## High Level Dose

There is no single value for absorbed dose that marks a sharp cutoff between a high-level and a low-level dose of ionizing radiation.69 For each harmful health

69Sometimes an absorbed dose above about 1 Gy is referred to as a "high-level" dose. The U.S. Nuclear Regulatory Commission refers to a "High Radiation Area" as one in which an individual effect, there is a range of values of dose within which the severity or the number of occurrences of the effect correlates with the dose in a statistically significant manner. Several types of relationship between dose and response have been observed. Examples are shown in Figure 13-21 for doses above background (the normal dose of ionizing radiation from natural radioactivity and cosmic radiation in the environment). The S-shaped curve in Figure 13-21a for a deterministic effect shows a threshold; that is, the response decreases to zero for a given type of dose greater than zero. In other words, with increasing dose starting at zero, there is no response until the dose has reached a minimum (threshold) value. At very high doses the curve becomes flat because the cells do not survive. Presumably, the mechanism for cell repair is effective below the threshold.

Most of the data used to establish the relationship between dose and response for a particular health effect have been obtained from laboratory experiments with animals. Because of the short lifetime and generation time for mice, for example, the health effects can be observed for a large population in experiments of reasonable duration. The key assumption is that the results of the animal experiments can be applied to human exposure.

In a number of instances, data on human exposure have been obtained directly from records of the dose received by patients exposed to ionizing

Deterministic effect

Stochastic effect

Stochastic effect

Deterministic effect

Stochastic effect

Stochastic effect

FIGURE 13-21 Examples of dose-response curves. (a) Curve showing threshold for a deterministic effect. (b) Linear curve for a stochastic effect with linear (dashed line) and nonlinear (dotted line) extrapolations to low-level dose (below ~ 1 Sv). (c) Linear-quadratic curve with linear extrapolation to low-level dose. In quadratic region, the response shows a marked increase with dose rate.

FIGURE 13-21 Examples of dose-response curves. (a) Curve showing threshold for a deterministic effect. (b) Linear curve for a stochastic effect with linear (dashed line) and nonlinear (dotted line) extrapolations to low-level dose (below ~ 1 Sv). (c) Linear-quadratic curve with linear extrapolation to low-level dose. In quadratic region, the response shows a marked increase with dose rate.

could receive (from external sources) "a dose equivalent in excess of 0.1 rem (1 mSv) at 30 centimeters from a radiation source or 30 centimeters from any surface that the radiation source penetrates." For a "Very High Radiation Area" an individual could receive from external sources "an absorbed dose in excess of 500 rads (5 grays) in 1 hour at 1 meter from a radioactive source or 1 meter from any surface that the radiation penetrates." These NRC definitions are given in the U.S. Code of Federal Regulations (10 CFR 20, 1003, January 2001).

radiation in medical procedures, radiologists exposed to x rays in their work, victims of accidents at nuclear facilities, and a population containing a statistically significant number of people exposed in known ways that can be documented. A few examples of populations studied in epidemiological investigations are workers who developed bone tumors, bone cancer, and anemia from ingesting luminous radium paint while painting clock and watch dials during the period from about 1915 to 1925; patients who developed malignancies after being given Thoratrast (a colloidal suspension of Th02) during the period 1930-1945 to improve the quality of diagnostic x-ray images of the liver; uranium miners who developed lung cancer; people exposed to ionizing radiation directly from nuclear weapons and from nuclear weapons tests; and people who were put at risk because of accidental release of radioactive material (e.g., the explosions at the Chernobyl nuclear power plant: Section 14.16.2.3).

Dose-response data for individuals in such groups who have received a dose high enough to cause a particular effect contribute to establishment of the solid-line section of the curves in Figures 13-21b and 13-21c.

