Give the signal room to spread
Start 12 cm away with gamma radiation and no shield. Double the distance to 24 cm. Predict the new rate before you move.
FIELD NOTE 06 / RADIATION DETECTIVE
The invisible leaves a trace.
What can a handful of counts tell you?
A SOURCE. A SHIELD. A QUESTION.
Start listening to chance.Press Start counting to collect your first sample.
Tracks are symbolic- Counts collected
- 0 counts
- Current expected rate
- — counts / s
- Measurement time
- 0 s
Move a detector, insert a shield and collect a sample. Separate changes in the expected rate from the randomness of individual counts.
Every second tells a slightly different story
Counts in each one-second intervalSample countsExpected counts per second
Read the measurements as a table
| Second | Counts | Expected |
|---|---|---|
| No counts collected yet. | ||
Try a starting point
Ready to explore.
Make a prediction. Change one thing. See what happens.
Model notes & references ↗FOLLOW THE SCIENCE
A pattern you can only see by counting.
A detector records interactions. Even with a steady source and an unchanged setup, counts arrive at unpredictable times. Repeat the same measurement and you will usually get a different number.
Change the distance or shielding and you also change the expected rate. This lab lets you distinguish a physical change in that average from the ordinary variation in a random sample.
A FEW QUESTIONS TO TRY
Let’s see what happens.
Put something in the way
Compare 5 mm of aluminium with 5 mm of lead. Which gives the lower uncollided gamma rate? Try the same materials with beta.
Ask the same question twice
Collect a full interval, then repeat it without changing the setup. Try 60 seconds: do relative fluctuations get smaller?
The source rate and the detector rate are different.
GEOMETRY & TRANSMISSION
What reaches the detector?
A small detector intercepts only part of the emission. Distance reduces that fraction. Material between source and detector can remove radiation from the beam.
COUNTING STATISTICS
What does one run tell you?
For a constant expected rate r over time t, the expected count is m = rt. Independent counts follow a Poisson model with standard deviation √m.
Far from a compact isotropic source, the geometric fraction approaches an inverse-square law. Twice as far means about one quarter of the source counts. The total rate does not follow that law exactly when a fixed background also contributes, or when air attenuation is significant.
| Model | What this experiment represents |
|---|---|
| Alpha | A short-range charged particle, stopped after a small material budget. The teaching model has an abrupt range cutoff. |
| Beta | Electrons with a spread of ranges. The teaching model removes a growing fraction as more material is added. |
| Gamma | 1 MeV photons with exponential removal from an uncollided beam. A thicker shield reduces the average; it does not set an absolute stopping distance. |
Physical ranges depend on energy and material. The qualitative alpha/beta comparisons follow the distinctions described by the Nuclear Regulatory Commission. The gamma calculation uses the tabulated coefficients linked below.
The mathematics, assumptions & references
Geometry and an ideal detector
f = [1 − d / √(d² + a²)] / 2
r = Q f T + b
r = Q f T + b
The source emits isotropically at Q = 20,000 particles or photons per second. The detector is a disk of radius a = 1 cm, facing a point source at distance d. f is its exact solid-angle fraction. Its intrinsic efficiency is set to 100%, so every model particle reaching the disk is counted. Background b = 0.5 counts/s is added independently.
Transmission is evaluated along the central ray for all accepted directions. That approximation is least accurate very close to the disk and near a particle’s stopping range. The shield covers the accepted beam. Tracks are slowed, sparsely drawn symbols; they do not show real speeds or every emitted particle.
Gamma: 1 MeV, uncollided beam
T = exp[−μaird − μshieldx]
μ = (μ / ρ) ρ · Half-value thickness = ln 2 / μ
μ = (μ / ρ) ρ · Half-value thickness = ln 2 / μ
Thickness x is converted from millimetres to centimetres. At 1 MeV, the NIST total mass attenuation coefficients used are 0.06146 cm²/g for aluminium and 0.07102 cm²/g for lead, with densities 2.699 and 11.35 g/cm³. Air uses 0.06358 cm²/g and 0.001205 g/cm³. Gamma attenuation by the thin paper sheet is neglected.
The model counts primary, uncollided photons only. It omits scattered photons returning to the detector, secondary radiation, energy response, dead time, source self-absorption and dose conversion.
Alpha and beta: teaching ranges
These are illustrative range models, not isotope-specific transport calculations. Material budget B is air density × distance plus shield density × thickness, in g/cm². Paper is represented as a 0.1 mm sheet at 0.93 g/cm³.
Alpha: T = 1 if B < 0.0048 g/cm²; otherwise 0
Beta: T = max(0, 1 − B / 0.45 g/cm²)²
Beta: T = max(0, 1 − B / 0.45 g/cm²)²
The alpha budget corresponds to about 4 cm of reference air. The beta formula assumes a chosen triangular distribution of material ranges up to 0.45 g/cm². Applying one mass budget to different materials is deliberately approximate. Energy loss, range straggling, backscatter and bremsstrahlung are not calculated.
Random counts
P(N = n) = e−m mn / n!
m = ∫ r(t) dt · σ = √m · σ / m = 1 / √m
m = ∫ r(t) dt · σ = √m · σ / m = 1 / √m
For a constant setup, m = r t. If you change the setup while counting, m adds up the rate × time for each part of the measurement. Already recorded detections are kept; only future arrivals use the new rate. The gold trace and the table show the expected count for each second under the settings used during that second. For a fixed schedule of rate changes, disjoint time intervals have independent Poisson counts; the total is their sum. The displayed expected spread is a standard deviation of repeated measurements, not a guaranteed interval. Four times the counting time halves the relative standard deviation for an unchanged positive rate.