Rutherford’s Atom — Podcast Script

I want to tell a story about a new technological era. Initially, the discoveries that were made were only of interest to a few specialists. Many people might have considered the research to be something bizarre, inexplicable, or too theoretical to impact their everyday lives. A few visionaries — or crackpots — suggested that, one day, this fundamental research might change the world — transform it from its present state into a paradise, with limitless energy, where humans could achieve incredible things. They were mostly ignored. But soon this changed. As the discoveries mounted, and people began to realise that this new technological force could be harvested — not just in science fiction, but for profit, not just to change the world as it was, but to create terrifying weapons of war and wield incredible power — people began to talk of entering a new era for the human species. An era so radically different from the present day. An era that would either lead the earth on the transformational path to a techno-utopia — or the shorter one, to a flaming, poisoned wreckage.

I want to tell you this story. But first, I want to highlight some of the characters who you might not hear about. In history, starting in the 19th century, there has been an ongoing debate about two alternative interpretations. One of them is the “great man theory”, and we’ll keep the misogyny because it’s an old-fashioned idea. This is the concept that the course of history is shaped by charismatic individuals — leaders who end up with large followings, who bend events to their will due to their charisma or talents. You can name some such individuals, of course. Julius Caesar. Jesus. Alexander the Great. Genghis Khan. Muhammad. Charlemagne. Napoleon. This is pretty Euro-centric, but most cultures and histories have such revered, titanic figures. In the modern era, their reputations can be a little more patchy; perhaps we remember better the brutalities of Stalin, Hitler, Mao. It makes a nice story; and it actually gives you a narrative framework for covering history that’s more convenient. Following all of the intricate threads of history — the interactions and interplay between various groups, trends, and forces; the relative importance of religion, economics, and so on — this is tricky to do. Maybe we as people can relate more to the story of an individual; seeing the world through their lens. And so, often, the history of Rome becomes the history of the lives of the Roman Emperors; the history of the United States becomes the story of each Presidential administration.

But there is of course a dissenting theory — that trends and forces are the most important. Like the anthropic principle, there are weak and strong versions of this theory. I guess the strong version of the theory suggests that the historical circumstances of the time make particular personalities inevitable. The German economy was in ruins during the Great Depression; they were bitter after the Treaty of Versailles had imposed a humiliating peace; some populist, aggressive, nationalist leader was bound to take control. If you had a time machine and killed Hitler, someone else would inexorably fill his place, and the war would have unfolded before. Individual humans are almost just pieces on a chessboard, or rational actors in some vast game theory set of equations. They might seem to be kings, when we pawns look at them. But they’re moved by forces larger than themselves. That’s the strong version. Perhaps in the weaker version, we argue that great personalities do exist, but they can only seize control of events when the trends and forces align correctly. After all — it seems almost ridiculously deterministic to say that Napoleon was destined from birth to change the face of Europe. If there was no French Revolution in 1789–93, how would he ever get his chance? And, similarly, this avoids the worrying thought that every great person goes onto shape the course of history. Some of them probably just end up being happy, instead.

As in history, so in the history of physics. It’s easy to point to individuals who changed the course of how we think. Aristotle. Galileo. Newton. Maxwell. Einstein. The list goes on and on. It’s true that some individuals make truly outstanding contributions to our knowledge of the Universe; that, in this specific realm, some people seem to have immense scientific gifts. There are scientists who are revered in hushed tones as being born with some unnatural genius. A scientific mind that arises once in a generation — once in a century, even. If anything, the so-called “Great Man theory” pervades our understanding of how science and technology develops more than it ever pervaded history. I’m guilty of this too, of course, with episodes on Newton already out, and more on Einstein sure to come. In the end, narrating history this way — through the story of these remarkable humans — is just too tempting.

Yet, at the same time, as any of these physicists would be the first to admit — it is very rare that you are not shaped by the science that has come before you. You’re building on a vast edifice of other people’s discoveries; your insights, your breakthroughs, are often impossible without the legwork that was done by previous geniuses. Not just previous geniuses, though; previous, unregarded, unnoticed, perhaps even completely forgotten figures from the history of science. Even if you develop a theory that’s almost completely unique to you — like some of those who discovered quantum mechanics, or Einstein and relativity, could perhaps claim to do — you’re building on the theoretical problems that you understand in the framework of a previous era. Physics is broken; there are these discrepancies; there is this piece of mathematics lying around — and all of the groundwork is laid for someone to come along — get a little lucky in the path they choose to take -make incredible advances, and take all the credit. The work done by the forgotten scientists — not just the ones who made it possible, but everyone who fruitlessly spent years confirming that a dead end truly is a dead end — is often unappreciated.

