Answer to Question #3991 Submitted to "Ask the Experts"
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I’d like to know how to calculate the effective dose for building materials, like dimension stones (granite). I’ve got the concentrations of 40K, 238U, and 232Th in a gamma ray spectrometer GS-512 Geofyzika/Scintrex in ppm, and I’d like to get the effective dose in mSv/year. One example of the measurements is eU = 4.2 ppm, eTh=22.4 ppm, and %K=7.3. How do I calculate the effective dose in mSv/year?
While it would be satisfying to be able to tell you that there is a simple relationship between the concentrations of radionuclides in building materials and the doses that they produce, I am not able to do so. I am assuming that your question relates primarily to external dose to individuals, although there may also be internal doses that come about from individuals inhaling or ingesting radionuclides in building materials. Internal doses may be a concern if concentrations of radium are high because radium decay leads to radon gas production, and some radon may be released from the building materials and be inhaled by occupants.
I shall address my subsequent comments to only external dose rates resulting from the radionuclides in the building materials. The external dose results from occupants being exposed to radiations emitted by the radionuclides and escaping from the building materials and irradiating occupants in the building. For the radionuclides you mention the major radiations that contribute to penetrating dose to individuals are gamma rays. Potassium-40, abundant to the extent of 0.0117 percent among all potassium, emits a single gamma ray of 1.46 million electron volts (MeV) energy in approximately one out of every nine decay events of 40K atoms. Uranium includes two major isotopes, 238U and 235U, each of which represents the lead member of a radioactive decay series in which the parent nuclide decays, as do subsequent product nuclei through many radioactive progeny, eventually to stable lead. Uranium-234 is also a uranium isotope that you would find present; it appears in the decay chain for 238U. The many uranium progeny emit a variety of gamma rays of varying energies and yields. The thorium decay chain is headed by 232Th that similarly decays through many radioactive progeny, eventually to another stable lead isotope. Based on the concentrations that you have given for potassium, uranium, and thorium, we can conclude that the contribution from radioactive 40K would dominate the external dose rate, with uranium and thorium and all their progeny contributing lesser amounts. This is so especially because of the high potassium concentration. Indeed, the value of 7.3 percent seems unusually high to me for many rocks, but I shall assume it is correct. You say you obtained the concentrations of 238U, 232Th, and 40K from gamma spectroscopy, but the concentrations you give—4.2 ppm, 22.4 ppm, and 7.3 percent, respectively—I assume are representative of mass fractions, and I use this assumption in the example evaluation below. I assume also that the concentrations of the radionuclides are uniform throughout the volume of building material, and the material has a fixed and uniform composition.
The approach to estimating the external gamma dose rate to an individual requires knowing several facts that include the following:
1. The identity and concentrations of radionuclides in the material.
2. The composition and mass density of the building material.
3. The shape and dimensions of the structure made of the material.
4. The position, relative to the structure, of the individual receiving the dose.
Given this information, one can then attempt to solve the problem from basic principles, using what is called a point-kernel approach, setting up the differential and integral equations that show how dose rate is related to the various parameters, taking account of shielding of the gamma radiation within the building material. Except for the simplest common geometry, a point isotropic source, the resulting equations cannot be resolved in an algebraic solution and require either mathematical approximations or, more commonly, numerical integrations to obtain results. Fortunately there is software available that can handle many of the more common geometries, following this deterministic approach. One of the most popular codes available commercially and easily used by individuals with relatively little training is called MicroShield (available from Grove Software, Inc.). For irregular geometries other approaches, especially probabilistic approaches such as Monte Carlo techniques, may be more suitable, although these require complicated computer codes that require considerable practice and expertise to implement and use with success. If you want more details about the various approaches to shielding problems, I would suggest you try to obtain a copy of a textbook such as that by Shultis and Faw (Radiation Shielding, Prentice Hall PTR, Upper Saddle River, NJ, 1996).
