HOMO, LUMO in Organic Chemistry

Transcript



Transcript



Transcript



Transcript

ATOM - The Greatest Discovery Ever

 

 

THE CLASH OF TITANS

This is the story of the greatest scientific discovery ever. The discovery that everything is made of atoms. The vast variety and richness of everything we see around us in the world and beyond, how it's built up, how it all fits together is all down to atoms and the mysterious laws they obey.

As scientists delved deep into the atom, into the very heart of matter, they unravelled Nature's most shocking secrets. They had to abandon everything they believed in and create a whole new science. A science that today underpins the whole of physics, chemistry, biology, and maybe even life itself.

But for me, the story of how humanity solved the mystery of the atom is both inspiring and remarkable. It's a story of great geniuses. Of men and women driven by their thirst for knowledge and glory. It's a story of false starts and conflicts, of ambition and revelation. A story that lead us through some of the most exciting and exhilarating ideas ever conceived of by the human race. And for a working physicist like me, it's the most important story there is.

On 5th October, 1906, in a hotel room near Trieste, a German scientist called Ludwig Boltzmann hanged himself. Boltzmann had a long history of psychological problems and one of the key factors in his depression was that he'd been vilified, even ostracised, for believing something that today we take for granted. He believed that matter cannot be infinitely divisible into ever smaller pieces. Instead, he argued that ultimately everything is made of basic building blocks - atoms.

It seems incredible now that Boltzmann's revelation was so controversial. But 100 years ago, arguing atoms were real was considered by most to be a waste of time. Although philosophers since the Greeks had speculated that the world might be made out of some kind of basic unit of matter, they realised that they were far too small to see even under the most powerful microscopes. Speculating about them was therefore a complete waste of time. But then, in the middle of the 19th century, whether or not the atom was real was suddenly a question of burning importance. The reason was this. Steam.

By the 1850s, it was changing the world. It powered the mighty engines, the trains, the ships, the factories of the Industrial Revolution. So figuring out how to use it more effectively became a matter of crucial commercial, political and military significance. Not surprisingly, then, it became the key question of 19th-century science. The demand to build more powerful and efficient steam engines in turn created an urgent need to understand and predict the behaviour of water and steam at high temperatures and pressures. Ludwig Boltzmann and his scientific allies showed that if you imagined steam as made of millions of tiny rigid spheres, atoms, then you could create some powerful mathematical equations. And those equations are capable of predicting the behaviour of steam with incredible accuracy.

But these same equations plunged Boltzmann and his fellow atomists into controversy. Their enemies argued that since the atoms referred to in their calculations were invisible, they were merely a mathematical convenience rather than real physical objects. To claim that imaginary entities were real seemed presumptuous, even blasphemous. Boltzmann's critics argued that it was sacrilegious to reduce God's miraculous creation down to a series of collisions between tiny inanimate spheres. Boltzmann was condemned as an irreligious materialist.

 The tragic irony of Boltzmann's story is that when he took his own life in 1906, he was unaware that he'd been vindicated. You see, a year before he died, a young scientist had published a paper which undeniably, irrefutably, proclaimed the reality of the atom. You might have heard of this young scientist. His name was Albert Einstein.

In 1905, the year before Boltzmann's suicide, Albert Einstein was 26 years old. His brash arrogance had upset most of his professors and teachers and he was barely employable. Then he got his girlfriend pregnant. That was followed by a hasty marriage. He needed a job. Any job.

Having not quite distinguished himself at university, he took up a job as a patents clerk here in Berne in Switzerland. He'd moved into this small one-bedroom apartment on Kramgasse with his young wife Mileva.

Despite dire personal straits, the young Einstein had a burning ambition. He was desperate to make his mark as a physicist. And in 1905, during one miraculous year, the mark he made was truly incredible.

Having an undemanding job meant that young Einstein had plenty of time on his hands both at work and here in this tiny apartment to think deep thoughts. In the space of just a few months, he was to publish several papers that would change science for ever. Now, everyone's heard of his Theory of Relativity, even if they don't understand it. His paper on the nature of light would win him the Nobel Prize a few years later.

But ironically, it wasn't either of these two papers that had the most impact on the discovery of atoms. The one that made all the difference was a short paper on how tiny grains of pollen danced in water.

