Exercises — Chapter 29
Natural Radioactivity and Internal Dose
Problem 29.1 ⭐ A 65 kg woman has a total body potassium content of 120 g.
(a) Calculate the number of ${}^{40}\text{K}$ atoms in her body, given that the isotopic abundance of ${}^{40}\text{K}$ is 0.0117% and $A = 40\,\text{g/mol}$.
(b) Calculate the activity of ${}^{40}\text{K}$ in her body in Bq, using $t_{1/2} = 1.248 \times 10^9\,\text{yr}$.
(c) What fraction of these decays produce the characteristic 1.461 MeV gamma ray?
(d) Estimate the number of 1.461 MeV gamma rays emitted from her body per second.
Problem 29.2 ⭐ A soil sample from a granitic region contains 5.0 ppm of uranium by mass.
(a) Calculate the specific activity of ${}^{238}\text{U}$ in this soil (Bq/kg). Assume all uranium is ${}^{238}\text{U}$ ($t_{1/2} = 4.468 \times 10^9\,\text{yr}$).
(b) Assuming secular equilibrium throughout the full ${}^{238}\text{U}$ decay chain (14 members), what is the total activity per kg of soil from the entire chain?
(c) In practice, secular equilibrium is broken because ${}^{222}\text{Rn}$ (a noble gas) escapes from the soil. If 40% of the radon escapes before decaying, what is the activity of ${}^{214}\text{Pb}$ (a post-radon daughter) relative to ${}^{238}\text{U}$?
Problem 29.3 ⭐ Carbon-14 is produced in the atmosphere by the reaction ${}^{14}\text{N}(n,p){}^{14}\text{C}$.
(a) Write the balanced nuclear reaction and verify that charge and mass number are conserved.
(b) The equilibrium ${}^{14}\text{C}/{}^{12}\text{C}$ ratio in the atmosphere is approximately $1.2 \times 10^{-12}$. A living organism contains 18% carbon by mass. For a 70 kg person, calculate the number of ${}^{14}\text{C}$ atoms.
(c) Calculate the ${}^{14}\text{C}$ activity in this person's body (Bq), given $t_{1/2} = 5{,}730\,\text{yr}$.
(d) After death, how long does it take for the ${}^{14}\text{C}$ activity to drop to 1% of its initial value?
Problem 29.4 ⭐⭐ The ${}^{232}\text{Th}$ decay chain has 10 steps (6 alpha, 4 beta) and terminates at ${}^{208}\text{Pb}$.
(a) Starting from ${}^{232}\text{Th}$, write out the complete decay chain, identifying each step as $\alpha$ or $\beta^-$ decay. Verify that you arrive at ${}^{208}\text{Pb}$.
(b) A kilogram of monazite sand from the Kerala coast contains 10% ThO$_2$ by mass. Calculate the ${}^{232}\text{Th}$ activity per kg of sand ($t_{1/2} = 1.405 \times 10^{10}\,\text{yr}$, $M_{\text{ThO}_2} = 264\,\text{g/mol}$, $M_{\text{Th}} = 232\,\text{g/mol}$).
(c) What is the total activity per kg from the entire chain in secular equilibrium?
(d) Compare this to the activity from typical soil (25 Bq/kg of ${}^{232}\text{Th}$) and explain why the Kerala coast is a natural high-background radiation area.
Cosmic Rays and Altitude
Problem 29.5 ⭐ Using the exponential approximation $\dot{D}(h) = \dot{D}_0 \, e^{h/h_0}$ with $\dot{D}_0 = 0.34\,\text{mSv/yr}$ and $h_0 = 1{,}500\,\text{m}$:
(a) Calculate the cosmic ray dose rate at the altitude of Denver (1,600 m), Bogota (2,640 m), and the summit of Mont Blanc (4,808 m).
(b) A hiker spends 14 days per year at altitudes above 3,000 m (average 3,500 m). What additional annual dose does this contribute beyond the sea-level baseline?
(c) At what altitude does the cosmic ray dose rate equal 10 times the sea-level rate?
Problem 29.6 ⭐⭐ An airline pilot flies 900 hours per year at an average cruising altitude where the dose rate is 5 $\mu$Sv/hr.
(a) Calculate the pilot's annual cosmic ray dose in mSv.
(b) Compare this to the ICRP occupational dose limit (20 mSv/yr averaged over 5 years). What fraction of the limit does this represent?
