This guide provides an expert-level analysis of the concepts and problem-solving methodologies required for the American Board of Health Physics (ABHP) Part II Comprehensive Examination. The content is synthesized from a detailed review of historical examinations and updated with key concepts from modern standards and recommendations. It is designed for candidates seeking a deep, operational understanding of health physics principles to demonstrate for certification.
Quick Reference: Constants & Conversions
A collection of fundamental constants and conversion factors frequently used in health physics calculations. Memorizing these is highly recommended.
Fundamental Constants
- Avogadro's Number ($N_A$): $6.022 \times 10^{23}$ atoms/mole
- Electron Rest Mass: $0.511$ MeV/c²
Activity Units
- 1 Curie (Ci) = $3.7 \times 10^{10}$ Bq (dps)
- 1 Becquerel (Bq) = 1 dps = $2.7 \times 10^{-11}$ Ci
- 1 $\mu$Ci = $2.22 \times 10^6$ dpm
Dose & Exposure Units
- 1 R = $2.58 \times 10^{-4}$ C/kg air
- 1 rad = 100 erg/g = 0.01 Gy
- 1 rem = 0.01 Sv
Key Half-Lives
- H-3: 12.3 y
- C-14: 5730 y
- Co-60: 5.27 y
- Sr-90: 29.1 y
- I-131: 8.02 d
- Cs-137: 30.1 y
- Ra-226: 1600 y
- Pu-239: 24,100 y
Rules of Thumb
- $E_{avg}$ for beta $\approx \frac{1}{3} E_{max}$
- Co-60 $\Gamma \approx 1.3 \frac{R \cdot m^2}{hr \cdot Ci}$
- Ir-192 $\Gamma \approx 0.5 \frac{R \cdot m^2}{hr \cdot Ci}$
- Cs-137 $\Gamma \approx 0.33 \frac{R \cdot m^2}{hr \cdot Ci}$
- HVL (Concrete) for Co-60 $\approx$ 2 in
- TVL (Lead) for Co-60 $\approx$ 2 in
Miscellaneous
- Std. Atmospheric Pressure: 760 mmHg
- Reference Man Breathing Rate: 1.2 m³/hr
- Working Year: 2000 hr
I. Radiation Physics & Interactions
This section covers the foundational principles of radioactive decay and the interaction of radiation with matter. A deep, quantitative understanding of these topics is essential, as they form the basis for all other domains of health physics.
1. Radioactive Decay & Energetics
Key Numbers & Data
- Electron Rest Mass Energy: $m_e c^2 = 0.511 \text{ MeV}$
- Pair Production Threshold: $2 m_e c^2 = 1.022 \text{ MeV}$
- Avogadro's Number ($N_A$): $6.023 \times 10^{23} \text{ atoms/mole}$
Key Calculation: Q-value from Mass Excess
Apply the conservation of mass-energy for each decay mode using atomic mass excesses ($\Delta$).
- Positron ($\beta^+$) Decay: $Q_{\beta^+} = \Delta_{parent} - \Delta_{daughter} - 2m_e c^2$
- Electron Capture (EC): $Q_{EC} = \Delta_{parent} - \Delta_{daughter}$
- Beta Minus ($\beta^-$) Decay: $Q_{\beta^-} = \Delta_{parent} - \Delta_{daughter}$
Parent-Daughter Equilibria
The activity of a daughter nuclide, $A_2$, at time t is given by the Bateman equation:
$$A_2(t) = \frac{\lambda_2}{\lambda_2 - \lambda_1} A_1(0) (e^{-\lambda_1 t} - e^{-\lambda_2 t}) + A_2(0)e^{-\lambda_2 t}$$- Transient Equilibrium ($T_{1} > T_{2}$): Occurs when the parent is longer-lived than the daughter (e.g., ${}^{99}$Mo/${}^{99m}$Tc). After several daughter half-lives, the daughter appears to decay with the parent's half-life. The activity ratio becomes constant: $\frac{A_2}{A_1} = \frac{\lambda_2}{\lambda_2 - \lambda_1}$.
- Secular Equilibrium ($T_{1} \gg T_{2}$): Occurs when the parent is much longer-lived (e.g., ${}^{90}$Sr/${}^{90}$Y). At equilibrium, the activities become equal: $A_2 \approx A_1$.
Decay Schemes & Nuclear Transitions
Beyond simple decay, you must understand the processes by which an excited nucleus reaches its ground state.
- Gamma Emission: An excited nucleus releases energy by emitting a photon (gamma ray) of a discrete energy corresponding to the difference between nuclear energy levels.
- Internal Conversion (IC): An excited nucleus transfers its energy directly to an orbital electron (usually from the K or L shell), ejecting it from the atom. This is a radiationless transition and is competitive with gamma emission. The ejected electron is called a conversion electron. IC is more probable in high-Z nuclei and for low-energy transitions.
- Isomeric Transition (IT): Occurs in nuclides with a metastable state (e.g., ${}^{99m}$Tc, ${}^{137m}$Ba). The nucleus remains in an excited state for a measurable half-life before de-exciting, typically via gamma emission or internal conversion.
2. Neutron Physics
Neutron Energy Classifications
- Thermal Neutrons: In thermal equilibrium with their surroundings (~0.025 eV).
- Epithermal Neutrons: Energy range from ~0.1 eV to ~100 keV.
- Fast Neutrons: Energy range from ~100 keV to ~20 MeV.
Neutron Sources & Interactions
- Sources: Be familiar with common neutron sources:
- Spontaneous Fission (SF): e.g., ${}^{252}$Cf.
- $(\alpha, n)$ Reactions: An alpha emitter mixed with a light element, e.g., AmBe or PuBe.
- Photoneutron $(\gamma, n)$ Reactions: High-energy photons (>~8 MeV) interacting with matter, common around high-energy accelerators.
- Interactions:
- Elastic Scattering: "Billiard ball" collision where kinetic energy is conserved. This is the primary mechanism for moderating (slowing down) fast neutrons, and it is most efficient with low-Z materials (like hydrogen in water or polyethylene).
- Inelastic Scattering: The neutron is captured and re-emitted with lower energy, leaving the target nucleus in an excited state. This has an energy threshold and is important for fast neutrons in high-Z materials.
- Radiative Capture $(n, \gamma)$: The dominant interaction for thermal neutrons. The nucleus absorbs the neutron and emits a prompt gamma ray. This is the basis for most activation calculations.
Key Calculation: Activity from Neutron Irradiation
The activity of a product nuclide after an irradiation time ($t_{irrad}$) followed by a decay time (t) is:
$$A(t) = N \sigma \phi (1 - e^{-\lambda t_{irrad}})e^{-\lambda t}$$Where $N$ is the number of target atoms, $\sigma$ is the cross-section, and $\phi$ is the neutron flux. The term $(1 - e^{-\lambda t_{irrad}})$ is the **saturation factor**. As $t_{irrad} \to \infty$, this term approaches 1, and the activity reaches its maximum possible value, the **saturation activity ($A_{sat} = N \sigma \phi$)**.
Key Calculation: Fast Neutron Shielding
For fast neutrons, an empirical "removal" cross-section ($\Sigma_R$) can be used for shielding calculations in a manner analogous to photon attenuation.
$$\phi(x) = \phi_0 e^{-\Sigma_R x}$$Where $\phi_0$ is the initial fast neutron flux, $\phi(x)$ is the flux after passing through a thickness x of shield material. This method is an approximation that accounts for the removal of fast neutrons from the beam by all types of interactions.
3. Interaction of Radiation with Matter
Photon Interactions: The "Big Three"
Understanding the relative importance of the three main photon interactions is crucial for shielding, dosimetry, and detector selection.
- Photoelectric Effect: An "all or nothing" absorption of a photon by a bound atomic electron. It is the dominant interaction for low-energy photons and in high-Z materials. The cross-section is approximately proportional to $\frac{Z^4}{E^3}$. This interaction is responsible for the high efficiency of NaI detectors at low energies and the effectiveness of lead shielding.
- Compton Scattering: An interaction with a "free" or loosely-bound electron. The photon scatters at an angle, losing some of its energy to the recoil electron. It is the dominant interaction for mid-energy photons (approx. 0.5-5 MeV) in most materials, including tissue. This is the primary source of scatter in shielding and the physical basis for the Compton continuum in a gamma spectrum.
