Question 5 of 7: Radiation Safety and Standards

Question 5: Radiation Safety and Standards (15 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. $T_{1/2}({}^{90}\text{Sr})=29.1$ yr, decaying by $\beta^-$ to ${}^{90}$Y ($T_{1/2}=64$ h, then stable Zr); $T_{1/2}({}^{137}\text{Cs})=30$ yr, decaying by $\beta^-/\gamma$ to ${}^{137m}$Ba; the "practically vanished" activity criterion (10 half-lives, activity down to $2^{-10}\approx0.098\%$ of its initial value) applied consistently across (e)(i) and (f)(ii).

Find. (a) the numeric occupational dose implied by "5× the acceptable exposure"; (e)(i) the time for ${}^{90}$Sr to practically vanish; (f)(ii) the fraction of ${}^{137}$Cs remaining at that same elapsed time.

Approach. Use the standard annual occupational effective-dose limit as the "acceptable exposure" baseline for (a); apply the standard 10-half-life "practically vanished" convention to (e)(i), then apply that same elapsed time as the argument of ${}^{137}$Cs's own decay law for (f)(ii); answer the remaining conceptual sub-parts from fission-product half-life/yield, chemistry-of-uptake, and gamma-vs-beta detectability arguments.

1. Part (a) — the implied dose value. The commonly cited annual occupational effective-dose limit for nuclear workers is $\approx 20$ mSv/year (the ICRP recommendation, averaged over five years; in Canada the CNSC limit for a Nuclear Energy Worker is 50 mSv in any one year and 100 mSv over a five-year dosimetry period, i.e. the same 20 mSv/yr average); five times that figure is $$\boxed{5 \times 20\text{ mSv} = 100\text{ mSv (in one hour, at the point measured)}}$$ consistent with contemporaneous reporting of the actual Fukushima measurement.
2. Part (b) — why Sr-90 and Cs-137 are named. Among the hundreds of fission products, ${}^{90}$Sr and ${}^{137}$Cs stand out because they combine a moderate half-life (29.1 and 30 years respectively) — long enough to persist in the environment for decades, short enough to carry substantial activity per unit mass (specific activity $\propto 1/T_{1/2}$) — with a relatively high fission yield and problematic biochemistry (Sr mimics calcium, Cs mimics potassium, so both are readily taken up biologically). Fission products with much shorter half-lives decay away within days to weeks of an accident; those with much longer half-lives (like ${}^{129}$I) have such low specific activity that they contribute comparatively little dose rate per becquerel of mass present.
3. Part (c) — why ${}^{129}$I and ${}^{131}$I are absent from the report. ${}^{131}$I has a short 8-day half-life, so by August 2013 — roughly 2.5 years (over 110 half-lives) after the March 2011 accident — essentially none of the originally released ${}^{131}$I remains; it is simply gone. ${}^{129}$I, conversely, has an enormously long half-life ($\approx 1.57\times10^7$ years), so even though some inventory remains, its specific activity (Bq per gram) is minuscule, contributing negligible dose rate compared to the moderate-half-life ${}^{90}$Sr and ${}^{137}$Cs highlighted in the report.
4. Part (d) — source of tritium. Tritium ($^3$H) is not itself a fission product in significant yield, but reactors produce it two ways: (i) ternary fission, in which roughly 1 in every $10^4$ fission events splits into three fragments rather than two, occasionally yielding a light nucleus such as tritium directly, and (ii) neutron activation of light nuclides present in the coolant or control materials — for example ${}^{10}\text{B}(n,2\alpha)^3\text{H}$ from boron used in control/shutdown systems, or $^6\text{Li}(n,\alpha)^3\text{H}$ where lithium is present, plus ${}^2\text{H}(n,\gamma)^3\text{H}$ capture on the deuterium naturally present in the cooling water itself. All of these mechanisms operate continuously during reactor operation, so tritium accumulates in reactor water independent of any fresh fission-product release.
5. Part (e)(i) — time for ${}^{90}$Sr to practically vanish. Using the standard "practically gone" convention of 10 half-lives (activity down to $2^{-10}\approx0.098\%$): $$\boxed{t = 10 \times T_{1/2}({}^{90}\text{Sr}) = 10 \times 29.1 = 291\text{ years}}$$
6. Part (e)(ii) — why ${}^{90}$Sr is still a hazard. The soil-shielding argument only removes the external beta hazard. ${}^{90}$Sr is chemically almost identical to calcium, so plants and animals take it up through the food chain and deposit it in bone (a "bone-seeker"), exactly where calcium goes. Once incorporated, its beta particles (and its daughter ${}^{90}$Y's, which are even more energetic) are emitted inside the body, directly irradiating adjacent bone marrow at short range with no soil, skin, or clothing to stop them — making ${}^{90}$Sr predominantly an internal (ingestion) radiological hazard rather than an external one.
7. Part (f)(i) — validity of the whole-body-counting statement. Valid. Whole-body counters detect gamma rays escaping the body from outside; ${}^{137}$Cs's daughter ${}^{137m}$Ba emits a strong, easily detected 662 keV gamma, so whole-body Cs-137 burdens are readily quantified externally. ${}^{90}$Sr and its daughter ${}^{90}$Y are essentially pure beta emitters with no significant gamma line, and beta particles cannot escape the body to reach an external detector — whole-body (gamma) counting is blind to ${}^{90}$Sr, which instead requires bioassay methods (urine or fecal sampling) to quantify.
8. Part (f)(ii) — remaining ${}^{137}$Cs after 291 years. Applying ${}^{137}$Cs's own decay law over the same 291-year interval found in (e)(i): $$n_{\text{half-lives}} = \frac{291}{30} = 9.7, \qquad \text{fraction remaining} = 2^{-9.7}$$ $$\boxed{\text{fraction remaining} = 2^{-9.7} \approx 1.20\times10^{-3} \approx 0.12\%}$$ Roughly one part in 830 of the original ${}^{137}$Cs activity is still present — small, but not yet at the same "practically vanished" threshold as ${}^{90}$Sr, since ${}^{137}$Cs's half-life is marginally longer.