(c) The pilot also receives the sea-level background dose during non-flying hours. Calculate the total annual dose from cosmic rays (flying + ground).
(d) EU Directive 2013/59/Euratom requires airlines to monitor crew doses. If the airline wants to ensure no crew member exceeds 6 mSv/yr from cosmic radiation, what is the maximum number of flying hours permitted? State your assumptions.
Radon
Problem 29.7 ⭐ A home has a measured radon concentration of 200 Bq/m$^3$ in the basement.
(a) Express this concentration in pCi/L.
(b) Does this exceed the EPA action level (4 pCi/L)? The WHO reference level (100 Bq/m$^3$)?
(c) Assuming an equilibrium factor of 0.4 (meaning the radon daughter activity is 40% of the radon activity, due to plate-out on surfaces and ventilation), and using the UNSCEAR dose conversion factor of 9 nSv per Bq$\cdot$h/m$^3$ for the equilibrium-equivalent concentration, estimate the annual effective dose to an occupant who spends 7,000 hours per year indoors.
Problem 29.8 ⭐⭐ A ${}^{226}\text{Ra}$ source with activity 1.00 kBq is sealed in a container.
(a) Using the secular equilibrium result from Chapter 12, what is the activity of ${}^{222}\text{Rn}$ in the container after a long time (many radon half-lives)?
(b) If the container is opened and the radon is released into a sealed 50 m$^3$ room, what is the initial radon concentration in the room (Bq/m$^3$)?
(c) After the container is closed again, how does the radon concentration in the room vary with time? Write the expression for $C(t)$ and calculate the concentration after 1 day, 1 week, and 1 month.
(d) Is the room above the EPA action level at any of these times?
Problem 29.9 ⭐⭐ The "radon diffusion length" in soil is defined as $l = \sqrt{D_e / \lambda}$, where $D_e$ is the effective diffusion coefficient of radon in soil gas ($D_e \approx 2 \times 10^{-6}\,\text{m}^2/\text{s}$ for typical soil) and $\lambda$ is the decay constant of ${}^{222}\text{Rn}$.
(a) Calculate the diffusion length $l$.
(b) Interpret this physically: what does $l$ represent in terms of radon transport?
(c) A house foundation is 2 m below the surface. If the radon production rate is uniform throughout the soil, approximately what fraction of the radon produced within the diffusion length of the foundation can reach the basement before decaying?
(d) Explain qualitatively why sub-slab depressurization is so effective at reducing indoor radon: how does it change the transport mechanism from diffusion to advection?
Dose Calculations and Radiation Protection
Problem 29.10 ⭐ A ${}^{137}\text{Cs}$ point source has an activity of 500 MBq.
(a) The specific gamma-ray dose constant for ${}^{137}\text{Cs}$ is $\Gamma = 76.8\,\mu\text{Sv}\cdot\text{m}^2/(\text{GBq}\cdot\text{h})$. Calculate the dose rate at a distance of 1 m from the source.
(b) How far must you stand to reduce the dose rate to 1 $\mu$Sv/hr?
(c) If the source is shielded by lead, how many half-value layers are needed to reduce the unshielded dose rate at 1 m to below 1 $\mu$Sv/hr? (HVL for ${}^{137}\text{Cs}$ in lead = 6.5 mm.)
(d) What thickness of lead (in mm) does this correspond to?
Problem 29.11 ⭐ Convert between dose units:
(a) A patient receives an absorbed dose of 0.5 Gy of X-rays to the whole body. What is the equivalent dose in Sv?
(b) A nuclear worker accidentally inhales ${}^{241}\text{Am}$ particles that deposit 2 mGy of alpha radiation to the lungs. What is the equivalent dose to the lungs? What is the contribution to the effective dose?
(c) A person receives the following doses in a year: 0.5 mGy of gamma rays to the whole body, 0.1 mGy of alpha particles to the lungs, and 0.02 mGy of neutrons (average $w_R = 10$) to the whole body. Calculate the total effective dose.
Problem 29.12 ⭐⭐ A radiation worker performs a task that exposes her to a ${}^{60}\text{Co}$ source ($E_\gamma = 1.17$ and $1.33\,\text{MeV}$). The unshielded dose rate at the working position is 200 $\mu$Sv/hr.
(a) If the task takes 30 minutes, what is the dose without shielding?
