Physics Lab

The Half life of Hershey®’s Kisses

Introduction:
When a radioactive material decays it does so at a rate which is directly proportional to the number of radioactive nuclei present. This is known as the law of radioactivity and is a result of the probabilistic nature of the decay of the individual nuclei in the material. During a given time interval each nucleus in the material has a certain probability of decay. The more nuclei present the more decays can be expected to occur. As the number of nuclei diminishes so the decays per unit time diminishes. The number of nuclei remaining N after a given time interval t follows an exponential relationship

where l is called the decay constant of the radioactive material and is the initial number of nuclei present. This relation can also be expressed as follows:
Where t1/2 is the half life of the material, which is the time it takes for half the nuclei to decay and is related to the decay constant by the expression
Another way to express the relation is
were a is the decay factor.

In this lab we will model nuclear decay by using Hershey®’s Kisses to represent the radioactive nuclei. When tossed, Kisses will land either with the pointed end up or not. A Kiss whose pointed end is up is said to have decayed. One whose pointed end is not up has not decayed. Refrain from eating decayed Kisses.

Procedure:
Count out about 40 Kisses and toss them onto a smooth surface (such as a tray). Remove those Kisses which are pointing up. Record the number of Kisses remaining after one toss (one unit of time). Now toss the remaining Kisses again and as with the first toss remove those Kisses which are pointing up. Record the number of Kisses remaining after two tosses. Repeat this procedure 5 times or until there are 10 or fewer Kisses remaining. The results of this simple experiment will be a data set with number of Kisses remaining after a given number of tosses (Don’t forget to include zero tosses in your data set). Unfortunately statistical variation can be quite high so it will be necessary to repeat this experiment several times and find the average number of tacks remaining after each toss. Then test the law of exponential decay by plotting average number of Kisses remaining versus the number of tosses. Find an exponential fit for the graph and hence determine an experimental value for the decay constant, l, the half life and the decay rate of Hershey®’s Kisses! What are the units for these constants?