Simulation: Geiger Counter and Radioactive Decay Half-Life


Simulation

Radioactivity is found in many things in everyday living. Granite countertops, for example, typically exhibit a small, but perceptible, amount of radioactivity. Many smoke detectors are based upon ionization caused by a small sample of a radioactive substance contained within the smoke detector. Medical uses of radiation in the treatment of cancer are common. Carbon-14 dating of archaeological antiquities is used to determine their age. The list can go on and on.

The rate of decay of a radioactive substance is often determined by the use of a Geiger counter. When the rate of decay is proportional to the amount of radioactive material present, the decay rate will decrease exponentially with time. The time required for the decay rate to become half of its original rate is known as the half-life of the radioactive substance.

This project will simulate both the decay process of radioactive isotopes and a Geiger counter used to measure the decay rate. The decay rate is simulated by a tone emitted by a synth speaker, with random clicks indicating that a simulated radioactive atom has decayed. Students collect data on decay rate vs. time for any one of ten simulated radioactive isotopes with half-lives varying from roughly 50 through 300 seconds. The teacher can assign a different isotope to each lab group.

Data collected automatically by a sketch (program) running on an Arduino module is imported into an Excel spreadsheet for student analysis.

Duration: About one class period

GRADE LEVEL
College/University (age 18+)
High School (ages 14-17)

DIFFICULTY
Intermediate

SUBJECT
Technology
Science

MODULES & ACCESSORIES USED (8)
slide dimmer (1)
slide switch (1)
power (1)
split (1)
synth speaker (1)
Arduino (1)
number (1)
battery + cable (1)

LESSON GUIDE

STEP 1 : Setup the Circuit

Simulation1

The picture above shows the entire circuit. The power connects to a split module. One end of the split connects to a slide dimmer (or alternatively to a dimmer). The other end of the split connects to a slide switch (or alternatively to a toggle switch). The slide dimmer is connected to the a0 input of the Arduino module. The slide switch connects to the a1 input of the Arduino module. The synth speaker connects to the d5 output of the Arduino, and the number module (set to “values”) connects tot the d9 output of the Arduino. A micro-USB cable connects the Arduino board to a computer that is running the Arduino IDE software. Both switches on the Arduino should be set to “analog”. (Note that you can use an LED instead of a synth speaker if you want a visual indication of “clicks”. You can also connect both a synth speaker and an LED in series to the d5 output if you want both sound and visual indications of “clicks”.)

Here is a link to the project that contains a list of bits used:

https://littlebits.cc/projects/simulation-geiger-counter-and-radioactive-decay-half-life

The isotope selector allows the student to select one of ten isotopes numbered with IDs from 0 through 9, each with a different half-life. The ID of the isotope selected is displayed in the number module. Once the simulation is started by turning the start simulation switch to the ON position, the isotope selected cannot be changed. The teacher can obtain a list of the half-life (in minutes) for each of the ten isotopes from an attached file. The synth speaker provides sound output, with random “clicks” indicating that a radioactive atom has decayed. A table of time and click counts is automatically recorded into the Arduino serial monitor by the Arduino sketch as the simulation proceeds. At the conclusion of data collection, the student can then import this data table into an Excel spreadsheet (provided as an attachment) for analysis.

STEP 2 : Ready the Arduino Module for Data Collection

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Note that the Arduino module’s micro-USB cable must be connected to your computer, and the computer must have the Arduino IDE software installed. THE ARDUINO SWITHCES SHOULD BOTH BE SET TO ANALOG.

Power up the Arduino module. Start the Arduino IDE software. Select Tools>Board>Arduino Leonardo. Then select Tools>Serial Port and select the serial port that the Arduino will use for communication. This will depend upon whether you are using a Windows, Mac, or Linux machine. Open the sketch file called DecayingAtoms.ino. With the start simulation switch in the OFF position, upload the sketch to the Arduino module. You will see the yellow rx/tx LEDs blink on the Arduino module while the sketch is uploaded.

Open the Serial Monitor in the Arduino software by clicking on Tools>Serial Monitor in the Arduino software.

Move the isotope selector slide dimmer until you see the ID (a number between 0 and 9) of the isotope assigned by your teacher displayed in the isotope number module.

You can then begin the simulation by turning the start simulation slide switch to the ON position. The synth speaker will produce a click every time a simulated radioactive atom decays. As time progresses, you will also see a detailed table of time and counts in the Serial Monitor window. A portion of what this table looks like is shown in the figure above. Time is in seconds and counts is the number of decays in intervals of 10 seconds each.

(If you need to start the simulation all over from the beginning:

1. Make sure the start simulation switch is set to OFF.

2. Re-upload the sketch to the Arduino module.

3. Open the Serial Monitor window.

4. Select the isotope ID from the slide dimmer.

5. Start the simulation by turning the start simulation switch to ON.)

STEP 3 : Transfer Data to the Excel File

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When you are done collecting decay data , then you can transfer the data from the serial monitor to Excel. Here is how to do that. First, uncheck Autoscroll in the bottom left corner of the serial monitor. Use your mouse to drag and select all of the data beginning with the data line containing the column headers “Time(s) Counts”. Open the attached Excel .xlsx file called Radioactivity_Simulator_Template.xlsx. Right-click on cell A1 in this worksheet and select Paste.

You should see the data in the Excel workbook on the far left. In addition you will see a chart displaying a graph of counts versus time. Note that “counts” is on the vertical axis, and the time axis (horizontal) is in seconds.

Your graph will look similar in shape to the graph shown above, but the numbers will be different.

STEP 4 : Data Analysis

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You will notice that your graph of counts rate vs. time has a blue line with data points shown, and a thin black line superimposed on the blue line. The blue line is your actual data.

(a) Why is the blue line “bumpy”, with random ups and downs?

(b) What is the original decay rate of your isotope? How much time has passed until it reaches a decay rate that is half of the original decay rate? This amount of time is known as the half-life of the isotope. It represents the time required for half of the radioactive atoms in the sample to decay into stable atoms.

(c) How much additional time is required for your isotope to reach a decay rate that is one-quarter that of the original decay rate?

The black line is Excel’s best-fit exponential trend line to your data. The equation for this best fit exponential trend line is shown in the upper left corner of the graph. y is the counts that is plotted along the vertical axis, and x is time that is plotted along the horizontal axis. You will notice that the equation for the trend line takes the form shown in the figure above.

(d) How does the value for the initial decay rate in the equation compare to the value you got by direct observation of your graph?

(e) Using a “littleBit” of algebra, you should be able to determine the relationship between the decay constant λ and the half-life t½ of the radioactive sample. Hint: After one half-life has elapsed, the decay rate of the sample is one-half of the original decay rate. (Answer: t½ = 0.693 / λ)

(f) Using the relationship between half-life and the decay constant shown in your graph, calculate the value of the half-life of your radioactive isotope. How does this value compare to the value that you obtained back in question (b)?