(b) A 5 cm lead shield (HVL for ${}^{60}\text{Co}$ in lead = 12 mm) is placed between the worker and the source. What is the dose rate behind the shield?
(c) With the shield in place, how long can the worker perform the task before accumulating 10 $\mu$Sv?
(d) If the worker performs this task once per week for 50 weeks, what is her annual dose from this source (with the shield)? Compare to the occupational limit.
Problem 29.13 ⭐⭐ A contaminated area has a uniform surface deposit of ${}^{137}\text{Cs}$ with an activity of 500 kBq/m$^2$.
(a) Using the rule of thumb that a surface contamination of 1 MBq/m$^2$ of ${}^{137}\text{Cs}$ produces a dose rate of approximately 5.4 $\mu$Sv/hr at 1 m above the surface, estimate the dose rate in the contaminated area.
(b) If a person spends 8 hours per day in this area for 365 days, what is the annual external dose?
(c) The contamination was deposited by the Chernobyl accident. Using the ${}^{137}\text{Cs}$ half-life of 30.17 years, what will the surface activity and dose rate be in 2056 (70 years after the accident)?
(d) What was the surface activity in 1986 (at the time of deposition)?
Biological Effects
Problem 29.14 ⭐⭐ A radiation accident exposes a worker to an estimated whole-body dose of 3 Sv of gamma radiation over a period of approximately 10 minutes.
(a) Classify the expected acute effects, referring to the dose thresholds in Section 29.5.2.
(b) The worker's blood is drawn at 6, 24, and 48 hours after exposure. Describe qualitatively what changes you would expect to see in the lymphocyte count.
(c) Estimate the worker's excess lifetime cancer risk using the ICRP risk coefficient.
(d) What is the approximate probability of survival with modern medical treatment? What supportive care measures would be indicated?
Problem 29.15 ⭐⭐⭐ The Life Span Study reports an excess relative risk (ERR) for solid cancers of 0.47 per Sv for the atomic bomb survivors.
(a) If the baseline solid cancer mortality rate is 25%, what is the absolute excess risk for a survivor who received a dose of 500 mSv?
(b) In a cohort of 10,000 survivors who each received 500 mSv, how many excess cancer deaths would the LNT model predict?
(c) The standard deviation of the number of cancer deaths in a group of 10,000 people (baseline 25%) is $\sigma = \sqrt{n \cdot p \cdot (1-p)} \approx 43$. Is the predicted excess detectable against this statistical background? (Hint: calculate the signal-to-noise ratio.)
(d) Repeat part (c) for a dose of 50 mSv. Comment on why the LNT debate is scientifically irresolvable at low doses.
Problem 29.16 ⭐⭐⭐ Consider two models for cancer risk at low doses:
- Model A (LNT): $R(D) = R_0 + \alpha D$, with $\alpha = 5\%\,\text{per Sv}$.
- Model B (Threshold): $R(D) = R_0$ for $D < D_{\text{th}}$; $R(D) = R_0 + \alpha(D - D_{\text{th}})$ for $D \geq D_{\text{th}}$, with $D_{\text{th}} = 100\,\text{mSv}$.
(a) Plot both models for doses from 0 to 1 Sv (sketch or calculate at several points). Assume $R_0 = 25\%$.
(b) What is the difference in predicted excess cancer risk between the two models at $D = 50$ mSv? At $D = 200$ mSv?
(c) Using the formula for required sample size from Section 29.5.3, estimate the number of subjects needed to distinguish between these two models at $D = 50$ mSv with 80% power.
(d) Compare your answer to the total number of atomic bomb survivors with doses in the 30–70 mSv range (approximately 15,000). Is the LSS large enough to resolve this question?
Nuclear Accidents and Environmental Monitoring
Problem 29.17 ⭐⭐ The Chernobyl accident released approximately $1.8 \times 10^{18}$ Bq of ${}^{131}\text{I}$ ($t_{1/2} = 8.02$ d).
(a) How many atoms of ${}^{131}\text{I}$ were released?
(b) What mass of ${}^{131}\text{I}$ does this correspond to (in grams)?
(c) After 80 days (approximately 10 half-lives), what fraction of the released ${}^{131}\text{I}$ remains?
(d) A child in the contaminated region drank milk contaminated with ${}^{131}\text{I}$ at a concentration of 100 kBq/L for one week (0.5 L/day), starting 3 days after the accident. Estimate the total ${}^{131}\text{I}$ intake (Bq), accounting for the radioactive decay during the week of consumption.
