Appendix F — Radiation Safety Quick Reference

This appendix compiles the essential radiation protection data referenced throughout this textbook, particularly in Chapter 16 (radiation interactions with matter), Chapter 27 (nuclear medicine), and Chapter 29 (radiation in the environment). It is organized as a quick-reference guide rather than a derivation-focused treatment. For the underlying physics, consult the relevant chapters; for legally binding regulations, consult the applicable national or institutional regulatory body (NRC, ICRP, or equivalent).

⚠️ Important: The values in this appendix reflect ICRP Publication 103 (2007) recommendations, which form the basis for radiation protection regulations in most countries. Regulatory limits vary by jurisdiction; always verify against the regulations applicable to your institution and country. The values here are recommendations, not universal legal limits.

F.1 Fundamental Quantities and Units

Key relationships:

• Equivalent dose accounts for the biological effectiveness of different radiation types through radiation weighting factors $w_R$.
• Effective dose accounts for the relative sensitivity of different organs through tissue weighting factors $w_T$.
• For photons and electrons, $w_R = 1$, so absorbed dose in Gy equals equivalent dose in Sv numerically.

F.2 Radiation Weighting Factors ($w_R$)

Radiation weighting factors reflect the relative biological effectiveness (RBE) of different radiation types at producing stochastic effects (cancer, hereditary effects) at low doses.

Neutron weighting factors (ICRP 103 continuous function):

ICRP 103 defines $w_R$ for neutrons as a continuous function of neutron energy $E_n$:

$$w_R = \begin{cases} 2.5 + 18.2 \, e^{-[\ln(E_n)]^2/6} & E_n < 1 \text{ MeV} \\ 5.0 + 17.0 \, e^{-[\ln(2E_n)]^2/6} & 1 \leq E_n \leq 50 \text{ MeV} \\ 2.5 + 3.25 \, e^{-[\ln(0.04 E_n)]^2/6} & E_n > 50 \text{ MeV} \end{cases}$$

where $E_n$ is in MeV. The peak near 1 MeV reflects the maximum energy transfer to hydrogen nuclei (proton recoils) in tissue.

💡 Physical Insight: The high $w_R$ for alpha particles and heavy ions reflects their high linear energy transfer (LET). A 5 MeV alpha deposits its energy over approximately 35 $\mu$m in tissue — comparable to a cell diameter — creating dense ionization tracks that are difficult for cellular repair mechanisms to fix. A 5 MeV gamma ray, by contrast, deposits energy sparsely over tens of centimeters.

F.3 Tissue Weighting Factors ($w_T$)

Tissue weighting factors represent the relative contribution of each organ to the total radiation detriment (cancer risk + hereditary effects). They sum to 1.0 by definition.

The "remainder" tissues include adrenals, extrathoracic region, gall bladder, heart, kidneys, lymphatic nodes, muscle, oral mucosa, pancreas, prostate/uterus/cervix, small intestine, spleen, thymus, and adipose tissue. Their collective weight is 0.12, distributed equally (0.00857 each).

F.4 Dose Limits

F.4.1 ICRP Recommended Dose Limits (Publication 103, 2007)

⚠️ Note on U.S. regulations: The U.S. NRC (10 CFR 20) specifies a total effective dose equivalent (TEDE) limit of 50 mSv/year for occupational exposure, without the 5-year averaging provision. Many U.S. facilities voluntarily adopt the ICRP 20 mSv/year recommendation as a more conservative administrative limit.

F.4.2 ALARA Principle

All dose limits are upper bounds, not targets. The fundamental principle of radiation protection is ALARA: keep doses As Low As Reasonably Achievable, taking into account economic and societal factors. In practice, this means that workers at well-managed facilities receive doses far below the limits — typically a few mSv/year or less.

F.5 Common Radiation Exposures

📊 Context: The average annual per-capita dose in the United States is approximately 6.2 mSv, roughly half from natural background and half from medical exposures. In countries with less medical imaging, the average is closer to the world average of 2.4 mSv.

F.6 Acute Radiation Syndrome (ARS) Thresholds

Acute radiation syndrome occurs after a large whole-body dose delivered over a short time (minutes to hours). The clinical manifestation depends on the dose level.

Latent period: Between the prodromal phase (first hours) and the manifest illness phase, there is often a latent period of apparent improvement lasting days to weeks. This is a characteristic and deceptive feature of ARS; it does not indicate recovery.

F.7 Shielding Principles

F.7.1 The Three Principles of External Dose Reduction

1. Time: Minimize the time spent near the source. Dose is proportional to exposure time: $D = \dot{D} \cdot t$.

2. Distance: Maximize distance from the source. For a point source in vacuum, dose rate falls as the inverse square of distance:

$$\dot{D}(r) = \frac{\dot{D}(r_0) \cdot r_0^2}{r^2}$$

Doubling your distance reduces your dose by a factor of 4.

3. Shielding: Place absorbing material between yourself and the source. The transmitted intensity through a shield of thickness $x$ is:

$$I(x) = I_0 \, e^{-\mu x} = I_0 \, e^{-(\mu/\rho)(\rho x)}$$

where $\mu$ is the linear attenuation coefficient (cm$^{-1}$), $\mu/\rho$ is the mass attenuation coefficient (cm$^2$/g), and $\rho x$ is the areal density (g/cm$^2$).

