Answer to Question #10388 Submitted to "Ask the Experts"
Category: Radiation Basics — Photons
The following question was answered by an expert in the appropriate field:
I am working on trying to determine actual gamma-dose rates based on a known source radionuclide and activity level, specifically 137Cs because that seems to be the industry norm for nonenergy discriminating scintillation detectors. I have either violated the boundaries of your dose equations or I have found a serious underestimation in the industry. I read an article on your site about the process of estimating X (R h-1) from the basic building blocks (activity, energy, mass absorption rate, . . .). This is more complex but I like it because I don't have to wonder what hand-waving assumptions are being made. In the process of doing my own dose calculations for 137Cs I stumbled upon a very unexpected result. When I consider only the dominant decay energy (661 keV at 85 percent) I see results consistent with online calculators and other resources. However, when I include the 4 keV decay that only makes up 0.9 percent of the radioactive photons emitted during disintegration, the calculated dose increases by 12%! That is astonishing to me. I assumed that such low-energy levels were fairly safe since they would lack the energy to penetrate the skin.
Are there practical boundaries that need to apply for the equations you derived (i.e., not valid for decay energies below a certain keV or above a certain MeV)? If this is not the case then how do we rectify the underestimation of dangerous level of 137Cs. Have we found a bad assumption in relating dose in air to dose in human tissue? I have a plot of my calculations for dose rate vs gamma energy level based on the resources listed here. The shape is a "V" starting at a high dose for 1 keV then dipping by 3.5 orders of magnitude at 90 keV and returning about 2 orders of magnitude by 20 MeV (all other variables remaining equal).
Some of the points you raise are completely justified. We often get so accustomed to performing particular tasks in a fixed way, according to routine procedures, that we sometimes forget or fail to recognize that the procedure we have been using incorporated certain assumptions that may not be valid for all situations; thus, your surprise at your results is likely quite legitimate. I am pleased to see that you have had the volition to pursue the topic of exposure rate dependencies on critical parameters. The use of the equation(s) in the reference that you cite is not theoretically restricted in terms of its applications to energies below any specified value. We sometimes impose a practical limit on upper energy values (about 3 MeV) because of the problem of satisfying certain requirements for determining the quantity, exposure.
In many situations, however, when people are concerned with exposure from external sources, the physical irradiation geometry precludes the likelihood of photons below some specified energy being a concern. For example, when sealed radioactive sources are used for irradiations the encapsulation of the source will prevent many low-energy photons from escaping. Similarly, there are often situations when the radioactive material, though not in a sealed configuration, is in a form such that self-absorption in the source medium will markedly attenuate low-energy photons. Thus when tabulations of gamma-ray exposure rate constants have been compiled, decisions have often been made to not consider photons below a particular energy. For example, in one of the more extensive compilations, ORNL/RSIC-45/R1, the choice was made to not include photons less than 10 keV in energy.
Recognizing such practical restrictions on energy, however, we must also be aware that there are situations in which low-energy photons should be included in the exposure or dose calculations. This is true, for example, in the case of internal dosimetry in which radionuclides taken into the body are dispersed to various tissues and because the radionuclides reside within the tissues, they may deliver dose from all radiations that are emitted.
In such instances we should recognize the importance of your observations. For the case of 137Cs that you deal with, the exposure rate from each photon energy is proportional to the photon energy, the respective mass energy absorption coefficient, and respective photon yield. As the reference you cite notes, the total exposure rate is proportional to the sum of the respective products of these three quantities for all photons being considered. Below are the major photon energies, mass energy absorption coefficients, and yields from the decay of 137Cs (137mBa).
Energy, MeV Mass energy absorption coeff., cm2 g-1 Yield, γ d-1
0.662 0.0293 0.851
0.0329* 0.1785* 0.0710*
0.00472** 49.8** 0.00835**
*Photons from 31.8 keV to 36.4 keV considered together.
**Photons from 3.95 keV to 5.81 kev considered together.
Energies and yields were taken from the Berkeley Laboratory Isotope Project's web page (click on element and then pick isotope). Mass energy absorption coefficients for air were taken from NIST tabulations.
If we were to compare the exposure rate from all the listed photons to the exposure rate from the 662 keV photons alone, we would find the exposure rates are given by the ratio:
[(0.662 MeV)(0.0293 cm2g-1)(0.851 γd-1)+(0.0329 MeV)(0.1785 cm2g-1)(0.0710 γd-1)+(0.00472 MeV)(49.8 cm2g-1)(0.00835 γd-1)]/[(0.662 MeV)(0.0293 cm2g-1)(0.851 γd-1)] = 0.01889/0.01651 = 1.144.
The implication is that the exposure rate, considering all the photons is almost 15% greater than that when only the 662 keV photons are considered. This is a similar conclusion to what you reached. Most of the increase is associated with the lowest energy group (0.00472 MeV) which, despite the less than 1% yield, pushes the exposure rate up because of the very high value of the mass energy absorption coefficient. Any differences between the above results and your findings are likely due to differences in the references used for energies and yields and possible differences in the ways energies were handled (i.e., grouped or individual).
The shape of the curve you describe for gamma dose rate vs energy is heavily influenced by the dependence of the mass energy absorption coefficient in air (or soft tissue if you are looking at tissue dose) on energy, dropping fairly quickly from very low to higher energies. At low energies the relative decrease in value of the mass energy absorption coefficient with increasing energies is much more rapid than the associated relative decrease in photon energy, hence the strong effect of the mass energy absorption coefficient.
The bottom line is that your findings are accurate and should serve as a reminder that published values of photon exposure rate and/or dose rate constants for radionuclides often do incorporate restrictions on photon energies and/or yields that affect the calculations. These restrictions may be unimportant for many applications in which such photons will be greatly attenuated before reaching a point of concern, but they can lead to possibly significant errors in situations when the lower energy/lower yield photons are able to reach the dose point of interest.
We should make perhaps one other observation to point out that the relationship between results calculated for low-energy vs high-energy photons may vary considerably depending on what specific dose quantity is of interest. For example, a given fluence rate of 10 keV photons at a point in air will deliver an exposure rate (e.g., R h-1) that is about 70% higher than the same fluence rate of 1 MeV photons at the same point. However, if we were interested in the personal dose equivalent at a 1 cm depth in soft tissue, the same fluence rate of 10 keV photons (at the surface of the body) would deliver a personal dose equivalent that is only about 1.5% of that from the same fluence rate of 1 MeV photons. This is largely because of the severe attenuation of the 10 keV photons compared to the 1 MeV photons in the 1 cm thickness of tissue overlying the dose point.
Thanks for your interest and for an important observation.
George Chabot, PhD