In the spirit of remembering the forgotten martyrs of physics, then, I’ll tell this story a little differently. In the early 1900s, there were two physicists called Geiger and Marsden. They worked under Ernest Rutherford, a hot-shot professor who had just won the Nobel Prize for Chemistry (which always annoyed him, because he thought of himself as a physicist). Rutherford had won the Nobel Prize — not only for discovering radioactivity took multiple forms, which he called alpha and beta particles, but also that the radioactive decay of elements involves one element transforming into another. The dream of the alchemists — that you could transmute elements into each other — had finally been realised — but it only applied to radioactive elements, and sometimes you had to wait thousands of years for the transformation to take place. Physics has a way of biting you on the bum.

We now understand that an alpha particle is pretty much the same thing as a helium nucleus; two protons, and two neutrons. That means it’s charged, which is important — both for the experiment I’m about to describe, and its high charge also explains why it can ionise other atoms when it interacts with them, tearing their electrons away. This is why alpha-emitters can cause immense damage to the body — and why the Russians used polonium-210, an alpha emitter, to kill Alexander Litvinenko. Luckily for most of us humans, alpha radiation can’t penetrate all that far through matter, so you should be safe as long as you don’t touch it and there’s minimal shielding involved. (or spies don’t feed it to you). We now know that when a radioactive alpha-emitter element’s nucleus is unstable, at some point, the alpha particle escapes via quantum tunnelling — that miniscule probability that it happens, by quantum chance, to be just outside the energy barrier that’s holding the atom together — and it’s emitted from the nucleus. You’re left with a new nucleus — a different configuration of protons and neutrons — and, hence, a new element.
But they didn’t know this at the time; no-one even knew that the nucleus existed, although a similar model was suggested by Japanese physicist Hantaro Nagaoka. Instead, the scientific consensus held that the atom was like a “plum-pudding” — electrons, the recently-discovered negatively charged particle, were embedded in a sphere of positive charge. This allowed the atom to be overall charge-neutral, so it wouldn’t interact as strongly as charged particles do with electric fields, while also containing electrons.

At any rate, Rutherford decided to use his recently discovered alpha particles to probe the structure of matter, and it’s here that he enlisted the help of poor Geiger and Marsden. They regularly used to turn off all the lights in the lab, until it was pitch black, and then sit there, eyes open, for half an hour.

Their eyes needed to adjust to the dark. The task that these physicists had was to watch a thin screen made of zinc sulphide. They were staring intently at the screen for tiny flashes of light. Whenever they saw one — and occasionally there were up to 90 a minute, or even more — they had to record the location of the flash, and the number of flashes that they’d seen. It was such a strain on the eyes and concentration that you could only achieve this for short bursts of a minute at a time before being overwhelmed by the flashes, these little pinpricks of light in the pitch darkness of the laboratory. Over the course of years, they recorded data from hundreds of thousands of tiny flashes. It’s no surprise that one of them would later spend many years developing an automatic detector — the Geiger counter — for just what he was trying to observe manually, by hand; so that no one ever had to go through that pain again.

So whenever you see a cool result in physics, or appreciate the benefits of modern technology, just think of all of the poor graduate students who had to suffer to bring you that information. Whenever you turn on a light-switch in France — think of poor Geiger and Marsden, counting their tiny flashes. Each flash was an alpha particle interacting with the zinc sulphide screen; this was the only way they could count them. This was the famous Rutherford gold foil experiment (or, in the spirit of giving them credit, the Geiger-Marsden experiment.) It was one of the pivotal moments in our understanding of the atom.

A common misconception about the Geiger-Marsden experiment was that the real revelation was that most of the alpha particles passed straight through the gold foil. This is how it’s sometimes presented: “Amazingly, most of the alpha particles passed straight through, showing that the atom was mostly empty space!” In fact, the current models of atomic physics suggested that the alpha particles should fly straight through the foil. Remember, they still had their plum-pudding model; and this is your ideal physics experiment; you have some idea of what you’re expecting to find, preferably with some specific calculation or number to check. If you find out you’re correct, the existing theory survives another test. If you find out your calculation disagrees with experiment, then you get incredibly excited, check the experiment a thousand times, 99.9999999% of the time you find you’ve made a stupid mistake in setting it up that’s giving you a ridiculous value, but 0.0000001% of the time you’ve discovered new physics! Fame, fortune, and Nobel prizes all around!

Anyway, such was the setup here. The charges were known, and so the electric fields could be calculated; they had Maxwell’s equations that described the theory of electromagnetism, and so they could calculate exactly how much the alpha particle, with its positive charge, would be deflected — and they thought that even a close interaction with an atom should only deflect the alpha particle by a tiny fraction of a degree. Even if the alpha particle found its way entirely through the gold foil that Geiger and Marsden were using, interacting with every atom along the way, it should only be deflected by a few thousandths of a degree — and most alphas should pass straight through with no measurable deflection.

