Reply #170: You didn't understand the secular equilibrium argument: given a natural mixture of radioisotopes

[struggle4progress]

of an element and its decay daughters in secular equilibrium, the total radioactivity of the top isotopic mixture of an element together with its daughter compounds can't exceed the activity of the top isotopic mixture times the length of the longest decay chain. This is because the daughters at each stage, if they all decay, must decay in combination at the rate of the immediate parent or (in the case of partially re-entrant chains) at the combined rates of the various parents, whereas if some are stable the total decay rate for the daughters will be less than the rate of the parent or combined rates of the parents. The path from U to Pb can't involve more than 7 or 8 alpha emissions, so I took the activity of natural U and multiplied by 10

<on edit: perhaps I should have used a factor of 14 or 15>
<on edit: practically, however, the factor of ten may be reasonably realistic for exposure purposes, since given the low concentrations, the beta emittors are likely to be trapped in a solid matrix and may not contribute much to surface radioactivity measurements>