Almost 80 years earlier, in 1827, a Scottish botanist called Robert Brown sprinkled pollen grains in some water and examined it through a microscope. What he found was really strange. Because instead of the pollen grains floating gently in the water, they danced around furiously, almost as though they were alive. Now, while this so-called "Brownian motion" was strange, scientists soon forgot about it. They found it mundane, even boring. Who cared if the pollen jiggled about in the water?

 And what had the jiggling to do with atoms anyway? For nearly 80 years, Brown's discovery remained a little-known scientific anomaly. Then Einstein changed everything.

In one staggering insight, Einstein saw that Brownian motion was all about atoms. In fact, he realised that the jiggling of pollen grains in water could settle the raging debate about the reality of atoms for ever.

His argument was simple. The pollen will only jiggle if they were being jostled by something else. So Einstein said that the water must be made of tiny atom-like particles which themselves are jiggling and continually buffeting the pollen. If there were no atoms, then the pollen would stay still.

So Boltzmann and his contemporaries had been rowing furiously about this question for nothing. The answer was there all along. Einstein proved that for Brownian motion to happen, atoms must exist.

Einstein's paper went way beyond just verbal arguments.

With flawless mathematics, he proved that the dance of the pollen revealed the size of the atom. And it's mind-numbingly tiny. One tenth of a millionth of a millimetre across! A single human hair, itself one of the narrowest things visible to the naked eye, is over a million atoms wide. Let me put it another way. There are more atoms in a single glass of water than there are glasses of water in all the oceans of the world! It sort of hurts your head just to think about it.

Einstein's paper ended the debate about whether the atom was real or not. And Boltzmann had been totally vindicated. The atom had to be real.

By the early years of the 20th century, the atom had arrived. Scientists who'd argued that the atom was real were no longer heretics. In a dramatic sudden reversal, they became the new orthodoxy. But they were to pay a huge price for their success. Before they'd had a chance to congratulate each other on discovering the atom, it ripped the rug out from under their feet and sent them spiralling into a bizarre and at times terrifying new world. And it all kicked off here in what by 1910 was the world's centre for atomic physics - Manchester.

Two of the most extraordinary men in the history of science worked here in the physics department of Manchester University between 1911 and 1916. They were Ernest Rutherford and Niels Bohr, on the face of it, two very different personalities and the unlikeliest of collaborators.

Rutherford was from a remote part of New Zealand and grew up on a farm. Bohr was born in Copenhagen, wealthy and erudite, virtually an aristocrat. Rutherford was the ultimate experimentalist. He loved technology and ingenious arrangements of batteries, coils, magnets and radioactive rocks. But he was also blessed with a profound intuition.

In contrast, Bohr was the ultimate theoretician. To him, science was about deep thought and abstract mathematics. Pen and paper, chalk and blackboard were his tools. Logic was his path to truth.

Although their approaches to their work couldn't have been more different, they had one thing in common.

They were prepared to ditch three centuries of scientific convention if it didn't fit what they believed to be true. They were genuine revolutionaries. Rutherford and Bohr were two of the most extraordinary minds ever produced by the human race. But it would take every bit of their dogged tenacity and inspirational brilliance to take on the atom.

In 1907, Ernest Rutherford took over the physics department in Manchester. This was a period of momentous scientific change. Just over ten years earlier, in Germany, came the first demonstration of weird rays that see through flesh to reveal our bones. These rays were so inexplicable. Scientists didn't know what to call them. So they were named x-rays.

And a couple of years after that, in Cambridge, it was shown that powerful electric currents could produce strange streams of tiny glowing charged particles that were called electrons.

And in 1896 in Paris, came the most significant discovery of all. One that, more than any other, would unlock the secrets of the atom. The metal uranium was shown to emit a strange and powerful energy that was named radioactivity. It seemed straight out of science fiction. Radioactive metals were warm to touch. They could even burn the skin. And the rays could pass through solid matter as if it wasn't there. It truly was a marvel of the modern age.

Rutherford was obsessed with radioactivity. All sorts of questions plagued him. How was it made? Why did it come in different forms? How far could it travel through a vacuum or through air? Did it alter the materials that it encountered?

In Manchester, together with his assistants, Hans Geiger - of Geiger counter fame - and Ernest Marsden, he devised a series of experiments that would probe the enigma of radioactivity.

1909. Manchester University. These are the props.

Gold leaf, beaten until it's just a few atoms thick. A moveable phosphorescent screen that flashed when struck by radioactive rays. And inside this box is the star attraction. A tiny piece of the metal radium.

