In 1955, in his last scholarly publication[1], Isaac Asimov calculated the radiation dose to the human body (or for that matter, any living cell) from endogenous sources (Potassium-40, Carbon-14, and Tritium) and found the total dose was roughly equal to the sea-level dose due to cosmic rays. 86% of the total endogenous dose is from K-40 and essentially all the rest from C-14, but the C-14 is believed to be much more significant biologically since carbon is integral to the DNA chain and bases while potassium is used only in metabolism. Still, the bulk of whole-body beta absorption is from K-40.
Since the half-life of C-14 is only 5700 years, the amount in the biosphere is in equilibrium between creation by cosmic rays and sequestration in biomass and carbonate rocks, and is presumably roughly constant over very long intervals (enough to average out magnetic field reversals, mass extinctions, volcanic outgassing, ice ages, etc.)
But K-40 has a half-life of 1260 million years, right in the mid-range of geological time, with the K-clock being wound by the supernova that expelled what became the solar nebula and continuing to run down ever since. Consider the following table, which takes the current K-40 dose as one and extrapolates over the age of the Earth and into the future. “Fraction remaining” arbitrarily starts at 1 at the time the Earth was formed—the actual isotopic abundance will vary from star to star depending on the properties of the medium from which it formed.
| Time, BP 106 y |
Fraction Remaining |
Relative Radiation |
Events |
|---|---|---|---|
| 4500 | 1 | 11.88 | Earth condenses from Solar nebula |
| 4250 | 0.871 | 10.36 | |
| 4000 | 0.759 | 9.029 | Lithosphere solidifies; most ancient rocks |
| 3750 | 0.661 | 7.869 | |
| 3500 | 0.576 | 6.857 | Fossils of most ancient prokaryotes |
| 3250 | 0.502 | 5.976 | |
| 3000 | 0.438 | 5.208 | Pre-Cambrian I (Catarchean) |
| 2750 | 0.381 | 4.539 | |
| 2500 | 0.332 | 3.956 | |
| 2250 | 0.290 | 3.447 | |
| 2000 | 0.252 | 3.004 | Pre-Cambrian II (Archean) |
| 1750 | 0.220 | 2.618 | |
| 1500 | 0.191 | 2.282 | Pre-Cambrian III (Proterozoic) |
| 1250 | 0.167 | 1.989 | |
| 1000 | 0.145 | 1.733 | Pre-Cambrian IV (Riphean) |
| 750 | 0.127 | 1.510 | |
| 500 | 0.110 | 1.316 | Cambrian era |
| 250 | 0.096 | 1.147 | Permian |
| 0 | 0.084 | 1 | The present |
| −250 | 0.073 | 0.871 | Future |
| −500 | 0.063 | 0.759 | |
| −750 | 0.055 | 0.661 | |
| −1000 | 0.048 | 0.576 | |
| −1250 | 0.042 | 0.502 | |
| −1500 | 0.036 | 0.438 | |
| −1750 | 0.032 | 0.381 | |
| −2000 | 0.027 | 0.332 | |
| −2250 | 0.024 | 0.290 |
When life appeared in the geological record, it incorporated potassium which gave it a radiation dose almost 7 times higher than typical contemporary lifeforms endure. This would both argue for a higher mutation rate, but also constrain the complexity by rendering a long genome with low redundancy too unreliable in such a high radiation environment.
Could it be that the long delay between the emergence of protists and metazoans—about 2.5 billion years, was due to the need for endogenous K-40 radiation to abate to a level compatible with the vastly greater complexity of eukaryotic metazoans?
If there is something to this, it would have all kinds of interesting anthropic consequences that constrain the time in which life must emerge based on the condensation of a star from a supernova remnant, and how long that star had to remain on the main sequence. Projecting into the future, one sees a dramatically falling K-40-induced mutation rate. Perhaps there is a relatively short window in which we are living during which the mutation rate is high enough to produce intelligent life and low enough to allow multicellular life at all.
[1] Asimov, I. “The Radioactivity of the Human Body”. Journal of Chemical Education, February 1955.