The Quant Discovers that Economic Reporters Can't Do The Math

by Cheryl Rofer

Bloomberg, that specialist in reporting financial information, tells us today that one of Lehman Brothers' less liquid holdings is a half-million pounds of yellowcake. It seems that the price of yellowcake has been dropping recently, and Lehman was sitting on a contract that expired. The amount of yellowcake might be "as much as 500,000 pounds." I am not sure why the qualification, or how uncertain this makes the total. After all, that statement could refer to anything down to pretty much zero.

But that's not the mathematical problem.

A supply of 500,000 pounds of yellowcake is just “slightly” less than the amount needed to make one bomb, or fuel one nuclear power reactor for a year, if the latest enrichment technologies are used, said Gennady Pshakin, an Obninsk, Russia-based nonproliferation expert.

Oh, dear. Looks like lazy reporting to me. It's not hard to calculate the amount of U-235 in a given amount of yellowcake; even reporters, particularly those who handle those financial numbers all the time, should be able to do it. Earlier in the article, they managed to multiply 500,000 pounds by $40.50 per pound to come up with $20 million. Or, whoops, no, the reporters seem to have asked a trader to do that for them.

A quick check of Wikipedia would have told the reporters that yellowcake is mostly U₃O₈ and that 0.72% of natural uranium is U-235. The hard part that you learn in chemistry is that those subscript numbers refer to the numbers of atoms in a molecule. So the molecular weight of U₃O₈ is 3 x 238 (for uranium) + 8 x 16 (for oxygen), or 842. Of that, 3 x 238, or 714, is uranium. So 714/842 of the 500,000 pounds is uranium, or 423,990 pounds.

Of that 423,990 pounds, 0.72% is U-235, or 30,527 pounds. That's a lot more than you need to make one nuclear weapon. If we take Wikipedia's number again, we see that 52 kilograms, or 114 pounds, is a critical mass of U-235. So that would make 267 bombs.

Lehman is the world's third- or fourth-largest nuclear power, ahead of all but Russia, the US and maybe China!

Of course, this is the same silly calculation that has been applied far too often to Iran. I've made some simplifying assumptions, like that U₃O₈ is the only uranium oxide in yellowcake, which isn't quite true, but even if you were more scrupulous about accounting for the oxygen, the number still comes out closer to 267 bombs than to 1.

With some thought, the reporters might have recognized that half a million pounds of yellowcake is a very large number relative to the amount of uranium needed for a bomb. This can be done qualitatively: yellowcake is a refined form of the ore, close to the metal, and uranium is a very heavy element, so it accounts for most of the weight. U-235 is about 1% of natural uranium. One percent of half a million is 50,000 pounds. And nuclear weapons are smaller than that.

One more example of reporters relying on what others say rather than digging out the facts themselves.