How Much Astatine Is Present in a Uranium Ore Rock?

Astatine is often described as the rarest naturally occurring chemical element. It is so rare because it is radioactive and has a short half-life -- 1.5 seconds for the most abundant naturally occurring astatine isotope, ²¹⁸At. The only reason astatine exists in nature is because it is a decay product of other, longer-lived radioactive elements.


If you're an element collector, it's obvious that having a visible sample of pure astatine isn't possible. The next-best thing you can do is get a sample of uranium ore rock. Because astatine is in the decay chain of uranium, and uranium is constantly decaying into its descendant elements, a small amount of astatine exists in the rock.

But exactly how small is a "small amount" of astatine? You can calculate this amount if you know the amount of uranium present, as explained below.

Each Decay-Chain Isotope Accumulates to Its Equilibrium Concentration

A decay chain is the sequence of elemental isotopes resulting from the decay of a particular "ancestor" isotope. For example, in the decay chain of uranium-238, also knows as the radium series, ²³⁸U decays into ²³⁴Th, ²³⁴Th decays into ²³⁴Pa, ²³⁴Pa decays into ²³⁴U, ²³⁴U decays into ²³⁰Th, and so on until the chain ends at a stable isotope, ²⁰⁶Pb. Each isotope in the chain has its own respective half-life, which is different from the half-lives of all the other isotopes. Some isotopes have a half-life of just a tiny fraction of a second, whereas the ultimate ancestor element ²³⁸U has a half-life of 4.5 billion years.

In a radioactive rock sample that has been sitting around undisturbed for millions of years, which is the typical experience of a rock, each isotope in the decay chain accumulates to its secular equilibrium concentration. For example, let's say that you have a rock containing 8 milligrams of ²³⁸U. This amount of uranium decays at a rate of 100 atoms per second, producing 100 atoms of ²³⁴Th per second. Meanwhile, the existing amount of ²³⁴Th in this rock decays at a rate of 100 atoms per second, producing 100 atoms of ²³⁴Pa per second. Meanwhile, the existing ²³⁴Pa in the rock decays at a rate of 100 atoms per second, and so on down the chain, until ²⁰⁶Th decays at 100 atoms per second into ²⁰⁶Pb. This final isotope of lead is stable and accumulates continuously without loss.

Why Do Accumulated Isotopes Decay at the Same Rate?

The rate of decay of a particular isotope is proportional to the amount of the isotope present. If there is less than the equilibrium amount present, it decays more slowly than it is being produced, so the amount grows. On the other hand, if there is more than the equilibrium amount present, it decays faster than it is being produced, so the amount shrinks.

In the foregoing example, 8 milligrams of ²³⁸U decays at 100 atoms per second into ²³⁴Th, while the accumulated ²³⁴Th decays at 100 atoms per second into something else, and so on. Suppose that you were to remove 10% of the ²³⁴Th from an old rock sample, leaving only 90% of the equilibrium amount. In that case, the reduced amount of ²³⁴Th would decay at a rate of only 90 atoms per second, because the rate is proportional to the amount of ²³⁴Th present. Meanwhile, the ²³⁸U would still decay at a rate of 100 atoms per second, producing 100 new atoms of ²³⁴Th per second. That would be a net increase of 10 atoms of ²³⁴Th per second, causing the total amount of ²³⁴Th to increase.

Conversely, suppose that you were to add an extra 10% of ²³⁴Th to rock. In that case, the new amount of ²³⁴Th present would decay at a rate of 110 atoms per second, while new ²³⁴Th is still being produced at 100 atoms per second. That would be a net loss of 10 atoms of ²³⁴Th per second, causing the total amount of ²³⁴Th to decrease. Whether there is too little or too much ²³⁴Th, after enough time passes, it will reach its final equilibrium concentration, with its production and decay rates both at 100 atoms per second.