Radium is an extraordinarily powerful source of the kind of radioactivity that Rutherford had named alpha-rays. They weren't really rays. They were more like a steady stream of particles. Radium spat out these particles like a machine gun that never ran out of bullets.

Rutherford set his students a simple-enough task: Use the radium gun. Shoot the alpha-radioactivity at the gold leaf and with the phosphorescent plate, count the number of particles that come out the other side. In practice, that meant sitting alone in the dark and counting tiny, almost invisible, flashes on the phosphorescent screen. It was deeply tedious, but Rutherford insisted that they keep at it.

Weeks passed and the team of researchers found nothing unusual. The alpha particles seemed to punch through the gold almost as though it wasn't there. Very occasionally, they would swerve slightly as they went through. Hardly front-page news!

Now comes what must be the most consequential off-the-cuff remark in the history of science. One that changed the world.

The story goes that Rutherford bumped into his assistant, Geiger, in the corridor outside the lab. Geiger reported that so far they'd seen nothing unusual.Now  in response, Rutherford could have easily nodded and walked on, but he didn't. He later claimed that he said what he said at the time for the sheer hell of it. But I don't believe him. Rutherford had great scientific intuition and I think he had a hunch that something was about to happen. Here's what he said to Geiger.

"Tell young Marsden to go back and  see if he can detect any alpha particles on the same side of the gold leaf as the radium source." In other words, see if any alpha particles are bouncing back.

Now, it's an extraordinary suggestion from Rutherford and one that he had no logical reason to make. After all, Geiger and Marsden had spent weeks seeing the alpha particles do nothing but stream straight through the gold leaf, almost as though it wasn't there. Why would any bounce back?

But Geiger and Marsden were young and in awe of the big New Zealander. They did their master's bidding and went back into their dark lab and watched patiently. For days, they saw absolutely nothing. They strained their eyes to the point of myopia but didn't see a single alpha particle bouncing back off the gold. It seemed that Rutherford's suggestion really was a stupid one. But then the impossible happened.

One afternoon in 1909, Geiger burst into Rutherford's office with some astonishing news. Very, very occasionally, an alpha particle would indeed ricochet back off the gold leaf. Geiger calculated that only one in 8,000 alpha particles would do this. It's a tiny percentage, but Rutherford's mind reeled with the news. He would later say it was like firing a shell at a piece of tissue paper and have it bounce back at you.

 There and then, Rutherford knew he'd struck physics gold. Although it would take him over a year to fully understand why the alpha particles would do this, when he did, he would show humanity for the first time the inside of an atom. People had barely got used to the idea that atoms existed. But now Rutherford knew that this minute world, one tenth of a millionth of a millimetre across, had its own internal structure. Within the atomic, there's a sub-atomic world. And Ernest Rutherford believed he knew what it looked like.

Rutherford realised that the bouncing alpha particle revealed an atom that was totally unexpected. It had no familiar analogy on Earth. So Rutherford looked for one in the heavens. He pictured the atom as a tiny solar system. Electrons, tiny particles of negative electricity, orbit around a minute positively-charged object called the nucleus. Rutherford calculated that the nucleus was 10,000 times smaller than the atom itself. That's why only one in 8,000 alpha particles bounced back. They're the ones that hit the tiny nucleus by chance. The rest whizz by without hitting anything. The first astonishing consequence of this idea is that Rutherford's atom is almost entirely empty space.That's why nearly all the alpha particles race through the gold atoms as if there's nothing there. There really is nothing there.

Consider the bizarre implications of Rutherford's atom by imagining it on a bigger scale. If the nucleus were the size of a football, then the nearest electron would be in orbit half a mile away. The rest of the atom would be completely empty space. Let me explain it another way. If you were to suck out all the empty space from every atom in my body, then I would shrink down to a size smaller than a grain of salt. Of course, I'd still weigh the same. If you did the same thing to the entire human race, then all six billion of us would fit inside a single apple! The atom was unlike anything we had ever encountered before. And it would only get stranger and stranger!

Almost immediately, a problem surfaced, and it was a big one. According to the tried and trusted science of the time, the electrons should lose their energy, run out of speed and spiral into the nucleus in less than the blink of an eye. Rutherford's atom contradicted the known laws of science.

