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Perhaps a minor point, but it initially threw me off, and perhaps
others, was Hugh's use of the letter p for the radioactive decay
constant. There is a standard symbol for the decay constant, and it is
lower-case lambda. Thus, the half life is ln(2)/lambda.
I'm not a nuclear physicist, so I don't have a keen sense of the
conventions used by nuclear physicists. However, my understanding of
radioactive decay is that, if lambda is the decay constant expressed in
number of nuclei decaying per time unit (e.g. in 1 s), then the
probability (p) of any ONE nucleus decaying in that same time unit is
equal to lambda, so p has "dimensions" of probability per unit time and
is numerically the same as lambda.