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RADIATION UNITS AND DOSE CALCULATIONS: Three concepts are used in measuring ionizing radiation: 1. Measurement of the electronic charge by an ionizing particle or ray. 2. Measurement of the energy imparted to matter by the ionizing particle or ray. 3. Assessment of the biological damage caused by radiation interaction. Each concept has unique units and some use in radiation protection. Terms which are related to measuring ionizing radiation are: • exposure • absorbed dose • biological dose equivalent • quality factor • activity 1 EXPOSURE: Exposure is defined as a measure of the charge produced in air by gamma and x-rays. The roentgen, R, is the unit of exposure. Here: 1esu 1R @STP Dry Air cm 3 where esu = electrostatic unit The roentgen is applicable to the measurement of charge in air from gamma and x-rays. The charge produced per unit time is the exposure rate (R/hr.) Example: A radiation worker has worked for two hours in a radiation field where the exposure rate is 25 mR/hr. Calculate the total gamma and x- ray exposure received by the worker. mR Exp. 25 2hr hr 50mR 2 ABSORBED DOSE: Absorbed does is the energy imparted per unit mass of matter by ionization and excitation caused by ionizing radiation. The unit of absorbed due is the RAD (Radiation Absorbed Dose.) RAD = any ionizing radiation that imparts 100 ergs/g to any form of matter. For example, the RAD applies to air, biological system, etc. The unit useful for particles that have limited ranges (alpha and beta) Absorbed Dose Rate= energy imparted to matter/unit time. (RAD/hr) Example: an alpha source delivers 100 RAD/hr to the air surrounding the source. Determines the absorbed dose, D, in m RAD imparted to the air in one hour. RAD 1, 000mRAD D 100 1hr hr RAD 100, 000mRAD 3 RELATIVE BIOLOGICAL EFFECTIVENESS: Biological effects depend not only on the total energy deposited per gram (or per volume) but also on the way in which the energy is distributed along the path of radiation. In particular the biological effect of any radiation increases with linear energy transfer (LET) of the radiation. For example, given the same absorbed dose, the biological effect damage due to alpha particles which produce dense tracks of ionization is much greater than the damage from gamma rays, which are less heavily ionized. RBE = 1 200 kev x-rays for a given tissue organ RBE depends upon the tissue, the biological effect under consideration, the dose and dose rate. 4 QUALITY FACTOR: The quality factor is a dimensionless factor that accounts for the difference in biological damage to humans, caused by radiation of different types and energies. This factor, QF, is based on the concept of linear energy transfer. A LET is measured for various energies and types of radiation using a sphere of water that approximates the size of a human body and the constituents of soft tissue. A QF is then assigned. Table 3.2 Linear Energy Transfer (LET) Quality Factor (QF) Relationship Linear