Answer to Question #2835 Submitted to "Ask the Experts"

I'm looking for a formula to use to calculate the amount of activity left in garbage and linen bags using the dose rate of these bags after an ¹³¹I therapy case (I need to dispose of them as waste).

There is a fundamental relationship between dose rate and the activity of a radionuclide resulting in that dose rate. However, for your question that relationship is dependent on the characteristics of the source, such as whether there is a single point source in the bags or whether is it distributed on materials in the bags, the density of the materials in the bag, the size and shape of the bag, and the distance from the bag at which the dose rate is measured. Therefore, a formula for this calculation must be specifically designed for the specific conditions at your facility.

The most fundamental relationship between activity and dose rate exists for a point (that is, small physical size) source. A point source of ¹³¹I has the following relationship:

1 Ci of ¹³¹I gives 283 mrem/hr one meter away from the source.

The dependence of dose rate on distance from a point source follows the inverse square law which is

H(2) = H(1) x [d(1)/d(2)]²

where

H(2) = dose rate at a second distance
H(1) = dose rate at a known distance
d(2) = the second distance
d(1) = the distance of the know dose rate

Therefore, the dose rate from 1 Ci of ¹³¹I at 2 meters is

H(2m) = 283 mrem/hr x [1 m/ 2 m]² = 283 mrem/hr x [1/4] = 70.8 mrem/hr

If the dose rate from your bags of contaminated materials varies by the inverse square law, the source appears as a point source regardless of its actual configuration and the relationship above can be used to calculate the activity of the bag. (You can tell if it follows the inverse square law by taking a dose rate at a known distance and see if the dose rate is 1/4 that value at twice the distance) The formula for this relationship is:

Activity (Ci) = [H(1m)/283] where H(1m) = dose rate in mrem/hr at 1 meter from the bag. If the dose rate does NOT vary by the inverse square law, then the size and material characteristics of the source are coming into play and a professionally developed relationship needs to be developed.

Regardless of whether you can use the point source formula or not I HIGHLY recommend you have a professional health physicist review your specific needs and provide you with a method to relate dose rate measurements to activity in the bags. You can find a health physicist in your area by contacting your State Radiation Control Program and asking for help or advice.

Keith H. Dinger, CHP