# Radioactive Decay Java Application

## Physics Background

From quantum mechanical principles, we can expect that radioactive species
will decay with a constant probability per unit of time. That is, if a sample
containing *N*_{0} undecayed atoms at an initial time *t*=0, then the probability
of each atom decaying in the next unit of time is λ. Therefore at any time
the expected number of atoms decaying in the next unit time interval is
λ *N*(*t*), where *N*(*t*) is the undecayed population
as a function of time. A simple first order
differential equation may then be written to predict the population of undecayed
atoms as a function of time:

The solution is a straightforward decaying exponential function of time:

Experimentally, we can measure radioactive decay events by using a Geiger
counter or similar instrument, and then we would expect the number of decay
events per unit time, or the decay rate,
to fall off with the same decaying exponential dependence:

## The Radioactive Decay Application

Click to Download

Run from a shell or command terminal in the download directory with:

java -jar RadioactiveDecay.jar

This application simulates the process of radioactive decay with an initial population
and a given probability per second λ, by simulating a discrete number of
atomic decay events over each one-second time interval. You may adjust the various parameters controlling the simulations by
moving the sliders. The plot displays the current undecayed count as a function of
time in seconds. Note that the verical population count axis is logarithmic, so
a series of populations count readings forming a straight line indicates
an exponential decay. If your computer has audio capability, a simulated audio response
from a Geiger counter is also provided, with one tick per decay event.

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