[Radioactivity as a function of time.]

Week 10 Notes: Random Processes

We study models that use random numbers to generate statistically predictable outcomes.  Examples include Monte Carlo methods and random walks on a lattice.  Many of the random walk models are described in Chapter 7 of An Introduction to Computer Simulation Methods.

Radioactivity and Half Life

The EJS Radioactive Decay Events Model simulates the measurement of a radioactive sample using discrete random events. If we start with N₀ radioactive nuclei and a wait a time  Δt, then some nuclei will decay spontaneously.  If we wait long enough half of the initial radioactive nuclei will decay and this time is call the half life of the sample.   It is, however, difficult to determine the half life from a single measurement of a small sample because each nuclear decay event is stochastic (random).  In order to determine the half life to within some experimental error we must fit the data to a theoretical model.

A typical half life experiment measures the number decay events in a time interval Δt.  Because the number of decay events ΔN is proportional to the number of radioactive nuclei, the radioactivity will decrease exponentially if the the sample consists of a single nuclear species decaying with decay constant λ.  For small time intervals the number of decay events is:

The Open Source Physics project has created a Data Tool that can perform data manipulations and data analysis and this tool is available within EJS models if the add data processing tools option is selected when the jar file is created.