Energy Transfer (keV / 10-6 inch) Quality Factor 3.5 or less 1 3.5 - 7.0 1-2 7.0 - 23.0 2-5 23.0 - 53.0 5 - 10 53.0 - 175.0 10 - 20 5 DOSE EQUIVALENT: The term Dose Equivalent (D) is used to denote the damage done to the human body by ionizing radiation. the unit = REM = Roetgen Equivalent Man D = R x QF = RAD x QF Dose equivalent rate (DR) is provided in rem/hr or millirem/hr. If radioactive material is deposited within the body then distribution of the material must be known. D = R x QF x Distribution Factor = RAD x QF x Distribution Factor Beyond the scope of study 6 Table 3.3 Radiation Quality Factors NCRP-39 Type of Radiation ICRP-9 10CFR20 x-rays 1 1 Gamma Rays 1 1 Beta Particles 1 E>0.03MeV 1 E<0.03 MeV 1.7 Neutrons 10 Thermal - 1 keV 2 10 keV 2.5 100 keV 7.5 500 keV 11 1 MeV 11 2.5 MeV 9 5 MeV 8 7 MeV 7 10 MeV 6.5 14 MeV 7.5 20 MeV 8 Protons 10 Alpha Particles 10 20 Heavy Recoil Nuclei 20 20 7 For most purposes, external radiation hazards may be considered as having a quality factor of one. 1 rem = 1 RAD Exposure to external radiation is measured by dosimeter of some type. Neutron Flux (N/cm2/sec) Dose 1 x109 thermal N/cm2 = 2.5x107 fast N/cm2 =1 rem Table 3.4 Neutron Flux Dose Equivalents Neutron Energy Neutrons/cm2 Equivalent To 1 rem (N/cm2) Thermal 970x106 100 eV 720x106 5 keV 820x106 20 keV 400x106 100 keV 120x106 500 keV 43x106 1 MeV 25x106 2.5 MeV 29x106 5 MeV 26x106 7.5 MeV 24x106 10 MeV 24x106 >10 MeV 14x106 8 PROBLEM: A worker receives an absorbed dose of : 2 RAD alpha 3 RAD Nts. 4 RAD's gamma Calculate the dose equivalent. SOLUTION: D 2QF a 3QF N 4QF 2(20) 3(10) 4(1) 74rem 9 PROBLEM: A worker is exposed to 100 keV Nt flux of 2.5x105 Nt/cm2/sec for three hours. Calculate the dose equivalent in rem. SOLUTION: t = 3 hrs(3600 sec/hr) t = 10800 sec D=DR x t = 2.5x105 Nt/cm2/sec x 10800 sec = 2.7x107 Nt/cm2 1 rem = 120x106 Nt/cm2 D = 0.225 rem 10 DOSE RATE CALCULATIONS: ergs DR S / A g S = C (Ci) 3.7 x1010 dps C Ci Ci = 3.7x1010C dps or gamma/sec = 3600 sec / hr x 3.7x1010C gamma/sec = 1.33x1014C gamma/hr E ( MeV ) 106 eV ergs 1.33x1014C gamma/hr 1.6 x1012 gamma MeV eV erg 2.13 x108 CE hr 11 Radiation emitted by the source is distributed uniformly over the surface area of a sphere of radius r. A 4r 2 ft 2 2 12in 2.54cm 2 4r ft 2 2 ft in 1.17 x104 r 2 cm 2 For tissue over the gamma range 0.2 to 4.0 MeV an approximate cm 2 value of of 0.03 . g Now, a rem of gamma radiation is absorbed when 100ergs are absorbed per gram of body tissue. 1rem DR S / A 100ergs g erg 0.03cm 2 2.13 x108 CE hr g ergs / g 1.17 x104 r 2 cm 2 100 1rem CE 5.46 2 r 6CE 2 r C - Ci E - MeV r - ft 12 Table 7.5 Gamma Decay for Selected Radionuclides Percent Dose Rate per Curie at Radionuclide Gamma Energy (MeV) Gamma Yield 1 Meter,G/10 (rem/hr) Celsium-134 E1 0.57 23 0.84 E2 0.605 98 E3 0.796 99 Celsium-137 E1 0.662 85 0.31 Cobalt-58 E1 0.511 30 0.53 E2 0.810 99 Cobalt-60 E1 1.173 100 1.40 E2 1.332 100 Chromium-51 E1 0.315 9 0.016 Iodine-131 E1 0.364 82 0.20 E2 0.284 5.4 E3 0.637 6.8 