How to Make an Apple Pie from Scratch

by Harry Cliff

  But back in Paris, Irène and Frédéric hadn’t given up their work on beryllium. Using a more precise method, the Paris pair were able to show that Chadwick got the mass of the neutron wrong; it actually weighed about 0.1 percent more than a proton. Rutherford was eventually forced to admit that the neutron wasn’t made of a proton and an electron after all.

  In fact, the whole idea that the nucleus was made of protons and electrons was wrong too. Physicists had fallen for the logical fallacy that because electrons come out of the nucleus, they must have been inside the nucleus to start with. It turned out that electrons are actually created at the moment a nucleus undergoes radioactive decay. The atomic nucleus is made not of protons and electrons, but of protons and neutrons. During radioactive beta decay, a neutron in the atomic nucleus transforms into a positively charged proton, which stays inside the nucleus, and shoots out a negatively charged electron.

  The neutron was soon promoted to a fundamental building block of the atom in its own right, alongside the proton and the electron. With these three particles you can make any atom you like, from hydrogen (1 proton and 1 electron) to uranium (92 protons, 92 electrons, and 146 neutrons). The question now is, how do these ingredients actually come together to make the chemical elements in our apple pie? To answer that question, physicists would have to look to the stars.

  Skip Notes

  *1 The word “proton” was inspired by William Prout’s hypothesis that the chemical elements were all made from hydrogen atoms, which he dubbed “protyls” when he had first published the idea in 1815.

  *2 There was one puzzling exception—hydrogen itself, which came out with a mass of 1.008. That little extra mass turns out to be a source of sunlight, starlight, and ultimately all the other elements in the universe, as we’ll see in chapter 5.

  *3 The fourth element in the periodic table after hydrogen, helium, and lithium—a rare soft silvery metal.

  *4 One solar mass (the mass of the Sun) is 2 million trillion trillion kilograms, so I weigh about 0.00000­00000­00000­00000­00000­00039 solar masses. Not a very convenient way of quantifying human bulk, I hope you agree, but I guess it does put any worries about one’s weight in perspective.

  *5 Remember that according to Rutherford a neutron is made of a proton and an electron.

  CHAPTER 5

  Thermonuclear Ovens

  A couple of years ago I passed through the sleepy English village of Culham on my way to visit one of the largest nuclear experiments in the world. Nestled in a sinuous curve of the upper reaches of the River Thames and surrounded by picturesque Oxfordshire countryside, Culham seems like an unlikely place to find scientists struggling to control one of the most powerful forces in the universe. A short drive from the village is a sprawling science campus where an international team are trying to pull off a truly promethean feat: they are trying to make a star on Earth.

  I was met at reception by Chris Warrick, the lab’s head of communications, who had kindly agreed to be my tour guide for the day. In principle I was there in my capacity as a curator at London’s Science Museum to see if there were any exciting bits of scientific equipment I could scavenge for the collections, but it was also a great excuse to see an experiment I had been itching to visit since I was a teenager—the Joint European Torus, or JET for short.

  JET is the world’s largest nuclear fusion reactor: a huge metal donut that heats hydrogen to temperatures of hundreds of millions of degrees. Under these extreme conditions, hydrogen nuclei fuse together to make helium, releasing tiny blasts of heat and light, replicating the energy source of the Sun and stars. The team at JET are working to tame and control this awesome power. If they can crack it, nuclear fusion could provide enough clean,*1 cheap energy to meet all our needs for millions of years.

  The dream of harnessing the power of the stars on Earth has inspired scientists and engineers since nuclear energy was first discovered in the 1930s. Today, the climate crisis makes the prize immeasurably greater. When I was thinking about whether to do a PhD back in the late 2000s I seriously considered applying to do research on nuclear fusion, and although in the end the chance to work on the newly minted Large Hadron Collider was just too good to pass up, I had always wanted to see a reactor up close.

  From reception, Chris led me across a road and into the large white building with a 1960s space-age look that would make it a good double for Starfleet HQ from Star Trek. After wending our way through a maze of corridors and security doors we stepped into the main hall. JET towered above us: a mass of pipes, cables, and machinery dominated by eight hulking iron transformer cores that protrude outward from the central reactor like huge orange buttresses. Confronted with the sheer bulk of the machine I couldn’t help but be left with the impression of some fearsome power being restrained within.

  As we walked around the reactor, Chris explained the challenges that his colleagues were grappling with. The extreme temperatures needed to achieve fusion makes it impossible to contain the burning hydrogen within any solid vessel. Instead it is kept away from the reactor walls using a powerful magnetic field that forces the hydrogen into a ring running around the center of the donut-shaped reactor. When JET was built in the early 1980s it was hoped that it would be the first fusion experiment to achieve breakeven—the point at which you get more power out of the fusion reactions than you put in. Unfortunately, this holy grail was never achieved thanks to a bunch of unforeseen effects that only became apparent once the reactor began operating. Instead, JET is now a test bed for an even bigger reactor currently being built in the south of France known as ITER. This €20 billion megaproject is meant to finally demonstrate the viability of nuclear fusion as a power source, but it has been beset by technical and political problems, leaving some doubting whether it will achieve its goal.

