Better Model for Radioactive Decay

[MisterX]

For the basic model for exponential decay, there is a decay constant, which is related to the half-life. The decay constant multiplied by the number of particles should give the decay rate per second (activity). However, the model I want is for small periods of time. For a small enough period of time, I can come to some conclusion like on average, there is 1/3 radiation event per period. The desired model will have the possibility for more than one event per period, even in this situation. So I could take a random nonnegative integer with probability distribution having 1/3 mean. But how do I find out what the distribution is? One thing that is apparent is there should be zero* probability of negative events. However the probability of any postitive number events it seems, would be nonzero. Thus, distribution would be asymmetric. Would you be able to point me to a model or a way to look up the distribution for a given isotope and mode of decay?*assuming the reverse reaction is treated probability

 

[sophiecentaur]

I think that Poisson statistics describe these sort of problems quite well. I know that a lot of processes are well described using Poisson.

 

[jtbell]

Indeed, Poisson statistics fits radioactive decay to a "T". You can think of the usual exponential distribution as the large-N limit of the Poisson distribution.

http://en.wikipedia.org/wiki/Poisson_process

 

[mathman]

The decay process has a Poisson distribution. The exponential that is used is the mean of the ratio of the current number of radioactive atoms to the original number.