F.7.2 Half-Value Layer (HVL) and Tenth-Value Layer (TVL)

The half-value layer is the thickness of a given material required to reduce the intensity of a radiation beam by a factor of 2:

$$\text{HVL} = \frac{\ln 2}{\mu} = \frac{0.693}{\mu}$$

The tenth-value layer (TVL) reduces intensity by a factor of 10:

$$\text{TVL} = \frac{\ln 10}{\mu} = \frac{2.303}{\mu}$$

After $n$ HVLs, the transmission factor is $(1/2)^n$. After $n$ TVLs, the transmission factor is $(1/10)^n$.

F.7.3 Half-Value Layers for Common Materials

⚠️ Caution: HVL values assume narrow-beam (good geometry) conditions. In broad-beam geometry, scattered radiation increases the effective transmitted intensity. Buildup factors $B$ correct for this: $I = I_0 B(E, \mu x) \, e^{-\mu x}$, with $B > 1$ always.

F.7.4 Shielding Guidance by Radiation Type

F.8 Useful Dosimetric Formulas

F.8.1 Dose Rate from a Point Gamma Source

The exposure rate at distance $r$ from a point source of activity $A$ emitting photons of energy $E_\gamma$ is:

$$\dot{X} = \frac{A \, \Gamma_\delta}{r^2}$$

where $\Gamma_\delta$ is the specific gamma-ray dose constant (also called the exposure rate constant or gamma factor), tabulated for common nuclides. The quantity $\Gamma_\delta$ has units of R$\cdot$cm$^2$/(mCi$\cdot$h) or, in SI, $\mu$Sv$\cdot$m$^2$/(GBq$\cdot$h).

Representative values of $\Gamma_\delta$ (in $\mu$Sv$\cdot$m$^2$/(GBq$\cdot$h)):

Example: What is the dose rate at 1 m from a 10 GBq $^{137}$Cs source?

$$\dot{H} \approx \frac{10 \times 87.6}{1^2} = 876 \;\mu\text{Sv/h} \approx 0.88 \;\text{mSv/h}$$

This exceeds the public dose limit (1 mSv/year) in just over one hour of continuous exposure.

F.8.2 Shielded Dose Rate

With a shield of thickness $x$ and buildup factor $B$:

$$\dot{H}(r,x) = \frac{A \, \Gamma_\delta}{r^2} \cdot B(\mu x) \cdot e^{-\mu x}$$

F.8.3 Internal Dose from Ingested or Inhaled Radionuclide

The committed effective dose from intake of activity $A_0$ is:

$$E_{50} = A_0 \cdot e(g)_{50}$$

where $e(g)_{50}$ is the committed effective dose coefficient (Sv/Bq) for ingestion ($g$) or inhalation, tabulated by the ICRP for each radionuclide and chemical form. For adults, representative values include:

💡 Physical Insight: The enormous dose coefficient for inhaled $^{239}$Pu (four orders of magnitude larger than ingested $^{137}$Cs) reflects the combined effect of alpha emission ($w_R = 20$), long biological retention in bone and liver, and long physical half-life (24,110 years). This is why plutonium contamination is treated with such urgency in nuclear security contexts (Chapter 28).

F.8.4 Inverse Square Law in Practice

For quick mental estimates:

$$\dot{D}_2 = \dot{D}_1 \times \left(\frac{r_1}{r_2}\right)^2$$

At 30 cm (1 foot): dose rate is 100$\times$ the 3 m value. At 1 m: dose rate is 9$\times$ the 3 m value. At 3 m (10 feet): reference distance. At 10 m: dose rate is 0.09$\times$ the 3 m value.

F.9 Emergency Action Levels (Generic)

The following are generic protective action guidelines, not binding regulations. Actual emergency response follows site-specific emergency plans.

F.10 Regulatory and Reference Documents

For deeper study of radiation protection, the following documents are authoritative:

• ICRP Publication 103 (2007): The 2007 Recommendations of the International Commission on Radiological Protection. Defines the dose limit system, weighting factors, and principles.
• ICRP Publication 118 (2012): Updated eye lens dose limits (reduced from 150 mSv/year to 20 mSv/year averaged over 5 years).
• ICRP Publication 137 (2017): Occupational intakes of radionuclides (Part 3). Updated dose coefficients.
• 10 CFR Part 20 (U.S. NRC): Standards for protection against radiation in the United States.
• NCRP Report No. 160 (2009): Ionizing radiation exposure of the population of the United States. Comprehensive breakdown of population dose by source.
• IAEA Safety Standards Series No. GSR Part 3 (2014): Radiation Protection and Safety of Radiation Sources: International Basic Safety Standards.

📊 Chapter Connections: The physics underlying every entry in this appendix is developed in Chapter 16 (radiation interactions). The medical applications of radiation dosimetry are in Chapter 27. Environmental radiation and the LNT debate are in Chapter 29.