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.

Object

To measure the decay constant of a typical short-half-life radioisotope.

Procedure

A "short" half-life gamma-ray emitting sample will be irradiated in the reactor for use. Following the instructions of the reactor operator and/or the instructor:

1. Extract the sample from its holder, using tweezers, and transfer the sample to the sample tray of the counter.
2. Monitor the transfer process with a portable detector.
3. Take successive one-minute counts of the sample, noting the starting time of each count.
4. Plot cpm vs. clock time as you take data (semi-log plot).
5. 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 decay constant for the radioisotope.
3. Does the value agree with published data?
4. Does the data generate straight lines? If not, why not?
5. Calculate the detector efficiency from the lab standard source.
6. Use the data to calculate the activity of the sample at the time t=0.
7. Determine the number of radioactive atoms in the sample at t=0.