A radiation measurement experiment uses a radiation detector to measure counting rates and investigate how background radiation, distance, shielding, measurement time, and other factors affect the measured values.
Radiation cannot be seen directly, but it can be detected by using its ability to ionize matter or produce fluorescence. In basic school and university experiments, GM counters and scintillation detectors are commonly used.
Radiation measurements show statistical fluctuations, so repeated measurements under identical conditions do not always produce the same count. Therefore, background-count correction, consistent measurement times, and evaluation of standard deviation are important.
This article assumes an experiment using a GM counter to measure natural radiation and an educational sealed source, and summarizes the introduction, precautions, result items, reference experimental values, calculations, sources of error, example results, and discussion examples.
Caution:
This article is a study reference for discussing results obtained in physics experiments at schools and universities. The experimental conditions and measured values shown here are illustrative examples and are not actual measurement results.
Handle radiation sources in accordance with laws, facility regulations, laboratory manuals, and instructions from the instructor or radiation safety officer. Never disassemble a source, remove it from its container, or bring it unnecessarily close to the body. Follow the basic principles of minimizing handling time, maximizing distance, and using appropriate shielding.
Some GM counters operate at high voltage. Do not touch terminals or internal wiring while energized, and turn off the power before changing connections.
- Basics of Radiation Measurement
- Background Radiation
- Distance and Count Rate
- Attenuation by Shielding
- Statistics of Radiation Counting
- Main Items to Record in the Results
- Reference Experimental Conditions
- Reference Experimental Values
- Calculation Methods
- Calculating Count Rate
- Mean Background Count Rate
- Background-Corrected Net Count Rate
- Standard Deviation of the Count
- Relative Standard Deviation
- Uncertainty After Background Correction
- Calculating Transmission
- Calculating the Attenuation Coefficient
- Calculating the Half-Value Layer
- Checking the Inverse-Square Law
- Main Sources of Error
- Example of How to Write the Results
- Points to Connect to the Discussion
- Discussion Example
- Summary
Basics of Radiation Measurement
A radiation detector converts energy deposited by radiation in matter into an electrical signal or another measurable form.
In a GM counter, radiation ionizes the gas inside the tube, producing an electron avalanche between the electrodes that is recorded as one pulse. The number of pulses recorded during a fixed period is the count.
If the measurement time is t and the count is N, the count rate R is:
R = N/t
Count rate is commonly expressed in cps (counts per second) or cpm (counts per minute).
Background Radiation
Even when no source is present, the detector records radiation from cosmic rays, naturally radioactive materials in the ground and buildings, radon in the air, and other sources.
This is called background radiation or background.
If the total count rate with the source present is Rtotal and the background count rate is Rbg, the net source count rate Rnet is:
Rnet = Rtotal − Rbg
Distance and Count Rate
When radiation from a point source spreads isotropically through space, the amount reaching a unit area ideally decreases in inverse proportion to the square of the distance.
R ∝ 1/r2
Here, r is the effective distance between the source and detector.
In actual experiments, deviations from the exact inverse-square law can occur because the source and detector are not points, as well as because of absorption in air, scattered radiation, background radiation, and an offset in the distance origin.
Attenuation by Shielding
When radiation passes through matter, some is absorbed or scattered, reducing the count rate detected.
For monoenergetic X-rays or gamma rays, the relationship between material thickness x and transmitted intensity I can be approximated by:
I = I0e−μx
Here, I0 is the intensity before shielding and μ is the linear attenuation coefficient.
The same relationship can be applied to background-corrected net count rates.
Statistics of Radiation Counting
Radioactive decay is probabilistic, so repeated measurements under identical conditions fluctuate.
If the count N can be regarded as following a Poisson distribution, its standard deviation is approximately:
σN ≈ √N
The relative standard deviation is:
σN/N ≈ 1/√N
Therefore, increasing measurement time and accumulating more counts reduces the relative fluctuation.
