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Knowing the decay constant lambda of a nucleus, find: (a) the probability of decay of the nucleus during the time from 0 to t, (b) the mean lifetime tau of the nucleus. |
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Answer» Solution :(a) The probability of survival(i.e., not decaying) in TIME `t` is `e^(-lambda t)`. Hence the probability of decay is `1-e^(- lambdat)` (b) The probaility that the particle decays in time `DT` around time `t` is the difference `e^(-lambda t)-e^(-lambda(t+dt))= e^(-lambdat)[1-e^(e lambda dt)]= lambda e^(-lambda t)dt` Therefore the mean LIFE time is `T= int_(0)^(oo)t lambdae^(-LAMBDAR)dt// int_(0)^(oo) lambdae^(-lambdat)dt=(1)/(lambda) int_(0)^(oo)xe^(-x)dx//int_(0)^(oo)e^(-x)dx=(1)/(lambda)` |
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