Question 9.10: The radioactive isotope ^40 K (odd Z and odd N ) is naturall......
The radioactive isotope ^{40}K (odd Z and odd N ) is naturally present in biological tissues and subjects humans to a certain amount of unavoidable internal radiation. The body of an adult weighing 70 kg contains about 170 g of potassium, mostly in intracellular fluids. The relative natural abundance of ^{40}K is 0.0118%, its half-life is 1.28\times 10^{9} years, and it emits b particles with an average kinetic energy of 1.40 MeV.
1. Calculate the total activity of ^{40}K, in millicurie, for a 70 kg adult.
2. Find the radiation dose rate in mrem/y.
Note: Potassium-40 is not included in Table 9.6 because human exposure to it is governed entirely by the body’s metabolic processes and its natural abundance. Therefore, it cannot be controlled by regulation.
| TABLE 9.6 | |||||||
| Calculated Concentrations (pCi/L) of \beta and Photon Emitters in Drinking Water Yielding a Dose of 4 mrem/year to the Total Body or to Any Critical Organ as Defined in NBS Handbook 69 | |||||||
| Nuclide | pCi/L | Nuclide | pCi/L | Nuclide | pCi/L | Nuclide | pCi/L |
| H-3 | 20,000 | Sr-85 m | 21,000 | Sb-124 | 60 | Er-169 | 300 |
| Be-7 | 6,000 | Sr-85 | 900 | Sb-125 | 300 | Er-171 | 300 |
| C-14 | 2,000 | Sr-89 | 20 | Te-125m | 600 | Tm-170 | 100 |
| F-18 | 2,000 | Sr-90 | 8 | Te-127 | 900 | Tm-171 | 1,000 |
| Na-22 | 400 | Sr-91 | 200 | Te-127m | 200 | Yb-175 | 300 |
| Na-24 | 60 | Sr-92 | 200 | Te-129 | 2,000 | Lu-177 | 300 |
| Si-31 | 3,000 | Y-90 | 60 | Te-129m | 90 | Hf-181 | 200 |
| P-32 | 30 | Y-91 | 90 | Te-131m | 200 | Ta-182 | 100 |
| S-35 inorg | 500 | Y-91 m | 9,000 | Te-132 | 90 | W-181 | 1,000 |
| Cl-36 | 700 | Y-92 | 200 | I-126 | 3 | W-185 | 300 |
| Cl-38 | 1,000 | Y-93 | 90 | I-129 | 1 | W-187 | 200 |
| K-42 | 900 | Zr-93 | 2,000 | I-131 | 3 | Re-186 | 300 |
| Ca-45 | 10 | Zr-95 | 200 | I-132 | 90 | Re-187 | 9,000 |
| Ca-47 | 80 | Zr-97 | 60 | I-133 | 10 | Os-188 | 200 |
| Sc-46 | 100 | Nb-93m | 1,000 | I-134 | 100 | Os-185 | 200 |
| Sc-47 | 300 | Nb-95 | 300 | I-135 | 30 | Os-191 | 600 |
| Sc-48 | 80 | Nb-99 | 3,000 | Cs-131 | 20,000 | Os-191m | 9,000 |
| V-48 | 90 | Mo-99 | 600 | Cs-134 | 80 | Os-193 | 200 |
| Cr-51 | 6,000 | Tc-96 | 300 | Cs-134m | 20,000 | Ir-190 | 600 |
| Mn-52 | 90 | Tc-96m | 30,000 | Cs-135 | 900 | Ir-192 | 100 |
| Mn-54 | 300 | Tc-97 | 6,000 | Cs-136 | 800 | Ir-194 | 90 |
| Mn-56 | 300 | Tc-97m | 1,000 | Cs-137 | 200 | Pt-191 | 300 |
| Fe-55 | 2,000 | Tc-99 | 900 | Ba-131 | 600 | Pt-193 | 3,000 |
| Fe-59 | 200 | Tc-99m | 20,000 | Ba-140 | 90 | Pt-193m | 3,000 |
| Co-57 | 1,000 | Ru-97 | 1,000 | La-140 | 60 | Pt-197 | 300 |
| Co-58 | 300 | Ru-103 | 200 | Ce-141 | 300 | Pt-197m | 3,000 |
| Co-58m | 9,000 | Ru-105 | 200 | Ce-143 | 100 | Au-196 | 600 |
| Co-60 | 100 | Ru-106 | 30 | Ce-144 | 30 | Au-198 | 100 |
| Ni-59 | 300 | Rh-103m | 30,000 | Pr-142 | 90 | Au-199 | 600 |
| Ni-63 | 50 | Rh-105 | 300 | Pr-143 | 100 | Hg-197 | 900 |
| Ni-65 | 300 | Pd-103 | 900 | Nd-147 | 200 | Hg-197m | 600 |
| Cu-64 | 900 | Pd-109 | 300 | Nd-149 | 900 | Hg-203 | 60 |
| Zn-65 | 300 | Ag-105 | 300 | Pm-147 | 600 | Tl-200 | 1,000 |
| Zn-69 | 6,000 | Ag-110m | 90 | Pm-149 | 100 | Tl-201 | 900 |
| Zn-69m | 200 | Ag-111 | 100 | Sm-151 | 1,000 | Tl-202 | 300 |
| Ga-72 | 100 | Cd-109 | 600 | Sm-153 | 200 | Tl-204 | 300 |
| Ga-71 | 6,000 | Cd-115 | 90 | Eu-152 | 200 | Pb-203 | 1,000 |
| As-73 | 1,000 | Cd-115m | 90 | Eu-154 | 60 | Bi-206 | 100 |
| As-74 | 100 | In-113m | 3,000 | Eu-155 | 600 | Bi-207 | 200 |
| As-76 | 60 | In-114m | 60 | Gd-153 | 600 | Pa-230 | 600 |
| As-77 | 200 | In-115 | 300 | Gd-159 | 200 | Pa-233 | 300 |
| Se-75 | 900 | In-115m | 1,000 | Tb-160 | 100 | Np-239 | 300 |
| Br-82 | 100 | Sn-113 | 300 | Dy-165 | 1,000 | Pu-241 | 300 |