- Pair Production: A high-energy photon interacts in the electric field of a nucleus and is converted into an electron-positron pair. It has a strict energy threshold of 1.022 MeV. The positron subsequently annihilates, producing two 0.511 MeV photons. This interaction is dominant for high-energy photons in high-Z materials.
Photon Interaction Dominance
Being able to sketch the regions of dominance for the "Big Three" interactions as a function of photon energy and absorber atomic number (Z) is a classic exam topic.

Key Calculation: Compton Scattering Kinematics
You must be able to calculate the energy of the scattered photon ($E_{\gamma'}$) and the recoil electron ($T_e$).
- Scattered Photon Energy: $$E_{\gamma'} = \frac{E_\gamma}{1 + \frac{E_\gamma}{m_e c^2}(1 - \cos\theta)}$$ Where $\theta$ is the photon scattering angle. The maximum energy transfer (minimum $E_{\gamma'}$) occurs at a 180° backscatter.
- Recoil Electron Energy: By conservation of energy: $$T_e = E_\gamma - E_{\gamma'}$$ The maximum electron energy, which defines the "Compton Edge" in a spectrum, occurs at 180° photon scatter.
Attenuation vs. Absorption Coefficients
It is critical to distinguish between the linear attenuation coefficient ($\mu$) and the energy absorption coefficient ($\mu_{en}$).
- Linear Attenuation Coefficient ($\mu$): Describes the fraction of photons removed from a narrow beam per unit thickness. It includes all interactions (photoelectric, Compton, pair production). It is used for shielding calculations: $I = I_0 e^{-\mu x}$.
- Energy Absorption Coefficient ($\mu_{en}$): Describes the fraction of photon energy that is deposited in the material via the kinetic energy of secondary electrons. It is always less than $\mu$ because it excludes the energy carried away by scattered photons, annihilation photons, and bremsstrahlung. It is used for calculating KERMA and absorbed dose.
Charged Particle Interactions
- Linear Energy Transfer (LET): The average energy deposited by a charged particle per unit path length. High-LET radiation (alphas, protons) is more biologically damaging than low-LET radiation (betas, gammas) for the same absorbed dose.
- Bragg Peak: Heavy charged particles (alphas, protons) deposit the majority of their energy at the very end of their track. This peak in energy deposition is called the Bragg peak and is the principle behind proton therapy.
- Beta Spectrum: Beta particles are emitted with a continuous spectrum of energies up to a maximum ($E_{max}$). This is because the decay energy is shared with a neutrino. This continuous spectrum is why beta attenuation in matter appears roughly exponential, even though individual electrons have a finite range.
Key Calculation: Alpha Particle Range in Air
A useful empirical formula for the range of an alpha particle in air at standard temperature and pressure is:
$$R_{air} (cm) = 0.32 E_{\alpha} (MeV)^{3/2}$$Bremsstrahlung Production
Bremsstrahlung ("braking radiation") is produced when a high-energy charged particle (typically an electron) decelerates rapidly in the electric field of a nucleus. This is a key consideration for beta shielding.
- Energy Dependence: The fraction of energy lost to bremsstrahlung is proportional to the initial electron energy (E) and the atomic number (Z) of the absorber: $$f \approx \frac{ZE}{800}$$
- Shielding Implication: To shield high-energy beta emitters (e.g., Sr-90/Y-90), a low-Z material (like plastic or aluminum) should be used as the primary shield to minimize bremsstrahlung production. A high-Z material (like lead) can then be placed outside the low-Z shield to attenuate the bremsstrahlung x-rays produced.
II. Shielding & External Dose Assessment
This section moves beyond simple point-source calculations to cover complex geometries, buildup physics, and specialized operational scenarios that are hallmarks of the Part II exam.
Core Concepts in Photon Shielding
Key Data & Definitions
- Gamma Constant ($\Gamma$): The unshielded exposure rate (e.g., R/hr) at a unit distance (e.g., 1 m) from a unit activity (e.g., 1 Ci) of a specific radionuclide. It is an empirical value that integrates the energy and yield of all photons from the source.
- KERMA vs. Absorbed Dose:
- KERMA (Kinetic Energy Released in Media): Energy transferred from uncharged particles (photons) to charged particles (electrons) per unit mass.
- Absorbed Dose: Energy deposited by charged particles per unit mass. Under conditions of Charged Particle Equilibrium (CPE), KERMA equals Absorbed Dose. A buildup cap on an ion chamber is used to establish CPE in the detector's sensitive volume.
The Buildup Factor (B)
The simple exponential attenuation equation, $I = I_0 e^{-\mu x}$, is only valid for narrow-beam conditions. For shielding calculations, you must account for scattered photons.
- Physical Basis: The buildup factor is a dimensionless multiplier ($B \ge 1$) that corrects the narrow-beam equation for the additional dose contribution from photons that have undergone Compton scattering within the shield but still reach the point of interest.
- Dependencies: B is a function of the initial photon energy, the shield material (Z), and the shield thickness in mean free paths ($mfp = \mu x$).
- Layered Shields: For a multi-layered shield, a common approximation is to use the buildup factor for the *final* material, but calculate it using the total number of mean free paths for the *entire* shield composite.
Shielding for Different Source Geometries
Line Sources
For a line source of activity per unit length $C_L$, the dose rate at a point P located at a perpendicular distance 'a' is given by:
$$\dot{D} = \frac{\Gamma C_L}{a} (\theta_2 - \theta_1)$$Where $\theta_1$ and $\theta_2$ are the angles (in radians) to the ends of the line. An equivalent form using distances along the line ($x_1, x_2$) is:
$$\dot{D} = \frac{\Gamma C_L}{a} \left(\arctan\frac{x_2}{a} - \arctan\frac{x_1}{a}\right)$$For an infinitely long line source, the dose rate simplifies to:
$$\dot{D}_{infinite} = \frac{\pi \Gamma C_L}{a}$$Area (Disc) Sources
For a circular disc source of radius R with activity per unit area $C_A$, the dose rate at a height 'h' above the center is:
$$\dot{D} = \pi \Gamma C_A \ln\left(\frac{R^2 + h^2}{h^2}\right)$$Specialized Shielding & Dosimetry Scenarios
Accelerator Shielding (NCRP 51)
This is a common problem type requiring use of provided graphs.
- Find Unshielded Dose Rate: Use the provided graph of $\dot{D}_0 I^{-1}$ vs. electron energy to find the dose index rate per unit current for the correct angle (0° or 90°). Multiply by the average beam current.
- Correct for 90° Spectrum: For the 90° direction, the spectrum is softer. Use a second graph to find an "equivalent electron energy" and use this lower energy for attenuation calculations.
- Find Required Shield Thickness: Use the required dose rate and the unshielded dose rate to find the necessary transmission factor. Then, use the provided transmission or TVL graphs for the correct material (e.g., concrete) and energy to find the required thickness.
Hot Particle Dosimetry
This is a localized skin dose calculation, averaged over an area of 1 cm² at a depth of 7 mg/cm².
The dose calculation is a direct multiplication where the area term is 1 cm²:
$$Dose~(rad) = \text{Activity}(\mu Ci) \times \text{Dose Factor} \left(\frac{\text{rad} \cdot \text{cm}^2}{\mu Ci \cdot \text{hr}}\right) \times \text{Time (hr)}$$III. Internal Dosimetry & Bioassay
This domain tests your ability to apply formalized dosimetry systems, understand their underlying models, and interpret bioassay data in complex situations.
ICRP Dosimetric Models
The ICRP 30 vs. ICRP 66+ Respiratory Tract Models
The exam questions are based on the ICRP 26/30 system, but awareness of the newer models shows advanced knowledge.
- ICRP 30 Model: A simple three-compartment model (Nasopharyngeal, Tracheobronchial, Pulmonary). Material is cleared from each region by mechanical processes or absorption into blood, with fixed rates for solubility classes D, W, and Y.
- ICRP 66+ Model: A much more detailed anatomical model (ET1, ET2, BB, bb, AI regions). It treats clearance as a competition between mechanical transport (e.g., mucus escalator) and absorption into blood. It replaces solubility classes with absorption Types F (Fast), M (Medium), and S (Slow). This model provides more realistic, particle-size-dependent dose estimates.