Iron-59 E1 1.095 56 0.66 E2 1.295 44 Manganese-54 E1 0.835 100 0.47 Nickel-65 E1 1.48 25 0.31 E2 1.12 16 13 PROBLEM: Calculate the dose rate, rem/hr, three ft. from a source containing one Ci of Mn-54. SOLUTION: E = 0.835 MeV C = 1 Ci r = 3 ft 6CE DR r2 MeV 6 1Ci 0.835 3 ft 2 0.557 rem / hr 14 PROBLEM: What happens when it emits two ’s? Calculate the does rate, rem/hr, 10 ft. from a 15 Ci Co-60 source. SOLUTION: E 1.173 1 1.332 1 2.505 MeV C 15Ci r 10 ft DR 6 15Ci 2.505 MeV / 10 ft 2 2.25rem / hr 15 PROBLEM: The dose rate 10 ft. from a pump is 10 rem/hr. Determine the dose rate 25 ft. from the pump. SOLUTION: DR10 10rem / hr 2 r DR25 DR10 10 r25 2 10rem 10 hr 25 rem 1.6 hr 16 INTERNAL RADIATION EXPOSURE: Internal exposures can be caused by beta, gamma, or neutron sources that are ingested, inhaled or enter the body by way of wounds. Internally deposited radionuclides are usually concentrated in localized areas with in the body depending on the chemical characteristics of the radioactive material involved. The exact length of time which it remains in the body (organs) depends to a great extent on the organs involved and the form of the radionuclides. Table 8.3 Critical Organs for Selected Radionuclides Radioisotope Critical Organ Hydrogen-3 (tritium) Whole Body Phosphorous-32 Bone Carbon-14 Fat Sulfur-35 Testes, whole body Chromium-51 Lower Intestine Cobalt-60 Lower Large Intestine Zinc-65 Liver, prostate Rubidium-87 Pancreas Technetium-99m Upper Large Intestine Iodine-131 (and I-125) Thyroid Cesium-137 Whole body, liver, spleen Gold-198 Lower Large Intestine Mercury-203 Kidney Iridium-192 Lower Large Intestine Radon-222 Lung Radium-226 Bone Uranium-235 Lower Large Intestine Plutonium-239 Bone 17 The biological half-life for a particular radionuclide is the time required to reduce the concentration of a radionuclide to 1/2. The effective half-life is the time during which a radionuclide may cause damage, and is determined by combining the effects of physical and biological half-lives: 1 1 1 T = half-life Teff TP TB TB TP TBTP TBTP Teff TB TP 18 Table 8.4 Effective Half-Lives of Common Radionuclides T2r T2B T2eff Physical Biological Effective Half-Life Half-Life Half-Life Radionuclides (Days) (Days) (Days) Hydrogen-3 4.5x103 8 8 Carbon-14 2.0x106 12 12 Phosphorus-32 14.3 1155 14.1 Sulfur-35 87.1 90 44.3 Chromium-51 27.8 616 26.6 Manganese-54 300 25 23.1 Iron-59 45.1 600 41.9 Cobalt-58 72 9.5 8.4 Cobalt-60 1.9x103 9.5 9.5 Zinc-65 245 933 194 Rubidium-87 1.8x1013 60 60 Strontium-90 1.0x10 4 1.8x10 4 6.4x104 Technetium-99m 0.25 20 0.25 Iodine-131 8 138 7.6 Cesium-134 840 70 64.6 Cesium-137 1.1x104 70 70 Iridium-192 74.5 20 15.8 Gold-198 2.7 120 2.6 Mercury-203 45.8 14.5 11 Radon-222 3.83 None (Inert Gas) 3.83 Radium-226 5.9x105 1.64x104 1.64x104 Uranium-235 2.6x1011 300 300 Plutonium-239 8.9x106 7.3x104 7.2x104 19 PROBLEM: Calculate the Teff of Cs-137 SOLUTION: T 1.1 x10 days 70days 4 1.1 x104 days 70days 70days PROBLEM: Calculate the effective half-life of S-35 