Question

A radiation detector records 8700 counts in 1.00 min. Assuming that the detector records all decays, what is the activity of the radiation source in (a) Becquerel and (b) curies?

Short answer

1. The activity of the radiation source in Becquerel is 145 Bq.
2. The activity of the radiation source in Curie is $3.92\times {10}^{-9}\mathrm{Ci}$.

Step-by-step solution

Given data

1. Number of counts recorded by the detector Disintegrations = 8700,
2. Time of record, t = 1 min or 60 s

Understanding the concept of activity of a source  

The strength of a radioactive source is called its activity, which is defined as the rate at which the isotope decays. Specifically, it is the number of atoms that decay and emit radiation in one second. Thus, the counts recorded by the detector are the number of decays or the disintegrations of a decay process.

Formulae:

Activity of the sample,$R=\frac{\mathrm{Disntegrations}/\mathrm{counts}}{\mathrm{time}}...........\left(1\right)$

The conversion of Curie to Becquerel, $1\mathrm{Ci}=3.7\times {10}^{10}\mathrm{Bq}...........\left(2\right)$

a) Calculation of activity in Becquerel

Now, using the given data in equation (1), we can get the activity of the radiation source in Becquerel as follows:

$$\begin{gathered} R=\frac{8700}{60\mathrm{s}} \\ =145\mathrm{Bq} \end{gathered}$$

Hence, the value of activity is 145 Bq.

b) Calculation of the activity in Curies

We have the activity value in Becquerel from part (a).

Now, using equation (2), the activity of the radiation source in Curies can be given as:

$$\begin{gathered} R=\frac{145\mathrm{Bq}}{3.7\times {10}^{10}\mathrm{Bq}/\mathrm{Ci}} \\ =3.92\times {10}^{-9}\mathrm{Ci} \end{gathered}$$

Hence, the value of activity is $3.92\times {10}^{-9}\mathrm{Ci}$.