See, for example, the Reuters article Polonium - deadly, hard to make and rare poison:

Radiation and chemistry experts say large-scale equipment, such as a nuclear reactor, would be needed to produce sufficient amounts to cause death. "It is not as simple as the idea that somebody might have broken into a radioactivity cabinet at some local hospital and walked off with some polonium," Dr Andrea Sella, a lecturer in chemistry at University College London, told Reuters. "You can't make this at home. This is in a different league," he added.

Maybe you can't make it at home, but I'm not so sure about the rest. To explain why, I have to start with some physics background.

Polonium 210 is the second to last entry in the
decay chain of
U-238 (uranium 238), the most abundant (99.275%) isotope of uranium in
nature. Unless they have been removed, all of these isotopes,
including Po-210, thus appear in small amounts with uranium wherever
it is found.
Marie Curie
discovered and separated polonium from pitchblende (a uranium ore
consisting mainly of uranium dioxide, UO_{2}) in 1897 using
purely chemical means. This was over a century ago. The first nuclear
reactor and even the particle accelerator were still decades away.

Like every other element heavier than iron (the end result of "normal" stellar thermonuclear fusion), the U-238 present today in the earth was created by the explosion of supernovae long before the solar system and earth were formed about 4.5 billion years ago. Because it has a 4.5 billion year half life, about half of the U-238 originally present in the earth at its formation is still here today. In undisturbed rocks and ores, U-238 exists in equilibrium with every isotope in its long decay chain. This chain ends with stable Pb-206 (lead 206), so as time passes lead accumulates and the radioactive elements (including the U-238) slowly disappear.

At equilibrium, each isotope in the decay chain is produced just as fast as it decays. So every radioactive isotope in the decay chain must have exactly the same radioactivity. That is, if a sample of undisturbed, unprocessed uranium ore contains 1,000 Bq (becquerel) of U-238, then it must also contain 1,000 Bq of thorium 234, 1,000 Bq of palladium 234, etc, all the way down to 1,000 Bq of polonium-210. (The becquerel is the SI unit of radioactivity, defined as one disintegration per second.) After another 4.5 billion years, assuming the sample is sealed to prevent the escape of gaseous elements such as radon, it will have only 500 Bq of U-238, 500 Bq of Th-234, etc, and 500 Bq of Po-210. Half of the U-238 present today will become Pb-206.

Although every isotope in the decay chain has the same
radioactivity, the number of *atoms* of each isotope will vary
widely because of their vastly different half lives. In fact, the
number of atoms of each isotope in the decay chain at equilibrium is
directly proportional to its half life. Polonium-210 has a half life
of only 138 days, so the number of Po-210 atoms will be only be 138
days / 4.5 billion years or about 10^{-10} (1 ten-billionth) of the number of
U-238 atoms.

Alpha particles are highly ionizing. Even a small amount of matter, such as a piece of paper or a few inches of air, will stop alpha particles and absorb their energy. A radioactive substance that emits only alpha particles is therefore easy to shield. But if the unshielded substance is taken into and spread throughout the body, then the alpha particles are absorbed by the adjacent tissues where they deposit their harmful energy. This makes alpha emitters like Po-210 potent radiological poisons, but only when they are injected, ingested or inhaled. Outside the body they cause little or no harm.

One gray is equal to an absorbed energy dosage of 1 joule per kilogram of absorbing material. The biological radiation weighting factor, i.e., the ratio of sieverts to grays, is the product of two values, Q and N. Q depends on the type of radiation (alpha, beta, gamma), and N depends on the particular body tissue. The Q value for alpha particles is 20, reflecting their highly ionizing nature. For human bone marrow, colon, lung and stomach, N=0.12; for several other organs, including the bladder, brain, breast, kidney, liver and small intestine, N=0.05. Taking the larger value of N=0.12 gives a QN product of 2.4. In other words, the deposition of 1 joule of alpha particle energy in 1 kg of human bone marrow (1 gray) would represent a dose of 2.4 sieverts.