Key Dosimetric Quantities
- Annual Limit on Intake (ALI): The activity of a radionuclide that, if taken in by Reference Man, would result in a CEDE of 5 rem (stochastic limit) or a CDE to any organ of 50 rem (deterministic limit). The more restrictive of the two values is the tabulated ALI.
- Derived Air Concentration (DAC): The concentration in air ($\mu$Ci/mL) that, if breathed for a working year (2000 hours at 1.2 m³/hr), results in an intake of one ALI. $DAC = ALI / 2400 m^3$.
Bioassay Interpretation and Calculation
Key Calculation: Intake Assessment from Bioassay
This is a cornerstone skill. The process involves using a measured biological sample to infer the original intake.
- Quantify the Bioassay Result: Determine the total activity in the sample or organ (e.g., total Bq in a 24-hr urine void). Be sure to scale up from an aliquot if necessary.
- Find the Intake Retention Fraction (IRF): The exam will provide a table of IRF values versus time post-intake for the specific nuclide and solubility class. The IRF is the fraction of the initial intake activity expected to be present in the measured compartment at that specific time.
- Calculate the Initial Intake (I): $I = \frac{\text{Measured Activity}}{\text{IRF}}$.
- Calculate the Committed Effective Dose Equivalent (CEDE): $CEDE~(rem) = \frac{I~(\mu Ci)}{ALI~(\mu Ci)} \times 5~rem$.
Key Calculation: MIRD Dose
For medical applications, the MIRD formalism is used. The mean absorbed dose to a target organ (T) from activity in a source organ (S) is:
$$\bar{D}(T \leftarrow S) = \tilde{A}_S \cdot S(T \leftarrow S)$$- Calculate Effective Half-Life ($T_{eff}$): $\frac{1}{T_{eff}} = \frac{1}{T_{phys}} + \frac{1}{T_{bio}}$.
- Calculate Cumulated Activity ($\tilde{A}$): This is the total number of disintegrations. $\tilde{A} (\mu\text{Ci} \cdot \text{hr}) = A_0 (\mu\text{Ci}) \times T_{eff} (\text{hr}) \times 1.443$.
- Calculate Absorbed Dose ($\bar{D}$): $\bar{D} (\text{rad}) = \tilde{A} \times S$, where S is the provided S-factor (rad/$\mu$Ci-hr).
Medical Interventions
For significant intakes, certain medical countermeasures can reduce the resulting dose.
- Blocking Agents (e.g., KI): Saturates the target organ (thyroid) with stable iodine, preventing the uptake of radioactive iodine. Must be administered *before or very shortly after* the intake to be effective.
- Chelation Therapy (e.g., DTPA): Binds with transuranics (Pu, Am) in the bloodstream to form a stable complex that is rapidly excreted. It is most effective when given quickly after an intake of *soluble* material.
- Lung Lavage: A high-risk medical procedure to physically wash *insoluble* material out of the lungs. Only considered in cases of extremely high, life-threatening intakes.
IV. Instrumentation & Measurement
This section covers the theory, application, and data analysis related to the instruments used in health physics. A deep understanding of detector mechanisms, efficiencies, and statistical limitations is required.
Gas-Filled Detectors
The Six-Region Curve
You must be able to identify and explain each region of the characteristic curve of pulse amplitude vs. applied voltage: Recombination, Ionization, Proportional, Limited Proportional, Geiger-Mueller (GM), and Continuous Discharge.

Proportional Counters
Operating in the proportional region allows for energy discrimination. The pulse height is proportional to the initial energy deposited.
- Gas Multiplication: Unlike ion chambers, the applied voltage is high enough to accelerate primary electrons, causing them to create secondary ionizations. This "gas amplification" (typically $10^2$ to $10^4$) results in a much larger, but still proportional, output pulse.
- Applications: Because they can distinguish between particle energies, proportional counters are excellent for spectroscopy of low-energy radiations (alphas, betas) and for discriminating between them (e.g., alpha counting in the presence of a high beta background).
Ion Chamber Temperature/Pressure Correction
For vented ion chambers, readings must be corrected to standard conditions (STP, often 22°C and 760 mmHg).
$$Corrected~Reading = Measured~Reading \times \left( \frac{P_{cal}}{P_{meas}} \right) \times \left( \frac{T_{meas}(K)}{T_{cal}(K)} \right)$$GM Detector Dead Time Correction
GM detectors have a significant "dead time" ($\tau$) after each pulse. For high count rates, the true rate (n) is higher than the measured rate (m).
$$n = \frac{m}{1 - m\tau}$$Scintillation & Semiconductor Detectors
Gamma Spectroscopy
You must be able to identify all key features on a gamma spectrum. The diagram below shows a representative spectrum from a high-resolution detector.

Semiconductor Detectors (HPGe)
High-Purity Germanium (HPGe) detectors are the gold standard for gamma spectroscopy.
- Superior Resolution: The energy required to create an electron-hole pair in germanium (~3 eV) is much lower than the energy to create an ion pair in a gas or a photoelectron in a scintillator. This results in a much larger number of charge carriers for a given photon energy, leading to vastly superior energy resolution (sharper peaks).
- Trade-offs: HPGe detectors are more expensive than NaI scintillators, have lower efficiency (due to smaller crystal sizes), and must be cooled to liquid nitrogen temperatures to reduce thermal noise.
Liquid Scintillation Counting (LSC)
This is the method of choice for low-energy beta emitters (${}^3$H, ${}^{14}$C). The most critical concept is **quenching**, any process that reduces light output. To get an accurate DPM, you must determine the efficiency for each *quenched* sample, typically by using an instrument-generated quench curve.
Neutron Detection
Neutron Detector Principles
- Slow/Thermal: Use high cross-section reactions like ${}^{10}B(n,\alpha)$ or ${}^{3}He(n,p)$. Be prepared to explain the "wall effect," where a reaction near the detector wall results in incomplete energy deposition and a smaller pulse.
- Fast: Use moderation (e.g., Bonner spheres) to thermalize neutrons before detection, or use proton recoil detectors.
- Bonner Spheres: A set of polyethylene spheres of different diameters with a thermal neutron detector (like a LiI scintillator) at the center. The varying moderator thickness makes each sphere most sensitive to a different neutron energy. By taking measurements with multiple spheres and using an "unfolding" algorithm, one can reconstruct the neutron energy spectrum.
Statistics and Quality Control
Key Calculation: Counting Statistics & MDA
- Calculate Net Rate: $R_{net} = R_g - R_b$.
- Propagate Uncertainty: $\sigma_{net} = \sqrt{\frac{R_g}{t_g} + \frac{R_b}{t_b}}$.
- Calculate MDA using the provided formula, e.g., $MDA (\text{dpm}) = \frac{2.71 + 4.65 \sqrt{R_b t}}{t \cdot \epsilon}$.
Chi-Square ($\chi^2$) Test
This test is used to determine if the observed variance in a set of repeated counts is consistent with the expected variance from a Poisson distribution.
$$\chi^2 = \sum_{i=1}^{N} \frac{(C_i - \bar{C})^2}{\bar{C}}$$The calculated $\chi^2$ value is compared to a table for N-1 degrees of freedom. A value that is too high or too low (typically outside the 5% to 95% probability range) indicates potential instrument malfunction.
V. Power Reactor Health Physics
This section covers the unique radiological challenges and calculations specific to commercial nuclear power plants. A CHP is expected to understand the sources of radiation, the operational controls, and the specific calculations related to reactor systems.
Key Concepts & Reactor Types
PWR vs. BWR Radiological Characteristics
Understanding the fundamental design differences is key to understanding their radiological signatures.
- Pressurized Water Reactor (PWR): The primary coolant loop is separate from the secondary loop that drives the turbine. The primary coolant is kept under very high pressure to prevent boiling. This design contains most of the fission and activation products within the containment building.
