COMPOUND RADIOISOTOPIC DECAY

Table of Contents

• Discussion
  
• Object
  
• Procedure
  
• Report

Discussion

The activity of a sample containing a single radioisotopic species will decay according to the following relationship:

Where:

• alpha = Sample activity, dps
• alpha_i = Sample activity at time t=0, dps
• t = Elapsed time, s

Note that at any time, the activity can be represented as:

Thus, N, the number of radioactive atoms in the sample can be easily computed.

When the radioisotope is counted by a detector, the count recorded during an interval of time t_c is proportional to the activity, the count time, and the efficiency of the detector.

If C₁ counts are recorded at t₁, and C₂ recorded at t₂, then:

where:

Taking the natural log of both sides of the expression, we obtain:

Which has the form y = B - Ax, and we realize that a plot of C vs. t would be linear on semi-log paper, provided:

• The source-detector distance and geometry remain constant during the measurements,
• Only one radioisotope contributes to the count, and
• Dead-time corrections for high count rates are applied, if required.

If two radioactive species are present in the sample, each will contribute to the count rate. If the half-lives of the components are reasonably different, a plot of activity vs time will appear as shown, with the longer-lived species determining the long-time behavior.

Projecting the long-time behavior linearly back to the t=0 line yields the dotted line shown.

Subtracting the values along that dotted line from the values on the solid data line above it will yield the contribution of the shorter-lived component. Plotting those values as shown will permit evaluation of the half-life of that component.

Object

To measure the decay constants of a two-component radioactive sample.

Procedure

A sample containing two gamma-ray emitting radioisotopes will be irradiated in the reactor for use. Following the instructions of the reactor operator and/or the instructor:

• Extract the sample from its holder, using tweezers.
• Transfer the sample to the sample tray of the counter.
• Monitor the transfer process with a portable detector.
• Take successive one-minute counts of the sample.
• Note the starting time of each count.
• Plot cpm vs. clock time as you take data (semi-log plot).
• Remove the foil, and, using one of the laboratory (small) sources which has a similar energy gamma (or beta), take a count to establish detector efficiency.

Report

1. Plot the data (cpm vs time) on semi-log paper.
2. Calculate the individual decay curves using the previously described technique.
3. Calculate the decay constant and half-life for each component.
4. Calculate the detector efficiency from the lab standard source.
5. Use the data to calculate the activity of each component at time t=0.
6. Determine the number of radioactive atoms in the sample at t=0.
7. Using the half-lifes and physical description of the sample , determine the likely radioactive components.
8. Discuss your conclusions.