Mathematical Modeling with Real Radiation Data Preview Close Preview

Japan in 2011 (1/12)

On March 11, 2011, a magnitude-9 earthquake shook northeastern Japan, unleashing a savage tsunami.

Do you know anything else about what happened during this earthquake and tsunami?

The Fukushima Power Plant (2/12)

The earthquake and tsunami that followed caused the safety mechanisms at the Fukushima power plant to fail, leading to a large explosion.

The video below explains why this happened.

What do you think the biggest danger would be after a nuclear power plant explodes? Why do you think so?

Radiation from Fukushima (3/12)

The tsunami caused a cooling system failure at the Fukushima Daiichi Nuclear Power Plant, which resulted in a level-7 nuclear meltdown and release of radioactive materials.

Radioactive materials were accidentally released in the initial explosion, and then on purpose by opening the vents to reduce gas pressure inside and discharging coolant water into the sea. Radioactive water continued to leak into the Pacific Ocean even years later.

The doctors in the video are using some sort of device to take a measurement. What do you think that device is measuring? Do you know what it is called?

How is Radiation Measured? (4/12)

Radioactivity is typically measured by a Geiger counter. Different models of Geiger counters detect and measure different kinds of radiation.


Geiger counters come in many forms, but they usually consists of three parts:


  1. Geiger tube – a gas-filled tube whose gas ionizes when charged particles or electromagnetic waves 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 electromagnetic waves that pass through the tube.

  2. Visual readout – a meter that keeps track of the number of radioactive particles or electromagnetic waves being detected by the Geiger counter.

  3. Audio readout – a meter that makes one “click” sound for each radioactive particle or electromagnetic wave counted by the Geiger counter. The clicks sound like this.

What does a Geiger Counter measure?

What does it mean when the Geiger Counter makes "clicking" sounds at a faster rate?

What does "counts per minute" or "counts per second" mean?

Open another browser and use the internet to look up "microSievert per hour". What does this mean? How does it differ from "counts per minute" or "counter per second"?

Radioactive materials around the Fukushima Power Plant (5/12)

The video below shows the Geiger Counter readouts as you drive towards where the Fukushima power plant is located.

What happens to the radioactivity measurements as the drivers get closer to the site of the Fukushima nuclear power plant?

Let's Do an Experiment with Radiation (6/12)

It seems like as you get closer to the Fukushima power plant, the level of radiation changes significantly. Let's take a closer look at this phenomenon.

To investigate this, you can design your own experiment to learn about how radiation moves through air. The instrument you will be using in this lab is located at the University of Queensland in Australia.


How does this lab work?

The lab equipment consists of:

  1. A Geiger counter
  2. A radioactive material (Strontium-90)
  3. A Circuit board that connects Geiger counter to the internet


The things that you can change in order to design an experiment are:

  1. The distances in millimeters from the strontium-90 source at which radiation can be measured. Radiation is measured in units of "particle counts", which means the number of particles emitted from the strontium-90 sample that were counted by the Geiger counter.
  2. The measurement time in seconds that each measurement of particle counts will last.
  3. The number of trials that will be conducted at the settings listed above.

What is strontium-90?

Research Question (7/12)

What are you trying to find out in this lab? What question are you trying to answer?

The last page gave you some information about the instrument you will be using to conduct an experiment about radiation. Now you need to develop the question you want to answer using this setup.

What is a research question? That is what your experiment is designed to answer. A “good” scientific research question is one that allows you to perform a test or experiment to show how your variables might be related. The results of the experiment will allow you to say something about how those variables are related. Your research question must be testable to make a strong statement about how the variables are related.

Your research question will guide your experimental design in the next step.

What is the independent variable in your remote labs experiment?

What is the dependent variable in your remote labs experiment?

Write your research question for your remote labs experiment.

Design Your Experiment (8/12)

Design your experiment by choosing values for the variables on the left. To learn more about each variable, click on the question mark icon next to the variable.

When you click "Run", the experiment will run on the instrument located at the University of Queensland in Australia.

Note that experiments are run one at a time, so you are being placed in a line or queue to run yours. If you don't want to wait, you can log out and come back later. Everything you have done up to now will be saved.

Radioactivity over Distance
Distance (mm)
Duration (s)
View your iLab Results (9/12)

Now let's take a look at the data you got from running your remote experiment.

You can review both your experimental design and the data you generated from your experiment in table form by clicking on the tabs below. Take a look at your data.

Do you notice any patterns in your data? If so, describe what those patterns are.

Analyzing your iLab Results (10/12)

Let's take a closer look at the results from your experiment.

By clicking on the tabs below, you can see the variables you chose for your experimental design, your data in table form, and a graph of your data.

Take a close look at the graph of your data in order to determine if there is a relationship between radiation (in particle counts) and distance. You can apply various best-fit functions to the graph in order to investigate the nature of this relationship, if there is one present.

Do you think a relationship exists between your two variables? What kind of relationship, and how do you know?

Is there an Equation to Describe the Relationship? (11/12)

Is there a way to describe the relationship between radiation intensity and distance mathematically? What is really happening here?

As the video mentions, light follows the inverse square law. Since all types of radiation travel through air the same way, just with different wavelengths, that means that all types of radiation follow the inverse square law. Here is another look at how this works with radiation in particular:

Write a mathematical equation to describe the relationship between radiation and distance.

Does your data exactly match what you would predict using the equation you developed? Why or why not?

Can We Predict Radiation Levels Near Fukushima? (12/12)

By analyzing the data you generated with your remote labs experiment and developing an equation to describe the relationship between radiation and distance, you have created a mathematical model of how radiation moves through space.

Earlier in the activity, you watched a video that showed radiation levels as you drove towards the site of the Fukushima nuclear plant. You can plug data from the dashboard Geiger Counters in the video into the mathematical model you created to predict radiation levels closer it the location of the Fukushima power plant and determine whether or not it is safe to approach.

The video is repeated in longer form below, for reference:

For further reference on the safety of different radiation exposure levels, click this link: Radiation Dosage Chart

See if you can answer the questions below with the information you now have:

How would you assess the goodness of fit of your model with the data from the video?

What does your model predict the radiation level will be at 1 km away from the site?

Explain how you came up with that answer.

Is it safe to be 1 km away from the site? Why or why not?