Problem 29.18 ⭐⭐⭐ After the Fukushima accident, ${}^{137}\text{Cs}$ contamination was deposited over a wide area. Consider a region with initial ${}^{137}\text{Cs}$ deposition of 1 MBq/m$^2$.
(a) Using the dose conversion factor from Problem 29.13, what is the initial external dose rate at 1 m above the ground?
(b) In addition to radioactive decay ($t_{1/2} = 30.17$ yr), the effective environmental half-life of ${}^{137}\text{Cs}$ is shorter due to weathering (rain wash-off, soil migration, etc.). If the environmental half-life is 5 years and the decay half-life is 30.17 years, calculate the effective half-life using: $$\frac{1}{t_{\text{eff}}} = \frac{1}{t_{\text{decay}}} + \frac{1}{t_{\text{weather}}}$$
(c) Using the effective half-life, when will the dose rate drop below 0.5 $\mu$Sv/hr (approximately the threshold for considering resettlement)?
(d) Contrast this with the result using only radioactive decay. Discuss the practical implications for evacuation zone management.
Problem 29.19 ⭐⭐⭐ The "bomb pulse" of ${}^{14}\text{C}$: atmospheric nuclear testing approximately doubled the ${}^{14}\text{C}/{}^{12}\text{C}$ ratio, peaking around 1963.
(a) The ${}^{14}\text{C}$ excess is decreasing exponentially with a half-life of approximately 16 years (due to mixing with the ocean, not radioactive decay). Write an expression for the atmospheric ${}^{14}\text{C}/{}^{12}\text{C}$ ratio as a function of time since 1963, given the equilibrium ratio is $R_{\text{eq}} = 1.2 \times 10^{-12}$ and the peak ratio was $R_{\text{peak}} \approx 2R_{\text{eq}}$.
(b) What was the ratio in 2023?
(c) A forensic scientist measures the ${}^{14}\text{C}/{}^{12}\text{C}$ ratio in a sample of human lens protein (which is not replaced after formation) and finds it to be $1.6 \times 10^{-12}$. Approximately when was this protein formed?
Dosimetry
Problem 29.20 ⭐ A TLD badge (LiF:Mg,Ti) is worn by a radiation worker for one month. Upon readout, the thermoluminescent glow curve indicates an absorbed dose of 0.45 mGy.
(a) The worker was exposed to a mixed field of photons and thermal neutrons. If 80% of the dose was from photons ($w_R = 1$) and 20% from thermal neutrons ($w_R = 2.5$), calculate the equivalent dose.
(b) If this is a whole-body dosimeter, what is the effective dose? (Assume uniform irradiation.)
(c) Project the annual dose assuming this monthly rate is constant. Does it approach any regulatory limit?
(d) LiF has an effective atomic number of 8.2, while tissue has an effective $Z$ of 7.4. For 50 keV photons, where the photoelectric effect dominates, would the TLD overestimate or underestimate the tissue dose? Explain qualitatively using the $Z$-dependence of the photoelectric effect.
Problem 29.21 ⭐⭐ After a suspected radiation exposure, a dicentric chromosome assay is performed on a blood sample.
(a) In 500 cells scored, 35 dicentric chromosomes are found. If the background rate is 1–2 dicentrics per 1,000 cells, and the dose-response for gamma rays follows $Y = 0.001 + 0.05D + 0.065D^2$ (dicentrics per cell, $D$ in Gy), estimate the absorbed dose.
(b) The uncertainty in the dicentric count follows Poisson statistics: $\sigma = \sqrt{n}$. What is the 95% confidence interval for the dicentric frequency?
(c) Propagate this uncertainty to estimate the uncertainty in the dose estimate.
Integration and Synthesis
Problem 29.22 ⭐⭐ Construct a complete radiation budget for the following individual: a 35-year-old non-smoking woman living in Denver, CO (altitude 1,600 m), in a home with radon concentration 100 Bq/m$^3$, who had two abdominal CT scans this year and works as a dental hygienist (occupational dose ~0.5 mSv/yr from dental X-rays).
(a) Estimate the annual dose from each source: cosmic rays, terrestrial, radon, internal, medical (the two CTs), occupational.
(b) What is her total annual effective dose?
(c) Which single source dominates? Would radon mitigation be recommended?
(d) How does her total compare to the US average of 6.2 mSv/yr?
