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
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?