Humans have used lead a bunch of different ways throughout history.

Ancient Romans used it to artificially sweeten their wine, modern dentists use it to shield your torso while they x-ray your mouth. And of course, alchemists tried very hard to turn it into gold.

But it turns out, nature does kind of the opposite. Because if you look at the periodic table, every element beyond lead is radioactive. Their atoms are unstable.

And the vast majority of  those atoms will eventually, if you give them enough time, decay into lead. And then they’ll stay that way, because lead isn’t just stable. It’s magic.

But I’m not using that word to reference the alchemists of yester-century. Modern scientists call lead, and many other elements, magic. And lucky for us, it can be explained with science. [Intro music]

Now before we get to any magic, we should start with some nuclear physics basics.

The nucleus of an atom is made up of particles  collectively called nucleons. You may know them better as protons and neutrons. It’s the number of protons that determines which element an atom is.

Every atom that has 82 protons is a lead atom, no matter how many neutrons it has. But different isotopes of the same element have different numbers of neutrons. And when we talk about them, we use both the element name and the total number of nucleons an isotope has.

Lead-208 has the requisite 82 protons plus 126 neutrons. Lead-206, meanwhile, only has 124 neutrons. And no matter what element you’re dealing with, a given isotope is either stable, meaning you can set a proverbial lump of it on your desk and it’ll stay that element forever… …Or, it’s radioactive, meaning you probably shouldn’t have a lump of any size sitting on your desk!

Sooner or later, the atoms will all decay. And as they do, they release radiation and often turn into a whole different element. The two types of radioactive decay we’re going to focus on today are called alpha and beta.

Alpha decay is when a nucleus emits an alpha particle, which is made of two protons and two neutrons. It’s basically the same thing as a helium-4 nucleus. And during beta decay, the unstable isotope emits a beta particle, which is either an electron or a positron depending on the exact kind of  beta decay you’re dealing with.

The most common kind converts one neutron to a proton, and releases a couple other particles we don’t care about for the topic of this video. Both alpha and beta decay change the number of protons in the nucleus, and therefore the element. Meanwhile, only alpha decay changes the total number of nucleons.

But you often find that one single decay, either alpha or beta, isn’t enough for an unstable  nucleus to become stable. It has to do it again, but it doesn’t have to stick to the same kind of decay every single time. So by putting a series of  alpha and beta decays together, you get what scientists call decay chains.

And if you know what isotope you’re starting with, you can consistently predict the exact steps it’s going to take to wind up stable, as well as what that final, stable isotope will be. The three main decay chains we see in nature are called the thorium series, actinium series, and the radium series, which is also known as the uranium series. these end with lead-208, lead-207, and lead-206 respectively. But these names are a bit confusing because they generally aren’t named after the isotope  you actually start with.

And on top of that, different  isotopes of uranium, thorium, and radium show up in all three series. So to make things a little clearer, let’s look at the thorium decay chain. It starts with the isotope thorium-232, which is less unstable than a lot of radioactive elements out there.

It has a half life of about 14 billion years. Which means if you ignored my instructions and plopped a lump of pure  thorium-232 on your desk, half of the atoms will no longer be thorium-232 when you check back in 14 billion years from now. But we don’t have to wait for half.

We just need one nucleus to decay. And when it does, it’ll spit out an alpha particle, turning itself into radium-228. Then it beta decays twice, first to actinium-228 and then to thorium-228. …and then four alpha decays later, it reaches lead-212.

But we’re not done yet, because that’s radioactive lead! So it beta decays to bismuth-212, then it has a proverbial choice. Sometimes it goes the alpha decay route, sometimes it goes with beta decay.

But either way, the nucleus does the other one next, and we wind up at lead-208 . Now, having walked through all of that, I should admit there is a fourth decay chain that doesn’t end with lead: the neptunium chain. But the isotopes in this chain  have such short half-lives, they’ve already gone though most of the steps.

Scientists say it’s “extinct in nature”... except for the very last step. The second to last isotope in the chain is bismuth-209, which has a half life of  nearly 20 quintillion years, which is 1.4 billion times  the age of the universe. But if we fast forward to the very far future, the final step in this chain is thallium-205.

And there are a couple other exceptions to lead being the ultimate fate for a radioactive nucleus, too. Like all the atoms that start with fewer nucleons than any lead isotope. Or the fact that, sometimes, a super massive nucleus that could become lead doesn’t even bother with a decay chain.

Instead, it undergoes this very fun reaction known as spontaneous fission, where it effectively cracks in two instead of just emitting small particles in an attempt to achieve stability. Fair enough. But that brings us to an important question: Why are some isotopes radioactive while others are stable?

If we zoom in to the nucleus, the protons are all positively charged, so they repel each other. Adding neutral neutrons can compensate. But the more protons you have, the more neutrons you need to keep things stable.

This leads to a pattern called the valley of stability. If we look at the number of neutrons and protons for all the known isotopes, and plot them out in a fancy chart, we can see that the stable ones all occur along the same line. But increasing the ratio of neutrons to protons only works for so long.

Eventually, the valley ends. Once you pass lead-208, everything is unstable. Everything is radioactive.

