The method and the results are on the nuclear decay lab. Do the analysis yourself first, then check the answers below.
Quick answer: Atoms have discrete energy levels, so they emit and absorb photons of fixed energy equal to the gap between levels. These answers go with the AP Physics 2 lab on nuclear decay: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Model answers use the sample table above. Your data will differ a little because the process is random, and a good answer comments on both the shape of the curve and the scatter of the points.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 15
The points form a falling exponential curve, steep at first and flattening, because each throw removes a fixed fraction of what is left.
Question 3 Half-life from the graph
N = 59 at throw 3 and 49 at throw 4, so N = 50 occurs at about 3.9 throws.
Question 4 Check from later readings
N falls from 49 at throw 4 to 24 at throw 8, which is about half in 4 throws, so T ≈ 4 throws, consistent with the graph.
Question 5 Theoretical value
n = ln 0.5 / ln(5/6) = −0.693 / −0.1823 = 3.80 throws. The experimental 3.9 is within about 3 % of this.
Question 6 Randomness
Each die is removed by chance, so the number removed fluctuates around the average. With 1000 dice the relative fluctuations shrink and the points would follow the curve much more smoothly.
Question 7 Change the rule
Removal probability is now 1/3, so survival is 2/3 and n = ln 0.5 / ln(2/3) = 0.693 / 0.405 = 1.71 throws, shorter because more dice are removed each time.
