ever seen with your own eyes? Perhaps a speck of dust floating in a sunbeam, or a flea. Well, they’re both bloody gigantic next to an atom.
Given th
eir mind-boggling smallness it’s pretty astounding that we can say anything at all about what atoms themselves are made from. That we can is ultimately down to four brilliant and, by today’s standards at least, staggeringly simple experiments carried out over a few decades around the start of the twentieth century.
This was the heroic age of experimental physics, when really profound discoveries could be made by just one or two people, beavering away in a dingy university laboratory. Today, making a major breakthrough in particle physics requires a gargantuan international effort involving thousands of physicists, engineers, and technicians and millions, if not billions, of euros, dollars, pounds, and yen. I work on the LHCb experiment with more than twelve hundred people from across the globe, and we’re actually the smallest of the four big detectors at the Large Hadron Collider, a machine that itself took almost four decades to plan, design, and build. On the other hand, the very first subatomic particles were all found using equipment cobbled together on a shoestring budget that could fit comfortably on a laboratory workbench.
So as we probe deep into the atom in search of the basic ingredients of our apple pie, I’d like to take you back to this heroic age when the basic ingredients of atoms were first discovered. But before we do, it’s worth recapping what was thought about the structure of matter at the end of the nineteenth century. From John Dalton we have the idea that every chemical element is made from a corresponding atom, the smallest possible unit of matter. However, the indivisibility of the atom wasn’t universally accepted. In 1815, the English chemist William Prout had argued that all the different elements might ultimately be made out of hydrogen atoms stuck together, which he based on the curious fact that all the elements appeared to have atomic masses that were roughly whole number multiples of hydrogen’s. However, Prout’s hypothesis wasn’t widely accepted, partly since he’d obtained his data from some distinctly dodgy experiments combined with a bit of judicious rounding; partly because of awkward elements like chlorine, whose atomic mass was 35.5 hydrogens; and also because many chemists were appalled by the prospect of resurrecting the alchemists’ old get-rich-quick scheme of converting lead into gold which, if Prout was right, became a simple matter of chipping a few hydrogens off a lead atom.
The other big piece of circumstantial evidence in favor of atomic substructure had come in 1869, courtesy of the Russian chemist, inspector of cheese factories, and hairdressers’ despair*1 Dmitri Ivanovich Mendeleev. After several long train journeys spent playing a game of chemical solitaire with cards representing the different elements, Mendeleev noticed that when he ranked the elements by atomic weight, their chemical properties repeated with a peculiar regularity. Laying out the elements to form the periodic table, Mendeleev was able to predict the existence of three brand-new elements, which he believed were required to fill the gaps in his scheme. Within a few years, they obligingly turned up—gallium, scandium, and germanium—with more or less the precise properties that he had predicted.
Where did these relationships between the chemical elements come from? At the very least, the periodic table showed conclusively that the elements were not a random collection of unrelated ingredients. There was clearly some sort of deeper order to the properties of atoms, and while that didn’t necessarily imply substructure, it was a tantalizing hint. However, the specter of alchemy loomed so large that it would take powerful experimental evidence to persuade chemists and physicists that atoms were really made of smaller things. Which brings us to heroic experiment number one, carried out in the dusty Cambridge laboratory where particle physics was born.
PLUM PUDDING
On a sleepy lane, nestled out of sight behind Cambridge’s Corpus Christi College, stands what should be one of the most famous buildings in the world, the original Cavendish Laboratory. Just a stone’s throw away on the bustling King’s Parade, crowds of tourists, boat tour touts, aggravated taxi drivers, and bicycle-riding students jostle for space, but here all is usually serene. Few on the tourist trail make it to the Cavendish, instead spending their time gawping at Cambridge’s medieval architecture or being taken on exorbitant punt rides up the river. But, every so often, you’ll see a small group gather outside the old lab, sometimes sheltering from the English drizzle under its arched entrance, while a guide shoots off a quick-fire list of world-changing discoveries that were made within its walls. Then after maybe five minutes, they shuffle off, normally in the direction of the Eagle pub, where Cavendish researchers Francis Crick and James Watson famously announced that they’d discovered “the secret of life” in the double-helix structure of DNA.
