A detector is used to measure the activity of a source with known half-life of 1

Question

A detector is used to measure the activity of a source with known half-life of 1 hour. The peak of the emitted particles (one particle per decay event) is observed and also contaminated by background counts from the environment and cosmic rays. Assume that the net counts corresponding to the real decay events of the source are the same as the background counts under the peak.

(a) How many in total count under the peak do we need if the statistical error of the activity is required to be 10%?

(b) Assume that the detector efficiency is 10% (i.e. it can detect only 10% of all the decay particles emitted in all directions). It takes two hours for the measurement to get the total count under the condition in (a). What is the activity of the source just before the measurement?

Explanation / Answer

Let the real count be N , so the std deviation for 10 accuracy s= 0.1N
The std deviation s is defined as
S= [real N + background N]
According to the problem background = N
So the std deviation s =[2N] = 0.1 N
Solve to get N= 200.

Part b..
Since the efficiency is 10
So the total actual count Nac =10×N
So Nac= 2000.
Decay constant k = 0.693/t.half
So k = 0.693 per hour.
The activity is given by
A= k x Nac = 0.693 x 2000
So A= 1386 per hour

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