Experiment 31

The Half-Life of a Radioactive Isotope

Objectives

To see that radioactivity of a sample declines in time and to measure the rate of decline.

Introduction

It is a relatively familiar fact that the number of atoms of a particular radioactive species decrease exponentially in time and that therefore the number of counts per minute of a counter recording this activity also vary exponentially in time according to the equation

where C_o is the initial rate at which the counter receives particles and C is the number of counts per minute at some subsequent time, t.  τ is the half-life, i.e., the time the species takes to decay to half the original number of atoms.  This half-life is characteristic of the species and cannot be altered by any known process.

Procedure

We will use a Geiger counter to record activity of the sample.  This instrument has counting characteristics of its own which must be known before the device can be used.  Below a certain voltage, the tube will not count and above a certain voltage it cascades giving many counts when only one particle has passed through it.  Between these values there is a region (the "plateau") where the response is uniform and largely independent of voltage fluctuations or drift.  Place a beta (green disc) source in the holder about 3 cm from the tube and set the voltage at 750 volts.  Count for 10 seconds, record the count, and raise the voltage at 50 volts and repeat the procedure.  Continue until the count begins to increase rapidly.  Multiply each count by 6 and sketch counts per minute vs. voltage.  Find the center of the voltage plateau and maintain that voltage for the rest of the experiment.

Remove the beta source but leave the rest of the holder in place.  Count for several minutes.  This count is the background count of radiation from natural sources.  It must be subtracted from all subsequent counts obtained from laboratory sources.

Obtain a sample of Ba 137.  Do not touch the upper surface of the sample and wash your hands after handling the sample.  Do not put things in your mouth during this experiment.  Place the sample in the holder where the beta source was.  Count for 10 seconds, wait 50 seconds, and then repeat for 8 minutes total time.  Obtain a new sample and repeat the measurement.

Evaluation

Graph the corrected counts/minute vs. the time of the count on a semi-log plot with counts on the log scale.  Draw a straight line through the data and calculate the half-life of Ba 137 for each data set.  Compare your average value with the known value.