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07 November 2009

Answer to Question #1236 Submitted to "Ask the Experts"

Category: Nuclear Medicine Patient Issues — Diagnostic Nuclear Medicine

The following question was answered by an expert in the appropriate field:

I am reinvestigating the validity of the formula used in calculating airborne effluent concentration of ¹³³Xe. Also, I am looking for the calculation method if the air is recirculated.

The formula is derived from the basic one-compartment model where removal occurs at an exponential rate. It is assumed that the material in the compartment is uniformly mixed prior to removal. The equation is the same as that used to calculate the activity of a radionuclide as it decays and determining at what time it reaches a certain activity. Only the variables differ. To calculate the removal of a radionuclide, for example, ¹³³Xe, the variables used in the equation are as follows:

The final activity (C) is given by the derived air concentration (DAC) found in Title 10 Code of Federal Regulations, Part 20, Appendix B, Table 1, Column 3, which is in µCi ml^-1 for that radionuclide;
The original concentration of the radionuclide in the room is the activity (A) in the container or vial in µCi divided by the volume (V) of the room in ml; and
The removal rate constant is the volume of the room (V) divided by the exhaust rate (Q). Again, the equation is solved for the time (t) when the concentration of radionuclide equals the DAC.

For the situation where there is continual recirculation of the air, the removal of the radionuclide would occur as it decays. In this case, the removal rate is the decay constant for the radionuclides, which is 0.693 divided by its half-life.

John Jacobus, MS, CHP

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