Name
Date
Measuring the Half Live of a Radioactive Sample
In this investigation you will be determining the half-life of
barium-137 using measurements of the gamma radiation emitted
when barium-137 (137Ba) decays from an excited state to its
ground state. The excited barium nuclei are produced when
cesium-137 decays by emitting a − particle, producing a barium
nucleus that is not in its lowest energy state. After this excited
nucleus is produced, the nucleons reorganize into the lowest
energy state and emit a gamma ( photon that can be detected
by the digital radiation monitor.
Figure 1: Vernier Digital Radiation Monitor.
The radioactive barium decays in a predictable way. The
Image Source: Digital Radiation Monitor manual.
probability that any nucleus will decay in a given second is
called the decay constant (k) and so the activity of the sample is proportional to the probability a
nucleus will decay and to the number of nuclei in the sample. As time passes, the number of
radioactive barium nuclei in the sample decreases, so the activity must also decrease. Activity is
typically indicated by the symbol R and its standard unit is a Becquerel, where 1 Bq = 1 decay
per second.
After half of the original sample of excited barium nuclei has emitted -radiation and decayed to
its ground state, the activity of the sample will also be half of its original value. This time period
for half of the sample to decay is called the half-life ( t1 / 2 ) of the nucleus. In this investigation,
you will measure the activity of the barium sample over 20 minutes and use that information to
determine the half-life of this nucleus.
Remember

 to follow ALARA principles at all times.
 to handle the equipment with care.
 that the mica window and grid is extremely fragile and nothing should touch it other than air.
Procedure:
1. Obtain a monitor, and a stopwatch.
2. Measure the background radiation at your location using the techniques you’ve used in
previous experiments.
3. Obtain a plastic bag containing a barium sample for your team.
4. Set your monitor to do counts per minute (CPM). Create a data table on a separate sheet of
paper in which to record the total time that has passed since you started the experiment, time
(t), and the activity (R) you measure of the sample. Don’t forget to record the units for your
measured quantities. How many measurements do you think you’ll be able to make over the
20 minutes of data collection? Don’t forget to allow for time to reset the stop watch and
radiation detector.
5. Have one team member start the stop-watch while another starts the radiation monitor.
6. Wait about 30 seconds and record the stop watch time (t) and the activity measured (R) for
that time.
7. Repeat Step 6 until 20 minutes have passed.
8. Graph the counts measured vs. time on your own paper.
9. Estimate the half-life of your sample from your graph. (Remember that the half-life is the
time it takes for ½ of the originally excited barium nuclei to emit radiation and convert to
ground-state barium nuclei. At this point how much radiation should be emitted?)
10. Compare your results to those of your classmates. Are they all the same or not? Explain.
11. If they are not the same, what might be the cause for the differences? Design a set of
measurements that could help you determine which causes have the largest affect.