The method and the results are on the radioactivity lab. Do the analysis yourself first, then check the answers below.
Quick answer: Radioactivity is the random decay of unstable nuclei, which emit alpha particles, beta particles or gamma rays. These answers go with the Physics 9-10 lab on radioactivity: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Model answers use the sample table. Your own numbers will be a little different because every throw is random, but the shape of the curve and the half-life of about 4 throws should appear in good results.
Level: Physics grades 9-10 (GCSE · IGCSE · O Level · Class 9-10) · Curriculum: HS-PS1-8, GCSE P4
Question 1 The analogy
A die represents one unstable nucleus; a throw represents a fixed interval of time; a six represents that nucleus decaying.
Question 2 Plotting the curve
The curve starts steeply and gets shallower. The number falls quickly at first and then more slowly, never quite reaching zero. This is an exponential decay shape.
Question 3 Half-life of the model
From 100 to 50: the graph reaches 50 at about 3.9 throws. From 50 to 25: the graph reaches 25 at about 7.5 throws, so 7.5 − 3.9 = 3.6 throws. Mean = (3.9 + 3.6) ÷ 2 = about 3.8 throws.
Question 4 Prediction
After throw 1: 100 × 5/6 = 83.3. After throw 5: 100 × (5/6)⁵ = 100 × 0.402 = 40.2. Sample results: 85 and 40, which are within a few dice of the predictions.
Question 5 Why not identical?
Each die falls at random, so the number removed varies from throw to throw, and with only 100 dice the chance fluctuations are large. Starting with more dice, or repeating the lab and averaging, would bring the results closer to the prediction.
Question 6 A different rule
Half-life: (2/3)ⁿ = 0.5, so n = ln 0.5 ÷ ln (2/3) = −0.693 ÷ −0.405 = 1.7 throws. The chance of decay in each throw is greater, so the sample halves faster, which is a shorter half-life.
Question 7 Limits of the model
Real nuclei do not interact or get thrown; the number of nuclei is vastly bigger than 100; and throws happen in discrete steps while real decay is continuous. Any two of these points are acceptable.
