Calculate count rates and convert their time units
Divide count by observation time and convert counts per second to counts per minute.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Divide numbers.
- Convert minutes and seconds.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is the rate for 120 counts recorded in 60 s?
What you will learn
- Divide count by observation time and convert counts per second to counts per minute.
- Calculate detected count rates with consistent intervals and distinguish an average from event timing.
Divide by the actual interval
Count is the number of recorded events; count rate is count per unit time. A record of 240 counts in 120 s gives 240/120 = 2 counts/s. The same mean rate is 120 counts/min because one minute contains 60 seconds.
A total of 240 counts is not itself a rate. Always retain the observation interval and chosen time unit. When time is given in minutes, divide by minutes for counts/min or convert time to seconds before finding counts/s.
Interpret the average properly
Counts/s and counts/min describe the same mean detection rate when converted consistently. A recorded interval average does not mean that exactly two events arrive every second; individual short-time counts fluctuate.
This Core calculation uses the supplied detected total as given. It does not subtract background unless a Supplement correction is explicitly requested. A detected count rate also differs from source activity, which concerns nuclear decays per second throughout the source.
Sources for this lesson
Pause and explain
A mean rate is 3 counts/s. Must every one-second interval contain exactly three events?
Worked example
A counter records 240 events in 120 s. Find the mean count rate in both listed units.
Show the worked solution
- Divide 240 by 120 s.
- The result is 2 counts/s.
- Multiply by 60 to obtain counts/min.
Answer 2 counts/s; 120 counts/min.
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Test this topic →From guided practice to a new situation
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.
Calculate the rate for 240 counts in 120 s.
Give me a hint
Use count divided by time.
Compare my reasoning
- Count is 240.
- Time is 120 s.
- The quotient is 2 counts/s.
2 counts/s.
Look for these in your work
- Keep the time unit.
- Report a rate rather than a count.
A record has 300 counts in 2 minutes. Find counts/min and counts/s.
Give me a hint
Use the original interval then convert the rate.
Compare my reasoning
- 300/2 = 150 counts/min.
- Divide that rate by 60.
- The rate is 2.5 counts/s.
150 counts/min; 2.5 counts/s.
Look for these in your work
- Keep equivalent rates.
- Use sixty seconds per minute.
A report compares 240 counts in 120 s with 300 counts in 2 min and says the first rate is larger. Check it.
Give me a hint
Convert both records to the same time unit.
Compare my reasoning
- The first rate is 2 counts/s.
- The second rate is 2.5 counts/s.
- The second is larger despite the report.
The second mean rate is larger: 2.5 versus 2 counts/s.
Look for these in your work
- Compare rates, not bare totals.
- Retain equal time units.
Common mistakes
- A count needs a time denominator.
- Multiply by 60 from per second to per minute.
- Mean rate does not give periodic arrival times.
What can you explain now?
How many seconds are in one minute?
Compare with the explanation
60
A minute contains sixty seconds, which sets the conversion between the count-rate units.
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Make it stick
Calculate detected count rates with consistent intervals and distinguish an average from event timing.
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.