It is useful to plot the activity of a nuclide as it changes over time. Plots of this type can be used to determine when the activity will fall below a certain level. This plot is usually done showing activity on either a linear or a logarithmic scale. The decay of the activity of a single nuclide on a logarithmic scale will plot as a straight line because the decay is exponential.

Example:

Plot the radioactive decay curve for nitrogen-16 over a period of 100 seconds. The initial activity is 142 curies and the half-life of nitrogen-16 is 7.13 seconds. Plot the curve on both linear rectangular coordinates and on a semi-log scale.

Solution:

First, use Equation (1-6) to calculate the decay constant corresponding to a half-life of 7.13 seconds.

Use the decay constant determined above to calculate the activity at various times using Equation (1-5).

Plotting the data points calculated above on both linear and semilog scales results in the graphs shown in Figure 11.

Figure l l Linear and Semi-log Plots of Nitrogen-16 Decay

If a substance contains more than one radioactive nuclide, the total activity is the sum of the individual activities of each nuclide. As an example, consider a sample of material that contained 1 x 10⁶ atoms of iron-59 that has a half-life of 44.51 days ( = 1.80 x 10⁷ sec^-1), 1 x 10⁶ atoms of manganese-54 that has a half-life of 312.2 days ( = 2.57 x 10^-8 sec^-1), and 1 x 10⁶ atoms of cobalt-60 that has a half-life of 1925 days ( = 4.17 x 10^-9 sec^-1).

The initial activity of each of the nuclides would be the product of the number of atoms and the decay constant.

Plotting the manner in which the activities of each of the three nuclides decay over time demonstrates that initially the activity of the shortest-lived nuclide (iron-59) dominates the total activity, then manganese-54 dominates. After almost all of the iron and manganese have decayed away, the only contributor to activity will be the cobalt-60. A plot of this combined decay is shown in Figure 12.

Figure 12 Combined Decay of Iron-56, Manganese-54, and Cobalt-60