## A Laboratory Exercise in Half-Life: Nuclear Physics M&Mium Experiment

Discussion: Many people have heard the term "half-life" and know that it is related to radioactive elements. This lab will help you understand exactly what is meant by half-life and how scientists use this idea to better understand the nucleus.

Purpose: To understand the statistical nature of half-life.

Procedure: You will be given a sample of a radioactive element known as M&Mium. Radioactive members of this isotope family are easily distinguished by the bold M&M emblazened across the front surface of the atom. Particle physicists are at a loss as to why the radioactive members of the species have this . . . perhaps you have a hypothesis? Place all members of the family in a box, MAKING SURE ALL ATOMS HAVE THE M&M LOGO UP SO YOU CAN READ IT!! Count the atoms as you place them in the box and record the total number you start with in a data table.

Next, close and shake the box one time. As you open the box and look inside you will see that several of the previously radioactive members of the group have decayed, and the M&M is no longer visible. This means that they are now considered "safe" and, since they are no longer radioactive, may actually be eaten withour fear of any harm to you! Please do so, and as you remove the edible atoms, count them so you may determine the number of atoms that have decayed in that particular shake.

You will need to continue in this manner until no radioactive members remain. Be sure to record the decayed atoms after each shake.

Analysis: Plot a graph of N (Number of decayed atoms) as a function of the number of shakes on a normal piece of quadrule paper.

Plot a second graph of N as a function of the number of shakes on the semi-log graph paper that has been supplied.

Questions:
1. Write an equation of the line found on the second graph. (Hint: Think about what the semi-log paper does for you.)
2. What is the half-life of M&Mium? (i.e., What number of shakes are necessary to reduce the radioactive members to one-half?)

Included in Catching the Sun, 1992, Fermilab.