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* probabilty of negative events. However the probabilty 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 seperately

 

[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.

 

[pmacias]

I would suggest looking into the Poisson distribution as a potential model for your desired decay process. The Poisson distribution is often used to model the number of events occurring in a fixed interval of time, and it is asymmetric with a probability of zero for negative events. It also has a parameter, lambda, which represents the average number of events occurring in the given interval. In your case, this parameter could be set to 1/3 to reflect your desired average number of events per period.

However, it is important to note that the Poisson distribution may not be the best fit for all types of radioactive decay. It is always important to consider the specific properties of the isotope and mode of decay in question when selecting a model. I would recommend consulting with other experts in the field or conducting further research to determine the most appropriate distribution for your specific scenario.