- Boiling Water Reactor (BWR): The water boils directly in the reactor vessel, and the resulting steam is sent directly to the turbine. This means that any radionuclides in the coolant are transported throughout the steam cycle, leading to contamination and radiation fields in the turbine building. The most significant radiological issue during operation is the creation of ${}^{16}\text{N}$ (from the ${}^{16}O(n,p){}^{16}N$ reaction), a high-energy (6.1 MeV) gamma emitter with a very short (7.1 s) half-life, which causes "turbine shine."

CRUD and Source Term Management
CRUD (Chalk River Unidentified Deposits) refers to activated corrosion products that are the primary source of occupational dose during reactor outages.
- Formation: Metal components (pipes, valves) corrode, releasing ions (e.g., Co, Ni, Fe) into the primary coolant. These ions circulate through the reactor core, where they are activated by the intense neutron flux.
- Deposition: These now-radioactive ions deposit on surfaces throughout the primary system, creating high dose rate "hot spots." ${}^{60}$Co is the most significant long-term contributor to this dose.
- Control: Source term reduction strategies, such as controlling coolant chemistry (e.g., pH) and using materials with low cobalt content, are critical ALARA measures.
Key Radionuclides & Their Significance
Major Source Terms
- Activation Products: These are the dominant source of occupational dose during maintenance and outages. They are formed when corrosion products (from pipes, valves, etc.) circulate through the core and are activated by neutrons.
- ${}^{60}$Co: The most significant long-term dose contributor. Formed from ${}^{59}$Co in steel alloys. $T_{1/2} = 5.27$ years.
- ${}^{58}$Co: Formed from ${}^{58}$Ni. A major dose contributor during the first year after shutdown. $T_{1/2} = 71$ days.
- ${}^{54}$Mn, ${}^{59}$Fe, ${}^{51}$Cr: Other common activation products.
- Fission Products: Released to the coolant through minor defects in the fuel cladding.
- Noble Gases (Kr, Xe): Gaseous and mobile. A primary component of gaseous effluent and a submersion dose hazard.
- Iodines (${}^{131}$I): Volatile and pose a significant internal hazard to the thyroid. A key nuclide in accident analysis.
- Cesium (${}^{137}$Cs): Soluble and chemically reactive. A major component of liquid waste and a long-term contamination concern.
- Tritium (${}^{3}$H): Produced by ternary fission and neutron activation of boron (used for chemical shim in PWRs) and deuterium. It is ubiquitous in reactor systems and difficult to remove.
Key Calculations in Reactor Health Physics
Key Calculation: Worker Stay Time
A fundamental ALARA calculation is determining the maximum time a worker can spend in a radiation field without exceeding a dose limit.
$$Stay~Time = \frac{\text{Dose Limit} - \text{Dose Already Received}}{\text{Dose Rate}}$$Ensure all units are consistent (e.g., mrem and mrem/hr).
Key Calculation: Activity Buildup in a Cleanup System
Problem Archetype: Reactor coolant containing a specific concentration of a radionuclide is passed through a cleanup system (like a demineralizer) with a given flow rate and efficiency. Calculate the activity accumulated in the system after a certain run time.
Solution Strategy:
- Calculate the Source Rate (S): This is the rate at which activity is removed from the coolant and added to the demineralizer. $$S (\text{Ci/s}) = \text{Coolant Conc.} (\text{Ci/mL}) \times \text{Flow Rate} (\text{mL/s}) \times \text{Efficiency}$$
- Apply the Activity Buildup Equation: The activity in the demineralizer, A(t), builds up over time, balanced by its own radioactive decay ($\lambda$). $$A(t) = \frac{S}{\lambda} (1 - e^{-\lambda t})$$
- Solve for A(t): Plug in the calculated source rate (S), the decay constant ($\lambda$) for the radionuclide, and the run time (t).
Key Calculation: Fission Product Inventory
Problem Archetype: A reactor operates at a specific power level for a given number of days. Calculate the core inventory of a key fission product (e.g., ${}^{137}$Cs) at shutdown.
Solution Strategy:
- Calculate the Fission Rate (F): Convert the thermal power of the reactor to fissions per second. $$F (\text{fissions/s}) = \frac{\text{Power (MWth)} \times (10^6 \text{ J/s/MWth})}{(\text{MeV/fission}) \times (1.602 \times 10^{-13} \text{ J/MeV})}$$
- Calculate the Production Rate (R) of the Fission Product: $$R (\text{atoms/s}) = F (\text{fissions/s}) \times \text{Fission Yield (Y)}$$
- Calculate the Equilibrium Activity: The number of atoms of the fission product, N(t), at time t is given by: $$N(t) = \frac{R}{\lambda}(1 - e^{-\lambda t})$$
- Convert to Activity: The activity is $A(t) = N(t)\lambda$. Therefore: $$A(t) = R(1 - e^{-\lambda t})$$ Plug in the production rate (R), the decay constant ($\lambda$) for the fission product, and the operating time (t).
VI. Environmental HP & Decommissioning
This domain covers the principles and practices for assessing environmental impacts, performing site characterization, and demonstrating that a site or facility meets radiological criteria for release from regulatory control.
The MARSSIM Framework
MARSSIM Process Overview
The Multi-Agency Radiation Survey and Site Investigation Manual (MARSSIM) provides a standard, technically defensible methodology for demonstrating compliance with a dose- or risk-based regulation. It is essential for decommissioning and license termination (e.g., per 10 CFR 20 Subpart E).
- Data Quality Objectives (DQOs): A 7-step planning process to ensure that the type, quantity, and quality of data collected are appropriate for the decision to be made. The steps include: stating the problem, identifying the decision, identifying inputs, defining boundaries, developing a decision rule, specifying error tolerances, and optimizing the design.
- Area Classification: Areas are classified based on their potential for contamination, which directs the level of survey effort (i.e., the number of samples).
- Class 1: Highest potential for contamination (e.g., > DCGL); requires the highest survey density.
- Class 2: Lower potential for contamination, but still some potential for levels > DCGL.
- Class 3: Lowest potential; not expected to contain any residual radioactivity above background.
- Survey Design: The FSS typically uses a systematic grid sampling pattern to ensure full coverage and avoid bias.
The Gray Region & Decision Errors
A key concept in MARSSIM survey design is the "Gray Region," which is the range of concentrations between the Lower Bound of the Gray Region (LBGR) and the DCGL. This is the range where decision errors are most likely to occur. The width of this region ($\Delta = DCGL - LBGR$) is a critical input for calculating the required number of samples. A smaller gray region (a more stringent survey) requires more samples to achieve the desired statistical confidence.
Derived Concentration Guideline Level (DCGL)
The DCGL is the radionuclide-specific surface or soil concentration that would result in a dose equal to the release limit (e.g., 25 mrem/yr). It is the operational benchmark for the Final Status Survey.
- DCGLw: The primary guideline, representing the average concentration over a wide area that meets the dose limit. It is calculated using pathway analysis models: $DCGL_W = \frac{\text{Dose Limit}}{\text{Pathway Dose Conversion Factor}}$.
- DCGLemc: An elevated measurement comparison for small areas of higher activity. It is calculated using an Area Factor (AF) from a table: $DCGL_{EMC} = AF \times DCGL_W$.
- Unity Rule: For multiple radionuclides, the sum of the ratios of their concentrations (C) to their respective DCGLs must not exceed 1: $$\sum_{i} \frac{C_i}{DCGL_{W,i}} \le 1$$
Key Calculation: Number of Samples (N)
The number of data points required for the Sign or WRS test is calculated to ensure the survey has enough statistical power to make a correct decision.
$$N = \frac{(Z_{1-\alpha} + Z_{1-\beta})^2}{4(\text{Sign } P - 0.5)^2}$$Where $Z_{1-\alpha}$ and $Z_{1-\beta}$ are quantiles from the standard normal distribution corresponding to the desired Type I ($\alpha$) and Type II ($\beta$) error rates. P is the probability that a random measurement will be less than the DCGL when the true median is at the Lower Bound of the Gray Region (LBGR).
MARSSIM Statistical Tests
Because measurements have uncertainty, statistical tests are required to make a decision with a known level of confidence. The **null hypothesis ($H_0$)** is always that the survey unit **exceeds** the release criterion.
- Sign Test: A simple non-parametric test used when the contaminant is not present in background. It compares each measurement directly to the DCGL. The goal is to reject $H_0$.
