Modelling half-life with dice
The question
Does a random process produce a predictable half-life, and how does sample size affect how well the model fits?
The age of the Solar System, about 4.57 billion years, comes from radioactive clocks in meteorites. Each nucleus decays at random, yet a large sample has a precise half-life.
Equipment
- 100 or more six-sided dice (or a spreadsheet random number generator)
- A tray and a results sheet
- A spreadsheet
Method
- Roll all the dice. Remove every die showing a six: those nuclei have decayed.
- Count the dice left and record. Repeat until fewer than five remain.
- Plot dice remaining against number of throws and read off the half-life.
- Repeat with 20 dice and with 500 simulated dice in a spreadsheet.
- What to measure
- Dice remaining after each throw, the half-life read from each graph, and how it compares with the theoretical value of about 3.8 throws for a 1 in 6 chance.
- How to present it
- Decay curves for each sample size, your half-lives, and an explanation of why large samples give precise ages.
- Take it further
- Find out why short-lived isotopes such as aluminium-26 let scientists date events in the first few million years of the Solar System.
Safety
No hazards beyond tidying up dice so nobody slips.