Perhaps because of the recent events in Japan and the somewhat-compromised Fukushima nuclear reactor, I have had a chance lately to think about radioisotopes and their half-lives. Like many things in physics, dealing with half-lives means dealing with astronomical numbers that are hard to digest. The difference between the shortest lived of isotopes and the longest lived of isotopes is one of attaseconds versus exayears, which is a difference of around 10^40. That is, as is common in physics, an astronomical number.

But what is paradoxically bewildering is that many isotopes seem to have half-lives that are on a scale that we can understand. Many, if not most isotopes, actually decay over seconds, hours, days or years. Strangely enough, much radioactive decay occurs on a timescale similar to that of chemical processes. Why should (for example), Au-195 and Au-198, decay at about the same rate as a pizza box and open jar of mayonnaise, respectively? There is a technical and non-technical answer to that question, but that question is just an introduction to the main point of this essay.

The main point of this essay is that in the long range of isotope half-lives, there is a certain window of ones who are important for geological processes. 100 million and 10 billion years are not arbitrary numbers, they are the half-lives that would enable an element to decay slowly enough that it would still be releasing heat after planetary accretion, but still fast enough that they are creating heat in the core faster than it can be radiated away into space. There are only five major isotopes with these characteristics:

  • Uranium-238: With a half life of 4.5 billion years, only half of the uranium that was present when our earth formed has decayed. Uranium is a rare, but not extremely rare element, and all of its isotopes are radioactive.
  • Uranium-235: With a shorter half-life of 700 million years, now forms a small part of the earth's remaining uranium, but it was a large fraction of the total uranium when the earth begin to form. Uranium-235 also undergoes spontaneous fission, which is important for its technological uses, but probably has no impact on its heating capacity.
  • Potassium-40: Has a half life of 1.25 billion years. Potassium-40 is a small part of existing Potassium, about one part in 10,000, but that would have been much greater in times past. However, since overall there is much more potassium than uranium in the earth, the contribution of potassium to the radioactive heating of the earth is on the same scale as the contribution of uranium.
  • Plutonium-244 has a half life of 80 million years, which is just under our nominal minimum, but is still enough that quantities of it probably existed right after planetary accretion.
  • Thorium-232, at 14.5 billion years, likewise is outside of our nominal time scale, but is still enough to add heat to our planet, especially since there is quite a bit of Thorium throughout the globe.
Those are then the major isotopes with half-lives that are active over the lifetime of our planet. There are a number of other isotopes that also fit this criteria, such as Lutetium-176, Platinum-190, and Samarium-146, but for the most part these exist in such small quantities that they would have not been able to play a geologically important role.

The fact that these isotopes exist, in these quantities, and with these half lives, is very important for the existence of life on earth as we know it. If these isotopes had a half-life under 100 million years, the earth as it was accreting would have been very hot, but all the heat would have radiated away into space, and there would have been no plate tectonics or geophysics to help biologically important elements cycle. There would have not been a molten iron core, and thus no magnetic field to protect the earth from cosmic rays. If, on the other hand, these five isotopes had half-lives over about 10 billion years, the heat they generated would have been able to dissipate away at the rate it was generated, and the earth could have never gotten a molten core. And, of course, if there were that many other elements, or greater quantities of these elements, the earth would be hot enough that a solid crust couldn't have formed. In other words, these five isotopes having the half-lives that they do, and being present in the proportion that they are, is key to our earth being the way it is. Given the great value of possible values for isotope half-lives, we should be happy that we ended up with isotopes whose geological age would match the time that our sun would exist on the main sequence.

Of course, too much shouldn't be read into this. It could be seen as a predictable example of the weak anthropic principle. Since these are the preconditions that allow our form of life to exist, they seem providential to us. But with a small use of imagination, we can imagine other forms of life thinking that the scale of isotopic half-lives are well suited for them. Perhaps several tens of billions of years in the future, argon crystal hive minds living on a cold planet circling a dim red dwarf will assume the slow, even decay of Samarium-148, which keeps their planet "heated" to a few degrees above absolute zero, and will for a hundred billion years, is the ideal, predestined conditions for "intelligent life".

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