Radioactive Cs 137 from Fukushima in the oceans

I've seen a lot of misinformation circulating about the consequences of the catastrophe at Fukushima, with nice world maps with ocean currents plotted on them showing how radioactive waste from Fukushima is going all around the world, supposedly making fish unfit for consumption all over the world. This is complete poppycock. Overstating the case wildly like this doesn't help at all – it just makes it easy for the pro-nuclear lobby to ridicule you. The problems at Fukushima are very real and affect a large area of land and sea and a lot of groundwater, but they really aren't a global problem. Here's why:

Cs133 is the only naturally-occurring isotope of Caesium. It is stable. It forms 0.5 ppb (parts per billion) of seawater, and 20 ppb of a human body.

A semicircular area of sea 50km in radius, to a depth of 30m, contains about 1.2 x 10¹¹ tonnes of water – so about 60 tonnes of Cs133.

A nuclear reactor typically contains about 70 tonnes of enriched uranium, of which about 4% is U235. Assuming a burn-up of about 6% (after which the fuel has to be changed because there's not enough U235 left to sustain the chain reaction*), about 0.24% of the uranium will have been converted into fission products. Cs137 is a direct or indirect product of about 6% of U235 fissions, so the total mass of Cs137 in the reactor can't be more than about 70 tonnes x 0.24% x 6% x 137/235 which is approximately 60kg. This is an approximate upper limit. Most of the time a lot of the fuel will be fresher than that, with more unreacted U235 and less fission products. Against that, there were several reactors at Fukushima, and a used fuel store (containing considerably more material than the reactors).

So if we distributed all the Cs137 from one reactor uniformly in the top 30m of that semicircular area of seawater, it would constitute about 0.1% of the caesium. In practice of course it's likely to be more concentrated in the middle, and less at the edge – but there could be some variations in the concentration at the edge. But by the far side of the Pacific, or by Hawaii, 6000 km away, it's going to be much less than that.

The human body contains about 20ppb of caesium. If 0.1% of that were radioactive Cs137 instead of stable Cs133, we'd have about 0.02 ppb of Cs137 in us.

The human body also contains about 2,000,000 ppb potassium, of which 0.0117% is radioactive K40 – that is, we contain about 234 ppb of K40. That's 11,700 times the amount of Cs137 that we're talking about. All these quantities are by weight, so that's 11,700 x 137/40 by numbers of atoms, that is about 40,000 times.

But K40 has a half-life of 1.277 x 10⁹ years, whereas Cs137 has a half-life of 30.07 years. The ratio is 4 x 10⁷ so 0.02 ppb of Cs137 is around 700 times as radioactive as 234 ppb of K40 – that's in terms of the number of atomic decays per second. There are two other things to consider.

Firstly, are the radiations produced by those decays the same? Not quite, but the difference is quite small. Cs137 decays by beta emission, with an energy of 1.176 Mev to a meta-stable state of Ba137, which has a half-life of 2.52 minutes, decaying to the stable state of Ba137 by an additional beta emission with energy 662 keV.

K40 also decays by beta emission, with an energy of 1.311 MeV, directly to stable Ca40.

Secondly, do potassium and caesium concentrate in different parts of the body, with different susceptibilities to radiation? No, caesium and potassium are biologically very similar; both are fairly uniformly distributed throughout the wet tissues, with lower concentrations in fat and bones.

So anyone eating a lot of fish caught in waters within about 50km of Fukushima may have been ingesting enough Cs137 to increase their internal radioactivity by quite a lot – not in general by as much as 700 times, unless their diet was exclusively fish or the fish are obtained particularly close to Fukushima, but quite significantly. Exactly how much increase in cancer risk is associated with such an increase in internal radiation is controversial, but I'd take a cautious view myself!

Then increase that 50km to the 6,000 km to Hawaii, or more to California, or very much more to the Atlantic – and allow for the fact that over such distances vertical mixing will be more than the typical 30m that occurs locally and rapidly. That's at least four orders of magnitude: there's going to be nothing important here. This is an oversimplification, of course: ocean currents can carry material over long distances without mixing it very much. However, they do mix it to a significant extent; add to that the effect of movement of fish in and out of the contaminated water, and the end result is that far from Fukushima, even someone who has a diet of mainly fish is at no real risk. In some places, the Cs137 may be detectable with sufficiently sensitive equipment, possibly even measurable, but not a real hazard.

Note that this analysis only concerns Cs137. The analysis for Cs135 is similar, except that its half-life is 2.3 million years, so it's very much less radioactive but will be around for far longer! The quantities produced in the reactor are very similar.

I131 is another one of concern: about 2.9% of fissions produce it, directly or indirectly, and it has a half-life of 8 days, decaying with a 971keV beta emission and a 164keV gamma ray (if you were getting enough of these gammas to matter, the corresponding betas would kill you instantly if it was internal!) Thus it's far more radioactive than the Cs137, but initially with half the quantity; and the quantity rapidly decreases as it decays to stable Xe131. Iodine is selectively concentrated in the thyroid, increasing the risk of locally higher concentrations. Iodine in the air (as from Chernobyl, but much less from Fukushima) is consequently a serious issue. Iodine in seawater is much less of an issue, for two reasons: firstly, there's a lot more ordinary, non-radioactive iodine in seawater to dilute the I131; secondly, the short half-life of I131 means that it's pretty much all gone before it travels very far by the relatively slow movement of seawater.

But there's a whole witches' brew of other isotopes to consider. See ie.lbl.gov/fission/235ut.txt