The long way to make a lead brick

kw: observations, analysis, science fiction

Many years ago I read something in a science fiction story that I passed over at the time. Since then, having learned a little more, I am kind of tickled by it. It seems people were exploring a long-abandoned alien planet, and someone turned up a block of heavy metal. They determine that it is lead, and somehow someone concludes that it started out as a block of uranium, which has completely decayed, as there is nearly no residual radioactivity.

The two uranium isotopes that have long enough half-lives for this to be impressive are ²³⁸U (4.5 Gy half life) and ²³⁵U (710 My). Now, how long has it been since the big bang? About 13.7 Gy (plus or minus a half Gy). The first generation of stars produced small (by modern comparison) amounts of all elements by about 12.5 Gy ago. So let's give some really ancient aliens the benefit of the doubt, that they could have arisen very quickly, let's say by 12 Gy ago, and they had enough uranium available that they could make a block of it as a really long-measuring clock. 12 Gy is 2.67 half-lives of ²³⁸U and 16.9 half-lives for ²³⁵U.

From this point the calculation is simple. After 2.67 half-lives, the first isotope has decayed to 0.157 (15.7%) of its former amount, and the second, which decays faster, has been reduced to 0.0000082 (0.00082% or one part in 122,000). In the first instance, having 1/6 of the original uranium still present would leave plenty of residual radiation. In the second, the story's point is more plausible, though one would not want to leave a very large block of ²³⁵U around, as it would self-fission and melt things, for many years (A nearly critical mass is a very interesting heat source).

But there is an added point. Nearly pure ²³⁸U, called "depleted uranium" these days, behaves one way, and the other isotope, "enriched uranium", in another, even in small amounts. I learned the following from a relative who has been a "nuke spook", someone who takes nuclear bombs apart and cleans the uranium or plutonium pieces periodically. Enriched nuclear fuel needs cleaning!

A piece of a self-fissile isotope gets dirty. The spontaneous fission produces all kinds of elements, particularly those in the middle of the periodic table, which are the transition metals, heavy metals, and "rare earth" elements. In the interior of a block of such material, the new isotopes just stay there, but near the surface, they are moving fast enough to escape. They slowly glom together into metallic oxides of all kinds, and the uranium block gets coated with fine dust. A nuke spook must brush this dust off and dispose of it as highly hazardous waste, every few years.

A block of ²³⁵U that sat around for ten or twelve billion years would have become a pile of dust by now. It would not be a lead block. So this story's lead block had to start out as ²³⁸U. But it would take much longer than the age of the universe for it to decay away as the story suggested.

I think very few people know about the different behavior of different kinds of uranium, so other than this entertaining quibble, the story is a good yarn. Now if I could just remember its title…