Teach lesson
Radiation intensity and distance
Measure how detector counts change with distance and test an inverse-square model.
Sign in with an educator account to prepare a class session. Students join with a class code.
New to LabsLand? Create your teacher account
Learning Outcomes
Correct repeated counts for background.
Test inverse-square behaviour using a transformed graph.
Apply and explain an ideal point-source model.
Student activity preview
Activity Content
Preview only. In a class session, students can fill in responses and submit their work to the teacher.
Measure background and source counts
30 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
Change the distance between source runs; keep the source, absorber and counting time fixed. Schematic, not to scale.
Keep the source, absorber and counting time unchanged while you vary distance. The corrected count is a measure of detector response under these fixed conditions.
Open the Radioactivity lab
Open the lab and use basic mode throughout this investigation. Follow the background settings below first, then measure the six source distances one at a time.
After changing a source or absorber, recheck the distance, duration and number of repeats: the lab may reset these controls.
First select basic mode, source None, absorber None, distance 15 mm, duration 10 s, and 3 repeats. Start the experiment and record the three separate results. Leave the absorber out. Calculate the mean background count: add the three counts and divide by three.
Background counts
Fill one row per result. Record pulses in 10 seconds, not pulses per second.
| Trial | Pulses in 10 s |
|---|---|
Calculate the mean background count, B, in pulses per 10 s. Show your calculation.
Now select Strontium-90, no absorber, 10 s and 3 repeats. Start at 70 mm, then repeat at 50, 40, 30, 25 and 20 mm. For each distance, record all three counts before changing the setting.
Calculate the mean M and the background-corrected count C:
$$M=(N_1+N_2+N_3)/3,\qquad C=M-B.$$
Counts at six distances
Fill all six rows. Each raw count covers 10 s. Calculate the mean and subtract your mean background; the last column is supplied for plotting.
| Distance (mm) | Count 1 | Count 2 | Count 3 | Mean / 10 s | Corrected / 10 s | 1/r² (m⁻²) |
|---|---|---|---|---|---|---|
Test the distance relationship
25 min
Use your corrected counts at 25 mm and 50 mm. Calculate C(25 mm)/C(50 mm). How many times smaller is the count when the distance doubles? Check the 20 mm and 40 mm pair too, then suggest a relationship between count and distance.
An ideal point source emitting uniformly in all directions suggests the model
$$C=\frac{k}{r^2}=k\left(\frac{1}{r^2}\right).$$
If this model describes the experiment, plotting C against 1/r² should give points close to a straight line through the origin. Use your measurements to test this prediction; do not force the points onto the predicted line.
Graph: corrected count against reciprocal square distance
On graph paper or in a graphing tool, plot all six points. Label the horizontal axis 1/r² (m⁻²) and the vertical axis corrected pulses per 10 s. Start both axes at zero and choose a scale that uses the space well. Draw a reasonable best-fit line without forcing it through the origin. Use Insert image in the answer toolbar for a clear PNG/JPEG image, or Attach file for a PDF.
Does your graph support the inverse-square model over the distances tested? Refer to the line, its intercept and any points that do not fit well.
Explain and apply the model
25 min
The same bundle of rays spreads out
The cross-sections intercept the same bundle of rays. Their linear dimensions increase in proportion to distance.
Use the diagram to explain why an ideal point-source intensity decreases with the square of distance.
Imagine handling a source with 12 cm tweezers instead of holding it directly, with your hand about 0.5 mm away. In an ideal point-source calculation, compare these two distances. By what factor does the distance increase, and by what factor does the model predict the intensity decreases? Show the unit conversion.
This very close-distance calculation illustrates the model. It does not establish a safe handling procedure or the actual dose to a hand.
For the next calculation, assume a point source of activity 100 kBq emits one particle per decay, uniformly in all directions. A non-absorbing cube has the source at its centre. Set a hypothetical design target of 4 particles per second per cm² on an imaginary sphere at the distance of the nearest face. This is a mathematical target, not a transport rule. Use the sphere area 4πr², with r in cm.
Calculate the minimum cube edge length in this model. First find the required radius r from the source to the nearest face, then relate r to the cube edge.
Turn this preview into a live class session
Continue to LabsLand Teach to use this lesson with your students and review the access available to your account.
New to LabsLand? Create your teacher account