The atom didn't care that it defied scientific convention. It's almost entirely empty space and it's gonna stay that way. I show no signs of shrinking down to the size of a grain of salt. And the Earth is, well, the size of the Earth. It's not getting smaller.

It's worth remembering the time scale. In six short years from 1905 through to 1911, the atom had announced its existence with the fact that it was unimaginably small. Then it revealed that it was mainly empty space. And now it didn't obey the known laws of physics. Not surprisingly, all the established scientists of the day, including Einstein, were baffled. Scientific ideas they'd put their faith in all their lives had failed completely to explain the atom. The atom now required a new generation of scientists to follow in Rutherford's footsteps. Bold, brilliant and above all, young. It was crucial they had no loyalty or attachment to ideas held by previous generations.

 One of the first of this new breed was Niels Bohr. He sailed from Denmark in 1911 and made his way to English soil.

Having finished his studies in Copenhagen, Bohr decided to move abroad and be at the centre of the new physics.

The trail led him to Britain, Manchester University and Ernest Rutherford.

Bohr had a brilliant mind, at times hampered by a pathological obsession with detail. In fact, the story goes that Bohr taught himself English by reading Dickens' Pickwick Papers over and over again.

Bohr was so captivated by Rutherford's picture of the atom that he made it his mission to solve the puzzles of why the atom didn't collapse and why there was so much empty space. As one of the new breed of theoretical physicists, he was fearless in his thinking and was prepared to abandon common sense and human intuition to find an explanation. So, in a leap of genius, he started to look for clues about the atom's structure not by looking at matter but by examining the mysterious and wonderful nature of light.

Now, atoms and light are clearly connected. Most substances glow when they're heated. And for centuries people had realised that different substances glow with their own distinctive colours, a bit like a signature. So the green of copper, the yellow of sodium and the red of lithium. These colours associated with different substances are called "spectra". And Bohr's great insight was to realise that spectra are telling us something about the inner structure of the atom, that they could explain all that empty space. Bohr's idea was to take Rutherford's solar system model of the atom and replace it with something that's almost impossible to imagine or visualise. So sensible ideas like empty space and particles moving around orbits fade away. They're replaced with something that is one of the most misunderstood and misused concepts in the whole of science - the quantum jump. Now, it takes most working physicists many years to come to terms with quantum jumps. And in fact, Bohr himself said that if you think you've understood it, then you haven't thought about it enough. So I'm going to take a deep breath and in under 30 seconds try and explain to you one of the most complicated concepts in the whole of science but one that underpins the entire universe.

Bohr described the atom not as a solar system but as a multi-storey building. The ground floor is where the nucleus lives, with the electrons occupying the floors above. Mysterious laws mean the electrons can only live ON the floors, never in-between. Other mysterious laws mean that sometimes they can instantaneously jump from one floor to another. These are what we call quantum jumps.

Now, Bohr had absolutely no idea what these laws were. But thinking like this allowed him to make a startling prediction. When an electron jumps from a higher floor to a lower one, it gives off light. More significantly, the colour of the light depends on how big or small the quantum jump the electron makes. So an electron jumping from the third floor to the second floor might give off red light. And an electron jumping from the tenth floor to the second floor, blue light.

To test his new theory, Bohr used it to make a prediction. Could it explain the mysterious signature in the spectrum of hydrogen? After months of calculating furiously, he finally came up with the result. And his prediction was surprisingly accurate. For the first time ever, it looked like the spectrum could be explained. And back in 1913, that was big news.

But Bohr's new idea rested on a single seriously-controversial supposition. Why should the electrons and the atom behave as though they were in a multi-storey building? And why should they magically perform quantum jumps from one storey to another? There was no precedent for it anywhere else in science.

When one physicist claimed that the jumps were nonsense, Bohr replied,

"Yes, you're completely right! But that doesn't prove the jumps don't happen, only that you cannot

visualise them."

But not being able to visualise things seemed to go against the whole purpose of science. Older scientists in particular felt that science was supposed to be about understanding the world, not about making up arbitrary rules that seem to fit the data. Conflict between the two generations of scientists was inevitable.

Bohr's weird new atom and his crazy quantum jumps were a shot across the bow of traditional classical science and the old school reacted angrily. Leading the traditionalists was giant of the physics world Albert Einstein. He hated Bohr's ideas and he was going to fight them. Anything to save the world of order and common sense from this assault by madness.

