# Mathematical Modeling Using Real Radioactivity Data

## Teacher Notes

A detailed Radioactivity iLab Guide is provided at the iLabCentral.org website. This website provides a very prescriptive approach to the lesson, and after reviewing the material provided there, teachers may decide that this approach is appropriate for their students.

As an alternative to the lesson described at iLabCentral.org, a less prescriptive lesson is detailed below. The lesson assumes that most students (and teachers) will not have much of a background on Geiger counters and radioactivity. The lesson outlined below provides background information and a real-world context to help make the data collection relevant.

Background info on Radioactivity: Radioactivity is typically measured by a Geiger counter (also called a Geiger-Mueller counter), which is an instrument that detects and measures ionizing radiation. Different models of Geiger counters detect alpha particles, beta particles, or gamma rays. When charged particles or photons from a radioactive material pass through the gas, the ions create a signal that can be measured, allowing the Geiger counter to count the number of radioactive particles or photons that pass through the tube. A visual readout keeps track of the number of radioactive particles or photons being detected by the Geiger counter (counts per minute, counts per second, or microSieverts per hour). An audio readout on the Geiger counter makes a "click" sound for each radioactive particle or photon detected. A microSievert is an SI unit of measure that quantifies the biological effects of radiation.

*Lesson introduction and problem set-up*

- Open lesson with video of tsunami that hit Japan in March of 2011.
- While watching the video, ask students to talk about anything they know about the event.
- Note: it is not necessary to watch the entire video. The first 2 or 3 minutes is enough to begin the conversation.
- The purpose of watching the video is to engage students and move towards a conversation about the explosion at the Fukushima Power Plant.
- More information about the tsunami, the earthquake that caused the tsunami, and the Fukushima Nuclear Power Plant can be found here.

- After turning the conversation to the Fukushima Nuclear Power Plant, view the image of the Fukushima Power Plant explosion and the image of a worker being tested for radiation exposure.
- Ask the students if anyone knows about the instrument that is being used to test for radiation exposure.
- Have students provide as much information about a Geiger counter as they already know.

- Ask students to work with a partner and use the internet to find the answers to the following questions. Students should cite their sources.

- What does a Geiger counter measure?
- What does it mean if the Geiger counter is making more clicking sounds?
- What is meant by “Counts per minute” or “Counts per second”?
- What is a microSievert per hour?

[In discussing the answers to these questions as a class, emphasize that more clicks, higher counts per minute, or higher microSieverts per hour all indicate higher levels of radiation. Emphasize the symbol for microSieverts per hour.]

Some students may need more direction to find the answers to the questions listed above.

4. Watch the video “Inside Fukushima's Nuclear Reactor Evacuation Zone with Geiger Counter” until time 2:10.

- On the board, copy down the two data points provided by the video.
- Does the video generate any student questions?

Some questions that may be asked:

- Are the radiation levels safe?
- Will the dogs get sick?
- Why are the traffic lights out?
- Why are the radiation levels changing?
- How high will the radiation levels get?

5. State to the students the objective of the lesson: The goal of this lesson is to create a model of the radiation levels based on the data from the Fukushima video, and use this type of model to predict the radiation levels at 1 km from the power plant.

6. Ask students to sketch a graph of the relationship between radiation levels and distance from the radiation source.

a. Tell the students that the purpose of the iLab is to gather data to allow a model to be created.

*Data gathering with iLab*

- Follow the instructions from the Radioactive iLab Guide to help students become familiar with the iLab setup.
- Use the simulation available on the iLabCentral.org to demonstrate how the Geiger counter can be adjusted to read various radiation levels.
- In addition to the Radioactive iLab Guide the student handout provides students instructions for data collection process.
- Students can work with a partner to gather data from the online Geiger counter at various distances from the radioactive material.
- Students should develop a model either by hand or using spreadsheet software.

Note: if modeling by hand, students can be guided to use two data points and the power function y = A*x^B. The value of B should be close to 2. Students may need to use logarithms to determine A and B. Students can be asked to analyze the goodness of fit by examining the sum of the squared errors of the model.

*Modeling and Presenting the Fukushima data:*

1. If students have modeled the iLab data by hand, they will be ready to model the Fukushima video data with the two data points.

- Otherwise, keep watching the video for additional data points to enter into a spreadsheet.
- Note: students may be confused by the use of microSieverts per hour in the video as compared to total counts used in iLab.

2. Students will use their model to predict radiation levels at 1 km from the power plant. What is the safety risk at that point?

- Note: Radiation risk level can be found here.

3. Students present Fukushima models and safety risk predictions.

**Pre-class Preparation**

Ensure internet connectivity for student computers.

**Materials and Tools**

**Assessment**

The teacher can use the student responses to the handout and their final presentations to assess student learning.

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