### 13.14.2 Low-Level Dose

Unfortunately, the dose levels of interest for establishing regulatory dose limits for stochastic effects are in the low-level dose region, below the minimum dose for which the dose-response characteristics are reasonably well known. As the dose from ionizing radiation in a controlled-exposure experiment or the dose received by the cohort of a group or population is lowered, the frequency of occurrence of a particular effect decreases to the "normal" value associated with other causative agents. With decreasing dose, it becomes increasingly difficult to determine any statistically significant increase in the frequency of occurrence that can be attributed to ionizing radiation. The problem is similar to that of establishing the toxic level value for the chemical toxicity or car-cinogenicity of a nonradioactive substance.

The usual procedure for predicting or estimating the value of a variable (response in this case) is to extrapolate the curve from the "known" region into the "unknown," low-level region. Dose-response predictions in the low-level dose region are customarily made by linear extrapolation (dashed straight lines in Figures 13-21b and 13-21c), which is based on what is variously referred to as the "linear theory," the "linear, no-threshold theory," the "linear hypothesis," or the "linear model."70 It is the simplest extrapolation, and it is based on the assumption that for stochastic effects any dose above zero is harmful. In

70The U.S. Environmental Protection Agency uses linear extrapolation from large doses to zero to evaluate the effect of small doses of chemicals that can damage DNA.

practice, zero dose is relative to background, which provides a chronic, low-level dose.

Over the years, investigators studying the response for stochastic effects to low-level radiation have observed responses with high statistical certainty (e.g., > 90%) that are less (perhaps by a factor of 2 or more) than the value predicted by linear extrapolation. One interpretation of this discrepancy is that there really is a threshold dose below which the response is zero. Some investigators interpret the data for bone cancers among watch-dial painters using radium-containing paint as showing a threshold. Those who support the existence of thresholds for stochastic effects at low doses point out that the linear extrapolation will overestimate the risk for an effect where there is a threshold. On the other hand, those who support linear extrapolation believe that it is prudent to be conservative in estimating health risks and setting regulations. Resolution of the controversy is important and awaits researchers with an innovative approach to work in this field, and probably the availability of new technology.

Various nonlinear extrapolations have been proposed. One is shown as the arbitrarily drawn, nonlinear dotted line in Figure 13-21b. One of the goals of ongoing population studies is to resolve the question of the existence or nonexistence of a threshold dose of ionizing radiation (external or internal exposure) for cancer.

Whereas high-level doses of ionizing radiation clearly have harmful (negative) biological effects, low-level doses of low-LET radiation have been reported by numerous investigators to have stimulating (positive) effects. This phenomenon, called radiation hormesis, is similar to chemical hormesis. Examples of radiation hormesis for low-level doses have been observed for plants, in which early growth can be stimulated, and for animals, in which increased growth and proliferation rates, have been reported, as well as increased longevity and reduction in the incidence of cancer.

### Additional Reading and Sources of Information

BEIR Reports. These are reports issued by the Committee on the Biological Effects of Ionizing Radiation, National Research Council, published by the National Academy Press, Washington, DC.

Cember, H., Introduction to Health Physics, 3rd ed. McGraw-Hill, New York, 1996. Choppin, G. R., J.-O. Liljenzin, and J. Rydberg, Radiochemistry and Nuclear Chemistry (2nd edition of Nuclear and Radiochemistry). Butterworth-Heinemann, London, 1995. CRC Handbook of Chemistry and Physics (Table of the Isotopes). Latest edition, CRC Press, Boca

Rations FL. Revised annually. Ehmann, W. D., and D. E. Vance, Radiochemistry and Nuclear Methods of Analysis, Vol. 116 of

Series of Monographs on Analytical Chemistry and Its Applications. Wiley, New York, 1991. Eisenbud, M. and T. Gesell, Environmental Radioactivity from Natural, Industrial, and Military Sources, 4th ed. Academic Press, San Diego, CA, 1997.

Firestone, R. B., and V. S. Shirley, eds., Table of Isotopes, 8th ed. Wiley, New York, 1997.

Friedlander, G., J. W. Kennedy, E. S. Macias, and J. M Miller, Nuclear and Radiochemistry, 3rd. ed. Wiley-Interscience, New York, 1981.