Main Items to Record in the Results
- Type of detector
- Source or object measured
- Measurement time
- Count
- Count rate
- Background count
- Background count rate
- Background-corrected net count rate
- Distance between source and detector
- Shielding material
- Shield thickness
- Transmission
- Attenuation coefficient
- Standard deviation
- Relative standard deviation
- Mean of repeated measurements
- Room conditions
- Applied voltage of the GM counter
- Orientation of the detector window
- Instrument resolution
Reference Experimental Conditions
| Item | Reference condition |
|---|---|
| Detector | GM counter |
| Measurement target | Natural radiation and educational sealed source |
| Measurement time per trial | 60 s |
| Number of repetitions | 5 |
| Distance range | 2–10 cm |
| Shielding | Paper, aluminum plate, acrylic plate, etc. |
| Room temperature | 23 ℃ |
| Detector orientation | Detector window facing the source |
Reference Experimental Values
Repeated Measurements of Background Radiation
| Trial | Measurement time (s) | Count (counts) | Count rate (cps) |
|---|---|---|---|
| 1 | 60 | 19 | 0.317 |
| 2 | 60 | 23 | 0.383 |
| 3 | 60 | 21 | 0.350 |
| 4 | 60 | 18 | 0.300 |
| 5 | 60 | 24 | 0.400 |
Source Measurement and Background Correction
| Trial | Total count (60 s) | Total count rate (cps) | Background count rate (cps) | Net count rate (cps) |
|---|---|---|---|---|
| 1 | 426 | 7.10 | 0.35 | 6.75 |
| 2 | 438 | 7.30 | 0.35 | 6.95 |
| 3 | 419 | 6.98 | 0.35 | 6.63 |
| 4 | 432 | 7.20 | 0.35 | 6.85 |
| 5 | 425 | 7.08 | 0.35 | 6.73 |
Distance and Net Count Rate
| Distance r (cm) | Total count rate (cps) | Background count rate (cps) | Net count rate (cps) | 1/r2 (cm−2) |
|---|---|---|---|---|
| 2.0 | 25.35 | 0.35 | 25.00 | 0.2500 |
| 3.0 | 11.45 | 0.35 | 11.10 | 0.1111 |
| 4.0 | 6.60 | 0.35 | 6.25 | 0.0625 |
| 6.0 | 3.13 | 0.35 | 2.78 | 0.0278 |
| 8.0 | 1.91 | 0.35 | 1.56 | 0.0156 |
| 10.0 | 1.35 | 0.35 | 1.00 | 0.0100 |
Shielding and Net Count Rate
| Shielding condition | Thickness (mm) | Total count rate (cps) | Net count rate (cps) | Transmission (%) |
|---|---|---|---|---|
| None | 0 | 7.15 | 6.80 | 100 |
| Paper | 0.10 | 6.95 | 6.60 | 97.1 |
| Aluminum | 1.0 | 4.43 | 4.08 | 60.0 |
| Aluminum | 2.0 | 2.80 | 2.45 | 36.0 |
| Aluminum | 3.0 | 1.82 | 1.47 | 21.6 |
| Acrylic | 5.0 | 3.75 | 3.40 | 50.0 |
Calculation Methods
Calculating Count Rate
If 426 counts are recorded in 60 seconds:
R = N/t
= 426/60
= 7.10 cps
Mean Background Count Rate
If the background counts are 19, 23, 21, 18, and 24 counts, the mean count is:
Nbg,avg = (19 + 23 + 21 + 18 + 24)/5
= 21.0 counts
Because each measurement lasted 60 seconds, the mean background count rate is:
Rbg = 21.0/60
= 0.350 cps
Background-Corrected Net Count Rate
Rnet = Rtotal − Rbg
= 7.10 − 0.35
= 6.75 cps
Standard Deviation of the Count
For a count of 426, the standard deviation based on Poisson statistics can be approximated as:
σN ≈ √N
= √426
= 20.6 counts
The standard deviation of the count rate is obtained by dividing by the measurement time.
σR = σN/t
= 20.6/60
= 0.343 cps
Relative Standard Deviation
Relative standard deviation = 1/√N
= 1/√426
= 0.0485
= 4.85%
Uncertainty After Background Correction
If the total and background counts are independent and both are measured for 60 seconds, the standard deviation of the net count can be combined as:
σnet = √(Ntotal + Nbg)
= √(426 + 21)
= 21.1 counts
The standard deviation of the net count rate is:
σR,net = 21.1/60
= 0.352 cps
Calculating Transmission
If the net count rate before shielding is 6.80 cps and after shielding is 4.08 cps:
Transmission T (%) = I/I0 × 100
= 4.08/6.80 × 100
= 60.0%
Calculating the Attenuation Coefficient
If a 1.0 mm shield gives a transmission of 0.600:
I = I0e−μx
μ = −ln(I/I0)/x
= −ln(0.600)/1.0
= 0.511 mm−1
Calculating the Half-Value Layer
The half-value layer is the thickness that reduces radiation intensity by half.