Bohr, though, was undeterred and as the 1920s dawned, the battle lines for one of the greatest conflicts in all science were drawn.

 Einstein spent much of the early 1920s arguing against Niels Bohr, with mixed success. His celebrity status gave him power so when he said he loathed ideas like quantum jumping that seemed plucked out of thin air, people listened.

Then in 1925, a letter landed on his desk that turned out to be manna from physics heaven. Here finally was an idea that described the atomic world with the tried and trusted principles of traditional science. Einstein was ecstatic.

He told friends, "Finally, a veil has been lifted on how the universe works."

The letter came with the PhD thesis of a young Frenchman. And behind it lay an extraordinary tale.

During the First World War, a young French student spent his time at the top of the Eiffel Tower, as a radio operator. His name was Prince Louis de Broglie. He came from French aristocracy but he was devoted to physics. He was so wealthy he built his own laboratory off the Champs-Elysees. After the war, De Broglie became gripped by the mysteries and controversies surrounding the atom. And then his war-time experience as a radio operator gave him an intriguing idea.

Perhaps radio waves could explain the atom. Because although invisible, they behave very much like water waves. Like ripples spreading out across a pond, radio waves obeyed mathematical equations that were reliable and well understood and had been worked out decades earlier. So for his PhD thesis, De Broglie imagined a kind of radio wave pushing the electron around the atom. He called it a “pilot wave”. This pilot wave would also hold the electron tightly in its orbit, stopping the atom from collapsing.

There were no strange instant quantum jumps, just intuitive common sense familiar waves. The relief felt by the traditionalists was palpable.

"The atom is all about waves",

they cried, and we understand what waves are. Einstein and the traditionalists felt that victory was within their grasp.

They believed they had Bohr and the new atomic science with its crazy quantum jumps on the ropes. But Niels Bohr wasn't the kind of man to roll over and give up. Even though he'd explained the spectrum of hydrogen, with his new revolutionary theory, he had nothing like Einstein's worldwide recognition. But in his native Denmark, his theory was enough to make him a star.

Flushed with success, Niels Bohr returned to Copenhagen in 1916, a conquering hero. His new-found celebrity status meant he found it very easy to raise money for research. In fact, it was funding from the Carlsberg brewery that helped build his new research institute. You could say it was beer that helped us understand the secrets of the atom!

This institute became a leading centre for research in theoretical physics that survives to this day. I came here in the early 1990s to carry out research on nuclear halos. And even then, this was the place to be to do that sort of research. This is the main lecture room in the Niels Bohr Institute. It doesn't look very impressive as far as lecture halls are concerned, but it's full of great quirky details. I remember lecturing here a few years back and I know that Niels Bohr himself designed some of the machinery that raised and lowered blackboards.

There's an incredible series of boards, one underneath the other, of boards filled with his formulae so that he wouldn't ever need to rub out any of his equations. It sort of goes on and on. Bohr's reputation for radical and unconventional ideas made Copenhagen a magnet for young, ambitious physicists. They were keen to make their mark and be a part of Bohr's innovative new science, which came to be known as quantum mechanics.

In 1924, in defiance of Einstein and De Broglie's traditional explanation of the atom, the radicals revealed a new theory, based on Bohr's quantum jumps. It was to be their most ambitious and most controversial idea yet. It was first developed by Wolfgang Pauli, one of Bohr's rising stars.

Pauli took Bohr's bizarre "quantum jumps" idea and turned it into one of the most important concepts in the whole of science. And I don't say that lightly. Pauli's idea goes by the uninspiring title of the Exclusion Principle. But I think a better title would be "God's best-kept secret" because it explains the vast variety of Creation. The question Pauli's idea tried to answer was this. Every atom is made of the same simple components. So why do they appear to us in so many different guises? In such a rich variety of colours, textures and chemical properties? For instance, gold and mercury. Two very different elements. Gold is solid, mercury is liquid. Gold is inert, mercury is highly toxic. And yet they differ by just one electron. Gold has 79 and mercury has 80. So how does one tiny electron make all that difference? What Pauli did was pluck another quantum rule out of thin air.

