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

Question

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?

Answer 1

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.