x1/2 = ln2/μ
= 0.693/0.511
= 1.36 mm
Checking the Inverse-Square Law
If the net count rate at 2.0 cm is 25.0 cps, the count rate expected at 4.0 cm from the ideal inverse-square law is:
R2 = R1(r1/r2)2
= 25.0 × (2.0/4.0)2
= 6.25 cps
Main Sources of Error
| Source of error | Effect on measurement | Typical tendency in results | Improvement |
|---|---|---|---|
| Statistical fluctuation of radioactive decay | Counts vary under identical conditions | Random differences between measurements | Increase measurement time and repetitions |
| Variation in background radiation | Background correction is not constant | Net count rate becomes too high or too low | Measure background before and after the experiment |
| Measurement-time error | Count-rate conversion becomes inaccurate | Greater effect for short measurements | Use an automatic timer |
| Source-detector distance error | Geometry changes | Count rate changes strongly at short distances | Use a fixed jig and measure effective distance |
| Offset in distance origin | Source center and effective detector surface are misidentified | Systematic deviation from inverse-square law | Confirm effective centers of the apparatus |
| Detector orientation | Effective area changes | Count rate decreases or fluctuates | Face the detector window toward the source |
| Source-position shift | Reproducibility decreases | Repeated values fluctuate | Fix the source with a holder |
| Scattered radiation | Radiation scattered from desks, walls, or shields is detected | Count rate remains high after shielding | Keep surrounding conditions constant |
| Shield-thickness error | Attenuation coefficient is miscalculated | Thickness-count-rate relationship is disturbed | Measure thickness at several points |
| Gaps in shielding | Radiation reaches detector without passing through shield | Transmission is overestimated | Cover the entire detector window |
| GM counter dead time | Some pulses are missed at high count rates | Measured rate is below true rate | Avoid high count rates and apply dead-time correction |
| Applied-voltage variation | Detection efficiency changes | Count rate varies over time | Use an appropriate voltage in the plateau region |
| Differences in detection efficiency | Sensitivity differs with radiation type and energy | Sources cannot be compared directly | Compare using the same detector and conditions |
| Finite source size | Point-source approximation fails | Deviation from inverse-square law at short distance | Measure at distances sufficiently larger than source dimensions |
| Absorption in air | Low-penetration radiation decreases with distance | Rate falls faster than inverse-square law | Use short distances and consider radiation type |
| Contamination of sample or surroundings | Unwanted radiation is detected | Background value increases | Check according to facility management procedures |
Why Counts Differ Each Time
Radioactive decay occurs probabilistically, so the number of atoms that decay during a fixed interval differs slightly each time. Therefore, statistical fluctuations occur even when all measurement conditions are identical.
Why Longer Measurement Times Improve Precision
For Poisson statistics, the standard deviation is √N and the relative standard deviation is 1/√N. Increasing the measurement time increases N, so although the absolute fluctuation increases, the fluctuation relative to the count becomes smaller.
Why Deviations from the Inverse-Square Law Are More Likely at Short Distances
The inverse-square law assumes that the source and detector can be approximated as points. At short distances, the physical sizes of the source and detector window cannot be ignored, and even a small error in effective distance has a large effect on the count rate.
Why the Count Rate Does Not Become Zero Even with Thick Shielding
Even with thick shielding, the total count rate may not become zero because background radiation, radiation scattered by the shield and surroundings, and highly penetrating components that pass through the shield can still be detected.
Example of How to Write the Results
Background radiation was measured five times for 60 seconds using a GM counter. The mean background count was 21.0 counts and the mean background count rate was 0.350 cps.
With the source placed at a fixed distance, the mean total count rate was 7.13 cps, and the mean net count rate after background correction was 6.78 cps.
When the source-detector distance was increased from 2.0 cm to 10.0 cm, the net count rate decreased from 25.0 cps to 1.00 cps. The net count rate was approximately proportional to 1/r2.
In addition, increasing the thickness of the aluminum plate caused the net count rate to decrease exponentially, and the transmission at a thickness of 1.0 mm was 60.0%.
Points to Connect to the Discussion
- How much did the background count rate fluctuate between repeated measurements?
- Was the fluctuation in counts approximately √N?
- Was background correction performed?
- Was the measurement time kept the same for all conditions?
- Was the net count rate inversely proportional to the square of distance?
- Did short-distance measurements deviate from the inverse-square law?
- Was distance measured from the source center to the effective detector surface?
- Did shield thickness and count rate show an exponential relationship?
- Was there an effect from radiation scattered by the shield?
- Could GM-counter dead time be neglected?
- Were detector orientation and source position kept constant?
- Were there enough measurement points and repetitions?
Discussion Example
In this experiment, a GM counter was used to investigate how background radiation, distance from the source, and shield thickness affect the count rate.