For exemplary purposes I have made some assumptions and carried out a calculation using the MicroShield code noted above. Since I did not have a specific material composition, I assumed a material made of concrete with the uniform mass concentrations of uranium, thorium, and potassium that you gave. I assumed a rectangular slab 10 meters by 10 meters by 15 cm thick with a mass density of 2.35 g/cm3. For conservatism I set the dose point at 1 meter opposite the geometric center of the surface of the 10 m x 10 m slab. For a mass percentage of 7.3 percent for potassium, we calculate a 40K activity concentration of 5.19 Bq/cm3, which is the value that is entered into the code. The code uses a numerical integration routine and outputs the deep dose equivalent rate (using conversion factors from Report 51 of the International Commission on Radiological Protection) that can be used to simulate effective dose rate. The result obtained for a rotational geometry (as if the body were rotated about the long axis to expose it from all directions) is 6.48 x 10-5 mSv/hr (equivalent to 6.48 x 10-3 mrem/hr). For 238U at 4.2 ppm, which translates to 1.217 x 10-1 Bq/cm3, and assuming complete equilibrium of all the radioactive progeny from 238U decay, we obtain a result from MicroShield of 1.67 x 10-5 mSv/hr, about 25 percent of the 40K dose rate. Uranium-235 and its progeny contribute an additional 2.02 x 10-7 mSv/hr. The 232Th at 22.4 ppm, or 2.15 x 10-1 Bq/cm3, along with all its decay progeny adds 4.26 x 10-5 mSv/hr, about two-thirds of the 40K value. The total estimated dose rate for this case is then 1.24 x 10-4 mSv/hr (or 0.0124 mrem/hr).
Since I don’t know the specific characteristics of the material or the structure you are dealing with, the above represents only an example of the kind of results you might obtain. I might mention one special case that can sometimes be helpful for making conservative estimations. This case applies when the structure is large, generally at least several meters in any areal dimension and tens of cm in thickness (for the radionuclides you have mentioned), and the dose point is at or close to the surface of the material. In such a case one can invoke a principle called energy spatial equilibrium in which, within the volume, the energy emitted per unit volume or per unit mass is the same as the energy absorbed per unit volume or mass. If we applied this principle to the 40K in the slab example that we used, we would calculate the gamma energy emitted per unit mass as:
Eemit = (5.19 Bq/cm3)(1 cm3/2.35 g)(0.1067 gamma/disintegration)(1.46 MeV/gamma)(3600 s/hr)(1 disintegration/sec-Bq) = 1.24 x 103 MeV/g-hr, which is also assumed to be the energy absorbed per unit mass per unit time.
This figure can be converted to the conventional absorbed dose rate at the concrete surface:
D = (1.24 x 103 Mev/g-hr)(1.6 x 10-13 J/MeV)(103 g/kg)(1 Gy/J/kg)(103 mGy/Gy)/2 = 9.91 x 10-5 mGy/hr.
The division by two is to account for the fact that the dose point at the surface is being irradiated from only one direction (unlike material within the volume of the slab). To estimate the soft-tissue dose rate we can multiply the above result by the ratio of mass energy absorption coefficients for water (simulates soft tissue) relative to concrete (for this gamma energy the ratio is about 1.16). The dose estimate would then be 1.15 x 10-4 mGy/hr, which for gamma radiation we may take as 1.15 x 10-4 mSv/hr. This would be an overestimate of effective dose, which accounts for dose distribution within the body. Because of this and because the slab we used was not thick enough to produce complete energy spatial equilibrium, the result of 1.15 x 10-4 mSv/hr is about 75 percent larger than the value of 6.48 x 10-5 mSv/hr obtained from the MicroShield code. Similar estimations could be made for uranium and thorium, but one must account for all the significant gamma radiation from all the decay progeny.
I realize this was rather a lengthy response to your question. I hope it provides you with some insight and possible avenues that you might follow. Good luck.
George E. Chabot, PhD, CHP
Answer posted on 12 October 2004. The information and material posted on this website is intended as general reference information only. Specific facts and circumstances may alter the concepts and applications of materials and information described herein. The information provided is not a substitute for professional advice and should not be relied upon in the absence of such professional advice specific to whatever facts and circumstances are presented in any given situation. Answers are correct at the time they are posted on the Website. Be advised that over time, some requirements could change, new data could be made available, or Internet links could change. For answers that have been posted for several months or longer, please check the current status of the posted information prior to using the responses for specific applications.
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