- Wilcoxon Rank Sum (WRS) Test: A non-parametric test used when the contaminant *is* present in background. It compares the distribution of measurements from the survey area to the distribution of measurements from a clean reference (background) area to determine if the survey area is statistically "dirtier" than the reference area.
- Decision Errors: You must know the definitions of Type I ($\alpha$) and Type II ($\beta$) errors.
- Type I Error ($\alpha$): Deciding the survey unit is clean when it is actually dirty (a "false positive" for the cleanup). This is the error MARSSIM primarily seeks to control.
- Type II Error ($\beta$): Deciding the survey unit is dirty when it is actually clean (a "false negative" for the cleanup, leading to unnecessary remediation).
RESRAD
The **RESRAD (RESidual RADioactivity)** family of computer codes, developed by Argonne National Laboratory, are the standard tools used to perform the pathway analysis needed to derive site-specific DCGLs. The codes model the transport of radionuclides from soil and surfaces through multiple environmental pathways (e.g., groundwater, plant uptake, inhalation, direct exposure) to calculate a dose to a defined human receptor.
Environmental Monitoring Program Design
Key Principles
The goal of an environmental monitoring program is to verify effluent controls, detect unexpected releases, and assess public dose.
- Indicator Locations: Placed where concentrations are expected to be highest based on modeling (e.g., downwind, downstream).
- Background Locations: Placed far from the site, in a location that is unimpacted by site activities, to measure natural background levels for comparison.
- Sample Media: Air, water (surface and ground), soil, sediment, and biota (e.g., vegetation, fish) are chosen based on the expected radionuclides and the most likely exposure pathways to the public.
Gaussian Plume Model (Centerline)
This is the standard model for estimating the downwind air concentration ($\chi$) from a continuous airborne release from a stack.
$$\chi(x,0,0) = \frac{Q}{\pi \sigma_y \sigma_z u} \exp\left(-\frac{h^2}{2\sigma_z^2}\right)$$Where Q is the source release rate (e.g., Ci/s), u is the wind speed, h is the effective release height, and $\sigma_y, \sigma_z$ are the dispersion coefficients, which are functions of downwind distance (x) and atmospheric stability class (A-F).
VII. Special Topics in Health Physics
This section covers specialized, high-consequence topics that require a synthesis of physics, engineering controls, and dosimetry. A CHP is expected to be the resident expert on these subjects.
Criticality Safety
The Six-Factor Formula and $k_{eff}$
The state of a fissile system is defined by the effective multiplication factor, $k_{eff}$, which is the ratio of neutrons in one generation to the generation before. $k_{eff} = k_{\infty} \cdot P_{NL}$, where $P_{NL}$ is the non-leakage probability.
- $k_{eff} < 1$: Subcritical. The chain reaction will die out.
- $k_{eff} = 1$: Critical. The chain reaction is self-sustaining.
- $k_{eff} > 1$: Supercritical. The chain reaction will rapidly increase in power.
The "Six Factors" are the physical parameters that are controlled to keep $k_{eff}$ safely below 1:
- Mass: Controlling the total amount of fissile material to stay below the critical mass for a given configuration.
- Geometry: Using "geometrically favorable" shapes (e.g., thin slabs, long narrow cylinders) that maximize neutron leakage. A sphere is the most reactive geometry.
- Moderation: Controlling the presence of hydrogenous materials (water, oil, plastic) that slow neutrons down to thermal energies, where the fission cross-section is much higher.
- Reflection: Controlling the proximity of materials (water, concrete, steel) that can scatter neutrons back into the fissile material, effectively reducing the critical mass.
- Concentration/Density: Ensuring the density of fissile atoms is below the critical value. This can involve mixing with non-fissile materials.
- Interaction/Poisons: Using materials with very high neutron absorption cross-sections (e.g., Boron, Cadmium, Gadolinium) to act as "poisons," removing neutrons from the system. Also includes ensuring safe spacing between multiple subcritical units.
The Double Contingency Principle
This is the fundamental safety philosophy in criticality safety. It requires that a process be designed to be safe, assuming that **two independent, concurrent, and unlikely changes** in conditions have occurred before a criticality accident is possible. In practice, this means that no single error or equipment failure should be able to cause a criticality.
Key Calculation: Criticality Excursion Yield
In an accident scenario, you may be given the total number of fissions and asked to calculate the dose.
Dose = $\frac{(\text{Total Fissions}) \cdot (\text{Particles/Fission}) \cdot (\text{Flux-to-Dose Factor})}{4 \pi d^2}$
You will be given the yield (e.g., 2.5 neutrons/fission, 8 gammas/fission) and the appropriate flux-to-dose conversion factor for the particles' energy.
Non-Ionizing Radiation
Laser Safety (ANSI Z136.1)
Laser safety focuses on preventing thermal or photochemical damage to the eye and skin.
- Maximum Permissible Exposure (MPE): The fundamental limit. It is the level of laser radiation to which a person may be exposed without hazardous effect or adverse biological changes in the eye or skin. It depends on wavelength, exposure duration, and whether the source is point or extended. An MPE table will always be provided.
- Nominal Ocular Hazard Distance (NOHD): The distance along the axis of the laser beam beyond which the beam irradiance or radiant exposure is less than the MPE.
- Laser Classifications: Know the general hazards of each class. Class 1 is safe for viewing. Class 2 is safe for momentary viewing due to the aversion response (0.25 s). Class 3R (formerly IIIa) is marginally unsafe for direct viewing. Class 3B (formerly IIIb) is hazardous for direct viewing. Class 4 is a hazard from direct, specular, and diffuse reflections and can be a fire hazard.
Key Calculation: Required Optical Density (OD)
Protective eyewear must reduce the potential exposure to below the MPE.
$$OD = \log_{10} \left( \frac{H_0}{MPE} \right) = \log_{10} \left( \frac{E_0}{MPE_{irradiance}} \right)$$Where $H_0$ or $E_0$ is the anticipated radiant exposure or irradiance at the eye.
Key Calculation: Nominal Ocular Hazard Distance (NOHD)
The NOHD is the distance at which the beam has spread enough for the irradiance to equal the MPE.
$$NOHD = \frac{1}{\phi} \sqrt{\frac{4 \Phi}{\pi \cdot MPE} - a^2}$$Where $\Phi$ is the total power, $\phi$ is the beam divergence, and 'a' is the initial beam diameter.
RF/Microwave Safety
The primary hazard from RF/microwave radiation is heating of body tissues.
- Near-Field vs. Far-Field: The boundary between the two is roughly at $R = \frac{2D^2}{\lambda}$, where D is the antenna diameter and $\lambda$ is the wavelength. In the far-field, the beam behaves as a plane wave and power density (S) decreases with the inverse square of distance ($1/d^2$). In the near-field, the relationship is complex, and direct measurements of both E- and H-fields are necessary.
- Specific Absorption Rate (SAR): The primary dosimetric quantity for RF exposure. It is the rate at which energy is absorbed per unit mass of body tissue, measured in watts per kilogram (W/kg). Exposure limits are based on keeping the whole-body average SAR below a certain level (e.g., 0.4 W/kg for controlled environments).
Key Calculation: Far-Field Power Density
$$S (\text{W/cm}^2) = \frac{P_{avg} G}{4 \pi d^2}$$Where $P_{avg}$ is the average power ($P_{peak} \times \text{Duty Factor}$), G is the dimensionless antenna gain, and d is the distance.
Ultraviolet (UV) Radiation Safety
UV radiation is typically categorized by wavelength, with each category having different penetration abilities and biological effects.
- UVA (315-400 nm): Long-wave UV, often called "black light." It penetrates deepest and is primarily associated with skin aging and wrinkling.
- UVB (280-315 nm): Mid-range UV, which is the primary cause of skin reddening (erythema) and sunburn. It is also the main cause of most skin cancers.
- UVC (100-280 nm): Short-wave UV, which is the most damaging but is almost completely absorbed by the Earth's ozone layer. It is commonly found in germicidal lamps. The primary hazards are to the eye (photokeratitis) and skin (erythema).
