Answer to Question #11547 Submitted to "Ask the Experts"

We measured International Atomic Energy Agency (IAEA) reference sample IAEA-448 using an ORTEC 3-inch by 3-inch, thallium-doped, sodium iodide (NaI[Tl]) detector to determine if radium-226 (²²⁶Ra) and its daughters lead-214 (²¹⁴Pb) and bismuth-214 (²¹⁴Bi) are in secular equilibrium.

From the measured spectrum, we obtained net counts of each radionuclide. For detector efficiency, standard gamma sources were used.

From our measurements, I'd like to know how I can determine that the activities are the same for:

1. ²²⁶Ra and its daughter ²¹⁴Pb.
2. ²²⁶Ra and its daughter ²¹⁴Bi.

I should note a few concerns I have before proceeding with a description of how the activity would be determined from your results.

Referring to the graphs and data that you sent to me under separate cover, your graph of the pulse-height distribution designates the sample size as 200 grams (g), although it was my impression that the IAEA-448 samples came in 100 g quantities. The values on the efficiency curve that you show appear to be consistent with what one might expect for a very small volume/area source placed close to the center of the flat face of the NaI detector. They do not appear consistent with what I would expect for a relatively large mass sample, such as 200 g. In order to get meaningful results, the geometry and physical characteristics of the standard(s) must be as close as possible to those of the sample(s) being measured.

I note also that you have no efficiency points for any photon energies less than 511 kiloelectronvolts (keV). This makes it very uncertain as to how reliably you can use any gamma energies less than the 609 keV ²¹⁴Bi gamma to estimate activities. You should obtain some efficiency points to cover the lower energies emitted by ²¹⁴Pb and ²²⁶Ra.

I would also recommend that you plot the efficiencies vs. energy on a log-log plot which will likely exhibit smoother behavior, often with a linear portion at the higher energies and a curved portion as energies decrease. The log-log presentation may make it easier to define a fitting function if desired and for interpolating efficiency values.

Also, because the resolution of the NaI detector is not very good, you will get some overlap of some gamma-ray energies lying within a given photopeak’s region of interest as well as photopeak tail overlaps that make for greater uncertainty in the net count analysis. You must be diligent in properly accounting for overlap as you go about calculating your Compton-subtracted net counts.

If you are using samples that have been removed from the original IAEA-448 container, you should ensure that they are well sealed to prevent possible loss of radon gas, which can lead to disturbance of equilibrium among the progeny. If you have repackaged samples, allow at least three weeks to elapse before counting to ensure reestablishment of equilibrium between the progeny and the ²²⁶Ra.

Once you are confident of the counting efficiencies and of the integrity of the samples, it is a simple matter to calculate the activity of any species at the time of counting from your results. For example, for the 609 keV energy from ²¹⁴Bi, the gamma yield (gammas per disintegration of the ²¹⁴Bi) is 0.461. If the determined counting efficiency (counts per gamma of said energy) were 0.15, as I determine approximately by doing a quick log-log plot of your data for 511 keV, 662 keV, and 1,170 keV, the determined activity in becquerels (Bq) for your count (c) of 727,270 in 10,800 seconds (s) would be:

A_214Bi = 727,270 c/[(10,800 s)(0.461γ Bq-s^-1)(0.15 c γ^-1)] = 974 Bq.

Since the usual IAEA quoted ²²⁶Ra activity of the 448 standard is 1.905 × 10⁴ Bq kg^-1, the expected activity for a 200 g sample would be 3.81 × 10³ Bq, almost four times higher than the above value for ²¹⁴Bi, which value we would expect to be equal to the radium activity under secular equilibrium conditions. Doing a similar analysis for the 351 keV photons from ²¹⁴Pb (using a photon yield of 0.371 and an efficiency of 0.48, based on extrapolation of the log-log line to this energy), I obtained an activity of 443 Bq, clearly different from the ²¹⁴Bi result and different from the expected result based on the ²²⁶Ra.

Assuming that the samples were properly packaged so as to ensure equilibrium of the progeny with the radium and that the 200 g sample was used, it seems likely that the efficiencies you are using are not appropriate, as they seem to be considerably higher than the true efficiencies. It is not appropriate to use the relative efficiencies obtained with small sources that exhibit little self-attenuation in an attempt to test for the condition of secular equilibrium between the progeny and the ²²⁶Ra because the effects of attenuation influence the photons of different energies differently so that the relative efficiencies for the small, low-mass standards are different from the relative efficiencies for the high-mass sample.

George Chabot, PhD