To compute the radiation dosage to the body from a given amount of ingested Po-210, we next need to know how much energy is released in its alpha particles. As mentioned above, each Po-210 decay releases an alpha particle with an energy of 5.407 MeV, so we can easily compute the total energy released by the complete decay of a given amount of Po-210 by multiplying the 5.407 MeV alpha energy by the number of polonium atoms. But we can't wait for all of the Po-210 to decay; we'll want to give our victim his fatal dose within, say, one week, and only half of it decays in about 138 days. (It took several weeks for Litvinenko's doctors to figure out what was wrong with him, and by then it was too late.)

Radioactive decay is an exponential process; the fraction of undecayed atoms left after time t is

*e*^{-t * ln(2)/h}, where h is the half-life.

The fraction of Po-210 remaining after one week is therefore

*e*^{-7 * ln(2)/138.376} = 0.9655

This means 1 - 0.9655 = 3.45% of the Po-210 will decay in one week, and we'll need 1/(1-0.9655) = 29 times as much Po-210 to deliver 10 sieverts in 7 days as we'd need to deliver 10 sieverts in infinite time (or 5 sieverts in one half life of 138.376 days).

One gram of Po-210 is 1/210 = 4.762 * 10^{-3}
mole.
Multiplying this by
Avogadro's number,
the number of atoms in a mole, we obtain

4.762 * 10^{-3} * 6.022 * 10^{23} = 2.87 * 10^{21}
atoms of Po-210.
If we multiply this many atoms by the alpha energy of 5.407 MeV, we
obtain a total energy release of

2.87 * 10^{21} * 5.407 MeV = 1.55 * 10^{28} eV.

One joule
equals 6.24 * 10^{18} eV, so this is equal to
2.48 * 10^{9} joules, or 2.48 gigajoules.

The average adult human male has a mass of 70 kg. If we assume the Po-210 is uniformly distributed throughout the body, then the whole-body radiation dosage from 1 gram of Po-210 in one week would be

0.0345 * 2.48 gigajoules / 70 kg * 2.4 sievert/gray = 2.9 * 10^{6}
sievert. This is a truly gargantuan dose, but 1 gram is a huge amount
of Po-210. If we only need 10 sieverts/week to kill our victim, then we only
need

10 sievert / (2.9 * 10^{6} sievert/gram) = 3.4 * 10^{-6} g.

That's 3.4 *micrograms*.

As discussed above, in a sample of natural uranium in equilibrium with
its decay chain, the relative abundance of Po-210 to U-238 is the
ratio of their half-lives. The half life of Po-210 is 138.376 days;
the half life of U-238 is 4.468 * 10^{9} years, or 1.63 *
10^{12} days (at 365.25 days/year). The Po-210/U-238 half-life (and
abundance) ratio is therefore

138.376 / (1.63 * 10^{12}) = 8.48 * 10^{-11} (or about
1 part in 10 billion, as mentioned earlier).

That's about one atom Po-210 per 11.8 billion atoms of U-238. But we only need 3.4 micrograms of Po-210. That corresponds to

(238/210) * (3.4 * 10^{-6} g / 8.48 * 10^{-11} =
4.54 * 10^{4} g = 45.4 kg U-238.

In other words, we only need as much natural uranium ore as contains 45.4 kg of U-238. That's not all that much, is it?

In any event, microgram amounts of Po-210 seem very dangerous indeed, so the utility, at least in theory, of chemical extraction cannot be ruled out.

If the *only* possible source of the Po-210 that killed
Alexander Litvinenko was a large nuclear laboratory, this would point
strongly at Russia, either for deliberately murdering him or for
failing to secure their inventories of Po-210. But counter to the
intuitive claims of the experts in the media, I don't think we can rule
out chemical extraction from manageable amounts of uranium ore with a
technique that was first developed (and published) over a century ago.

It is also worth pointing out that, unlike a finite stockpile of Po-210 produced in a reactor or particle accelerator, uranium ore is a nearly infinitely renewable source of Po-210. After extraction, a significant amount is replenished in a matter of weeks by further decay of the parent isotopes in the U-238 decay chain. I think this might have some practical implications vis a vis use of pure Po-210 (stolen or allocated) for international political assassinations. Once pure Po-210 is used, it cannot be reused -- but the stock of uranium ore used to breed it could be. Po-210 also decays relatively rapidly -- a consideration if the international smuggling of radioactive isotopes is time consuming (and I have no way of knowing). Uranium ore, on the other hand, would be an assassin's gift that keeps on giving.

Phil Karn, v 1.02, 26 November 2006