Instead, they saw that some alpha particles — a tiny fraction — were deflected through angles of more than 90 degrees — some were deflected entirely by the thin gold foil. They realised that the electric field strength required to totally deflect an alpha particle were huge. After all these are hefty beasts with a measurable mass moving at quite some speed they were firing at the foil. And this totally wrecked the concept of a plum-pudding model for the atom; you needed a very strong electric field, concentrated across a tiny area, to make this work.

The electric field on a sphere of charge depends on the radius of that sphere, and the amount of charge. If the same amount of charge is smeared across a larger sphere, the electric field will be smaller — the charge is more spread out, and the electric field strength really measures the gradient, the difference in the force as you move from place to place. The only way they could get the kind of results they were seeing is if the atoms contained a tiny, positively charged nucleus. That way, the vast majority of alphas would pass straight through the foil, while a tiny fraction would pass close enough to the strong electric fields surrounding the nucleus that they’d be deflected by these large angles — what you might call a head-on collision. To be electrically neutral overall, the electrons would have to somehow orbit around this nucleus. This was the new model of the atom, and probably the one we all picture when we try to picture an atom (although often, in our mind’s eye, the size of the nucleus is exaggerated — its radius is something like 1/10,000th the radius of the whole atom, as a rule of thumb.)

This is a classic physics experiment due to the simplicity of the setup, the richness of the inference, and of course the fact that it disproved an old model while presenting a shiny new one to investigate. Rutherford later described his surprise at the experiment by saying:

“It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backward must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive centre, carrying a charge.”

As soon as Rutherford had the idea, he realized that the results they’d seen were easier to explain if the nucleus was tiny — and the deflection was caused entirely by an inverse-square force law; deflections via the electric field of the nucleus. You can calculate the scattering angles that you’d expect for an alpha particle passing close to a nucleus — in fact it’s a calculation they made us do in undergraduate physics — and, lo and behold, the theory of a dense positively-charged nucleus in the centre of the atom with orbiting electrons gave the correct answer, and the plum-pudding model ended up cast into the dustbin of history. The system works!

Rutherford would later make other great contributions to nuclear physics, the field that he helped to discover — because the model was far from finished. Later experiments conducted by Rutherford used alpha particles to convert nitrogen into oxygen — a process that emits a proton, or a hydrogen nucleus, same thing. In the process, Rutherford realised that — since all atoms had masses that were roughly multiples of the proton mass, and charges that were multiples of the proton charge — the proton must be the building block of the nucleus. This helped explain the masses and charges, and the process by which elements could be turned into each other — nuclear reactions, where the nucleus lost or gained protons from the alpha particle bombardment — but it created more problems. If protons could be knocked out of the nucleus, and the nucleus was made up of many positively charged protons, what stopped their electrostatic repulsion from tearing the nucleus apart? This required the idea of the strong nuclear force; and with it, another entirely new branch of physics. Rutherford was one of those who proposed a new particle — the neutral electron, or neutron — which sat in the nucleus and helped to bind together the protons. And, in 1935, a few years before Rutherford died, he would get to see his scientific colleague James Chadwick win a Nobel Prize for proving his neutron theory correct by discovering the neutron in an experiment. Even then, all of the questions provoked by Rutherford’s discovery hadn’t been resolved: after all, if the electrons are “orbiting” the positively charged nucleus as you’d expect due to their mutual electrostatic attraction, there was a problem. Accelerating charges radiate away their energy; it’s how electromagnetic radiation is formed, after all. And the electrons in orbit around the nucleus were constantly accelerating, as anything does when it’s changing direction in an orbit: the electrons should have been emitting all of their energy and spiralling into the nucleus in a very short amount of time. A model of the atom that doesn’t allow for any atoms to exist for longer than a few seconds is obviously not ideal. This is a problem that would require quantum mechanics to solve; and that’s for another day.

Given the huge wealth of physics that was opened up by the gold foil experiment, it’s no wonder that it’s gone down in the annals of history as one of the most famous experiments ever conducted, revolutionising our understanding of the fundamental building-blocks of matter — and in an elegant, simple-to-explain way. Rutherford expressed shock at the results of the experiment, but he might have been even more surprised if he’d had any inkling what the discovery of this nucleus could possibly mean, how it would not only open up whole new branches of physics but come to change the course of history; that it would create both incredible hope and incredible fear for the human species. Next episode, we’ll skip forward in time to explain the “liquid drop model” for the energy of a nucleus — which will hopefully then allow us to explain why joining nuclei in fusion and splitting them in fission can both, depending on the nucleus, liberate energy. Join us then.