This is the first lab of a three-lab sequence on radioactivity. In this lab, you will get some practice handling radioactive sources and measuring intensities, as well as getting a feeling for how different materials shield against radioactive particles. Your work in this lab will prepare you for the next modules which explore the lifetimes of radioactive materials how we can use that information to perform radiodating. 

By the end of this lab, students will have…

• … observed alpha, beta, and gamma decay;
• … studied the randomness of radioactive decay;
• … learned to use a Geiger-Mueller particle detector and counter;
• … studied how different materials shield against radiation.

Working with radiation requires some additional safety precautions.

We will be working with radioactive sources which emit alpha, beta, and gamma particles. The sources we use are all relatively low activity and are sealed so you cannot access the radioactive material directly. Your potential exposure is low and well below safe limits.

• If you discover that a radioactive source is broken open or damaged, alert the TA immediately.
• Do not remove sources from the room.
• Do not place source in your pockets or bags.
• Use only one radioactive source at a time, and return sources to their storage location after use.

One of the materials we will be using as shielding is lead.

• Use nitrile gloves whenever handling lead blocks.
• Wash your hands after finishing lab (whether you touched lead or not).
• There is absolutely no food or drink allowed in the lab. Food which comes in contact with lead (or lead contaminated surfaces) can lead to lead ingestion.
• If you need to eat or drink during lab, wash your hands and step outside the room.

The TA will introduce you to the Geiger-Mueller detector and counter and will show you where the radioactive sources are kept. You will begin by making some observations about count rate using different emitters and different shielding materials and conditions. Based on what you see, you will make a hypothesis that leads to a prediction, and you will design an experiment to test that hypothesis.

In this experiment, we want a device which can detect when a radioactive particle passes through it and which will then produce an electronic pulse which can be counted. There are many different types of detectors – some of which can provide additional information such as particle energy or particle type – but for this experiment we will use what is called a Geiger-Mueller (GM) tube.

A GM tube is a sealed cylinder filled with an inert gas (like xenon or argon) which has a wire running down the center which is held at a constant voltage. When a high-energy radioactive particle passes through the gas, it ionizes the gas (i.e., it strips off electrons from the atoms) and the liberated electrons are attracted to (and collected on) the central wire. This accumulation of electrons causes the voltage on the wire to momentarily drop, which can be read out as a detection. If a GM tube is connected to an electronic counter, the pulses can be tallied. 

Spontaneous decays of radioactive particles occur randomly. If we look at a large collection of particles of the same type, we can say something about the average (mean) lifetime of particles of that type, but we can’t say anything for sure about any one particular member of the group. It may decay right now, 1 second from now, 1 year from now, etc.

Because of the random nature of nuclear decay, there is an inherent uncertainty when we measure count rates. If we count the number of decays that happen in a radioactive source for a time interval $t$, the number we observe, $N$, will fluctuate from trial to trial. If we look at the distribution of these times (after repeating the trial many times), it will form a Gaussian (or Normal) Distribution.

To be a bit more mathematical, suppose that you make $n$ measurements of the count within a fixed time period $t$. The distribution will have a mean given by

and a width (or standard deviation) of

In a Gaussian distribution, about 68% of events happen within one standard deviation of the mean. That means that the range $\mu-\sigma \leq N \leq \mu+\sigma$ contains about 2/3 of the events, and the range outside that contains about 1/3.

For counting experiments with a large mean value, the standard deviation is equal the square root of the mean number of counts,

Gaussian (Normal) distribution, showing mean value and standard deviation

We can observe this scatter in counts (and the width of the distribution of counts) by repeating a measurement many many times. (Or, if we only have the opportunity to measure a quantity once, we would report our best estimate of the count as $N \pm \sqrt{N}$.)

It may be observed that the Geiger counter produces pulses even without any radioactive sources nearby. These pulses are due to ionizing radiation from cosmic rays or naturally occurring radioactivity in building materials or in the earth. Thus, the counting rate observed in the laboratory will never drop to zero. This residual rate is called the background. To measure the background, one should record the counts after removing the radioactive sources from the proximity of the counter.

The statistical precision in the background count depends on the total number of background counts obtained. Suppose, for example, you want to know the background rate to within $\pm 10\%$. In order to have a measurement with this precision, $N$ counts are required (with uncertainty $\sqrt{N}$) such that

Therefore, you would need to count until $N = 10^2 = 100$.

Check that the cable from the Spectech ST-370 counter is plugged into the USB port of the computer. Place a strontium-90 ($^{90}$Sr) radioactive source on the plastic tray and slide it into the top slot of its holder under the GM tube.