  Chris and I sat in his office later that day discussing the prospects for fusion power. He for one remains convinced that we will eventually get there. Slowly but surely, the technical challenges are being overcome and, if nothing else, the promise of limitless clean energy is just too good to give up on. That said, the engineering hurdles remain formidable.

  The problem that the scientists and engineers at Culham are trying to solve is the same one we’re now confronted with in our search for the ultimate apple pie recipe. Having gotten our hands on the basic ingredients of all atoms—electrons, protons, and neutrons—we now need to find a way to fuse them together to make the chemical elements in an apple pie. Hydrogen is easy—just take some protons and electrons, shake thoroughly. Carbon and oxygen, which have nuclei made of six protons and six neutrons and eight protons and eight neutrons, respectively, are going to be more of a challenge.

  In fact, before we can even begin to think about how to make carbon and oxygen we need to find a way to make an element that apple pies don’t contain at all: helium. As the second element in the periodic table, with a nucleus made of two protons and two neutrons, there is no route to carbon and oxygen that doesn’t first go through helium.

  Unfortunately, as the good people at JET will tell you, making helium from hydrogen turns out to be bloody difficult. To understand why, I’d like to indulge in a little thought experiment. Imagine, if you will, that we are in a nuclear kitchen. In front of us on the work surface are two bowls containing our basic ingredients: protons and neutrons. Our dish of the day is the helium nucleus, a simple combination of two protons and two neutrons. This is nuclear cooking 101. What could be simpler?

  As we saw earlier, the thing that makes a helium atom a helium atom is its nuclear charge—in other words the number of protons in the nucleus—so let’s begin by picking up two protons. As we start to bring them together we immediately encounter a problem. The two positively charged particles start to repel each other, and as we force them closer and closer together that repulsive force becomes stronger and stronger. Electrical repulsion between two
charges follows what is known as an inverse square law—in other words, the force between two charges quadruples every time you halve the distance between them. This means that long before we get the protons anywhere near touching a terrific force sends them slipping out of our hands and flying across the room, perhaps smashing some nuclear crockery in the process.

  This is precisely the problem that led Ernest Rutherford to speculate about the existence of the neutron. A neutral particle encounters no repulsive force and so bringing a proton and a neutron together should be a doddle by comparison. However, as we turn to the bowl of neutrons we discover to our dismay that while we were looking the other way almost all of them have disappeared, leaving only protons and electrons behind.

  This is the second big problem—neutrons are unstable. Outside the safe confines of a nucleus a neutron lives a short and uncertain existence, surviving for only fifteen minutes on average until it spontaneously decays into a proton, an electron, and a third ghostly particle called a “neutrino” (more on that shortly). Ironically, this instability means that although neutrons were invented to explain how the elements get made, today they play almost no role in forming elements lighter than iron.*2 They just don’t hang around long enough.

  We seemed to have reached an impasse. The only way forward is to find some way of overcoming the vast electrical repulsion that conspires to keep two protons apart. In fact, we need two different things to happen. First of all, we need another force, an attractive one, that will bind the protons together if we can only get them close enough. The first hints of such a force were found by James Chadwick and a young physicist named Étienne Bieler in 1921. While bouncing alpha particles off hydrogen nuclei they discovered that when they got within a few thousandths of a trillionth of a meter of each other an attractive force started drawing them together. This, it turned out, was the first sign of an entirely new force of nature—the strong nuclear force—so called because it is strong enough to overcome the enormous electrical repulsion between two protons.

  In the 1920s physicists had almost no understanding of the strong nuclear force, beyond the fact that it must exist to explain how the nucleus holds together and that it only starts to act when two protons are within touching distance of each other. This leads us to the second piece of the puzzle. If we are to fuse protons together to make helium, then we need to find a way to get them close enough for the strong nuclear force to kick into action. However, at this distance—around a thousandth of a trillionth of a meter—the electrical repulsion between two protons is stupendously large: equal to the pull of the Earth’s gravity on a 5-kilogram dumbbell. That may not sound like a lot, but bear in mind this is the force on a single proton, and a proton’s mass is just 0.00000­00000­00000­00000­00000­017 kilograms.

  You can think of the repulsive electric field surrounding the nucleus as like the steeply rising ramparts of a heavily fortified castle. To storm the keep, a proton needs to be moving fast enough so that it can “jump” to the top of the walls, at which point the strong nuclear force takes over and pulls it into the nucleus. This can only happen if the protons are moving fantastically quickly, and such terrifically high speeds require terrifically high temperatures, temperatures of tens of millions of degrees. This is precisely why the scientists at JET need to heat the hydrogen to such fantastically high temperatures, and why mastering nuclear fusion has proven to be so difficult. However, even if we haven’t figured out how to do it on Earth yet, there are places in the universe where such temperatures do exist.