National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY 11973-5000. http://www.nndc.bnl.gov/

Nuclear Regulatory Commission, Code of Federal Regulations, Title 10, Part 20. U.S. Government Printing Office, Washington, DC. Revised annually. One URL is http://www.access.gpo.-gov/nara / cfr/cfr-table-search.html.

Parrington, J. R., H. D. Knox, S. L. Breneman, E. M. Baum, and F. Feiner, Nuclides and Isotopes (Chart of the Nuclides), 15th ed. General Electric Nuclear Energy, San Jose, CA, 1996.

Spinks, J. W. T., and R. J. Woods, Introduction to Radiation Chemistry, 3rd ed. Wiley, New York, 1990.

Turner, J. E., Atoms, Radiation, and Radiation Protection, 2nd ed. Wiley, New York, 1995.

EXERCISES

13.1. Calculate the average binding energy (MeV) per nucleon for

The isotopic masses of *H and % are 1.007825032 and 1.008664924, respectively.

13.2. Calculate Q (MeV) for the following nuclear reactions:

The isotopic masses (amu) are *H, 1.007825032; *n, 1.008664924; 2H, 2.014101778; 4He, 4.002603250; 14C, 14.0003241; 14N, 14.003074007; 27Al, 26.9815384; 24Na, 23.990961; 59Co, 58.933200; and 60Co, 59.933819.

13.3. Calculate Q for the thermal neutron fission of 235U into 100Mo + 134Sn and 2 neutrons. The isotopic masses in amu are xn, 1.008664924; 100Mo, 99.90748; 134Sn, 133.92783; and 235U, 235.043922.

13.4. A "rich" sample of pitchblende contains 60.0% U308 by weight. How many kilograms of 238U, 235U, and 234U are present in one metric ton of the ore? How many becquerels and how many curies of 226Ra are present in the same quantity of ore? How many kilograms of 226Ra and of 222Rn are present? Assume that all members of the uranium series are in secular steady state. Natural uranium contains 99.2745 at. % 238U, 0.720 at. % 235U, and 0.0055 at. % 234U.

13.5. For the ore in Exercise 13.4, assume that all the 222Rn could be removed quickly from one metric ton of ore, collected completely, and transferred to a l.0-liter evacuated flask at 273 K. Calculate the initial pressure of the radon in pascals. Calculate the initial power output in watts for the a radiation (5.4895 MeV per disintegration).

13.6. A bottle with the original seal intact contains 1.0 kg of "chemically pure" U3O8 that is 2.0 years old. How many becquerels, microcuries, and micrograms of 234Th and of 234Pa does it contain?

13.7. Prepare a semilog plot of the following experimental data for the decay of a single radionuclide. (All data were obtained in a radiochemistry laboratory course. No measurement was made on the 28th day because of spring break.) Determine the half-life of the radionuclide. The data were obtained with a Geiger-Muller (GM) tube and have been corrected for the background counting rate in the absence of a sample and for coincidence losses at high counting rates.

Days |
Counts/min |
Days |
Counts/min |
Days |
Counts/min |

0 |
6297 |
35.0 |
1170 |
63.0 |
313 |

7.0 |
4502 |
42.0 |
852 |
70.0 |
221 |

14.0 |
3249 |
49.0 |
610 |
77.0 |
161 |

21.0 |
2298 |
56.0 |
441 |

13.8. (a) Prepare a semilog plot of the following activity data in disintegrations per minute for a mixture of two independent radionuclides, A and B.

(b) Determine the half-life of A, the longer-lived component, extrapolate its decay curve back to t = 0, and determine AA.

(c) Subtract values on the decay curve for component A from the total activity curve to obtain the decay curve for component B. Draw the decay curve for B and determine the values of tj/2 and AB.

