Answer to Question #8184 Submitted to "Ask the Experts"
The following question was answered by an expert in the appropriate field:
A radioactive check source has appeared mysteriously on my desk. The source is Na-22, and the activity on 8/1/68 was 3.7 x 105 Bq. Using a GM survey meter, what count rate (cps) can I expect to get from the check source? Additionally, what further evaluation would you conduct on the source?
I recall from an earlier incarnation as the RSO (radiation safety officer) at a university several experiences similar to yours in which sources of unknown origin and history emerged from unexpected locations or appeared without the identifiable presence of another human being. I got to view such occasions as positive events in that the sources found their way to appropriate supervision and control rather than ending up in somebody’s trash or worse. For the case you describe, it does not appear that the impact of whatever fate the source might have suffered would be of undue concern.
Since the half-life of 22Na is 2.61 years, and more than 40 years have elapsed since 1968, there will not be much of the activity remaining. At the current date, there should be about 7.8 Bq present. This amount of activity is not going to produce much of a response on a typical GM detector. You do not specify the type of GM detector, but we can do a simple estimation for a case of a commonly used detector, a pancake-type probe such as the Ludlum Model 44-9 thin-window detector with an active area of 15 cm2 (radius of 2.19 cm).
I shall assume that the source is encapsulated so that the positrons from the 22Na decay lose all their energy in the encapsulation and the annihilation photons (with a yield of 1.8 photons per disintegration) are emitted from the source along with the 1.275 MeV gamma ray associated with the decay. The gamma ray soft tissue dose rate constant for 22Na is about 9.8 x 10-7 μGy s-1 Bq-1 at one cm. If we assume the detector window is centered above the source and that the source may be treated as a point isotropic source, it is easy to show that the dose rate averaged over the facial area of the window is given by
Davg = (AΓ/R2)ln((H2 + R2)/H2),
where A is the source activity in Bq, Γ is the dose rate constant, H is the distance from the source to the detector window, R is the radius of the active window area, and ln refers to the natural logarithm. If we assume a close distance of H = 0.1 cm, and if we use the value above, we obtain
Xavg = [(7.8 Bq)(9.8 x 10-7 μGy s-1 Bq-1 cm2)/(2.19 cm)2]ln((0.12 + 2.192)/0.12)= 9.8 x 10-6 μGy s-1.
If the GM detector had been calibrated in terms of soft tissue dose rate using a 137Cs source, the typical response is 1.98 x 104 cps per μGy-s-1. For the above exposure rate the expected count rate would then be (9.8 x 10-6 μGy s-1)( 1.98 x 104 cps per μGy s-1) = 0.19 cps. Since the typical background reading for this detector is on the order of 0.6 cps, the added 0.19 cps would not be very significant, especially if you were viewing the output rate on an analog display. For an analog ratemeter with a nominal 10-second RC (resistance capacitance) time constant, the relative standard deviation in a background count rate of 0.6 cps is about 30 percent; at the 95 percent confidence level, this would mean that the gross count rate would have to exceed about 0.96 cps before it could be identified as a meaningful, non-background rate. This implies a net count rate of 0.36 cps, which is considerably higher than the 0.19 cps we estimated above. You would likely conclude that the response was not different from background.
If you fed the output of the detector to a digital scaler on which you could select the counting interval, you would have more flexibility that might help in determining the net count rate, but you might require relatively long counting times. For example, if we counted the background and sample each for 15 minutes, the critical net count rate would be about 0.06 cps, implying that we could identify the 0.19 cps as representative of real activity. For a 100-minute counting interval for background and sample, the critical level would be reduced to a net count rate of about 0.02 cps.
If the source had considerably more activity associated with it, I would also recommend taking a surface wipe of the source and analyzing the wipe to determine whether the source was leaking. If this is a plastic encapsulated source and the activity were greater, leakage should be suspected for a source of this age. Given the very low activity currently, I do not feel this is necessary.
The original source activity of 3.7 x 105 Bq was equivalent to the 10 CFR 30.71 Schedule B license-exempt quantity for 22Na, and the current calculated activity of this source is almost 50,000 times less than this. Measurement with a typically accepted GM survey instrument would likely lead one to conclude that the reading was indistinguishable from background, and the source could likely be disposed of as nonradioactive waste. If you do this, however, you must make sure that all markings and symbols that identify the source as radioactive are removed.
One last caveat—if the source is not encapsulated to prevent release of positrons, the above discussion would need modification. In particular, for a point source of 22Na of 7.8 Bq positioned very close to the detector and with no attenuation of the positrons in the source material, the expected positron count rate on a thin-window GM of the type noted above would be roughly 2 cps, a rate that would be easily distinguishable from background. This would clearly alter our conclusions about the presence of detectable activity.
I did not spell out the statistical justifications for the relative standard deviation in the background rate for the analog ratemeter above and the value obtained for the critical level for the digital scaler. If you want more information on these please see the answer to Question 8067 on the HPS Ask the Experts Web site.
George Chabot, PHD, CHP