Key Takeaways — Chapter 29

Core Concepts

1. Natural background radiation is ubiquitous and unavoidable. The global average annual dose is approximately 3.0 mSv/yr; the US average is ~6.2 mSv/yr (higher due to greater medical imaging use). The three primordial sources are ${}^{238}\text{U}$ ($t_{1/2} = 4.47$ Gyr), ${}^{232}\text{Th}$ ($t_{1/2} = 14.0$ Gyr), and ${}^{40}\text{K}$ ($t_{1/2} = 1.25$ Gyr).

2. You are radioactive. A 70 kg human contains ~4,400 Bq of ${}^{40}\text{K}$ and ~3,700 Bq of ${}^{14}\text{C}$, for a total internal activity of ~8,700 Bq. This activity is maintained by homeostasis and cannot be reduced by dietary changes.

3. Radon-222 ($t_{1/2} = 3.82$ d), from the ${}^{238}\text{U}$ decay chain, is the single largest contributor to natural radiation exposure (~37% of the US total). The health hazard comes from its alpha-emitting daughters (${}^{218}\text{Po}$, ${}^{214}\text{Po}$) deposited in the bronchial epithelium. The EPA action level is 148 Bq/m$^3$ (4 pCi/L).

4. Cosmic ray dose increases exponentially with altitude: $\dot{D}(h) \approx \dot{D}_0 \, e^{h/h_0}$ with $h_0 \approx 1{,}500$ m. At jet cruising altitude (~10 km), the dose rate is ~5 $\mu$Sv/hr, making airline crew a significantly exposed occupational group.

5. Medical radiation, principally from CT scanning, is the largest man-made contributor (~48% of the US total, ~2.96 mSv/yr). A single CT abdomen (~10 mSv) delivers the equivalent of 3 years of natural background.

6. Deterministic effects (tissue reactions) occur above dose thresholds: nausea/vomiting at ~500 mSv, clinical radiation sickness at ~1 Sv, LD$_{50/60}$ at 3–5 Sv without treatment. Severity increases with dose.

7. Stochastic effects (cancer): the excess relative risk is ~0.47/Sv for solid cancers, based on the LSS of atomic bomb survivors. The ICRP nominal fatal cancer risk coefficient is 5% per Sv.

8. The LNT model ($R = R_0 + \alpha D$) is the regulatory standard but is scientifically unproven below ~100 mSv. The fundamental limitation is statistical: the predicted excess is smaller than the noise in the baseline cancer rate. Distinguishing LNT from a threshold model at 50 mSv would require ~2 million subjects per group.

9. Radiation protection principles: Justification (benefit must outweigh risk), Optimization (ALARA — as low as reasonably achievable), and Dose Limitation (occupational: 20 mSv/yr averaged over 5 yr; public: 1 mSv/yr above background).

10. Dose quantities form a hierarchy: Absorbed dose ($D$, Gy) $\to$ Equivalent dose ($H_T = \sum w_R D_{T,R}$, Sv) $\to$ Effective dose ($E = \sum w_T H_T$, Sv). The radiation weighting factor $w_R = 20$ for alpha particles is the key reason radon dominates the effective dose budget.

Essential Numbers to Remember

Threshold Concept

The LNT model is a regulatory assumption, not a proven biological law. The cancer risk from low-dose radiation (<100 mSv) is too small to measure directly against the large statistical background of spontaneous cancer. This epistemic limitation — not ideology or incompetence — is what makes the LNT debate genuinely unresolvable with current data. Understanding this limitation is essential for honest risk communication and sound policy.

Connections to Other Chapters

• Chapter 12 (Radioactivity Fundamentals): The decay law and secular equilibrium govern radon production and all environmental radioactivity.
• Chapter 16 (Radiation Interactions): The Bethe-Bloch formula, photon interaction coefficients, and radiation units developed there underpin all dose calculations in this chapter.
• Chapter 26 (Nuclear Energy): The reactor accidents discussed here connect to the reactor physics and safety analysis of Chapter 26.
• Chapter 27 (Nuclear Medicine): Medical radiation exposure, the dominant man-made source, uses the radiopharmaceuticals and imaging modalities discussed in Chapter 27.
• Chapter 23 (Explosive Nucleosynthesis): The primordial radionuclides (${}^{238}\text{U}$, ${}^{232}\text{Th}$) were synthesized in the r-process events discussed in Chapter 23.