Time (hj |
Bq |
Time (hj |
Bq |

0 |
1100 |
24 |
185 |

2 |
868 |
31 |
139 |

4 |
698 |
38 |
108 |

6 |
572 |
45 |
84 |

8 |
478 |
52 |
66 |

10 |
406 |
59 |
51 |

13 |
328 |
66 |
40 |

17 |
258 |

13.9. The initial ratio of activities of 131I (8.0207d) to that of 24Na (14.95 h) in a sample is 2.0. What is the ratio 7.0 days and 14.0 days later? 13.10. Iodine-131 (8.0207d) emits a 0.608-MeV p ray in 89% of the decays and a 0.364-MeV y ray in 81.1% of the decays (Figure 13-10). How many 0.608-MeV p rays and how many 0.364-MeV y rays does a sample having an initial activity of 370 MBq (10.0 mCi) emit in 24 h?

13.11. Strontium-90 (28.78 y) decays into 90Y (2.67 d) and Y-90 decays into stable 90Zr. (see Figure 13-13). A sample of freshly separated 90Sr has an activity of 3.7 GBq (100 mCi). Prepare a semilog plot showing the activity of 90Sr and 90Y and the total activity out to 30 days. What is the total p-ray emission rate per second in the sample after 30 days?

13.12. Transient equilibrium can be illustrated by the following fission product chain: 140Ba (12.75 d) ^ 140La (1.678 d) ^ 140Ce(s). Prepare a semilog plot of the activities of 140Ba, 140La, and the total activity out to 30 days, assuming that at t = 0 the sample consists of 74 MBq (2.0 mCi) of radiochemically pure 140Ba. When do the parent and daughter activities become equal? Show how the activity curves would change if the initial sample were not pure and contained 7.4 MBq (0.20 mCi) of 140La.

13.13. Prepare a semilog plot of the total activity and the activities of 143Ce and 143Pr out to 30 days for the following fission product chain: 143Ce (1.377d) ^ 143Pr (13.57d) ^ 143Nd(s) for a sample initially containing only 296 MBq (8.0 mCi) of pure 143Ce.

13.14. Derive equation (13-23).

13.15. Derive equation (13-24) from equation (13-23).

13.16. From equation (13-23) with AB = 0, derive an equation for the time when Ab reaches a maximum. Write the resulting equation in terms of half-lives. What is the ratio of AB to Aa when AB is at its maximum?

13.17. A sample of NaCl weighing 0.100 g is placed in a nuclear reactor and is irradiated in a thermal neutron flux of 1013 neutrons cm-2s-1 for 5.0 h. The thermal neutron activation cross sections (oy, for the n, y reaction) for the production of24Na (14.95 h) and 38Cl (37.2 m) from 23Na (100 at. %) and 37Cl (24.23 at. %) are 0.53 and 0.43 barn, respectively. Rf for the activation reaction is 9oyN, where 9 is the thermal neutron flux and N is the number of atoms in the target having the oy. Calculate the activity of 24Na and 38Cl in becquerels and millicuries at the end of the irradiation. Why is the activation of 35Cl (75.77 at. %, oy = 43.6 barns) to form 36Cl (3.01 x 105y) not important?

13.18. Calculate the weight of pure 137CsCl (30.07y) needed to make a 3.7-TBq (100-Ci) source.

13.19. Carbon-11 (20.3 m) decays to nB (s) by emission of a positron (Emax = 0.960 MeV) without y-ray emission. The isotopic mass of nB is 11.0093055 amu. What is the isotopic mass of nC?

13.20. Zinc-65 (243.8 d) decays to 65Cu (s) with the emission of a 1.115-MeV y ray in only 50.75% of the disintegrations. What is the mode of p decay? Isotopic masses (amu): 65Zn, 64.929243; 65Cu, 64.927793 amu.

13.21. Beryllium-7 (53.28 d) decays to 7Li (s) with the emission of a 0.477-MeV 7 ray. What is the mode of decay? Isotopic masses (amu): 7Be, 7.016928; 7Li, 7.016003.

13.22. Calculate the energy (MeV) available for decay of 32P by negatron emission into stable 32S. Isotopic masses (amu): 32P, 31.973907; 32S, 31.972070.