Problem 29.23 ⭐⭐⭐ Compare the radiation doses and risks from two energy-producing technologies.
(a) A 1 GW$_e$ nuclear power plant operates for one year and, under normal conditions, releases radioactive effluent producing a maximum dose of 0.01 mSv to the nearest resident. If 100,000 people live within 30 km, estimate the collective dose (person-Sv) and the predicted number of excess cancers (using LNT).
(b) A 1 GW$_e$ coal power plant burns 3 million tonnes of coal per year, each tonne containing 2 ppm of uranium and 5 ppm of thorium. The fly ash concentrates these by a factor of ~10. If 1% of the ash is released to the atmosphere, estimate the total ${}^{238}\text{U}$ and ${}^{232}\text{Th}$ activity released per year.
(c) Discuss the limitations of using LNT-derived collective dose calculations for such comparisons. When is collective dose a useful concept, and when is it misleading?
Problem 29.24 ⭐⭐⭐ (Design problem) A hospital is building a new CT suite. The maximum dose rate in the adjoining corridor (occupied area) must not exceed 0.02 mSv/week. The CT scanner produces a dose rate of 5 mSv/hr at 1 m from the isocenter, operates 40 hours/week at 50% utilization (beam-on time), and the corridor is 3 m from the isocenter.
(a) Calculate the unshielded dose rate in the corridor during beam-on time.
(b) Calculate the weekly unshielded dose in the corridor, accounting for the beam-on utilization factor.
(c) What attenuation factor is required to meet the dose limit?
(d) How many HVLs of lead are needed? (Use HVL = 0.28 mm Pb for the effective CT beam energy of ~70 keV.)
(e) What thickness of lead is needed? Is this a practical amount?
Problem 29.24a ⭐⭐ (Shielding design — neutrons) A research laboratory has an Am-Be neutron source (average neutron energy ~4.5 MeV) with an emission rate of $10^7$ neutrons/s. The unshielded dose rate at 1 m is approximately 0.85 mSv/hr.
(a) If the lab must maintain the dose rate below 10 $\mu$Sv/hr at the operator's position (2 m from the source), what is the required total attenuation factor (accounting for both distance and shielding)?
(b) The shield will be borated polyethylene (${}^{10}\text{B}$-loaded, density 0.95 g/cm$^3$). The effective HVL for Am-Be neutrons in this material is approximately 6 cm. How many HVLs are required, and what is the total shield thickness?
(c) Why is lead ineffective for neutron shielding? What role does the ${}^{10}\text{B}$ play after the neutrons have been moderated by the polyethylene?
(d) A 5 cm layer of lead is added outside the polyethylene. What is its purpose? (Hint: consider what happens when neutrons are captured by ${}^{10}\text{B}$.)
Problem 29.24b ⭐⭐ (Practical dosimetry) A radiation safety officer must choose a personal dosimeter technology for three different work environments. For each, recommend the most appropriate technology (TLD, OSL, EPD, or film badge) and justify your choice:
(a) A hospital radiology department where technologists receive low, chronic doses and dosimeters are read monthly.
(b) A nuclear power plant maintenance crew entering a high-dose-rate area ($> 1$ mSv/hr) during a reactor outage.
(c) A research laboratory in a developing country with limited readout infrastructure and unreliable electricity.
(d) For the nuclear plant scenario in (b), the EPD alarms at 100 $\mu$Sv cumulative dose and 500 $\mu$Sv/hr dose rate. If the actual dose rate in the work area is 2 mSv/hr, how long after entering the area will each alarm trigger?
Research Problems
Problem 29.25 ⭐⭐⭐⭐ (Research) Read the executive summary of BEIR VII (2006), available from the National Academies Press.
(a) Summarize the committee's conclusions regarding the LNT model in 3–4 sentences.
(b) What alternative models did the committee consider, and why did they find them less well-supported by the evidence?
(c) The BEIR VII report estimates that a dose of 100 mSv increases the lifetime cancer risk by approximately 1% above the 42% baseline. Calculate the number of subjects needed to detect this 1% increase with 95% confidence and 80% power.
(d) Given that the total LSS cohort is ~120,000 and doses are distributed across a wide range, critically evaluate whether the LSS can resolve the shape of the dose-response curve below 100 mSv.
Problem 29.26 ⭐⭐⭐⭐ (Research) The Ramsar high-background region in Iran has areas with natural radiation doses up to 260 mSv/yr — roughly 100 times the global average.
