Teach lesson
Statistical variation in radiation counts
Collect 30 counts, construct a histogram and compare the spread with a counting model.
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Learning Outcomes
Record and organise 30 observations at fixed settings.
Choose equal-width histogram bins.
Compare individual-count spread with the square root of the mean.
Student activity preview
Activity Content
Preview only. In a class session, students can fill in responses and submit their work to the teacher.
Collect 30 observations
25 min
You will use a Geiger-Müller detector to count pulses from a radioactive source. Each result is the number of pulses detected during 10 seconds, not a dose measurement. You work remotely and do not handle radioactive material. The lab plays recorded experiments with real apparatus and their measured results. After a run, select or hover over each result bar to read its exact count. Record the numbered results in order, rather than estimating from bar lengths. Copy each completed result into your table before starting another run. If the lab timer runs out, return to this activity and choose Open lab again, then restore your settings and continue from your next empty row.
Source, detector and counter
Keep the source, distance and counting time fixed while collecting repeated counts. Schematic, not to scale.
Even with unchanged settings, radioactive decay and detection produce varying counts. Your task is to investigate the spread of individual counts around their mean.
Open the Radioactivity lab
Select basic mode, Strontium-90, no absorber, 20 mm, 10 s, and 5 repeats.
Start a display and record its five individual results in the next five rows of the table.
Compare each new group of five counts with the groups already recorded. If all five counts match an earlier group in the same order, skip that replay and request another display.
Continue until you have six different groups and 30 counts. Keep every setting unchanged and record each accepted group in the order shown. Keep unusual results; skip only exact repeated groups.
The lab chooses among recordings you have not yet seen at these settings before repeating them. Still compare complete groups to avoid counting a replay twice. An equal individual count is normal and is not a reason to discard a group. If repeated groups prevent you from reaching 30 counts, ask your teacher rather than inventing values.
Thirty observations
Fill all 30 rows in order: five individual counts from each of six different groups. Record counts, not the displayed mean.
| Observation | Group | Pulses in 10 s |
|---|---|---|
Calculate the mean and choose categories
15 min
Calculate the mean of your 30 counts. Show the sum and the divisor. Retain extra digits for the following calculations.
Choose ten categories of equal width that include every observation. For integer counts, categories such as 321-330, 331-340 and 341-350 each contain ten possible values. Choose limits suited to your own results. Each count must belong to exactly one category.
Frequency table
Use ten equal-width categories spanning your observations, including empty categories with frequency 0. Both limits are inclusive; adjacent categories must not overlap. The frequencies must sum to 30.
| Category | Lowest count included | Highest count included | Number of observations |
|---|---|---|---|
Draw and annotate your histogram
20 min
Draw a histogram with count categories on the horizontal axis and number of observations on the vertical axis. Use touching bars because the categories form a continuous sequence. For integer counts 321-330, draw bin boundaries at 320.5 and 330.5.
Blank histogram grid
Use this grid as a drawing guide, or create your own axes. Add the category boundaries and a frequency scale that fit your results.
For a Poisson counting model, the standard deviation of individual counts is the square root of the true mean. Estimate it using your sample mean:
$$\widehat{\sigma}=\sqrt{\overline{N}}.$$
Draw a solid vertical line at your mean. Draw dashed vertical lines at the mean minus its square root and the mean plus its square root.
Calculate the comparison interval
Calculate all three values using your unrounded mean. Record at least one decimal place.
| Quantity | Value (counts) |
|---|---|
Your annotated histogram
Submit one clear photograph or exported graph showing your ten bars, both labelled axes, the solid mean line and both dashed interval lines. Use Insert image in the answer toolbar for PNG/JPEG, or Attach file for a PDF. Choose an axis scale that allows all three lines to be shown.
Using the original 30 values, count how many fall between your two interval limits, including the endpoints. Calculate this as a percentage of 30 and show the calculation.
Compare with the statistical model
10 min
For a normal distribution, approximately 68.3% of values lie within one standard deviation of the mean. This is a useful approximation to a Poisson distribution when its mean is sufficiently large. A set of only 30 observations is not expected to give exactly this percentage.
Calculate the absolute difference between your percentage and 68.3%. Give the result in percentage points.
Explain why your percentage may differ from 68.3%. What kind of additional measurements would make the comparison more informative? Include what repeated lab displays can and cannot add.
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