20.2 Radioactive decay

Stochastic mechanisms

These are some suggestions for virtual "experiments" that students can investigate or questions that students can try to answer:

Distribution of decay results:

• What proportion of the results are close to the expected result?

• Why is there a range of outcomes?

  • Does varying the number of particles per trial affect the range of outcomes?

  • Does varying the number of trials affect the range of outcomes?

The teacher may want to point out the difference between number of trials and proportion of trials.

Decay over time:

• How would you describe the trend?

• Explain why the number of remaining particles follows this curve.

• Explain why the activity over time follows this curve.

Analysing radiation data: Are bananas radioactive?

Pre-requisites:

• Familiarity with how to handle error and uncertainty in measurements

• Knowledge of how to use spreadsheet software to calculate averages, and to find minimum and maximum values.

  • Additionally, understanding of histograms is also useful but not necessary.

Students should have access to the following equipment:

• Sample of radioactive material from daily life.

  • For the SLS lesson, a banana is used. This can be substituted with a range of materials such as (but not limited to) low sodium salt, brazil nuts, and some types of milk powder. For commercial products, the teacher may want to test the samples beforehand to verify their radioactivity before providing them for the class to use.

• Geiger-Muller (GM) counter(s)

• Laptop(s)

• Link to the SLS lesson

Process:

1. The SLS resource begins with an introduction to sources of radiation in daily life. The teacher may want to reassure students while facilitating productive discussion. The Interactive Thinking Tool provides a question for discussion.

2. Students will then take short measurements of background radiation and the sample. The interactive thinking tool on these pages direct students to estimate radiation levels and the precision of their measurement, and to evaluate the radioactivity of the sample. Teachers may want to allow students to work independently, while students key in their responses during class itself.

3. Students will then set the GM counter to logging mode so that measurements of background radiation and the sample can be taken over longer periods of time.

   • The teacher needs to set aside space for the setups to be undisturbed between lessons.

   • If more than one GM counter is available, teachers may want to facilitate students in checking whether the readings between two counters are comparable, and then running them simultaneously between classes to log background radiation and readings from the sample to save time.

4. In the next class, students should continue their work by analysing the logs from the GM counter.

   • The teacher should highlight that the readings will show a bell-curve-like distribution.
     In the H2 Physics syllabus, students use an error range x ± Δx which implicitly assumes a flat distribution (i.e. it is equally likely to obtain readings of x, x+Δx, or anywhere within the range). Hence, for usual practical questions, it is sufficient to evaluate a claim by stating whether the discrepancy is within the range of error. In this case, the student is likely to find that the difference between background radiation and the measurement of the sample is within the range of error, but due to the bell-curve (and considering standard deviation), the measurement of the sample can be expected to be significantly different from background radiation. If the students have learned statistical testing in their H2 Mathematics, this is a good opportunity to review cross-curricular connections.

The following resources are provided:

• Template for analysis

• Sample data for students without access to GM counters

Teachers can also make use of the following resources:

• About radiation 

• International Atomic Energy Agency guide to radiation and safety

• Dosage from common items or experiences:

  • Singapore Food Agency guide to radiation and food

  • USA Environmental Protection Agency guide to radioactive sources and materials

  • Low sodium salt, smoke detectors and granite  (this page also contains a sample calculation)

  • Human bodies

  • Concrete and other building materials and steel

  • CT scans