After reaching equilibrium, the decay of  ²³⁴Th feeds the next element in the chain, ²³⁴Pa, at a rate of 100 atoms per second. ²³⁴Pa also accumulates and eventually reaches its equilibrium concentration, which feeds the next element in the chain at 100 atoms per second, and so on. After enough time passes, each isotope in the entire chain decays at a uniform decay rate of 100 atoms per second, with some exceptions that we'll get to later.

One of the elements in the decay chain is radon, an inert gas. Although any radon near the surface of a rock escapes by diffusing out, most of the radon usually remains trapped in the rock for its entire lifetime. The part that escapes can work its way through cracks and soil to the Earth's surface, occasionally causing harmful accumulation in homes and buildings. Helium gas, a stable product of radioactive decay, also accumulates in the rock. The alpha particles produced by decay are just charged helium atoms. A lot of helium remains trapped in the rock, but a little bit escapes into underground natural gas deposits. That's where we get our helium for toy balloons and blimps. Helium in the atmosphere, being very light, tends to rise up and escape into outer space, so our only Earthly source of this element is from underground radioactive decay.

Radium Content of a Uranium Ore Rock

So how much is the equilibrium concentration of each isotope in the decay chain? It is simply the ratio of the half-life of that isotope relative to that of any other isotope in the chain. For example, radium-226 is in the decay chain of uranium-238. The half-life of ²³⁸U is 4.5 billion years and the half-life of ²²⁶Ra is 1,602 years, a ratio of roughly 3 million to one. Since radium decays 3 million times faster than uranium, for both elements to decay at the same rate of 100 atoms per second, there must be 3 million times more uranium than radium in the rock.

In any rock containing uranium, radium accumulates until it reaches an equilibrium concentration of one 3-millionth that of the uranium. This explains why Marie Curie had to spend years of hard work, processing a ton of uranium mining waste, to obtain one-tenth gram of radium. The payoff for her labor was a weighable radium sample, which she used to establish the atomic weight of radium.

Astatine Content of a Uranium Ore Rock Sample

So much for radium. How about astatine? Astatine-218 is in the decay chain of Uranium-238 and has a half-life of 1.5 seconds. However, there's another consideration aside from the half-life ratios. Astatine is produced at a branch in the decay chain. The immediate ancestor to ²¹⁸At is ²¹⁸Po, which can decay into either of two different elements: ²¹⁴Pb, with a probability of 99.98%, or ²¹⁸At, with a probability of 0.02%. So the equilibrium concentration of ²¹⁸At is reduced by a factor of 0.0002 compared to what you would calculate from the half-life ratio alone.

For example, suppose that you have a uraninite rock similar to the one shown here. If your rock has a volume of 1 cubic centimeter, weighs 8 grams, and contains 12% uranium by weight, its uranium content is 1 gram.

Photo credit: Rob Lavinsky, iRocks.com, via Wikipedia Commons

In 1.0 gram of natural uranium, all isotopes in the main branch of the decay chain decay at a rate of 13,000 atoms per second, or 13,000 becquerels (13 kBq). However, when ²¹⁸Po decays, of the 13,000 new atoms produced each second, only a few are astatine atoms; the rest are lead atoms.

To calculate the equilibrium concentration of astatine compared to uranium, take the half-life of ²¹⁸At (1.5 seconds), divide by the half-life of ²³⁸U (4.5 billion years converted into seconds), and multiply this ratio by 0.0002. The result is 2 x 10^-21. Thus, the number of astatine atoms in a rock is the number of uranium atoms multiplied by 2 x 10^-21.

Uranium has an atomic weight of 238 grams per mole and there are 6 x 10²³ atoms in a mole. Put this information together, and you'll find that for a rock containing 1 gram of uranium, there are about 5 astatine atoms, each having an average lifetime of 2.2 seconds. New astatine atoms are created at rate of 2.6 atoms per second, and they decay away at the same rate. If you could actually see the astatine atoms, they would appear and disappear randomly, as shown in the simulation on the right.

