Answer to Question #14107 Submitted to "Ask the Experts"

How would one determine the decayed activity for a "mock" or "simulated" iodine-131 (¹³¹I) source containing 0.38 Bq cesium-137 (¹³⁷Cs) and 3.96 Bq barium-133 (¹³³Ba)? The total (effective) activity of ¹³¹I is 3.45 Bq. Would it be more appropriate to use an effective half-life (as you would in biokinetics calculations) or by calculating the decayed activity amount of each isotope and summing them together?

Generally, the useful life of a mock ¹³¹I source of this sort is governed by the ¹³³Ba because its half-life is about three times less than that of the ¹³⁷Cs, and decay-correcting the ¹³³Ba is usually most important to judge whether the source is suitable for your purposes. Additionally, in ¹³¹I decay, the 364 keV photons (simulated by the ¹³³Ba) are about nine times more abundant than the 600⁺ keV photons, making them the greatest contributor to count rate. Decay correcting each radionuclide's activity and adding the activities together does yield the true total activity, but this is not necessarily useful in evaluating how well the source simulates ¹³¹I. The use of an effective half-life is not appropriate. I'll elaborate a bit on this.

The mock source is initially prepared with quantities of the two radionuclides that provide emission rates of the photons of concern, those around 360 keV from the ¹³³Ba and around 660 keV from the ¹³⁷Cs, that are in relative amounts similar to what is expected for the respective 364 keV and 637 keV (the 643 and 723 keV contributions from ¹³¹I may also be included) emissions from an ¹³¹I source of a specified activity. The ¹³³Ba has a 10.5 year half-life while the ¹³⁷Cs half-life is about 30 years. After five years, the gamma emission rate from the barium is reduced to about 72% of its original value while the cesium gamma emission rate is 89% of its original value. This results in the 660 keV to 360 keV ratio being about 25% greater than it should be for an ¹³¹I source. This may be tolerable, depending on your acceptance criteria, as I will attempt to demonstrate in a later example. The disparity increases with passing time. The pertinent question is what level of disagreement between the mock source and an actual ¹³¹I source relative to photon emission rates is acceptable for your purposes. The answer to this depends likely on how you are using the source and how much accuracy is required in your procedure. If you are using it simply in a calibration procedure to determine the iodine counting efficiency using a specific gamma energy such as only the high energy gamma rays (>637 keV) in a gamma spectrometric analysis, then simply correcting the decay of the ¹³⁷Cs activity to obtain the correct photon emission rate may be sufficient to determine the photopeak counting efficiency (of course, in this situation you don't really need a mixed radionuclide mock iodine source since a single ¹³⁷Cs source would suffice). However, if you are doing something like wide window counting, inclusive of most of the gamma radiation spectrum, the efficiency estimations will incur progressively larger errors as the mock source ages and the relative frequencies of the photons of interest change compared to what is expected for ¹³¹I.

Detection efficiencies at specific gamma energies depend on the energy, the detector configuration (e.g., dimensions and solid cylindrical vs. well detector) and the source-detector geometry. As an example of how things might change, I will assume the activities that you cite for the ¹³³Ba and ¹³⁷Cs in the mock source are initial activities, and will assume we are counting with a 7.5 cm × 7.5 cm NaI(Tl) well counter with the standard near the bottom of the well and that we are counting in a wide window that extends from about 250 keV to 775 keV. I shall also assume a detection efficiency of about 0.50 counts per gamma ray for the ¹³³Ba photons that extend from about 276 keV to 384 keV and an efficiency of about 0.25 counts per gamma for the ¹³⁷Cs gamma rays of 662 keV. The photon emission rate of interest from the ¹³³Ba would be about 3,800 min^-1 and the photon emission rate from the ¹³⁷Cs would be about 320 min^-1. The expected count rate, R, would then be R = 0.5 (3800 min^-1) + 0.25 (320 min^-1) = 1980 min^-1. After the source has aged five years, the expected count rate would be R₅ = 0.5 (3,800)e^{-(ln2/10.5)(5)} + 0.25(320)e^-(ln2/30)(5) = 1,440 min^-1. Ideally, we would have liked for the ¹³⁷Cs to have decayed with the same half-life as the ¹³³Ba to maintain the similarity to ¹³¹I. Had that been possible and the entire source activity had been decay-corrected, assuming only the half-life for the ¹³³Ba, we would have obtained an expected count rate. R_A, of R_5A = 0.5(3,800)e^{-(ln2/10.5)(5)} + 0.25(320)e^{-(ln2/10.5)(5)} = 1,420 min^-1. Thus, the error incurred as a consequence of the difference in half-lives between the barium and the cesium is (1,440-1,420)/1,420 = 0.014 = +1.4%, most likely an acceptable error. Even after ten years, for the system we are considering, the error that would accrue by decay-correcting both the barium and cesium activities using the ¹³³Ba half-life would be only about +2.2%.

I do not know specifically what counting system you are using and exactly how you are using the mock standard so you can only use what I have done as representative of an approach to validate the use of the mock source, including decay correction of the source. I have attempted to use values in the example that are realistic.

I hope this is helpful.

George Chabot, PhD, CHP