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”the sort of fallout radiation provided by standard thermonuclear weapons […] decays by a factor of ten for each factor of seven increase in time—in other words, after seven hours, the radiation has decreased tenfold. After two weeks, it’s down to one thousandth. 14 weeks, one ten thousandth.”

With a mix of radiation sources of varying half lifes, it won’t be a 100:1 decrease after 14 hours, but is this, as I guess, just a rough fairly easy to remember fit to some sample curve, or is there some simple mathematical model behind this?

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It's a rule-of-thumb. The fission of Uranium and Plutonium results in an incredible diversity of both isotopes and nuclear isomers.

Most of these isotopes exist on distinct decay chains. An unstable nuclear state may decay in more than one mode, each with a distinct time constant. Many of these decays occur as groups of decay chains that occur on extremely short time-scales, and may temporarily remain in metastable states (isomers).

So this general rule results from the superposition of many thousands of reactions, that proceed stochastically with distinct time constants and energy released.

There is a mathematical rule relating the time constants and energies of these reactions, but it is not simple: https://en.wikipedia.org/wiki/Fermi%27s_golden_rule

According to the golden rule, rate constants are not directly connected to "energies of reactions", but to matrix elements $<f|H'|i>$ for different eigenfunctions i,f. The energy gap between two eigenfunctions may be very large, but the corresponding element may be zero and the rule would predict rate of transition as zero. It is only approximate rule, so the transition may still happen.

For short-term radiation, https://en.wikipedia.org/wiki/Nuclear_fallout#The_Seven_Ten_... :

> The danger of radiation from fallout also decreases with time, as radioactivity decays exponentially with time, such that for each factor of seven increase in time, the radiation is reduced by a factor of ten. For example, after 7 hours, the average dose rate is reduced by a factor of ten; after 49 hours, it is reduced by a further factor of ten (to 1/100th); after two weeks the radiation from the fallout will have reduced by a factor of 1000 compared the initial level; and after 14 weeks the average dose rate will have reduced to 1/10,000th of the initial level.

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