Question 1 of 7: Fukushima Cooling-Water Isotopes and Caesium's Effective Half-Life

Question 1: Fukushima Cooling-Water Isotopes and Caesium's Effective Half-Life (13 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Fukushima Daiichi is light-water cooled; discarded cooling water has been treated to remove caesium and strontium but not tritium; caesium's biological half-life $T_b=70$ days, physical half-life $T_p=30.17$ years.

Find. (a)–(f) qualitative explanations of isotope production, hazard and treatment choices; (g) the effective half-life $T_{\text{eff}}$ of caesium in the body.

Approach. Classify each isotope by its production mechanism (direct fission product vs. neutron-activation product), use each isotope's decay mode/half-life/chemical behaviour to identify the dominant hazard isotope and its removal difficulty, then combine biological and physical clearance in part (g) via the reciprocal-half-life rule.

1. Part (a) — production mechanisms. Caesium (¹³⁴Cs, ¹³⁷Cs) and strontium (⁹⁰Sr) are direct fission products: when a ²³⁵U nucleus splits, the two mid-mass fragments land in the mass regions around $A\approx90$–100 (Sr) and $A\approx134$–137 (Cs), either directly or after a short chain of $\beta^-$ decays from the primary (more neutron-rich) fragment. Tritium (³H), by contrast, is not a fission product of that mass region; in a light-water reactor it arises from (i) rare ternary fission (roughly 1 in $10^4$ fissions ejects a third light fragment, occasionally ³H), and (ii) neutron activation — $(n,\alpha)$ capture on trace ¹⁰B/⁶Li in control materials and coolant chemistry, and $(n,\gamma)$ capture on the small natural abundance of deuterium already present in ordinary water. Both routes make far less tritium than a heavy-water reactor, but the volumes of coolant and years of operation still accumulate a measurable inventory.
2. Part (b) — isotope of caesium of greatest concern. ¹³⁷Cs ($T_{1/2}=30.17$ y) is of most concern, not ¹³⁴Cs ($T_{1/2}=2.06$ y). Its long physical half-life means it persists in the environment and in stored water for decades rather than decaying away within a few years; it is also a strong photon emitter (via its short-lived daughter ^137mBa, 662 keV gamma) and, chemically, caesium behaves like potassium, so it is readily taken up and distributed through soft tissue if ingested.
3. Part (c) — isotope of strontium of greatest concern. ⁹⁰Sr ($T_{1/2}=28.8$ y) is of greatest concern. Strontium is chemically similar to calcium, so ⁹⁰Sr is a classic "bone-seeker": once ingested it substitutes for calcium in bone mineral and is retained there for years, delivering a prolonged internal beta dose directly to the bone marrow — a far more damaging exposure pathway than a similarly-sized dose to soft tissue that clears quickly.
4. Part (d) — why iodine is absent from the report. Radioiodine (¹³¹I, $T_{1/2}=8.02$ days) was indeed released in the accident, but by April 2016 — more than five years and over 200 physical half-lives after the March 2011 accident — its activity has decayed to a physically negligible fraction ($2^{-200}$) of its original value. There is simply no detectable ¹³¹I left to report in water stored and treated years later; its short half-life is precisely why it is an acute, not a long-term, hazard.
5. Part (e) — why tritium survives the cleansing. The treatment system (ALPS, an ion-exchange/co-precipitation train) removes caesium and strontium because they exist as dissolved cations (Cs$^+$, Sr$^{2+}$) chemically distinct from the water molecule itself, so they can be captured on exchange resins. Tritium instead exists as tritiated water (HTO) — the tritium atom has replaced a hydrogen atom in the water molecule, so it is chemically indistinguishable from ordinary water. No conventional filtration or ion-exchange process can separate HTO from H$_2$O; only expensive, large-scale isotope separation (e.g. cryogenic distillation) could, which is impractical at the volume involved.
6. Part (f) — tritium's hazard mechanism. ³H decays by $\beta^-$ emission (${}^{3}\text{H}\rightarrow{}^{3}\text{He}+\beta^-+\bar\nu$) with a very low average beta energy ($\sim$5.7 keV, 18.6 keV maximum) and a range in tissue of only tens of micrometres — too short to penetrate the skin's outer dead layer, so tritium poses essentially no external hazard. Its danger is entirely internal: because it is chemically identical to hydrogen, HTO is freely taken up by ingestion, inhalation or skin absorption and distributes through the body's water (∼60% of body mass), irradiating tissue from within at short range. Its 12.32-year physical half-life is long, but its biological half-life as body water ($\sim$10 days) is short, so a single intake clears relatively quickly — the real hazard from a leak like Fukushima's is chronic, repeated intake, not one large dose.
7. Part (g) — effective half-life of caesium. The physical and biological clearance processes act in parallel, so their rate constants add: $$\frac{1}{T_{\text{eff}}} = \frac{1}{T_b} + \frac{1}{T_p}$$ Converting $T_p=30.17$ y to days ($30.17\times365.25=11{,}019.6$ d) and substituting $T_b=70$ d: $$\frac{1}{T_{\text{eff}}} = \frac{1}{70} + \frac{1}{11{,}019.6} = 0.014286 + 0.0000908 = 0.014376\ \text{d}^{-1}$$ $$\boxed{T_{\text{eff}} = \frac{1}{0.014376} \approx 69.6\ \text{days}}$$ Because $T_p\gg T_b$ here, $T_{\text{eff}}$ is dominated by (and lands close to, but slightly below) the biological half-life $T_b=70$ d — physically, the body clears caesium almost as fast as it would clear any chemically similar, non-radioactive tracer, since 30 years of physical decay barely registers over a 70-day biological residence.