# How can I describe a distribution of decay times for an individual unstable nuclei

by elduderino
Tags: decay, distribution, individual, nuclei, times, unstable
 P: 57 Hey, just for the record I was able to do it. Since the exponential decay is a truly random memory-less process, we have to start with a method which mimics this. I was able to "solve" this problem (of recreating the exponential distribution from the individual atom's "perspective") by using two different monte carlo approaches. One was what we can call a "time discretization" approach. In this, you take discrete time steps, and associate each unstable atom in your ensemble with a parameter $$u$$which has a uniform random distribution and compare it to $$\lambda$$ (decay constant) for each atom, then increment the number of times $$u>\lambda$$ to get your distribution. The second is a more mathematical and less programmatic one. Its called the "inverse transform method". I have the programs written down for both of these in ROOT (basically C++) so if anyone needs them just send me a PM.