SOLUTION: T 87.1days 90days 87.1days 90days 44.3days 20 PROBLEM 1: Calculate the maximum critical dimensions of the core. A thermal homogeneous reactor has a cylindrical bare core: •height equals its diameter •1.3% enriched uranium metal •light water as a moderator Possible Data 1.0558 TR 0.45 0.830 D Given: LM 2.88 L2 (on tables) f 0.870 a LSM 5.74 1.40 Table in Problem Statement SOLUTION: k 1.067 L2 2.88 8.2944cm 2 2 L2 5.74 32.95cm 2 2 S M 2 L2 L2 41.24cm 2 S d E 0.71 0.45cm 0.32cm k 1 1.0673 1 v f a B2 0.00163 2 M2 41.24 D 2 2 2.405 B 2 H e Re Re R d e H e H 2d e 2 R 2d 2 Re 2 2 2.405 0.00163 2 Re Re Re 71.14cm R 70.82cm H 2 R 141.64cm 21 PROBLEM 2: Calculate the maximum critical dimensions of the core. A thermal homogeneous reactor has a cylindrical bare core: •height equals its diameter •1.3% enriched uranium metal •light water as a moderator Possible Data 1.0558 TR 0.45 0.830 D Given: LM 2.88 L2 (on tables) f 0.870 a LSM 5.74 1.40 Table in Problem Statement SOLUTION: k 1.067 L2 2.88 1 f 1.078cm 2 2 L2 1.10 5.74 36.242cm 2 2 S M 2 L2 L2 37.320cm 2 S d E 0.71 0.45cm 0.32cm k 1 1.0673 1 B2 2 0.0018cm 1 M 37.320 2 2 2.405 B 2 H e Re 2 2 2.405 0.0018 2 Re Re Re 67.705cm H 2 R 135.4cm 22 PROBLEM: Calculate Slowing Down Length: LS2 SOLUTION: 1 D L2 N f S f TR f or a S 3 Initial E 1 E Ni Nf ln Final E E Nf E ln S f 2 S f 2 E L2 N f 3 1 Cos 3 1 Cos S 23 PROBLEM: Determine k00 if the mass of U235 (f = 0.024 g/cc) in a homogenous reactor ~6kg. The reactor core is a cube with water as moderator. SOLUTION: Assume- critical dimentions Assume d = 0.71 to be small 2 Bg 3 2 S k 1 v f a Bm m2 D Critcal----> Bg = Bm 2 k 1 3 S 2 M 2 k 3 M 2 1 S 24 PROBLEM: Calculate S and M2 First determine S. Mass (g) = fS3 6, 000 gram S 63cm 3 g 0.024 cc Next, M2. 33, Provided in Tables M L 2 L 2 S 2 Dt Dt 0.18cm L2 a af am 0.02cm 0.037cm M 2 33 3 36 2 k 3 36 1 63 1.27 25 TABLE 6.1 Moderator Density Dt L M2 Water 1.00g/cc 0.18cm 2.88cm 33cm2 41cm2 Heavy Water 1.10 0.85 100 120 10,120 Beryllium 1.84 0.61 23.6 98 655 Graphite 1.62 0.92 50.0 350 2,850 26 EXTERNAL EXPOSURE: Neutrons - Energy Dependent Tabulated graphically Gamma’s for a beam with a single energy air • R 8 a X 1. 83 *10 IE sec photons 's where I - Intensity or cm 2 * sec cm 2 * sec E - Energy MeV a cm 2 mass absorption coefficient g in mR/hr air • mR X 0. 0659IE a h Dose from External Exposure tis • mrad D 0. 0576I a h or tis a • mrad • D 0. 0874 X h a air Equivalent Dose • • HfD where f energy dependent function which depends on the type of tissue. 27 INTERNAL EXPOSURE: Gamma and Charged particle • rad 5. 92 *10 4 C t E D sec M where C(t) Ci M mass of the organ grams E is energy in MeV Equivalent dose • • H DQ for a multi mode decay • • H D Retention function R t C 0 qe b t q is describes mode of internalization i.e. ingestion or inhalation Single intake 51.1C d qe e t • rem H day M Continuous Intake t e t Cd q C t Cd q e Ct 1 e e t e 0 28 Then • rem H 51.1C d q 1 e et day M e 29

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