A student is asked to determine the half-life of a radioactive source in a school laboratory. The apparatus available includes a sealed radioactive source s...
Question 1 Report
A student is asked to determine the half-life of a radioactive source in a school laboratory. The apparatus available includes a sealed radioactive source stored in a lead-lined box, a Geiger-Müller tube, a counter (scaler), a timer, and tongs. Fig. 50.1 shows the experimental setup. The student must first measure the background count rate before bringing the source near the detector. She must then place the source at a fixed distance from the tube and record the count rate at regular time intervals. The background count rate must be subtracted from each reading to give the corrected count rate. The student then uses the corrected readings to determine the half-life. The teacher provides the student with a checklist of safety precautions to follow throughout.
(a) Describe how the student should measure the background count rate. [2]
(b) Describe the procedure the student should follow to collect data for determining the half-life. [3]
(c) Explain how the student uses the corrected count rate data to determine the half-life. [2]
(d) State two safety precautions the student should follow during this experiment. [2]
Answer Details
(a) Measuring the background count rate [2]
First, remove all radioactive sources from the area (or ensure the source remains sealed in its lead-lined box) so that only natural background radiation reaches the detector [1]. Then record the total count on the counter over a measured time period (for example, 5 minutes), and calculate the count rate in counts per minute. Repeat this measurement several times and take an average to reduce the effect of random variation in the background count [1].
(b) Procedure for collecting half-life data [3]
- Using tongs, place the sealed radioactive source at a fixed distance from the GM tube [1].
- Start the timer and record the count rate at regular time intervals (for example, every 30 seconds or every minute) [1].
- Continue recording readings for at least four or five half-lives to obtain enough data points for an accurate determination. This gives a clear exponential decay curve [1].
Keep the distance between source and detector constant throughout, and do not move the apparatus during the experiment.
(c) Using the data to find the half-life [2]
Subtract the background count rate from each measured count rate to obtain the corrected count rate for each time interval [1]. Then find the time taken for the corrected count rate to fall to exactly half its initial value. This time interval is the half-life. Alternatively, plot the corrected count rate against time and read off the time for the value to halve [1]. Repeating this for several halving intervals (e.g., from the initial value to half, then from half to a quarter) and averaging gives a more reliable result.
(d) Two safety precautions [2]
- Handle the source with tongs (never bare hands) to keep it at a distance from the body and reduce the radiation dose to the hands [1].
- Return the source to its lead-lined container immediately after the experiment is finished, and minimise the total time spent near the source [1].
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