A classroom alternative to simulate radioactive decay of nuclei

Abstract

In this work we present a classroom alternative to simulate radioactive decay of nuclei. It consists of a game in which the students in a classroom are invited to participate in a kind of lottery. The students (around 45 in a typical classroom) take 20 “tickets” numbered at random from 1 to 50. As a whole we have 900 initial “tickets”. Then one student is asked to give a random number between 1 and 50 (for example 34) and the teacher gives a range of numbers from 34 to 38 or 30 to 34. The students cross the numbers in their list that coincide with the numbers given by the teacher. These numbers are the “lucky” ones and represent “nuclei” which decay, then someone gives another number and the process is repeated and the number of “lucky” tickets put in a list. Repetition of the process gives a sequence of numbers which are the number of “nuclei” surviving
as the time goes on. The nuclei decaying are considered as stable ones. A plot of the surviving “nuclei” as a function of time (number of times the students are asked to cross the lucky numbers) gives a typical exponential decay. When one considers the case of nuclei A decaying into nuclei B decaying to nuclei C and this one is a stable one, using the corresponding differential equations one obtains the normal curves of nuclei as a function of time.