13.23. The isotopic masses of 64Ni, 64Cu, and 64Zn are 63.927968, 63.929765, and 63.929145 amu, respectively. Which nuclide is radioactive? Calculate the transition energy (MeV) available for it and identify the mode(s) of decay.

13.24. Samarium-147 (1.06 x 1011 y) decays by a-particle emission. Calculate Q and the Coulomb barrier height in MeV for the transition. Isotopic masses (amu): 147Sm, 146.914894; 143Nd, 142.909810; 4He, 4.002603250.

13.25. Calculate the binding energy (MeV) of 4He. (For M values, see Exercise 13-2.)

13.26. Calculate the power output in watts of a source containing 1 kg of 238Pu. Plutonium-238 has a half-life of 87.7 years and emits a particles with energy 5.498 (71.1%) and 5.4565 (28.7%). Gamma-ray intensities are low and can be neglected.

13.27. A sample of a single radionuclide, A, has an activity of 9473 Bq 1.0 day after preparation. The activity is 7519 Bq 5.0 days later. The decay product, B, which was absent initially, is stable. How many atoms of B are present 21.0 days after preparation of A?

13.28. If 3.7 GBq (100 mCi) of 222Rn is released into a sealed room that has the dimensions 10 ft x 10 ft x 8 ft (3.05 m x 3.05 m x 2.44 m) and if all of the 210Pb daughter becomes uniformly adsorbed on the walls, ceiling, and floor of the room, what will be the surface concentation in atoms and the activity concentration in becquerels and picocuries per square meter 60 days after the radon release?

13.29. If the proton is unstable, its half-life must be exceedingly long. Assuming that the half-life is 1032 y, calculate the proton activity in becquerels per year in 1000 metric tons of water.

13.30. Describe with a sketch and explanation what you would expect to see in a cloud chamber photograph when a source emitting only 7 rays is placed inside and near the wall (brass) of a cylindrical cloud chamber if E7 = (a) 0.050 MeV, (b) 0.50 MeV, and (c) 2.50 MeV.

13.31. Although the 4.147-MeV a transition in 238U occurs in 23% of the disintegrations (Figure 13-16), the 49-keV 7 ray is emitted in only 0.32% of the disintegrations. Explain.

13.32. Cobalt-60 (5.271 y) emits two 7 rays per disintegration (1.173 and 1.332 MeV) (Figure 13-9). Estimate the exposure rate in coulombs per kilogram per hour and milliroentgens per hour at 1.0 m from an unshielded 7.4-GBq (200-mCi) point source of 60Co. For a one-hour exposure, what would be the values of the absorbed dose in the units of grays and rads and the equivalent dose in terms of sieverts?

13.33. A collimated beam of 1.0-MeV y rays passes through 2.0 m of air. What fraction of the energy of the beam is absorbed by the air at room temperature and pressure?

13.34. Phosphorus-32 emits negatrons (Emax = 1.709 MeV) without y rays. Should the p-shielding container be made of lead, aluminum, or plastic (containing H, C, and O and having a density of 1.20g/cm3)? Why? What thickness (cm) of the correct shielding material would be required to stop all the negatrons?

13.35. A small 370-MBq (10-mCi) source of 60Co (Figure 13-9) is placed in a lead cylinder having a 2.54-cm-thick wall and an outside diameter of 7.62 cm. Estimate the exposure rate in coulombs per kilogram per hour and milliroentgens per hour at the outer surface of the cylinder from the two y rays. Estimate the fraction of the most energetic bremsstrahlen that will be absorbed in the cylinder wall.

13.36. While walking in a parking lot, you find what looks like a small pearl. You pick it up and decide to hold it tightly in your fist to avoid dropping it. The "pearl" is a 3.7-TBq (100-Ci) source of 137Cs (Figure 13-11). Estimate the absorbed dose to your hand in grays if you hold the source for 30 minutes. Assume that all the p radiation is absorbed in your hand. The mass energy absorption coefficients for bone and muscle are 0.0315 and 0.0326 cm2/g, respectively, for 0.60-MeV y rays, and the value changes slowly with energy at this energy. (Note that for the same two types of tissue, the values are 19.0 and 4.96, respectively, for 10-keV photons.) The fraction of the incident y-ray energy absorbed can be calculated from the decrease in y-ray intensity in passing through your hand.