When background radiation was measured five times for 60 seconds each, the counts ranged from 18 to 24, with a mean of 21.0 counts.
The counts did not agree exactly even at the same location and for the same measurement time because radioactive decay occurs probabilistically. If the count follows a Poisson distribution, the standard deviation is approximately √N.
For a mean count of 21, the expected standard deviation is about 4.6 counts, and the observed variation was within this range. Therefore, the variation in background counts can mainly be attributed to the statistical nature of radiation counting.
The net count rate due to the source was obtained by subtracting the background count rate from the total count rate. Without background correction, the source count rate would be overestimated, especially at large source distances or with thick shielding.
As the distance between the source and detector increased, the net count rate decreased. It was 25.0 cps at 2.0 cm and 6.25 cps at 4.0 cm, so doubling the distance reduced the count rate to approximately one quarter.
This occurs because radiation emitted from a point source spreads over a spherical surface whose area increases with the square of distance, so the number of particles reaching a unit area decreases in inverse proportion to the square of distance.
Actual measurements may deviate slightly from the inverse-square law. Possible causes include the finite sizes of the source and detector, uncertainty in the distance origin, absorption in air, radiation scattered from the surroundings, and statistical fluctuations in the background count.
Especially at short distances, an error of only a few millimeters in the distance from the source center to the effective detector surface can significantly change 1/r2. Distance should therefore be measured using the effective center of the source and effective detector surface rather than the outer surfaces of the apparatus.
In the shielding experiment, the net count rate decreased as the aluminum thickness increased. This is because radiation is absorbed or scattered in the shielding material, reducing the amount reaching the detector.
The transmission was 60.0% at 1.0 mm, 36.0% at 2.0 mm, and 21.6% at 3.0 mm. Thus, each additional 1.0 mm reduced the transmission by a factor of about 0.60, which is consistent with exponential attenuation.
Because the total count rate after shielding includes background radiation, the background-corrected net count rate must be used when calculating the attenuation coefficient.
The count rate did not become completely zero even with thicker shielding. This can be attributed to background radiation, radiation scattered from the shield, desk, or walls, and highly penetrating radiation components.
At high count rates, GM-counter dead time can also cause error. For a short period after detecting one radiation event, the counter cannot detect the next event, so the measured count rate becomes lower than the true rate.
The count rates in this experiment were not extremely high, so the effect of dead time was considered relatively small. However, dead-time correction may be required when the source is placed too close to the detector.
Measurement precision can be improved by increasing the measurement time for each condition, repeating measurements and taking averages, measuring background radiation before and after the experiment, fixing the source and detector positions, and keeping the detector orientation constant.
In conclusion, radiation counts exhibit statistical fluctuations, making background correction and uncertainty evaluation necessary. The count rate generally decreased according to the inverse-square law as distance increased and showed an exponential decrease as shield thickness increased.
Discussion Example When the Count Rate Was Higher Than Expected
A higher-than-expected count rate may have resulted from the actual source-detector distance being shorter than the set value, failure to subtract background radiation, detection of radiation scattered from surrounding objects, or the source shifting closer to the center of the detector window.
Discussion Example When the Count Rate Was Lower Than Expected
A lower-than-expected count rate may have resulted from the source-detector distance being longer than the set value, the detector window not facing the source directly, unintended shielding between the source and detector, or missed counts caused by GM-counter dead time at a high count rate.
Discussion Example When the Inverse-Square Law Was Not Observed
Possible reasons for deviation from the inverse-square law include measurements made at distances too short to treat the source and detector as points, an offset in the distance origin, absorption in air, background radiation, scattered radiation, and statistical fluctuations in counting.
Discussion Example When Exponential Attenuation Was Not Observed
Possible reasons why shield thickness and net count rate did not show a simple exponential relationship include a non-monoenergetic radiation spectrum, scattered radiation from the shield, gaps in the shielding, errors in thickness measurement, and insufficient background correction.
Summary
In radiation measurement, the count rate is calculated from the number of counts recorded during a fixed time, and the net count rate is obtained by subtracting background radiation.
Because radioactive decay is probabilistic, counts show statistical fluctuations. Increasing the measurement time and repeating measurements reduces the relative fluctuation.
For a point source, the count rate ideally decreases in inverse proportion to the square of distance. Radiation may also attenuate exponentially with shield thickness.
In the discussion, it is important to relate background radiation, statistical fluctuations, distance measurement, scattered radiation, shield thickness, and GM-counter dead time to deviations in the measured values.