Remember Bohr's multi-storey atom? The nucleus is the ground floor with the electrons progressively filling the floors above. Pauli said there's another quantum rule which states crudely that each floor can only accommodate a fixed number of electrons. So if we want to add another electron to the atom, it has to check for a vacancy in the top floor. And if that floor is full, another floor or shell is created above it for the electron. In this way, a single electron can radically change the shape of the atom and this, in turn, affects how the atom behaves and how it fits together with other atoms.

So Pauli's principle really is the basis upon which the whole of chemistry, and ultimately biology, rests. Pauli's Exclusion Principle was a major breakthrough for Bohr's quantum mechanics. For the first time, it seemed to offer us a real understanding of the incredible variety in the world around us and possibly life itself. Its success blew a large hole in Einstein's defence of the old physics. And like quantum jumping, it was straight out of the weird rule book of atomic physics.

Pauli didn't explain why his principle worked. He said it just did. Einstein and the traditionalists hated it. For them, this sounded like arrogant, unscientific nonsense. But they needed to hit back, and hit back hard.

So far, the debates about the new atomic physics had been polite and gentlemanly. Now the two sides wheeled out their biggest guns. Two of the greatest names in physics. They were two very contrasting characters who loathed each other.

For the new revolutionary science was a buttoned-up, uber-competitive German called Werner Heisenberg. For the conservatives was a debonair, Byronesque Austrian called Erwin Schroedinger.

Erwin Schroedinger, passionate and poetic, a philosopher and a romantic. He wrote books on the Ancient Greeks, on philosophy, on religion, he was influenced by Hinduism. He was also a very flamboyant character, cool, suave, sophisticated, a dapper dresser and a big hit with the ladies.

Schroedinger's promiscuity was legendary. He had a string of girlfriends throughout his married life, some much younger than him. In 1925, 38-year-old Schroedinger stayed at the Alpine resort of Arosa in Switzerland for a secret liaison with an old girlfriend whose identity remains a mystery to this day. But their passion proved to be the catalyst for Schroedinger's creative genius. Another physicist said of Schroedinger's week of sexually-inspired physics,

"He had two tasks that week.

"Satisfy a woman and solve the riddle of the atom.

"Fortunately, he was up to both."

He took De Broglie's idea of mysterious pilot waves guiding electrons around an atom one crucial step further. He argued that the electron actually was a wave of energy vibrating so fast it looked like a cloud around the atom, a cloud-like wave of pure energy. What's more, he came up with a powerful new equation which completely described this wave and so described the whole atom in terms of traditional physics.

The equation he came up with we now call Schroedinger's wave equation. It's incredibly powerful. What's unique about it is that it features a new quantity called the wave function which Schroedinger claimed completely described the behaviour of the sub-atomic world.

Schroedinger's equation and the picture of the atom it painted, created during a sexually-charged holiday in the Swiss Alps, once again allowed scientists to visualise the atom in simple terms. It's hard to over-estimate the relief Schroedinger's idea brought to the traditional physics community.

Strange though his picture of the atom was, at least it was a picture and scientists love pictures. They allowed them to use their intuition.

But there was still a deep nagging problem, one that the radicals feltSchroedinger just couldn't reconcile. His new theory still couldn't account for Bohr's strange, instantaneous quantum jumps. The time had come for the radicals to hit back.

In the summer of the same year, one of Niels Bohr's protegees, Werner Heisenberg, was travelling to an obscure island off the north coast of Germany. He was fiercely competitive and took Schroedinger's ideas as a personal affront. He felt strongly that the strangeness of the instant quantum jumps was actually the key to understanding the atom. He thought the atom was so unique and unusual, it shouldn't be compromised through a simple analogy like a wave or an orbit, or even a multi-storey building. He believed it was time to give up any picture of the atom at all.

Werner Heisenberg, one of the true geniuses of the 20th century. Young, athletic, a great mountain climber, an excellent pianist, he was also an exceptional student. At the age of just 20, he was well on his way to finishing his PhD and being courted by the great universities across Europe. Now, in the summer of 1925, he was suffering from a particularly bad bout of hay fever. His face was swollen up almost beyond recognition. He decided to escape alone, here, to this beautiful but isolated island of Helgeland. He walked along the beaches, he swam, he climbed the rocks and he pondered.

Ever since he'd encountered atomic physics, Heisenberg felt in his bones that all human attempts to visualise the atom, to model it with familiar images, would always fail. The atom, he believed, was too capricious, too strange to ever be explained that simply. So he decided to abandon all pictures of it and describe it using pure mathematics alone.