But even within the valley of stability, you’ll see there are some weird patterns. Like why does indium, atomic number 49, only have 2 stable isotopes… but its periodic table neighbor tin has a whopping 10? Well, back in the 1940s, this particular quirk did not go unnoticed by a chemist named Maria Goeppert Mayer.

While she was working on a project to map the abundance of various isotopes, she noticed that isotopes with a particular number of  either protons or neutrons were more likely to be stable. These numbers were 2, 8, 20, 28, 50, 82, and 126. She proposed this was evidence of the nuclear shell model, where protons and neutrons occupy specific energy levels inside a nucleus.

You can think of them as shells, and each can hold a particular number of nucleons. When the outermost shell is completely full, the atom holds onto its nucleons tighter. That translates to the isotope having a better chance of being stable.

Now if you’re wondering why all this sounds a little familiar to you, it’s probably because you learned something very similar happens with electrons. Chemistry textbooks often describe electrons as  orbiting the nucleus in “shells”. And when the outermost shell is full, the element is less reactive.

This gives us the noble gasses on the far right of the periodic table. They’re inert because they have full outer electron shells. But while electron shells were accepted by the time Goeppert Mayer proposed her nuclear shell model, many physicists were  reluctant to accept her ideas.

Instead, they were using the liquid drop model, which suggested a nucleus is basically a blob of protons and neutrons. One physicist named Eugene Wigner  was particularly skeptical, but he couldn’t deny the patterns that Goeppert Mayer had discovered. So he called these stability  numbers magic numbers, because the liquid drop  model couldn’t explain them.

But it wasn’t magic, it was a revelation in nuclear physics. And Goeppert Mayer published her findings in 1948, at nearly the exact same time as the German physicist Hans Jensen was figuring the same thing out, himself. But rather than this leading  to an academic rivalry, or the attempted erasure of a certain someone’s contributions  to the world of science, this story has a happy ending.

They went on to work together, and in 1963 they shared  the Nobel Prize in Physics. Despite not being magic, the term magic numbers stuck. And these days, the accepted ones are still those that Goeppert Mayer first identified: 2, 8, 20, 28, 50, 82, and  at least for neutrons, 126.

Some scientists think that 114 is more likely to be the seventh  magic number for protons, but that hasn’t been proven experimentally. Either way, magic numbers explain why tin has more stable isotopes than indium. Tin has 50 protons, one of our magic numbers.

But some isotopes are doubly magic because both their proton and neutron counts are just right. The simplest is helium-4, with two protons and two neutrons. And the extreme stability of this isotope is partly why radioactive elements like thorium-232 undergo alpha decay.

Because remember, alpha particles are identical to helium-4 nuclei. Now, having a magic number doesn’t guarantee stability, it just makes it more likely  given the other factors, like the physical size of a nucleus. For example, all isotopes of lead have 82 protons, so they’re all magic.

But there are still many radioactive forms of it. And then there’s lead-208, which has 126 neutrons, making it doubly magic. That makes it more stable  than it would otherwise be given its large size, and it winds up being the heaviest stable isotope… as far as we know.

So to sum up, so many radioactive elements decay into lead because lead is magic, and one isotope of lead is doubly magic. But that’s not the end of the story, because physicists are still on the lookout for new magic numbers. And which ones are actually magical is a subject of debate!

Magic numbers can be predicted  through theoretical calculations, but scientists have to do experiments to actually test the real  world properties and stability of a given isotope. For example, in 2013, separate studies suggested that both 32 and 34 were magic numbers. But a follow up study in 2021 looked at 32 by measuring the size of  specific potassium nuclei.

If a potassium nucleus started with 32 neutrons, and 32 were a magic number, you’d measure a big jump in its size if you added one more neutron. Because remember, magic numbers refer to filled outer shells, so that 33rd neutron would have to go in a new outer shell that makes the whole nucleus bigger. But when the team actually tested this, they didn’t observe that change.

So they concluded there was nothing magical about the number 32. But potassium isn’t exactly new ground to explore. So it’s worth highlighting that magic numbers can also help scientists  extend the periodic table, and predict the stability of  yet-to-be discovered elements.

Everything heavier than lead-208 is radioactive, but as we go farther and farther away, to heavier and heavier elements, things get very unstable. I’m talking half lives that are just milliseconds  or microseconds long, max. But somewhere beyond the known elements, there’s a hypothetical island of stability.

A group of isotopes that could be stabilized by unconfirmed magic numbers. They would still be radioactive, but their half lives would be longer than the other superheavy isotopes around them. Predictions range from minutes  up to millions of years.

The center of the island could be Flerovium-298, which according to some  scientists would be doubly magic with 114 protons and 184 neutrons. We’ve still got a ways to go though. As of 2023, the heaviest element we’ve synthesized is Oganesson-294, made up of 118 protons and 176 neutrons.

So while they may not be “real” magic, magic numbers can tell us a lot about how the fundamental building  blocks of our universe work. They may be the key to  extending the periodic table. And they explain how a lump of gray metal that makes you sick from radiation poisoning can turn into a lump of a different gray metal that makes you sick from lead poisoning, without any alchemists in sight.

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