Quick answer: Atoms have discrete energy levels, so they emit and absorb photons of fixed energy equal to the gap between levels. This AP Physics 2 lab on nuclear 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 for each nucleus, yet a large sample decays in a predictable way. You will model this with dice, plot the decay curve and find the half-life of your model.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 15
Aim
Model radioactive decay with dice, plot the number of remaining dice against throw number, and find the half-life of the model sample.
Equipment
- 100 identical dice (or 100 coins and a rule that tails decay)
- large shallow tray with edges
- graph paper or spreadsheet
- pencil
Safety
Throw the dice gently into the tray and never at another person. Pick up any dice that fall on the floor straight away, because they are a slipping hazard.
Method
- Place 100 dice in the tray. This is throw 0 with N = 100.
- Shake and tip the dice out, then remove every die that shows a six. These represent nuclei that have decayed.
- Count and record the dice still in play.
- Throw the remaining dice again and repeat until fewer than 15 dice are left.
Results
Sample data from Mei in Singapore:
| Throw number | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| Dice left N | 100 | 84 | 70 | 59 | 49 | 41 | 35 | 29 | 24 |
Analysis questions
Question 1 Fraction remaining
Calculate N / N₀ for each throw.Question 2 Plot the graph
Plot N against the throw number and draw a smooth curve through the points. Describe its shape.Question 3 Half-life from the graph
Read the number of throws needed for N to fall to 50. This is the half-life of the model.Question 4 Check from later readings
Use the readings at throw 4 and throw 8 to give a second value of the half-life.Question 5 Theoretical value
Each die has a 5/6 chance of surviving a throw. Calculate the theoretical half-life using (5/6)ⁿ = 0.5 and compare with your result.Question 6 Randomness
Explain why the points do not lie exactly on a smooth curve, and what would happen with 1000 dice.Question 7 Change the rule
Predict the half-life if dice showing a one or a two are removed, and explain.