Astatine decay-chain simulation by Steve Byrnes

You'll need at least one-fifth of a gram of uranium in your rock to maintain an average of one astatine atom. If your rock has less than that, don't despair. It still has astatine atoms, just not all the time.

The astatine isotopes 219At and 215At both appear in the decay chain of the actinium series, which starts with 235U. However, they appear in very rare branches of the chain, and 235U makes up less than 1% of natural uranium, so the resulting astatine isotope concentrations are insignificant compared to the 218At appearing in the radium series. Similarly, in the decay chain of thorium, 216At appears in a very rare branch and has a half-life of just 0.0003 second, so it has a negligible contribution to the total amount of astatine existing in nature.

Astatine Content of Depleted Uranium, Uranium Compounds, Fiestaware ...

So far we've been discussing the presence of astatine in natural uranium-bearing rocks. What about other forms of uranium, such as depleted uranium metal, uranium salts, and uranium-glazed Fiestaware plates and bowls?

In these forms, the uranium has been extracted from the natural rock chemically, leaving behind all the decay-chain isotopes in the waste discarded by the mining company. The extracted uranium comes out pure, but it immediately starts decaying into its decay-chain isotopes. Since the uranium is starting out "fresh", the decay products start accumulating from zero.

The first two isotopes in the chain below ²³⁸U, ²³⁴Th and ²³⁴Pa, build up rapidly because they have short half-lives. But the next one, ²³⁴U, has a half-life of a quarter million years, a major bottleneck in the decay-chain buildup. If you do the calculations, you'll find that 1 gram of pure uranium produces fewer than 100 astatine atoms per century.

Total Astatine Content if the Earth's Crust

The Earth is one large, old rock, with its uranium content decaying in equilibrium with the isotopes in its decay chain, including astatine. Since we don't know about the uranium content of the core, we'll restrict this discussion to the crust.

The concentration of uranium in the Earth's crust is about 2 parts per million. The mass of the Earth is 6.0 x 10²⁴ kg and the crust makes up about one-half of one percent of the mass of the Earth. Almost all natural uranium is ²³⁸U, which is the start of the radium series in which ²¹⁸At appears. Put this information together, and you'll find that the total amount of astatine in all of the Earth's crust is about one-tenth of a gram.

Astatine Content in an Ionization Smoke Detector 

So much for natural elements. How about artificial ones? An ionization smoke detector contains 0.3 microgram of synthetic americium-241, with a half-life of 432 years. Americium-241 appears in the the decay chain of the neptunium series, and astatine-217 is a descendant isotope. Could you break open a smoke detector and keep the radioactive source as your astatine sample?

The americium in a smoke detector is created "fresh" in a laboratory, so the decay-chain isotopes start accumulating from zero. Two isotopes in the chain below ²⁴¹Am are ²³⁷Np and ²³³U, having half-lives of 2 million years and 160,000 years, respectively, creating major bottlenecks in the decay-chain buildup. If you do the calculations, you'll find that 0.3 microgram of pure ²⁴¹Am produces fewer than 20 astatine atoms per century, each such atom having a half-life of only 0.032 second.

None of the isotopes in the neptunium series have a significantly long half-life on a geological time scale. Therefore, these isotopes have all decayed away do not exist naturally in the Earth's crust.

Conclusion: Get a Rock

If you want an authentic sample of astatine for your element collection, get a uranium ore rock, like the ones available for purchase from United Nuclear:

Source for cloud chamber, $35 5,000 to 10,000 CPM

5 dram vials of small chunks, $15 each (5 drams = 18 ml = 1.2 Tablespoon)

2 to 3 inch rocks, $12 each 1,000 to 3,000 CPM

Or just pick up any old rock that looks like the ones shown here. Who will know the difference?

More information: How Much Astatine Is Present in the Earth's Crust?