ACGIH UV Threshold Limit Values (TLVs)
The American Conference of Governmental Industrial Hygienists (ACGIH) sets TLVs for UV radiation. For the actinic region (UVC and UVB), the TLV is based on a spectral weighting function, $S(\lambda)$, to account for the varying biological effectiveness at different wavelengths.
- The TLV for the actinic region (200-315 nm) is **3 mJ/cm²** effective irradiance, integrated over an 8-hour day.
- For UVA (315-400 nm), the TLV is **1 J/cm²** for exposure times greater than 1000 seconds.
VIII. Regulatory & Standards Frameworks
A CHP must not only know the dose limits but also understand the philosophy behind them, how they are applied in practice, and the specific requirements for different situations like transportation and effluent control.
Occupational Dose Limits & Summation
Key Dose Limits (10 CFR 20 & ICRP)
- Total Effective Dose Equivalent (TEDE): 5 rem/year (50 mSv/year)
- Lens Dose Equivalent (LDE): 15 rem/year (150 mSv/year) per 10 CFR 20.
Note: ICRP 118 (2012) recommends a lower limit of 20 mSv/year, averaged over 5 years, with no single year exceeding 50 mSv. - Shallow Dose Equivalent (SDE) to skin/extremities: 50 rem/year (500 mSv/year)
- Declared Pregnant Worker (to fetus): 0.5 rem (5 mSv) over the entire gestation period.
Key Update: ICRP 60 vs. ICRP 103
While U.S. regulations (10 CFR 20) are based on ICRP 26/30 and 60, a modern CHP should be aware of the 2007 recommendations in ICRP 103.
- Tissue Weighting Factors ($w_T$): ICRP 103 updated the list of tissues and their weighting factors. For example, the gonad weighting factor was reduced from 0.20 to 0.08, while breast was increased from 0.05 to 0.12. A "remainder" category was also changed.
- Radiation Weighting Factors ($w_R$): The concept of a continuous Quality Factor Q(L) was replaced with specific $w_R$ values for radiation types (e.g., 20 for alpha particles, a continuous function for neutrons).
- Effective Dose: The term "Effective Dose" (E) is used instead of "Total Effective Dose Equivalent" (TEDE), though the concepts are functionally similar for regulatory purposes.
Planned Special and Emergency Exposures
Situations may arise where exceeding the standard occupational dose limits is necessary. These are tightly controlled.
- Planned Special Exposure (PSE): Authorized by a licensee in advance for an exceptional situation. Per 10 CFR 20, a PSE is allowed only if it does not exceed the annual limits (5 rem TEDE, 50 rem to any organ) and the lifetime dose from all PSEs does not exceed 5 times the annual limit (i.e., 25 rem TEDE).
- Emergency Worker Guidelines (NCRP/EPA): These are not regulations but guidance for emergency response.
- ~10 rem: All activities during an emergency.
- ~25 rem: Protecting valuable property.
- >25 rem (up to ~100 rem): Lifesaving activities or protecting large populations, only for volunteers who are fully aware of the risks.
Key Calculation: Total Effective Dose Equivalent (TEDE)
TEDE is the sum of the deep dose equivalent (DDE) from external sources and the committed effective dose equivalent (CEDE) from internal sources.
$$TEDE = DDE_{ext} + \sum_j CEDE_j$$The CEDE for an intake of radionuclide 'j' is calculated as:
$$CEDE_j = \frac{\text{Intake}_j (\mu Ci)}{ALI_j (\mu Ci)} \times 5 \text{ rem}$$For multiple internal and external sources, you must sum all components to ensure the total does not exceed the 5 rem limit.
The Sum of Fractions Rule
To control exposure to multiple sources (internal or external), the sum of the ratios of the exposure to the applicable limit must not exceed 1.
$$\frac{DDE}{5 \text{ rem}} + \sum_j \frac{\text{Intake}_j}{ALI_j} \le 1$$Public Dose & Effluent Control
Dose Limits for Members of the Public
- The annual limit is 0.1 rem (1 mSv) TEDE from licensed operations.
- The dose rate in any unrestricted area from an external source must not exceed 2 mrem in any one hour.
- Effluent Concentration (EC) values in 10 CFR 20 Appendix B are derived such that if a member of the public were continuously exposed to that concentration in air or water, they would not exceed the 0.1 rem annual limit.
- The limit for license termination (decommissioning) is **25 mrem/year** to an average member of the critical group (10 CFR 20.1402).
Radioactive Materials Transportation (49 CFR 173)
Package Labeling Criteria
The required label is determined by the highest value of either the surface dose rate or the Transport Index (TI).
- Transport Index (TI): The maximum dose rate in mrem/hr at 1 meter from the package surface. For fissile material, the TI also includes a criticality component.
- White-I: Surface dose rate $\le 0.5$ mrem/hr AND TI = 0.
- Yellow-II: Surface dose rate $\le 50$ mrem/hr AND TI $\le 1$.
- Yellow-III: Surface dose rate $\le 200$ mrem/hr AND TI $\le 10$. (A reading > 200 mrem/hr requires the shipment to be under exclusive use).
IX. Problem-Solving Methodologies
This section focuses on the practical application of fundamental principles to solve complex problems. It covers how to combine formulas and model dynamic scenarios, which are key skills for the exam.
Order of Magnitude Estimations
Before beginning a complex calculation, perform a quick, "back-of-the-envelope" estimate to determine if your potential answer is reasonable. This can prevent significant errors caused by unit conversions or calculator mistakes. Use rules of thumb and round constants to simplify the math (e.g., $\pi \approx 3$).
Example: If asked for the dose rate from 1 Ci of Co-60 at 1 meter, you should immediately know the answer is ~1.3 R/hr. If your detailed calculation yields a result in the mR/hr or thousands of R/hr, you have made an error.
Working Backwards from the Answer
For multi-step problems, a useful strategy is to start with the final desired quantity and work backwards to the information you are given.
- Identify the Goal: What is the final unit and quantity you need to calculate (e.g., CEDE in rem)?
- Find the Final Equation: What is the immediate precursor formula to get that answer? (e.g., $CEDE = (\text{Intake}/ALI) \times 5$ rem).
- Assess Inputs: For each input in that formula (Intake, ALI), is it given or does it need to be calculated?
- Repeat: For each input that must be calculated, repeat the process, identifying the precursor formula and its inputs, until you have a chain of calculations that connects the initial given information to the final answer.
Unit Analysis & Formula Derivation
Building Equations from Scratch
On the exam, you may not be given the exact formula you need. A critical skill is the ability to derive a formula on the fly using dimensional analysis (i.e., making sure the units cancel correctly). Start with what you're given, what you need to find, and then find the conversion factors and constants that bridge the gap.
Example: Derive an equation for the dose rate (mrem/hr) at 1 meter above an infinitely large, uniformly contaminated surface, given the contamination level in dpm/100 cm².
- Start with the Goal Unit: $\frac{mrem}{hr}$
- Introduce the Given: You have $\frac{dpm}{100 cm^2}$. You need to convert this to a flux ($\frac{\gamma}{cm^2 \cdot s}$). This requires knowing the gamma yield (Y, $\frac{\gamma}{dis}$) and assuming an emission geometry (e.g., $2\pi$ for a surface).
- Build the Conversion Chain: $$\frac{mrem}{hr} = \left( \frac{dpm}{100 cm^2} \right) \times \left( \frac{1 dis}{dpm} \right) \times \left( \frac{Y \gamma}{dis} \right) \times \left( \frac{1 min}{60 s} \right) \times \left( \frac{60 min}{1 hr} \right) \times \left( \frac{100^2 cm^2}{m^2} \right) \times ...$$
- Bridge Flux to Dose Rate: The final link is a flux-to-dose-rate conversion factor, which will be given in a form like $(\frac{mrem/hr}{\gamma/cm^2 \cdot s})$. By carefully arranging these factors, you can cancel all intermediate units and arrive at the desired final unit.