(a) Research and summarize the epidemiological studies conducted in Ramsar. What cancer rates have been observed compared to control populations?
(b) What are the major confounding factors that limit the statistical power of these studies?
(c) Some hormesis advocates cite Ramsar as evidence against LNT. Critically evaluate this claim: what would a definitive study require?
(d) If the LNT model were exactly correct, how many excess cancers per year would you predict in a population of 2,000 exposed to 50 mSv/yr (a moderate level for Ramsar)? Compare this to the expected statistical fluctuation.
Problem 29.27 ⭐⭐⭐⭐ (Research) The concept of "collective dose" (total dose summed over a population, in person-Sv) is used in regulatory assessments but is controversial.
(a) Define collective dose and explain how it is calculated.
(b) The global population (8 billion) receives an average of 3 mSv/yr from natural background. What is the collective dose? Using the LNT risk coefficient, how many "radiation-induced" cancers per year does this predict?
(c) Is this number meaningful? The ICRP explicitly warns against using collective dose to predict cancer cases in populations exposed to very low individual doses. Explain the statistical and philosophical reasons for this warning.
(d) Propose a scenario where collective dose is a genuinely useful concept for decision-making, and one where it is clearly misleading.
Problem 29.28 ⭐⭐ (Computational) Using the dose comparison calculator from this chapter's code exercise (or your own implementation):
(a) Generate a complete radiation budget for a hypothetical resident of Guarapari, Brazil (annual terrestrial dose: 15 mSv, radon: 3 mSv, cosmic: 0.35 mSv, internal: 0.29 mSv, medical: 0.6 mSv).
(b) Compare this graphically to the US average and to a resident of Denver who has had three CT scans in a year.
(c) Calculate the LNT-predicted excess lifetime cancer risk for each scenario, assuming 70-year exposure at the annual rate.
(d) Discuss the validity (or invalidity) of this calculation.
Problem 29.29 ⭐⭐ (Environmental monitoring) After a hypothetical nuclear accident, a gamma spectrometer at a monitoring station 50 km downwind detects ${}^{131}\text{I}$ (364 keV), ${}^{137}\text{Cs}$ (662 keV), and ${}^{134}\text{Cs}$ (605 and 796 keV) in an air filter sample.
(a) The ${}^{134}\text{Cs}/{}^{137}\text{Cs}$ activity ratio can distinguish reactor accidents from weapons fallout. Explain why: what is the origin of ${}^{134}\text{Cs}$ in a reactor, and why is it absent from weapons fallout? (Hint: ${}^{134}\text{Cs}$ is produced by neutron activation of stable ${}^{133}\text{Cs}$, which is itself a fission product.)
(b) For the Fukushima accident, the initial ${}^{134}\text{Cs}/{}^{137}\text{Cs}$ activity ratio was approximately 1.0. Given their half-lives (${}^{134}\text{Cs}$: 2.065 yr; ${}^{137}\text{Cs}$: 30.17 yr), what will the ratio be 10 years after the accident? 30 years after?
(c) A soil sample collected in 2025 from northern Japan shows a ${}^{134}\text{Cs}/{}^{137}\text{Cs}$ ratio of 0.0047. Verify that this is consistent with Fukushima-origin contamination (accident date: March 2011).
(d) Why is the ${}^{131}\text{I}$ detected in the air filter but not in the soil sample collected years later?
Problem 29.30 ⭐⭐ A radiological emergency dispatcher must estimate doses to first responders entering a contaminated area. The measured ambient dose equivalent rate at the area boundary is 500 $\mu$Sv/hr.
(a) If a team of two enters the area for a 20-minute search-and-rescue mission, what dose does each team member receive?
(b) The ICRP recommends an emergency reference level of 500 mSv for life-saving actions and 100 mSv for actions that bring no direct individual benefit. How many 20-minute missions could a single responder perform before reaching the life-saving reference level?
(c) If 50 responders each perform one 20-minute mission, what is the collective dose (in person-mSv)? Using the LNT risk coefficient, what is the predicted number of excess cancers? Comment on whether this calculation is meaningful for such a small collective dose.
(d) The contamination source is ${}^{137}\text{Cs}$. The dose rate decays with the half-life of 30.17 years. How long until the boundary dose rate drops below 1 $\mu$Sv/hr (approximate threshold for unrestricted access)?