Physics and Engineering of Radiation Detection

16 Chapter 1. Properties and Sources of Radiation

versus time in such a case will deviate from a straight line of single isotopes. The
best way to understand this is by assuming that the composite material has one
effectivedecay constant. But this decay constant will have time dependence since as
time passes the sample runs out of the short lived isotope. Hence equations 1.3.20
and 1.3.21 will not be linear any more.
Figure 1.3.3 shows the activity plot of a composite radioactive material. Since
we know that each individual isotope should in fact yield a straight line therefore
we can extrapolate the linear portion of the graph backwards to get the straight
line for the isotope with longer half life. We can do this because the linear portion
shows that the shorter lived isotope has fully decayed and the sample now essentially
contains only one radioactive isotope. Then the straight line for the other isotope
can be determined by subtracting the total activity from the activity of the long
lived component.

ln(A)

Time

Slow decaying component

Fast decaying component

Measured activity

Figure 1.3.3: Experimental de-

termination of decay constants

of two nuclides in a composite

decaying material.

Example:

The following table gives the measured activity in counts of a composite ra-

dioactive sample with respect to time. Assuming that the sample contains two

radioactive isotopes, compute their decay constants and half lives.

t(min) 0 30 60 90 120 150 180 210 240 270 300

A(cts/min) 2163 902 455 298 225 183 162 145 133 120 110

Solution:

Following the procedure outlined in this section, we plot the activity as a

function of time on a semilogarithmic graph (see Fig.1.3.4). It is apparent from

theplotthataftert= 120 minutes ln(A) varies linearly with time. Using least

square fitting algorithm we fit a straight line through points betweent= 150

andt= 300 minutes. The equation is found to be

ln(A)=− 3. 28 × 10 −^3 t+5. 68.