Modeling Simultaneous Processes: Release & Decay
The Governing Differential Equation
Many complex operational problems (e.g., a radioactive gas leak into a ventilated room) can be modeled with a simple first-order differential equation. The rate of change of activity in a volume is the difference between the rate at which activity enters and the rate at which it is removed.
$$\frac{dA}{dt} = (\text{Source Rate}) - (\text{Removal Rate}) = S - \lambda_{eff}A(t)$$The key is to correctly define the **effective removal constant**, $\lambda_{eff}$. It is the sum of all removal constants:
$$\lambda_{eff} = \lambda_{Radiological} + \lambda_{Ventilation} + \lambda_{Other}$$Where $\lambda_{Ventilation}$ is the ventilation rate (in air changes per hour/minute) and $\lambda_{Other}$ could be a cleanup filter, etc.
Key Scenarios: Puff vs. Continuous Release
The solution to the governing equation depends on the source term (S):
- "Puff" Release (S=0 after t=0): An instantaneous release of activity $A_0$ into a room. The activity concentration $\chi(t)$ decreases over time. $$\chi(t) = \chi_0 e^{-\lambda_{eff}t}$$ The total integrated intake (I) over a time T is: $I = \int_0^T B \cdot \chi(t) dt = \frac{B \cdot \chi_0}{\lambda_{eff}}(1-e^{-\lambda_{eff}T})$
- Constant Leak (S > 0): A constant leak into a clean room. The activity concentration builds up to an equilibrium value. $$\chi(t) = \frac{S}{\lambda_{eff} V} (1 - e^{-\lambda_{eff}t})$$ The total integrated intake (I) over a time T is: $I = \int_0^T B \cdot \chi(t) dt = \frac{B \cdot S}{\lambda_{eff} V} \left[ T - \frac{1}{\lambda_{eff}}(1-e^{-\lambda_{eff}T}) \right]$
Where B is the breathing rate and V is the room volume.
X. Common Mistakes & Exam Pitfalls
Calculation & Unit Errors
- Unit Mismatches: The most common error. Forgetting to convert Ci to $\mu$Ci, hours to minutes, or cm to meters can change an answer by orders of magnitude. Always write out your units and make sure they cancel.
- Forgetting Buildup (B): Shielding calculations for broad beams always require a buildup factor. Forgetting it will result in an underestimate of the dose rate.
- $E_{avg}$ vs. $E_{max}$ for Betas: Dose calculations require the average beta energy ($E_{avg}$), which is roughly 1/3 of the maximum energy ($E_{max}$). Using $E_{max}$ will significantly overestimate the dose.
- Decay During Irradiation: Forgetting the $(1 - e^{-\lambda t_{irrad}})$ saturation factor when calculating activation will overestimate the final activity, especially when the irradiation time is short compared to the half-life.
Conceptual Errors
- Confusing Dose Quantities: Be precise with your terminology. Absorbed Dose (rad/Gy), Dose Equivalent (rem/Sv), and Exposure (R) are not interchangeable.
- Misinterpreting Statistical Tests: Remember that for MARSSIM, the null hypothesis ($H_0$) is that the area is dirty. The goal is to *reject* the null hypothesis to prove the area is clean.
- Ignoring Special Cases: Forgetting that some rules have exceptions (e.g., the need for low-Z material to shield high-energy betas first) is a common pitfall.
XI. Key Formula Sheet & Applications
This section summarizes key equations from the provided formula sheet and explains their typical application on the exam. This is not an exhaustive list; understanding how to derive and combine these formulas is key.
Basic Decay & Dose
- $A(t) = A_0 e^{-\lambda t}$
Use: Basic radioactive decay. - $SA (Ci/g)=\frac{1.14\times10^{13}}{T_{1/2}(s)\cdot \text{Atomic Mass}}$
Use: To calculate the specific activity of a radionuclide. - $\dot{D}(x) = \frac{\Gamma A}{x^2}$
Use: Point source dose rate calculation. - $D(x) = D_0 B e^{-\mu x}$
Use: Shielding calculation with buildup factor (B).
Flux to Dose Rate Conversion
- $\dot{D} (\frac{rad}{hr}) = 5.767 \times 10^{-5} \cdot \phi \cdot E \cdot \frac{\mu_{en}}{\rho}$
Use: To calculate the absorbed dose rate in a medium from a known photon flux ($\phi$), photon energy (E), and mass energy absorption coefficient ($\mu_{en}/\rho$).
Internal Dosimetry
- $\frac{1}{T_{eff}} = \frac{1}{T_{phys}} + \frac{1}{T_{bio}}$
Use: Calculating effective half-life. - $CEDE~(rem) = \frac{I~(\mu Ci)}{ALI~(\mu Ci)} \times 5~rem$
Use: Calculating CEDE from a known intake and ALI. - $I = B \times t \times \chi$
Use: Basic intake calculation from air concentration ($\chi$).
Statistics
- $\sigma_{net} = \sqrt{\frac{C_g}{t_g^2} + \frac{C_b}{t_b^2}}$
Use: Propagating uncertainty for net count rate. - $L_D \approx 4.65 \sqrt{R_b / t_b}$
Use: Simplified Currie formula for the Lower Limit of Detection (in cps). - $\chi^{2}=\frac{\sum_{i=1}^{n}(C_{i}-\overline{C})^{2}}{\overline{C}}$
Use: The Chi-Square test for counter performance.
XII. Integrated Practice Problems & Detailed Solutions
This section applies the guide's principles to full, multi-part exam questions to demonstrate integrated problem-solving.
Practice Problem 1: The Reactor Coolant System Demineralizer
Scenario: A worker must perform a 30-minute maintenance task at a distance of 2.74 meters from a demineralizer tank. The tank contains 60 Ci of ${}^{60}$Co as a point source. The source was placed in the tank 6 months ago. To reduce dose, a 2-inch thick lead shield is placed between the worker and the tank.
Task: Determine if this shielding is sufficient to keep the worker's dose for this specific job below an administrative limit of 300 mrem. You are given that the buildup factor for this energy and shield thickness is B=2.15, and the linear attenuation coefficient for lead is 0.65 cm⁻¹.
Solution Walkthrough:
- Decay Calculation: First, calculate the current activity of the source. $A(t) = A_0 e^{-\lambda t} = (60 \text{ Ci}) \cdot e^{-(\frac{0.693}{5.27y})(0.5y)} = (60 \text{ Ci}) \cdot (0.936) = \textbf{56.2 Ci}$.
- Unshielded Dose Rate: Calculate the dose rate at the worker's location without the shield using the gamma constant. $\dot{D}_{unsh} = \frac{\Gamma A}{d^2} = \frac{(1.3 \frac{R \cdot m^2}{hr \cdot Ci}) \cdot (56.2 \text{ Ci})}{(2.74 \text{ m})^2} = 9.73 \frac{R}{hr} = \textbf{9730 mrem/hr}$.
- Shielded Dose Rate: Apply the attenuation equation, including the buildup factor, to find the dose rate with the shield in place. Note the conversion of inches to cm (2 in = 5.08 cm). $\dot{D}_{sh} = \dot{D}_{unsh} \cdot B \cdot e^{-\mu x} = (9730 \frac{mrem}{hr}) \cdot (2.15) \cdot e^{-(0.65 cm^{-1})(5.08cm)} \approx \textbf{770 mrem/hr}$.
- Total Dose: Calculate the total dose for the 30-minute (0.5 hr) job. Dose = $770 \frac{mrem}{hr} \times 0.5~hr = \textbf{385 mrem}$.
- Conclusion: The projected dose of 385 mrem **exceeds** the 300 mrem limit. The shielding is not sufficient, and further ALARA actions (e.g., more shielding, reducing time, increasing distance) are required.
Practice Problem 2: Fetal Dose from Diagnostic X-Rays
Scenario: A patient undergoes a series of diagnostic imaging procedures, including a pelvic CT (2 scans at 1.2 rad/scan) and a pelvic fluoroscopy procedure (10 minutes at 4 R/min ESE). Later, she discovers she was 2 months pregnant at the time.
Task: Estimate the total fetal dose and discuss the potential risks. You are provided with a table indicating the fetal dose conversion factor for this type of fluoro exam is 421 mrad/R.
Solution Walkthrough:
- Calculate Dose from CT: The dose is given directly. Dose (CT) = 2 scans $\times$ 1.2 rad/scan = 2.4 rad = 2400 mrad.
- Calculate ESE from Fluoro: Calculate the total Entrance Skin Exposure (ESE). ESE (Fluoro) = 4 R/min $\times$ 10 min = 40 R.
