Calculation of Shielded Dose Rate in Sieverts from Contaminated Surface
Assume a surface, which is contamined by 1.0 Ci of 137Cs. Assume that this contaminant can be aproximated by the point isotropic source which contains 1.0 Ci of 137Cs, which has a half-life of 30.2 years. Note that the relationship between half-life and the amount of a radionuclide required to give an activity of one curie is shown below. This amount of material can be calculated using λ, which is the decay constant of certain nuclide:
About 94.6 percent decays by beta emission to a metastable nuclear isomer of barium: barium-137m. The main photon peak of Ba-137m is 662 keV. For this calculation, assume that all decays go through this channel.
Calculate the primary photon dose rate, in sieverts per hour (Sv.h-1), at the outer surface of a 5 cm thick lead shield. Then calculate the equivalent and effective dose rates for two cases.
- Assume that this external radiation field penetrates uniformly through the whole body. That means: Calculate the effective whole-body dose rate.
- Assume that this external radiation field penetrates only lungs and the other organs are completely shielded. That means: Calculate the effective dose rate.
Note that, primary photon dose rate neglects all secondary particles. Assume that the effective distance of the source from the dose point is 10 cm. We shall also assume that the dose point is soft tissue and it can reasonably be simulated by water and we use the mass energy absorption coefficient for water.
See also: Gamma Ray Attenuation
See also: Shielding of Gamma Rays
The primary photon dose rate is attenuated exponentially, and the dose rate from primary photons, taking account of the shield, is given by:
As can be seen, we do not account for the buildup of secondary radiation. If secondary particles are produced or if the primary radiation changes its energy or direction, then the effective attenuation will be much less. This assumption generally underestimates the true dose rate, especially for thick shields and when the dose point is close to the shield surface, but this assumption simplifies all calculations. For this case the true dose rate (with the buildup of secondary radiation) will be more than two times higher.
To calculate the absorbed dose rate, we have to use in the formula:
- k = 5.76 x 10-7
- S = 3.7 x 1010 s-1
- E = 0.662 MeV
- μt/ρ = 0.0326 cm2/g (values are available at NIST)
- μ = 1.289 cm-1 (values are available at NIST)
- D = 5 cm
- r = 10 cm
The resulting absorbed dose rate in grays per hour is then:
1) Uniform irradiation
Since the radiation weighting factor for gamma rays is equal to one and we have assumed the uniform radiation field (the tissue weighting factor is also equal to unity), we can directly calculate the equivalent dose rate and the effective dose rate (E = HT) from the absorbed dose rate as:
2) Partial irradiation
In this case we assume a partial irradiation of lungs only. Thus, we have to use the tissue weighting factor, which is equal to wT = 0.12. The radiation weighting factor for gamma rays is equal to one. As a result, we can calculate the effective dose rate as:
Note that, if one part of the body (e.g.,the lungs) receives a radiation dose, it represents a risk for a particularly damaging effect (e.g., lung cancer). If the same dose is given to another organ it represents a different risk factor.
If we want to account for the buildup of secondary radiation, then we have to include the buildup factor. The extended formula for the dose rate is then:
Buildup Factors for Gamma Rays Shielding
The buildup factor is a correction factor that considers the influence of the scattered radiation plus any secondary particles in the medium during shielding calculations. If we want to account for the buildup of secondary radiation, then we have to include the buildup factor. The buildup factor is then a multiplicative factor which accounts for the response to the uncollided photons so as to include the contribution of the scattered photons. Thus, the buildup factor can be obtained as a ratio of the total dose to the response for uncollided dose.
The extended formula for the dose rate calculation is:
The ANSI/ANS-6.4.3-1991 Gamma-Ray Attenuation Coefficients and Buildup Factors for Engineering Materials Standard, contains derived gamma-ray attenuation coefficients and buildup factors for selected engineering materials and elements for use in shielding calculations (ANSI/ANS-6.1.1, 1991).