For counting, we will use the STX x64 software (which should be bookmarked on the desktop). Open the application.

Near the left side of the toolbar running along the top of the application window are buttons for the following:

• Start Counts: This button shows a green square when the STX application is ready to begin collecting data.
• Stop Counts: This button shows a red circle while data collection is active.
• Erase All Data: This button labeled “X” is active only when the application is not taking data.

Located on the righthand side of the application window are a column of boxes for setting and viewing the parameters: Preset Time, Elapsed Time, Runs Remaining, and High Voltage. Boxes for parameters which the user can change contain an up and down arrow as well as a text box for entering new values. Each of these parameters can also be accessed via the Setup and Preset menus.

Set the high voltage to 950 volts (and press Enter). This is a good operating voltage for the tube. Click on the Start Counts button. Do you see the number increasing in the Counts window? Remove the $^{90}$Sr source and verify that the count rate drops almost to zero. The residual counts are due to background radiation, caused by cosmic rays and other natural radioactivity.

Every time you hit “stop”, the software will automatically record a “run” and display the number of counts and the time.

• If the “preset time” is set to zero, the software will run until you select “stop”.
• If the “preset time” is set to any finite number of seconds, it will run for that amount of time and then automatically stop.
• If you increase “runs remaining” to any finite value, it will execute consecutive runs, each for a length of time set by “preset time”, erasing the data between runs.

The STX software

Click on the Stop Counts and Erase All Data buttons to clear old data. Set the Preset Time to 2 (seconds), and Runs Remaining to 100. Replace the $^{90}$Sr source in the top slot of the GM holder and click Start Counts. Data should begin to accumulate in the data table.

When the runs are complete, save your .tsv file somewhere on the computer where you can locate it.

We'll be using a Google Colab notebook to load, process, and plot the data from the software. Follow the instructions there.

Be sure to include plots of you data in your notebook.

Alpha particles are helium nuclei and consist of two protons and two neutrons bound together. We wish to study the effect of the double charge of the alpha particle on its ability to penetrate matter. Note that a particle which loses energy very quickly in matter will be able to penetrate only a short distance.

You can test penetrating power of alpha particles from an Americium-241 source. Observe count rates from the source itself and with a sheet of paper inserted between the source and GM tube.

Check the penetrating power of the beta particles from a strontium-90 source. To do so, place the Sr-90 source on the plastic tray in the 4th slot from the top of the GM holder.

Note that the radioactive material inside the strontium-90 sources is not placed directly in the middle of the button. You will find that the count rate is lower when the source is oriented face up (label showing) compared to when it is face-down (label hidden).

Measure the count rate with a single sheet of paper between the Sr-90 source and the GM tube. Repeat with wood of several thicknesses and with one square of lead.

Beta particles are energetic electrons and therefore have a single charge. Charged particles moving through a magnetic field experience a force and are thus deflected by the field. This fact may be used to determine whether the particles from Sr-90 are charged and what the sign of the charge is. Your lab TA will use the apparatus shown in Fig. 4 to demonstrate the charge of the particles from Sr-90.

Figure 4: Apparatus for determining the sign of the beta particle charge

Question 9: Sketch the magnet, showing the position of its north (N) pole. On your sketch, show the approximate path the beta particles took.

Question 10: From the path the betas took and the direction of the magnetic field (north to south pole), deduce the sign of the charge of the beta particles.

Gamma particles are high energy electromagnetic radiation and have no charge. Test the penetrating power of gammas with wood, iron, and lead. To do so, place the cesium-137 ($^{137}$Cs) source in the plastic tray in the 4th slot from the top. The count rate may be lower, so you might need to count for longer times. Set Preset Time equal to 60 seconds and Runs Remaining equal to 1. Click on the Stop Counts and Erase All Data buttons before each new data run.

Test how effective wood, iron, and lead are at stopping gamma radiation. (You only need to do 1 run each for these.)

Using 0, 1, 2, 3, and 4 lead squares, measure the counting rate as a function of thickness of lead placed between the Cs-137 source and the detector. Plot the count rate vs. number of pieces of lead absorber. Qualitatively, how does the count rate depend on the number of pieces of lead used to absorb the gamma particles?

At the end of the lab, you will need to record your final conclusions (about 1 or 2 paragraphs) in your lab report summing up the important results and take-away points from your experiment. Remember that you should only draw conclusions which are supported by the data, so be ready to back up any statements you make!

When you're finished, save your file as a PDF and upload it to Canvas. (Only one student needs to submit the report, but make sure everyone's name is on it!) If you make a mistake, you can re-submit, but work done after the end of the lab period will not be accepted.