- Calculate Fetal Dose from Fluoro: Convert the ESE to fetal dose using the given factor. Dose (Fluoro) = 40 R $\times$ 421 mrad/R = 16840 mrad.
- Sum the Doses: Add the contributions from both procedures. Total Dose = 2400 mrad + 16840 mrad = 19240 mrad $\approx$ **19.2 rad**.
- Conclusion & Risk Discussion: The estimated fetal dose is approximately 19.2 rad. At this dose level and at this stage of gestation (period of major organogenesis), there is a significant risk of deterministic effects (e.g., malformations, >15-20 rad threshold) and an increased lifetime risk of stochastic effects (cancer). This information must be clearly communicated to the patient and her physician to inform their medical decisions.
Practice Problem 3: Environmental Pathway Analysis
Scenario: Routine environmental monitoring detects ${}^{137}$Cs in a river downstream of a facility at a concentration of $0.881$ pCi/mL. A member of the public regularly fishes from this river.
Task: Calculate the annual dose (CEDE) to this individual, assuming they consume 250g of fish per day. You are given a bioaccumulation factor for Cs-137 in fish of 2000 L/kg and an ingestion ALI of 100 $\mu$Ci.
Solution Walkthrough:
- Calculate Concentration in Fish ($C_{fish}$): Use the bioaccumulation factor to find the concentration in fish from the concentration in water. $$C_{fish} = (0.881 \frac{pCi}{mL}) \times (\frac{1000 mL}{L}) \times (2000 \frac{L}{kg}) = 1.76 \times 10^{6} \frac{pCi}{kg}$$
- Calculate Annual Intake (I): Calculate the total activity ingested over a year. $$I = (1.76 \times 10^{6} \frac{pCi}{kg}) \times (0.25 \frac{kg}{day}) \times (365 \frac{day}{yr}) = 1.61 \times 10^{8} \frac{pCi}{yr}$$
- Convert to CEDE: Convert the intake to $\mu$Ci and use the ALI to find the CEDE. $$I = 1.61 \times 10^{8} pCi \times \frac{1 \mu Ci}{10^6 pCi} = 161 \mu Ci$$ $$CEDE (\text{rem}) = \frac{161 \mu\text{Ci}}{100 \mu\text{Ci}} \times 5 \text{ rem} = \textbf{8.05 rem}$$
- Conclusion: The calculated annual dose of 8.05 rem is well above the public dose limit of 0.1 rem/yr. This indicates a significant radiological concern that requires immediate investigation and potential remedial action, such as issuing a fish consumption advisory.
Practice Problem 4: MARSSIM Final Status Survey
Scenario: A room is being decommissioned. The primary contaminant is ${}^{137}$Cs, which is not present in background. The DCGLw is 15,000 dpm/100 cm². A final status survey of 10 measurements is performed.
Task: The results are (in dpm/100 cm²): 12k, 11k, 14k, 16k, 9k, 13k, 10k, 11.5k, 14.5k, 8k. Do these results pass the Sign Test at a 95% confidence level ($\alpha=0.05$)?
Solution Walkthrough:
- State Null Hypothesis ($H_0$): The median concentration of the survey unit exceeds the DCGL. We want to reject this hypothesis to show the area is clean.
- Calculate Differences: For each measurement, calculate the difference: $D_i = \text{Measurement}_i - DCGL_W$.
- 12000 - 15000 = -3000
- 11000 - 15000 = -4000
- 14000 - 15000 = -1000
- 16000 - 15000 = +1000
- 9000 - 15000 = -6000
- 13000 - 15000 = -2000
- 10000 - 15000 = -5000
- 11500 - 15000 = -3500
- 14500 - 15000 = -500
- 8000 - 15000 = -7000
- Count the Signs: Count the number of positive differences. This is the test statistic, S+. Here, S+ = 1.
- Compare to Critical Value: From MARSSIM Table I.3 for N=10 measurements and $\alpha=0.05$, the critical value (k) is 8. This means we need 8 or more measurements to be less than the DCGL to be confident the area is clean. Equivalently, we reject $H_0$ if S+ $\le$ (N - k) = (10 - 8) = 2.
- Conclusion: Our calculated test statistic S+ = 1. Since 1 is less than or equal to the critical value of 2, we **reject the null hypothesis**. This means there is sufficient statistical evidence to conclude that the median concentration of the survey unit is less than the DCGL, and the area passes the release criterion.
XIII. Glossary of Key Terms & Acronyms
- ACGIH: American Conference of Governmental Industrial Hygienists - Sets occupational exposure limits for non-ionizing radiation (TLVs).
- ALI (Annual Limit on Intake): The activity of a radionuclide that, if inhaled or ingested, would result in a CEDE of 5 rem or a CDE of 50 rem to any organ.
- ALARA: As Low As Reasonably Achievable - The guiding principle of radiation protection.
- AMAD (Activity Median Aerodynamic Diameter): The median aerodynamic diameter of an aerosol, used to characterize particle size distribution for internal dosimetry.
- ANSI: American National Standards Institute - Develops consensus standards, including for laser safety (Z136.1).
- Buildup Factor (B): A correction factor used in shielding calculations to account for the contribution of scattered photons to the dose.
- BWR (Boiling Water Reactor): A type of nuclear reactor where water boils in the core, and the resulting steam directly drives a turbine.
- CDE / CEDE: Committed Dose Equivalent / Committed Effective Dose Equivalent - The dose received over 50 years from an intake of radioactive material.
- CPE (Charged Particle Equilibrium): A condition where the energy of charged particles leaving a volume is balanced by the energy of charged particles entering it. Under CPE, KERMA equals absorbed dose.
- Cross Section ($\sigma$): A measure of the probability of an interaction between a particle and a target nucleus, typically measured in barns ($10^{-24}$ cm²).
- DAC (Derived Air Concentration): The airborne concentration of a radionuclide that, if breathed for a working year, would result in an intake of one ALI.
- DCGL (Derived Concentration Guideline Level): A radionuclide concentration limit used in decommissioning to demonstrate that a site meets the release criterion (e.g., 25 mrem/yr).
- DDE (Deep Dose Equivalent): The external dose equivalent at a tissue depth of 1 cm (1000 mg/cm²).
- DQO (Data Quality Objective): A systematic planning process used in MARSSIM to ensure that the data collected will be sufficient to support the desired decision.
- HVL (Half-Value Layer): The thickness of a material required to reduce the intensity of a radiation beam to one-half its original value.
- ICRP: International Commission on Radiological Protection - An international body that provides recommendations and guidance on radiation protection.
- KERMA (Kinetic Energy Released in Media): The energy transferred from uncharged particles (photons, neutrons) to charged particles per unit mass of a medium.
- LET (Linear Energy Transfer): The rate at which a charged particle deposits energy as it travels through matter.
- MARSSIM: Multi-Agency Radiation Survey and Site Investigation Manual - A standardized methodology for decommissioning surveys.
- MPE (Maximum Permissible Exposure): The highest level of laser radiation to which a person can be exposed without hazardous effects.
- NCRP: National Council on Radiation Protection and Measurements - A U.S. organization that issues recommendations on radiation protection.
- NOHD (Nominal Ocular Hazard Distance): The distance from a laser at which the beam irradiance equals the MPE.
- PAG (Protective Action Guide): A projected dose at which a specific protective action (e.g., sheltering, evacuation) is recommended during an emergency.
- PWR (Pressurized Water Reactor): A type of nuclear reactor with separate primary (reactor) and secondary (turbine) coolant loops.
- Q-value: The total energy released in a nuclear reaction or decay.
- SAR (Specific Absorption Rate): The rate at which RF/microwave energy is absorbed per unit mass of body tissue.
- TEDE (Total Effective Dose Equivalent): The sum of the external deep dose equivalent (DDE) and the internal committed effective dose equivalent (CEDE).
- TLV (Threshold Limit Value): Exposure guidelines for occupational health hazards, including non-ionizing radiation, issued by the ACGIH.
- TVL (Tenth-Value Layer): The thickness of a material required to reduce the intensity of a radiation beam to one-tenth its original value.
- WRS (Wilcoxon Rank Sum) Test: A statistical test used in MARSSIM when the contaminant is also present in the background.