Final answer:
The true count rate of the sample when a detector with a resolving time of 100 microseconds yields 174,000 net counts in a one-minute sample is 4084.5 counts per second.
Step-by-step explanation:
The question at hand deals with determining the true count rate of a sample, given that a detector with a certain resolving time has produced a certain number of net counts within a minute. Specifically, if a detector with a resolving time of 100 microseconds yields 174,000 net counts during a one-minute sample count, to find the true count rate we use the formula:
T = N / (1 - Nτ)
Where:
- T is the true count rate,
- N is the observed count rate,
- τ is the resolving time of the detector.
In this case:
- N = 174,000 counts/min,
- τ = 100 × 10-6 seconds.
To find the observed count rate per second, we divide by 60:
- N (per second) = 174,000 / 60 = 2900 counts/second
Now we apply the formula:
- T = 2900 / (1 - 2900 × 100 × 10-6)
- T = 2900 / (1 - 0.29)
- T = 2900 / 0.71
- T = 4084.5 counts/second (rounded to two decimal places)
This is the true count rate of the sample. Note that deviations from the true rate can occur due to the finite resolving time of the detector.