Correct radiation records with unequal observation intervals
Convert each total to a common rate before subtracting background.
Section 5.2.1 · Detection of radioactivity
Extended only (Supplement); Physics 0625, 2026–2028. Use labelled nuclides, supplied count intervals and stated background conditions. Model drawings are not to scale. Written practice is self-checked.
Before you begin
- Calculate count rate.
- Subtract background in matching units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the background rate for 90 counts in 60 s?
What you will learn
- Convert each total to a common rate before subtracting background.
- Correct unequal-duration observations and pool compatible background exposure consistently.
Give each count its own denominator
When observation intervals differ, raw counts cannot be subtracted directly. Source-present 720 counts in 120 s gives 6 counts/s. Background 90 counts in 60 s gives 1.5 counts/s. The corrected detected rate is 4.5 counts/s.
Equivalently, the estimated background count over 120 s is 1.5 × 120 = 180, so corrected count over that interval is 720 − 180 = 540. Dividing 540 by 120 gives the same 4.5 counts/s. State whether the requested answer is a rate or an interval count.
Combine reference records by total exposure
For background records taken under comparable unchanged conditions, combine their counts and durations before dividing. A record of 60 counts in 30 s plus 90 counts in 60 s gives 150/90 = 5/3 counts/s, not an unweighted mean of rates with unequal durations.
A pooled estimate is valid only when combining compatible conditions; changed shielding or locations can make pooling inappropriate. The calculation remains a statistical estimate of detected background. It is not a biological dose or a universal environmental constant.
Pause and explain
Comparable background records have unequal durations. How should their overall mean rate be obtained?
Worked example
Correct 720 counts in 120 s using background 90 counts in 60 s.
Show the worked solution
- Gross rate is 720/120 = 6 counts/s.
- Background rate is 90/60 = 1.5 counts/s.
- Corrected rate is 6 − 1.5 = 4.5 counts/s.
Answer 4.5 counts/s.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find corrected rate for 720/120 s gross and 90/60 s background.
Give me a hint
Compute both rates in counts/s.
Compare my reasoning
- Gross gives six.
- Background gives one and a half.
- Subtract to obtain four and a half.
4.5 counts/s.
Look for these in your work
- Use both durations.
- State the corrected rate unit.
Pool background 60 counts in 30 s and 90 counts in 60 s under matched conditions.
Give me a hint
Add counts and exposure times separately.
Compare my reasoning
- Total counts are 150.
- Total time is 90 s.
- Mean rate is 150/90.
5/3 counts/s ≈ 1.67 counts/s.
Look for these in your work
- Use exposure weighting.
- Do not average unequal-duration rates unweighted.
For the supplied 120 s gross interval, find the estimated corrected count using 1.5 counts/s background and 720 gross counts.
Give me a hint
Convert background rate back to the gross interval first.
Compare my reasoning
- Background estimate is 1.5 × 120 = 180 counts.
- Corrected interval count is 720 − 180 = 540.
- 540/120 recovers 4.5 counts/s.
540 estimated corrected counts over 120 s.
Look for these in your work
- State the interval.
- Distinguish corrected count from rate.
Common mistakes
- Convert totals to rates first.
- Weight pooled records by duration.
- Do not pool different measurement conditions silently.
What can you explain now?
Can totals from different time intervals be subtracted as though durations match?
Compare with the explanation
No
Each count needs its own observation time before a comparable rate correction is made.
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Make it stick
Correct unequal-duration observations and pool compatible background exposure consistently.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.