But as he pondered, he realised the atom didn't just defy visualisation, it even defied traditional mathematics.

It was while he was here on Helgeland that Heisenberg had an incredible revelation. He realised that in order to describe certain properties of atoms, he had to use a strange new type of mathematics. It seems that certain properties like where an electron is at a given time and how fast it's moving, when multiplied together, the order in which you multiply them matters.

Let me try and explain. If we multiply two numbers together, it doesn't matter which order we do it in. So three times four is clearly the same as four times three. But when it came to atoms, Heisenberg realised that the order in which he multiplied quantities together gave a different answer. This quickly led him to other discoveries and he was convinced that he'd cracked a code in the atom, that he'd somehow found the hidden mathematics within. He was so excited. He was also very scared. That night, he climbed to the top of a rock and sat there waiting till dawn. He called it his "Night of Helgeland". When he return to the university in Goettingen, he told his colleague Max Born about it and they then worked together intensely for several months developing a whole new theory of the atom. A theory that today we call matrix mechanics.

Matrix mechanics uses complex arrays of numbers, rather like a spreadsheet. By manipulating these arrays, Heisenberg and his mentor the brilliant physicist Max Born could accurately predict atomic behaviour. But for Einstein and the traditionalists, this was pure scientific heresy. An atom can't actually be a matrix of numbers. Surely we're made of atoms, not numbers?

Back in Copenhagen, Bohr and Pauli were thrilled with matrix mechanics. So what if we couldn't imagine the atom as a physical object?  They exalted in the purity of the mathematics and launched into vicious attacks against Schroedinger's vulgar sensual waves.

Heisenberg wrote, "The more I reflect on the physical portion of Schroedinger's equation, the more disgusting I find it. In fact, it's just bullshit."

But Schroedinger was equally scathing of Heisenberg, saying he was repelled by his methods and found his mathematics monstrous.

In Munich in 1926, their enmity began to reach boiling point.

Schroedinger was to give a lecture on his wave equation. Heisenberg scraped together the money to travel to Munich for the lecture. To finally come face to face with his rival. What was at stake was more than just Heisenberg's reputation. He believed Schroedinger's simplistic approach wasn't just misguided, but totally wrong. And his intention was nothing less than to destroy Schroedinger's theory.

Schroedinger delivers his lecture on the new wave mechanics to a packed audience. Standing room only. He writes down his new wave equation. To Schroedinger, this describes a real physical picture of the atom with electrons as waves surrounding the atomic nucleus.

24-year-old Werner Heisenberg is in the audience. He can hardly contain himself. At the end of the lecture he stands up and delivers a monologue attacking Schroedinger's approach. For Heisenberg it's impossible to ever have a picture of what the atom is really like.

The audience is on Schroedinger's side. They much prefer his simple physical interpretation to Heisenberg's abstract, complicated mathematics. Heisenberg is booed. He's told to sit down and be quiet. He leaves the lecture sad and depressed.

Heisenberg returned to Copenhagen with his confidence severely dented. There at the institute, he and Bohr reached their darkest moment. Almost all of the scientific community was against them. They felt isolated, desperate. Their backs were against the wall. Despite this, they stubbornly refused to give up their controversial theory.

This attic room was Heisenberg's study back in 1926. Bohr would come up here night after night where he and Heisenberg would argue about the meaning of the new quantum mechanics. They would argue so passionately, that on one occasion Heisenberg was reduced to tears.

And then, as Heisenberg stared out of his attic window in despair at the park below, an extraordinary thought occurred to him. It struck him why an atom can't be visualised, why it can't be understood intuitively. It's not just because it's tiny, tricky and difficult. It's because it's inherently unknowable.

He realised that there was a fundamental limit to how much we can know about the sub-atomic world. For instance, if we know where an electron is at a particular moment in time, then we cannot know how fast it's moving. But if we knew its speed, we wouldn't know its position. This ambiguity isn't a shortcoming in the theory itself. Nor is it due to the clumsiness of the way we carry out our measurements, but a fundamental truth about the way Nature behaves at the sub-atomic scale. It became known as Heisenberg's Uncertainty Principle. And it's probably the most profound, incredible, yet unsettling concepts in the whole of science.

