Answer to Question #4307 Submitted to "Ask the Experts"

At Oak Ridge National Laboratory, I have a small plastic bag of DAW (dry active waste) (paper, plastic, PPE) weighing approximately 10 lbs. It contains a 50/50 mixture of ¹³⁷Cs and ⁹⁰Sr. The contact dose rate is 900 mR/hr closed window. I can calculate the cesium gamma activity but how do you calculate activity from a pure beta emitter such as ⁹⁰Sr?

You state that you are able to calculate the cesium activity, presumably based on the closed window reading obtained. You also state that the waste is a 50/50 mixture of ¹³⁷Cs and ⁹⁰Sr. I am not clear as to what the 50/50 means. If it refers to the distribution of the respective activities of the two radionuclides then it would be a simple matter to equate the ⁹⁰S activity with the ¹³⁷Cs activity that you determined from the measurement. I assume that the 50/50 is not an accurate estimation of the activity distribution, and you are looking for a technique to evaluate the ⁹⁰Sr activity based on additional measurements. This is not so simple. While the ¹³⁷Cs activity can be estimated from a measurement of exposure rate at some fixed distance from the bag (for a small bag with negligible attenuation of the gamma radiation this is most easily done by placing the detector at a distance from the center of the bag equal to at least three times the maximum bag dimension, assuming a point source geometry, and using the gamma ray exposure rate constant, Γ, in an appropriate expression that relates activity to exposure rate, X, and distance, [e.g., A = Xd²/Γ]). One may also do attenuation corrections if felt necessary and if one has a reasonable understanding of how the activity is distributed in the bag.

For the beta-emitting ⁹⁰Sr and its daughter ⁹⁰Y, the situation is more difficult, as you imply, because the measurement itself is more difficult to make and the attenuation of the beta radiation within the bag contents usually cannot be neglected. Two rather extreme geometries that we might consider for ⁹⁰Sr activity distribution within the bag are (1) a small (point) source of activity localized somewhere within the bag and (2) a more or less uniform distribution of activity throughout the waste volume in the bag. For the kind of waste you describe the second geometry may be more appropriate since I assume that the activity may be spread among the various dry materials within the bag. If we assume a weight of 10 pounds and a reasonably small bag size, say something with linear dimensions in the one- to two-foot range, and that the ⁹⁰Sr activity is uniformly distributed throughout the bag contents, we can apply a principle called energy spatial equilibrium (ESE) to relate a measured dose rate at the bag surface to the ⁹⁰Sr activity. This does require being able to make a reasonable measurement of the beta dose rate at contact with the bag surface. You said you made a closed window measurement of the ¹³⁷Cs exposure rate at contact. This leads me to believe that you probably used an ionization chamber type instrument that has a movable attenuator that can be moved to an open-window position. Such instruments are often used for gamma- and beta-radiation measurements, closed window for the gamma and open window for beta plus gamma. In practice the soft tissue or air beta dose rate is usually estimated by subtracting the closed window reading from the open window reading and multiplying the result by a correction factor, a number usually greater than one that accounts for under-response to the beta radiation. This correction factor may be available from the instrument manufacturer or it may be evaluated by the user through measurements of known radiation sources/fields. It is important to evaluate the thickness of the attenuator used in the closed window reading to ensure that the thickness is greater than the range of the beta radiation being assessed so that the beta radiation does not contribute to the closed window reading.

Let us assume that you have made the required measurements at the bag surface and have established a beta dose rate of D mrad/hr at the bag surface; we will now apply the principle of ESE to estimate the ⁹⁰Sr activity. We shall assume further that the bag wall itself contributes negligible attenuation and that ⁹⁰Y is in secular equilibrium with the ⁹⁰Sr so that equal activities of both radionuclides are present. The ESE principle, as applied to beta radiation, states that at any point within a uniform volume source, such point being removed from any source boundary by at least the range of the beta radiation being emitted, the beta energy absorbed per unit volume will be equal to the beta energy emitted per unit volume. At the surface of such a volume source the energy absorption rate will be approximately 1/2 of what it is at the point within the volume, since source material will be present only on one side of the dose point (2 π geometry as opposed to 4 π geometry). This energy absorption rate will likely be somewhat high because of the lack of backscatter material outside the bag. If A_Sr is the ⁹⁰Sr activity in the bag, and it is distributed uniformly among a mass, m, of material in the bag, the ⁹⁰Sr activity mass concentration is given by C =  A_Sr/m. We will assume that the units of C are curies/g. ⁹⁰Sr emits beta radiation with an average beta energy of 0.196 MeV and ⁹⁰Y emits beta radiation with an average energy of 0.935 MeV. The expected beta dose rate at the bag surface is then

D = C(3.7x10¹⁰ s^-1 Ci^-1)(0.196 MeV + 0.935 MeV)(1.6x10^-6 ergs MeV^-1)(1 rad/100 ergs-g^-1)(3600 s/hr)/2 .

The division by 2 is to account for the reduced dose rate at the surface compared to internally in the bag. For a determined value of D (in rad/hr), we may solve the above expression for C, and from this we can obtain the ⁹⁰Sr activity, A_Sr. There is an implicit assumption here that the dose rate in the material in the bag would not be significantly different from the dose rate in soft tissue if the latter replaced the mass of material in the bag. For the low atomic number material you cite, this assumption is reasonable. As an example, let's assume that you measured a beta dose rate of 1.3 rad/hr at contact. Using the above equation we solve for C and obtain C = 1.08x10^-6 Ci/g; since A_Sr = Cm and, for m = 4.54x10³ g (10 pounds), we obtain A_Sr = 4.9x10^-3 Ci = 4.9 mCi. (Note that we did not include the contribution from the cesium-137 beta emission and the conversion electrons from the metastable barium-137 daughter in the above  expression for beta dose rate. The combined average beta plus conversion electron energies are 0.248 MeV, and their contribution to dose rate could be accounted for using an equation analogous to the above but with the energy terms replaced by this value and with C equal to the cesium mass concentration.)

There are other possible approaches that one might adopt if it is known that the activity is localized at discrete spots in the bag, but they require making assumptions as to where the activity is within the bag. If you have access to the beta dose code Varskin 3 (recent version completed to upgrade/replace the earlier Varskin Mod 2), written by Jim Durham and intended for use in estimating skin doses from beta and gamma sources, you can play some games with various source geometries and source activities to evaluate possible ranges of activity that might be present. The code is intended primarily for doing skin dose estimations when activity is on the skin or on protective clothing, but it can be used for other situations as well. The code may be purchased from the Radiation Safety Information Computational Center at Oak Ridge National Laboratory. The Web site to order the code is http://www-rsicc.ornl.gov/. Select the letter "V" on the Package index line, and it will lead you to the page for ordering the code. I hope this proves helpful to you. 

George Chabot, PhD, CHP