Topic 4 of 9
Random decay and measured counts
An individual decay is unpredictable, while a large collection has a statistical trend. A detector records counts, which must be interpreted using the observation time, its response and the background.
Spontaneous means nuclear decay does not need an external triggering event. Random means we cannot predict the exact time at which a particular unstable nucleus will decay. Ordinary changes of temperature, pressure or chemical state do not provide a way to set that time in this model.
Activity is not automatically count rate
Activity is the rate of nuclear decays. Its unit is the becquerel:
Detector count rate = recorded counts / counting time
Some emissions miss the detector or are not registered, while background adds other counts. An activity and a count rate therefore need not be numerically equal. Bq is a decay-rate unit, not a radiation-dose unit. Here activity A is distinct from a nuclide's nucleon number A.
Identify the background contribution
Background includes cosmic radiation and natural radionuclides in the environment, materials and bodies. Artificial sources can also contribute. A comparable background measurement excludes the investigated source while retaining the relevant detector and surroundings.
Keep the detector conditions fixed for the background comparison
Measure source-plus-background and background as separate conditions with otherwise comparable settings. Use each actual interval to calculate a rate. The source is absent for background; subtracting an unmatched raw count would not make the rates comparable.
Equal intervals fluctuate around a statistical mean
Each point is a count in 10.0 s. Their mean is 400 counts per interval, giving a total rate of 40.0 counts/s. Scatter about this mean does not by itself imply detector failure or a smoothly falling source activity.
Worked background correction
Convert counts to rates before subtracting
A rate of order 40 counts/s over 10 s gives hundreds of counts; background of order 4 counts/s gives tens. These constructed teaching records describe a source whose expected rate changes negligibly during the short observations. Each interval lasts 10.0 s.
| Interval | Source + background | Background |
|---|---|---|
| 1 | 412 | 38 |
| 2 | 389 | 42 |
| 3 | 405 | 36 |
| 4 | 394 | 44 |
| 5 | 400 | 40 |
Background rate = 200 counts / 50.0 s = 4.0 counts/s
Net source rate = 40.0 - 4.0 = 36.0 counts/s
The corresponding means are 400 and 40 counts per 10.0 s. If durations differ, subtract their rates, not the unmatched raw counts. Pool a stable-rate series using total counts divided by total duration rather than an unweighted mean of unequal-duration rates.
Fluctuations between equal intervals are evidence of the random nature of decay, not proof that the detector is broken. A smooth expected decay curve does not mean each nucleus decays on schedule.
Evaluate the counting method
Compare rates with source-detector positions, absorber, detector window and timing method fixed. A longer observation can reduce fractional random scatter when the expected rate is sufficiently stable, but it can blur a rapid decay change. Repetition does not correct an omitted background, incorrect time interval or changed geometry.
Changing detector efficiency and dead time at high rates can limit the result. Background can fluctuate or drift too. Retain the supplied records and explain a specific limitation rather than deleting points simply to obtain a smoother pattern.