Quick answer: Radioactive decay is the random change of an unstable nucleus, and a sample decays exponentially with a fixed half-life. This Physics 11-12 lab on radioactive decay gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
Radioactive decay is random, yet a large sample decays in a smooth, exponential way. In this lab you model the decay of 120 nuclei with dice, plot the results and use them to find the half-life of the model, then compare it with the value predicted from the chance of decay.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: IB E.3-E.5
Aim
To model radioactive decay with dice, to find the half-life of the model from a graph and from the gradient of ln N against the number of throws, and to compare it with the value predicted from the chance of decay.
Equipment
- 120 identical dice (or 120 small cubes with one face marked)
- a large tray or shoebox lid with a rim
- a second container for removed dice
- graph paper or a spreadsheet
- calculator with a ln key
Safety
This is a model: no radioactive source is used. Throw the dice gently inside the tray so that none fall on the floor, where they are a slipping hazard, and pick up any stray dice at once.
Method
- Put all 120 dice in the tray and record N = 120 for throw 0.
- Shake the tray so that all the dice are thrown, and remove every die showing a six: these represent nuclei that have decayed.
- Count the dice that remain in the tray and record N for throw 1.
- Throw only the remaining dice and repeat the removal until you have done 10 throws, or until fewer than 10 dice are left.
- Plot N against the number of throws n, and also calculate ln N for each throw.
Results
Sample results from one run:
| Throw n | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Dice left N | 120 | 102 | 90 | 74 | 61 | 48 | 39 | 35 | 33 | 27 | 22 |
Analysis questions
Question 1 Why results vary
Explain why a second run with the same number of dice would give different counts, and why this is realistic for radioactive decay.Question 2 Expected values
Each die has a 1/6 chance of being removed in each throw. Calculate the expected number left after 10 throws and compare it with the sample result of 22.Question 3 Half-life from the graph
Plot N against n for the sample data and use the graph to find the number of throws taken for N to fall from 120 to 60.Question 4 Straight-line plot
Calculate ln N for each throw, plot ln N against n and find the gradient of the best-fit line. State what the gradient represents.Question 5 Half-life from the gradient
Use the decay constant found in the previous question (λ = 0.17 per throw) to calculate the half-life in throws.Question 6 Prediction from probability
The chance that a die decays in one throw is 1/6. The fraction left after each throw is 5/6. Show that the model has λ = ln(6/5) per throw, calculate the predicted half-life, and compare it with your result.Question 7 Improving the reliability
State why the last few readings are the least reliable, estimate the percentage fluctuation for N = 22, and suggest one improvement.
