The purpose of this laboratory is the study of random nuclear processes.

In this lab rather than using programs built in to the webpage you use an excel spreadsheet which you can either download from here on find on the desktop of the lab computer and enter your data in to that. There is **no** worksheet that you need to print out for this lab.

If you need the .pdf version of these instructions you can get them here.

- “Geiger” Counter box
- 1 blue/yellow or orange
^{137}Cs radioactive source (long-lived: T_{1/2}= 30 Years) - 1
^{137}Ba source (low intensity – short-lived – prepared by the instructor: T_{1/2}= 2.6 minutes) - Stopwatch
- Lead absorber plates (one with 1 mm thickness, 6 with 3 mm thickness) (5 sets per lab)

**Although none of the radioactive sources in this experiment are dangerous it is important that they are returned to the TA at the end of the lab. Also absolutely no food must be consumed in the lab, and you should wash your hands before eating after handling radioactive sources and the lead plates.**

A common radiation detector (a “Geiger counter”) will be used in these experiments to count γ-rays. Measurements will be made on:
I. Fluctuations in random counting rates.
II. γ-ray attenuation in an absorbing material, and
III. the half-life of a γ-decaying excited state of the nucleus ^{137}Ba .

A sketch of a Geiger counter is shown below:

The principle of operation is simple: energy loss or absorption of any type of radiation that enters the counter gas results in free pairs of electrons and positive ions. Due to the voltage applied across the counter, electrons move toward the anode (charged positive), and ions toward the cathode (charged negative). The transient current due to the moving charges through the resistor R appears as a voltage pulse. These pulses are fed into a “scaler” which registers each count on a neon display tube. There are two slightly different Geiger counters in the labs, but their operation is extremely similar.

As there are only 5 sets of lead plates per lab you may have to do part II before part I. Your TA will organize which part you will do first.

Measurements of random events are always subject to fluctuations in the number actually measured. Nuclear decay is a random process, i.e. it is impossible to predict exactly when a given nucleus will decay. Only averages can be predicted, e.g. “on average, in this sample 10 nuclei decay every second”. If one measures the number of counts accumulated in the same time interval (which is chosen to be small compared to the half life of the radioactive nucleus – see Ch24 sheet 23) repeatedly, one finds that this number of counts, , fluctuate about an average, . On average, nuclear decay behaves according to Poisson statistics. This means that about 2/3 of the measurements will yield a number of counts, , which lies in the interval (where the “Standard Deviation”, the “statistical error” of is . This represents the absolute error in the count due to statistics from nuclear decay being a random process). In Part I, you verify these assertions and in Part II and III you use for as the statistical error for a number of counts, .

In this part you use a long-lived radioactive source (^{137}Cs , T_{1/2} = 30 years) to study fluctuations in random counting rates. For this part of the lab you measure and record the number of counts every ten seconds continually for 10 minutes. The half-life of the source chosen is 30 years, which is large compared to the duration of your experiment. This is necessary to keep the average counting rate constant during the experiment.

Turn the Geiger counter voltage on. The HIGH VOLTAGE should be at ~600 V. Do NOT change this setting during your experiment! It will distort your data if you do.

Notice the counter counts, even when the radioactive source is far from the counter. These are “background counts”. Count the background for 5 min with the source far removed from the counter and **write it down.** You will need this background count later in Part III.

In this part you ignore the background, which has a constant counting rate as the source has. If they counting rate for the background is constant, then it will have the exact same effect on each 10 second interval, so you do not need to consider the background for this part of the experiment.

Position the ^{137}Cs source such that you get roughly 60 counts/min. You will have to place the source about 15 cm away outside the counting box in order to get this rate. Make sure you leave the source in this position during Part I of this experiment or else you will change the average count rate, which will result in incorrect data.

Now, working with a partner, observe the number of counts displayed over a period of 10 minutes, or 600 seconds. Use the continuous or manual mode for this measurement. In this period, one of you should watch the counter for the entire period. At each 10 second interval, read the number of counts off of the counter. Your partner should record this number (They can do it directly in to the spreadsheet). At the end of the 10 minutes, you should have 60 data points. Make sure you are taking this data continuously (No Stopping!) over the 10 minute time interval.

