Answer to Question #126567 in Atomic and Nuclear Physics for Vidurjah Perananthan

Question #126567
In a cupboard at the Department of Physics you will find an old Strontium preparation 90Sr which
is 14 years old. A protocol showed that the activity was then measured at 2780 pulses / minute at a background radiation of 210 pulses / minute. The half-life of strontium 90 is 29.1 years.
How many pulses should be measured today, if the background radiation is the same now as then?
1
Expert's answer
2020-07-17T08:40:46-0400

The activity (pulses/minute) of the radioactive sample obeys the radioactive decay law:


"A(t) = A_02^{-t\/T}"

where "A_0 = 2780\\space pulses\/minute" is the initial activity, "T = 29.1\\space years" is the half-life of strontium 90 and "t = 14\\space years" is a time.

Thus, the activity after 14 years will be:


"A(14) =2780\\cdot 2^{-14\/29.1}\\approx 1992\\space pulses\/minute"

In order to calculate the total pulses we should add the background radiation:


"A_{tot} = 1992+210=2202 \\space pulses\/minute"

Answer. 2202 pulses/minute.


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