| Rb-86 | 600 | Sn-125 | 60 | Dy-166 | 100 | Bk-249 | 2,000 |
| Rb-87 | 300 | Sn-122 | 90 | Ho-166 | 90 | ||
| Source: From EPA, Implementation Guidance for Radionuclides, United States Environmental Protection Agency, Office of Ground Water and Drinking Water (4606M), EPA 816-F-00-002, March 2002, www.epa.gov/safewater. | |||||||
1. First calculate the decay rate constant, k, with units of s^{-1}
k=\frac{0.693}{t_{1/2}} =\frac{0.693}{(1.28\times 10^{9} y)(3.16\times 10^{7} s y^{-1})} =1.71\times 10^{-17} s^{-1}Let the number of {^40}K atoms = N
\mathscr{N} = \frac{170 g of K}{40.0 g/mol}\times (\frac{1.18\times 10^{-4} mol ^{40}K} {mol K})\times 6.02\times 10^{23} atoms/mol = 3.02\times 10^{20} atoms of ^{40}KActivity = \mathscr{A} = k\mathscr{N} = (1.71\times 10^{-17} s^{-1})(3.02\times 10^{20} atoms) = 5.16\times 10^{3} atoms/s(dps)
Converting to curies gives
2. Number of curies per kilogram = \frac{1.4\times 10^{-7} Ci} {70 kg} = 2.0\times 10^{-9} Ci/kg
Disintegrations per second per kilogram = \frac{5.16\times 10^{3} dps}{70 kg} = 73.7 s^{-1} kg^{-1}
Joules per \beta particle = (1.40\times 10^{6} eV)(1.60\times 10^{-19} J/eV) = 2.24\times 10^{-13} J
Joules × dps per kilogram = (2.24\times 10^{-13} J)(73.7 s^{-1} kg^{-1}) = 1.65\times 10^{-11} J/s/kg
Joules per kilogram per year = (1.65\times 10^{-11} J/s/kg)(3.16\times 10^{7} s/year) \\ = 5.22\times 10^{-4} J/kg=/year
The number of rems is the number of centijoules (10^{-2} J) of radiation energy absorbed per kilogram of tissue weight multiplied by the RBE factor. From Table 9.5, RBE = 1.
Since ^{40}K is distributed throughout all body tissues, we can assume that essentially all the \beta radiation energy is absorbed within the body.
Number of rem per year = \frac{5.22\times 10^{-4} J/kg/year} {10^{-2} J/kg/rem}
= 5.22\times 10^{-2} rem/year = 52.2 mrem/yearTable 9.7 shows that the annual dosage from all natural radiation sources received by a person is about 399 mrem, which shows that about 13% of our natural radiation exposure is from ^{40}K and is unavoidable because it is part of our body’s chemical makeup.
As shown in Table 9.7, about 84% of the total average annual effective dose is from natural sources of radiation, and of that, most is from radon. Of the other 16%, the majority is from medical diagnosis and treatments.
| TABLE 9.5 | ||||
| RBE (Relative Biological Effectiveness) Values for Several Types of Radiations, Based on Whole-Body Exposure | ||||
| Radiation | RBE | |||
| x- and \gamma-Rays | 1 | |||
| \beta-Rays and electrons | 1 | |||
| Thermal neutrons | 2 | |||
| Fast neutrons | 10 | |||
| High-energy protons | 10 | |||
| \alpha Particles | 20 | |||
| Fission fragments, heavy particles of unknown charge | 20 | |||
| Heavy ions | 20 | |||
| Note: RBE values are also called quality factors or weighting factors. | ||||
| TABLE 9.7 | ||||||
| Sources of Environmental Radiation in the United States and Estimated Annual Dose Contributions to Individuals. The Total Annual Dose Is about 399 mrem/year | ||||||
| Sources | Approximate Average Annual Dose to a Person in the United States (mrem/year) |
Approximate Percent of Total Dose Received |
||||
| Natural sources 84% of total (about 334 mrem/year) | ||||||
| Inhaled radon | 200 | 50 | ||||
| Ingested with food | 40 | 10 | ||||
| Cosmic radiation | 27 | 7 | ||||
| Terrestrial radiation | 28 | 7 | ||||
| Internal body | 39 | 10 | ||||
| Man-made sources 16% of total (about 65 mrem/year) | ||||||
| Medical x-rays | 39 | 10 | ||||
| Nuclear medicine | 14 | 4 | ||||
| Consumer products | 9 | 2 | ||||
| Occupational exposure | 0.9 | 0.2 | ||||
| Weapons testing fallout | <0.9 | <0.2 | ||||
| Nuclear fuel cycle | 0.4 | 0.1 | ||||
| Miscellaneous | 0.4 | 0.1 | ||||