Aside from a small plaque fixed to its front wall, there’s precious little evidence that anything of much significance happened here, which is a source of eternal frustration to me. If particle physics were a religion, this would be its holiest of holies. Hordes of pilgrims would throng to the old Cavendish every year to walk the corridors and touch the stones where men and women once split atoms and uncovered new building blocks of nature. Perhaps there’d be a gift shop selling kitsch porcelain figurines of Ernest Rutherford and J. J. Thomson. Anyway, particle physics isn’t a religion, which is probably for the best, so instead when the physics department abandoned the creaking Victorian building for more spacious digs on the edge of the city in the mid-1970s, the university filled the old lab with social scientists and whacked up a plaque as a sop to history.
That hasn’t stopped the odd pilgrim making their way here over the years. Just after the apple pie scene in episode 9 of Cosmos, Carl Sagan himself turns up in the Cavendish’s old lecture theater, which he declares to be the place where “the nature of the atom was first understood.” That’s a bit of an exaggeration as we’ll see, but Cavendish physicists certainly had a claim to a large part of the puzzle, the first piece of which was found in the dying years of the nineteenth century, by the lab’s top prof, Joseph John Thomson.
“J.J.,” as he was known affectionately to his students, had been a bit of an odd choice to head up one of Britain’s leading experimental laboratories. He was a mathematical physicist by training and notoriously clumsy, to the extent that his laboratory assistant often did his best to keep his boss from handling the delicate glass bulbs that they used in their work. However, Thomson did have a knack for designing ingenious experiments and a keen nose for an interesting problem, one of which arrived like a bolt from the blue at the start of 1896. In Germany, Wilhelm Röntgen had discovered a miraculous new type of ray that could penetrate human flesh and reveal the bones beneath. He caused a worldwide sensation when he shared a macabre photograph of the bones of his wife Anna’s hand; horrified by the image, she remarked, “I have seen my death.” The mysterious new form of radiation was given a suitably enigmatic name: the X-ray.
Röntgen had found X-rays emanating from the end of a Crookes tube, a glass bulb with most of the air pumped out and two electrodes inside. It had been known for several decades that when a high voltage was connected to the tube, so-called cathode rays would flow from the negative electrode (the cathode) toward the positive electrode (the anode), creating an eerie green glow where they hit the end of the tube. Röntgen’s X-rays appeared to be coming from the place where the cathode rays struck the glass, but despite having been known about since the 1860s, no one was sure what cathode rays actually were.
Inspired by Röntgen’s discovery and the scientific potential of the new X-rays, Thomson set himself the task of uncovering the true nature of cathode rays. At the time there were broadly two schools of thought: either they were some form of electromagnetic wave, like radio, light, or the new X-rays, or they were a flow of negatively charged particles, most likely electrically charged atoms known as ions. Thomson, who had spent most of the past few years breaking gases apart into ions using electricity, was firmly of the latter view. The question was, how to prove it?
In 1895, Jean Baptiste Perrin had shown that if you fired a beam of cathode rays into a
metal cup, a negative electric charge built up, which he took as evidence that they were indeed negatively charged particles. However, many physicists weren’t convinced, arguing that the negative electric charge might just be a side effect of the cathode rays, rather than an intrinsic part of them.
Picking up where Perrin had left off, J.J. carried out a modified version of the experiment, but this time he placed the cup at an angle, out of the firing line of the cathode rays. When the tube was switched on, the rays traveled in a straight line, missed the cup, and no negative charge built up. However, when Thomson used a magnetic field to bend the cathode rays off their straight path and into the cup, hey presto! Negative charge was detected. In other words, the electric charge seemed to go wherever the cathode rays did. If he had any doubts before, J.J. was now absolutely convinced that cathode rays were negatively charged particles, but what type of particle was still unclear. Were they atoms, or something else entirely?
To figure it out once and for all, J.J. needed to know the mass of a cathode ray. If his guess that they were negatively charged atoms was correct then he’d expect them to have a larger mass than the lightest known atom, which was hydrogen. The tricky part was how to measure the mass of something so fantastically tiny. Remember that we’re still more than a decade away from being able to measure the size of an atom, even indirectly.