Modeling Halflife by Joe Rowing
last updated 8/27/2017

# Theory:

Radioactive decay is based on the assumption that the disintegrations are entirely at random.
This can be modelled using dice to represent the atoms of a radioactive isotope.

## Activity

In this experiment you are crudely modelling radioactive decay with dice. The activity formula - $\frac{dn}{dt}=- \lambda N$ Then must have the form: $\frac{dn}{dt}= -\frac{1}{6} N$ That is, every roll of the dice should cause approximately one-sixth of the dice to decay”

## Results and graph

You will need to take enough results to plot a graph showing the exponential decay, you can compare this to the theoretical decay curve: $N= N_{0} e^{- \lambda t}$ Where t” is the number of throws, here representing the passage of one second.

# Apparatus:

1000 dice
10 ×cups to hold 100 dice each

# Further guidance

The Cubes with only one side coloured come as a kit from Philip Harris catalogue number B8G85951.
This is the kit

# Method:

Each student should have an equal share of the 1000 dice (or cubes) and a cup.
Throw the dice onto the table.

Suppose all the dice with the number 1 uppermost have disintegrated.
Remove these dice and count the number remaining.
Repeat this for a further 9 throws (making 10 in all) and note down the number of throws and the number of dice remaining each time.
When complete combine the results of the class so you have data for 1000 dice rolled 10 times.
Plot a graph of number of dice remaining (y-axis) against number of throws (x-axis). This should give an exponential curve with a half-life of about 3.8 throws.

## Model equation

The equation of the theoretical curve is: $N= N_{0} e^{- \lambda t}$

# Simulation

Below we have some python code that will simulate your results.
You will notice a number of variables that you might like to investigate to see how they might affect your investigation - these include the initial population (the number of dice you start with) and the number of experiments you do (they will be automatically averaged)
Each time you chage a variable, click Evaluate” to re-run the code.