What Heisenberg had uncovered through his abstract matrix mechanics was a deep and shocking truth about the atomic world. Atoms are wilfully obscure. We can never fully know an atom's position and speed simultaneously. The atomic world just refuses to allow that to happen. It was completely mind-boggling. But once they accepted it, Heisenberg and Bohr found the boost of confidence to be even more bold. They realised uncertainty forced them to put paradox right at the very heart of the atom.

Atoms are not just unimaginable. They're self-contradictory. They behave both like particles and waves. And it gets weirder. When you're not looking at an atom, it behaves like a spread-out wave. But when you look to see where it is, it behaves like a particle. This is insane! First, atoms couldn't be visualised at all, now they change completely in character depending on whether or not you're looking at them.

 The Uncertainty Principle had changed everything. It revealed a shocking contradiction at the heart of Nature. Everything we see is made of atoms. And yet atoms themselves are unknowable. They can only be understood through mathematics. For the first time for Bohr and Heisenberg everything about the atom fell into place.

By the autumn of 1927, full of confidence and smarting for a fight, they knew they were finally ready to take on the conservatives.

For this physics showdown, they chose the Solvay Conference in Brussels. All the world's leading atomic physicists would attend. If Bohr and Heisenberg were successful, they would lead a total scientific revolution.

This is amazing. I'm looking at original footage of the Solvay delegates coming out of these doors. There's Bohr talking to Schroedinger and there's Heisenberg behind them. There's Pauli, strange-looking guy. There's Einstein coming down with a big smile on his face.

For the week of the conference, all that the delegates could think and talk about was Bohr's quantum mechanics. With uncertainty now a central plank, it was a truly formidable theory. And over the week, the final showdown played out between Bohr and his arch-rival, Albert Einstein.

Einstein hated quantum mechanics. And every morning he'd come to Bohr with an argument that he felt picked a hole in the new theory. Bohr would go away, very disturbed, and think very hard about it, and by the end of the day he'd come back with a counter-argument that dismissed Einstein's criticism. This happened day after day until by the end of the conference, Bohr had brushed aside all of Einstein's criticisms and Bohr was regarded as having been victorious.

And with that, his vision of the atom, which became known as the Copenhagen Interpretation, was suddenly at the very heart of atomic physics.

 At the end of the conference, they all gathered for the team photo. Never before or since have so many great names of physics been together in one place. At the front, the elder statesman of physics, Hendrik Lorentz, flanked on either side by Madame Curie and Albert Einstein.

Einstein's looking rather glum because he's lost the argument. Louis de Broglie has also failed to convince the delegates of his views. Victory goes to Niels Bohr. He's feeling very pleased with himself. Next to him, one of the unsung heroes of quantum mechanics, the German Max Born who developed so much of the mathematics. And behind them, the two young disciples of Bohr, Heisenberg and Pauli. Pauli is looking rather smugly across as Schroedinger, a bit like the cat who's got the milk. This was the moment in physics when it all changed. The old guard was replaced by the new. Chance and probability became interwoven into the fabric of Nature itself and we could no longer describe atoms in terms of simple pictures but only using pure abstract mathematics. The Copenhagen view had been victorious.

Although Einstein went to his grave never believing quantum mechanics, Solvay 1927 was the turning point at which the rest of the science establishment came to embrace the Copenhagen Interpretation. And that interpretation is still accepted today.

All the physics that I use in my research, certainly the quantum mechanics that I teach my students and that fills the text books on my shelves is based on ideas that were hammered out and crystallised here at the Solvay Conference in October 1927. In a sense, everything I know about the way the world around me is made up started here.

The quantum mechanical description of the atom is one of the crowning glories of human creativity. Over the last 80 years, it has been proven right, time after time and its authority has never been in doubt. It's a monumental scientific achievement.

Between 1905 and 1927, science changed our view of the world. It also changed our view of science itself. As scientists probed the tiniest building blocks of matter, they created the most successful and powerful theory ever - quantum mechanics.

It allows us to describe what everything in the universe is made of, how it interacts and how it all fits together. But it comes at a huge price. At its most fundamental level, we have to accept that Nature is ruled by chance and probability. Heisenberg's Uncertainty Principle dictates that there are certain limits on the sorts of questions we can ask the atomic world.

Most crucially, while we now know so much more about what an atom is and how it behaves, we have to give up any possibility of imagining what it looks like. Our human nature has forced us to ask questions of everything we see around us in the world. What we've discovered has been beyond our wildest imagination.