  THE IMPOSSIBLE SUN

  The first person to come up with a decent estimate of the temperature at the center of a star was the English astronomer Arthur Stanley Eddington. Eddington’s love affair with astronomy had begun in 1886 during nighttime walks with his mother along the promenade in the seaside town of Weston-super-Mare. Four-year-old Arthur would gaze up into the inky black and try to count all the stars in the night sky.

  By 1920, as director of the Cambridge Observatory, Eddington was grappling with the age-old mystery of the Sun and stars—why do they shine? In total, the Sun blasts 383 trillion trillion watts of power continuously out into space, enough to keep 150 billion trillion kettles permanently on the boil. That’s a lot of cups of tea.

  Since the mid-nineteenth century a debate had been raging over the source of this tremendous power and, crucially, how long it could keep the Sun shining. On one side were the geologists and naturalists, including the great Charles Darwin, who argued that the Earth and Sun must be hundreds of millions, perhaps even billions of years old in order to explain the agonizingly slow processes of rock formation and evolution of living things by natural selection. Arrayed against them were the physicists, led by Lord Kelvin, the guy with his own temperature scale, who arrogantly dismissed this as nonsense. There was simply no known power source that could keep the Sun shining at its current rate for more than a few million years, and who were these rock botherers to argue with the laws of physics?

  After decades of confusion a vital clue had arrived in 1919. Just down the road from the tranquility of Eddington’s tree-lined observatory on the edge of Cambridge, Francis Aston had been laboring away in a dingy basement at the Cavendish Laboratory, weighing atoms using his newly invented mass spectrograph. Aston’s great triumph had been to show that every atom had a mass that was equal to a whole number of hydrogen atoms, providing convincing evidence that hydrogen nuclei (protons) were the building blocks of atoms. But there was one puzzling exception to this whole number rule.

  Aston’s spectrograph could only weigh atoms relative to one another, and so you needed to choose a reference element to compare all your other weights to. In those days, oxygen, which has an atomic mass of 16 (eight protons plus eight neutrons), was the reference element of choice, which meant that the basic unit of atomic mass was defined as one-sixteenth the mass of an oxygen atom. On this scale, one element stuck out: hydrogen itself. By rights a hydrogen atom should have had a mass of exactly one, but instead it came out ever so slightly higher at 1.008.

  When Eddington heard about Aston’s peculiar result, he immediately realized its significance. If, as Rutherford and Aston argued, all atoms where made of hydrogen, then that little excess mass might just be the true source of the Sun’s power. In 1905, Albert Einstein had argued that mass and energy were interchangeable, an idea expressed by the most famous equation in science: E = mc2.*3

  Now the speed of light (c) is a very big number (299,792,458 meters per second to be precise), which means that the speed of light squared is a very, very big number. In other words, this equation tells us every kilogram of mass (m) has the potential to unleash a cataclysmic blast of energy (E). If four hydrogen atoms could be fused together to make helium then that little bit of extra mass from each hydrogen atom would be converted into energy. Eddington worked out that if hydrogen made up just 7 percent of the Sun then this process of nuclear fusion could easily keep it shining long enough to keep Darwin and the geologists happy.

  Eddington was acutely aware that his ideas were speculative; no one had managed to fuse hydrogen to make helium in the lab. The big question now was whether the center of the Sun was hot enough to overcome the electrical repulsion between protons and force them together. Fortunately, Eddington had recently created the very tool needed to attack this question—the first realistic theoretical model of the internal workings of a star.

  Using his model, Eddington calculated the temperature at the very heart of the Sun—a blistering 40 million degrees Celsius. But despite being far, far hotter than any temperature yet created in a lab, it fell well short of the estimated 10 billion degrees needed to get two protons to fuse. As we saw in our nuclear kitchen, two protons would only be able to overcome their enormous electrical repulsion if they were moving at fantastically high speeds, and even at 40 million degrees they wouldn’t be moving anywhere near fast enough.

  Undeterred,
Eddington was certain that the Sun and stars were fusing helium out of hydrogen, famously retorting, “We do not argue with the critic who urges that the stars are not hot enough for this process; we tell him to go and find a hotter place.” (Perhaps the most genteel way that anyone has ever been told to go to hell.) For Eddington to be right protons must somehow be breaking the accepted laws of physics. Luckily, breaking the laws of physics was all the rage in the early years of the twentieth century thanks to a revolutionary new theory that was turning the subject on its head.

  QUANTUM COOKING

  My first encounter with the weird and wonderful world of quantum physics was when my parents gave me a short paperback for my eleventh birthday called Mr. Tompkins in Wonderland. The book follows the adventures of the titular hero, “a little clerk of a big city bank” with a habit of dozing off and dreaming of fantastical worlds inspired by physics. Through Mr. Tompkins’s adventures we get to explore what the world would be like if everyday objects behaved in a quantum way, leading to, among other things, a very confusing game of snooker and concerns about lions and tigers spontaneously appearing outside their enclosures at the zoo. The author of this charming piece of whimsy was one of the most inventive physicists of the twentieth century, George Gamow. It was his insight that would eventually allow physicists to untangle the paradox of nuclear fusion in the stars.