Question: As a sample of radioactive atoms decays, the number of atoms steadily diminishes and the sample's radioactivity decreases in proportion. To study this effect, a nuclear physicist monitors the particles ejected by a radioactive sample for 2 hours. She counts the number of particles emitted in a 1-minute period and repeats the measurement at half-hour intervals, with the following results:
Time elapsed, t (hours): 0.0 0.5 1.0 1.5 2.0 Number counted, v, in 1 min: 214 134 101 61 54
(a) Plot the number counted against elapsed time, including error bars to show the uncertainty in the numbers. (Neglect any uncertainty in the elapsed time.) (b) Theory predicts that the number of emitted particles should diminish exponen-tially as v = v. exp( - rt), where (in this case) v. = 200 and r = 0.693 11-1. On the same graph, plot this expected curve and comment on how well the data seem to fit the theoretical prediction.