ManInStone

Bismuch decay

From the question on the exponential decay page: the equation is dN/dt = γN = [ln2/t(1/2)]N. If t(1/2) is 1.9e19 years = 6e26 sec and N is 2.9e27, then dN/dt is 3.35 disintigrations per sec. From here, you have to know that you need to calculate from the Poisson distribution the 0.05 probability time for 0 events, when gamma (expected event rate) is 3.35/sec, is exp-(γ*t), where the lamba here is the total expected event rate for our entire mass, not the one for each atom. So 0.05 = exp-(3.35*t). Solve for t and you get a time about 0.893 sec. You have to wait that long for a 95% chance to see a single disintigration with an expected rate of 3.35/sec. SBHarris 02:07, 28 July 2007 (UTC)