Once you have collected your data, if you have not done so already, enter it in the excel sheet. You should notice that the count number you recorded each 10 seconds represents the total count up to that point, and not the count in the previous 10 second interval, which is what you need to use to analyze your data. The computer will calculate this quantity for you. The sheet now calculates the frequency of occurrence of each number of counts/10secs and plots it as a histogram. (This is similar to the way we display your grades, for each score, (scores are on the horizontal axis), the histogram plots the frequency on the vertical axis)). The sheet also calculates the average count and plots the Poisson distribution based on this average. You should satisfy yourself that the Poisson distribution is a good fit to the data. The sheet also calculates and shows lines on the graph which mark the interval . Is it true that about 2/3 of the number of counts/10sec measurements lie between these lines?

In part II you verify that the number of γ-rays that penetrates an absorbing material decreases exponentially with the material thickness. This happens because, unlike charged particles, γ-rays do not lose energy continuously, but either pass through the material or are absorbed. The number of γ-rays that are absorbed, i.e. the decrease in the number of γ-rays after traversal of a thin layer of material, is proportional to the number N of γ-rays incident to the material and the layer thickness . One writes where λ is a proportionality constant called the “absorption constant” which depends on the material density, composition, and γ-rays energy. This equation looks exactly like the equation describing radioactive decay (see Ch24 sheet 22 and 23) if one simply replaces and with and . There λ is the decay constant. Thus, the number of γ-rays present after traversing a thickness of material is , where is is the number of γ-rays incident.
In this part you use the long-lived radioactive source (^{137}Cs, T_{1/2} = 30 years) to study absorption of γ-rays. There are 5 sets of Lead absorption plates available for this part. Each set includes a 1 mm plate and 6 plates 3 mm thick. Since there are not enough sets of plates for every group, they will have to be shared, so you may have to collect data for this part of the experiment before you do Part I.

Place the source holder in the bottom slot of the counting box and cover it with the 1 mm thick plate. The source emits γ and β rays (electrons emitted by the nucleus) and you want to eliminate the “background” β rays for this part, in order to study the absorption of γ rays. The β rays are stopped by the 1 mm plate and most of the γ rays penetrate through it.

**Define the measurement with the 1 mm thickness only as absorber thickness “0”. You do not count the 1 mm plate when you calculate the thickness of the subsequently added absorber plates.**

Add one lead plate over the source and 1 mm plate. Count for 1 minute and record the number of counts. Continue to add lead plates one at a time until you have used all the plates. Again, count for 1 minute each time you add an additional plate and enter the data on the sheet for Part II on the Excel Sheet.

The sheet will calculate the error in each measurement ( ) and plot counts/1min against absorber thickness. It will also fit it to an exponential function, , allowing you to work out the absorption constant λ. Does the fitted line pass within most of the error bars? When you have the absorption constant write it on the board at the front of the lab so that you will be able to compare all the different values that are obtained by different groups of lab partners.

In part III, you measure the half-life, T_{1/2} , of an excited state of the ^{137}Ba nucleus. The half-life is of the order of minutes, a convenient time for this experiment. Your instructor will prepare the source for you when you are ready for this part of the experiment

Set up your Geiger counter so you can begin counting right away when your TA gives you the source. Count for 10 time intervals of 30 seconds each. As in Part I, these time intervals should be continuous, so you should count for 5 minutes, recording the number of counts each 30 seconds. Enter your cumulative counts on to the sheet for part III on the Excel Sheet, which will then calculate the counts per ~30 sec time, given by the symbol N.

In Part I you collected background counts for an interval of 5 minutes. In this part of the experiment you will be observing time intervals of 30 seconds. Using the background counts you collected, determine the number of background counts per 30 seconds and enter this in the box on the Excel Sheet. This number will be subtracted from your recorded data and the result will be plotted against time and fitted to . Does the fitted line pass within most of the error bars?

You can get the decay constant λ from the fit to as you did in Part II for the absorption constant.

The half-life T_{1/2} from is (Ch24 sheet 23).

Calculate the half-life and write it on the board at the front of the lab so that you will be able to compare all the different values that are obtained by different groups of lab partners.