The half-life T1/2 is not the average lifetime T of a radioactive nucleus. We find the average lifetime by multiplying t by the probability per unit time P(t) that the nucleus will "live" that long, then integrating over all time, (a) Show that P(t) should be given by λe-λl. (Hint: What must be the total probability?) (b) Show that r = T1/2/ln 2.
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