13.37. For the purposes of various radiological health calculations, a "reference man" (reference person) weighs 70 kg. A reference man also contains 140 g of potassium, which has a natural content of 0.0117 at. % of 40K (1.27 x109y). Potassium is distributed mainly in soft tissue (e.g., muscle).

(a) Calculate the total becquerels and picocuries of 40K in the reference man.

(b) Calculate the number of negatrons emitted in the reference man over a period of 80 years, assuming a constant amount of potassium (see Figure 13-15).

13.38. Using the results of Exercise 13.37 and the decay scheme for 40K (Figure 13-15), estimate the absorbed dose in grays per year and the equivalent dose in sieverts per year from the p radiation from 40K in the soft tissue of a reference man.

13.39. The reference man contains 12.600 kg of carbon.

(a) Calculate the total activity in becquerels and the number of nega-trons emitted per year by 14C in the reference man. (Assume a pre-nuclear-weapons-testing equilibrium value of 0.255 Bq/g of carbon.)

(b) Estimate the absorbed dose in rads per year and in grays per year, and the equivalent dose in sieverts per year.

13.40. How long could you stand 10 ft from a 18.5-TBq (500-Ci) point source of 60Co (Figure 13-9) before receiving a total-body dose corresponding LD50? What would the time be at a distance of 30ft?

13.41. How far (meters) from an unshielded 1.85-GBq (50-mCi) point source of 60Co should you stand in an open area so that (a) the negatrons (see Figure 13-9) and (b) the y rays do not reach you? How far should you stand from the source so that the y-ray exposure rate is 2.58 x 10-6Ckg_1h_1 (10 mR/h)? At this distance, what would the absorbed dose be in rads, and grays, for an exposure of one hour? Recalculate the values for a 185-GBq (5.0-Ci) source.

13.42. Calculate the absorbed dose rate (Gy/h) from the p~ radiation from 111 MBq (3.0 mCi) of 131I uniformly distributed in a thyroid gland weighing 20 g. Eave for p~ particles from 131I is 0.19 MeV.

13.43. Derive equation (13-66) and the following equation for estimating exposure rate in roentgens per hour for a source with an activity of C curies: R/h at 1 ft) = 6nCEy. (Use the absorption coefficient given in footnote 65.)

13.44. If the biological half-life of manganese is 17 days for the total body and the radioactive half-life of 54Mn is 312.1 days, what is the effective total-body half-life of 54Mn?

13.45. Prepare an essay, a class presentation, or a term paper on one of the following.

(a) A summary of the work that has been done to date to find a chemical substance ("protective agent") that could be ingested to protect a person from the effects of ionizing radiation. What type of substance (chemical properties) would be required?

(b) How much the absorbed dose received by patients from x rays in the dental office environment has been reduced, and how the reduction has been achieved for the period of 1930 to date.

(c) Results of research on methods to reduce the biological half-life of elements such as plutonium.

(d) A summary of the methods that have been used and are being used to study neutrinos and antineutrinos.

(e) The methods used by Madame Curie to isolate and purify radium. What connection was there between her laboratory work and her death?

(f) A summary of the properties of stable nuclides that led to the discovery of "magic numbers" and to the formulation of the Nobel Prize-winning shell model for the atomic nucleus.

(g) A brief summary of the chemistry of the hydrated electron.

(h) A summary of the repair mechanisms for damaged DNA.

(i) The status of the controversy on the existence of a threshold for stochastic health effects of ionizing radiation.

(j) The evidence, based on current literature, for and against radiation hormesis.

(k) The latest information about the flux of cosmic rays and solar neutrinos reaching the earth's surface.

(l) An update on any changes in recommended quantities and units for dosimetry of ionizing radiation and any changes in regulations involving changes in such quantities and units.

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