本文是理论物理学家L. Motl 写的辐射剂量科普，适合非核物理专业人士阅读。
Unfortunately, the nuclear crisis in Japan hasn't managed to converge closer to its end on Tuesday: quite on the contrary, some people might say that it got out of control.
I have only passed one course in "applied nuclear energy" - as an undergrad in Prague - but I have also studied the subject "informally" (and because of qualifying exams etc.) over the years and many TRF readers know much more about the subject and they may correct my mistakes and contribute their own comments.
Some theory background
Existing nuclear power plants are based on fission, i.e. splitting of nuclei. Most of the energy from the fission of uranium may be attributed to the electromagnetic energy. This means that according to the liquid-drop model of the nucleus, the energy mostly comes from the Coulomb term (because of the large concentration of positively charged protons). There are several terms in this model, namely a volume term, surface term, Coulomb term, asymmetry term, and pairing term.
Despite the suggestive name of the two non-electromagnetic, non-gravitational fundamental forces, the "strong and weak nuclear force", most of the nuclear energy we're getting from the power plants arises from electromagnetic energy. (The liquid-drop model can't predict the magic numbers etc., something that requires the shell model. All these things are approximations of QCD which becomes incalculable in practice for those extremely complicated bound states of quarks and gluons.)
Nuclear power plants and nuclear bombs are based on chain reaction: a neutron breaks a uranium nucleus which releases something like 2.5 neutrons and they either escape from the material or cause additional disintegrations of other nuclei. If more than 40% of the neutrons do the latter, the reaction exponentially grows. The minimum mass needed to reduce the escaped neutrons below those 60% or so is called the critical mass. The potential exponential growth is deliberately unregulated in an atomic bomb; people try to regulate it in nuclear power plants.
However, many things keep on "burning" at the nuclear level even when the rods were moved to "turn off" the reactor: about 3% of the normal output of the nuclear power plant survives once the reactors were "turned off" by shifting the rods right after the earthquake. And be sure that 3% of the burning of those materials is still much stronger than the burning coal... Nuclear reactors are messy machines that can't be "fully turned off" too easily. That's why some cooling remains essential now.
The chain reaction is a "stimulated" nuclear process. Most nuclei decay "spontaneously", too. For an unstable nucleus species, the amount of so-far undecayed nuclei decreases exponentially with time, as "N(t) = N(0)*exp(-t/t_0)", where "t_0" is the lifetime of the nucleus; for a short period of time "dt", "N(0)*dt/t_0" nuclei decay. Also, "exp(-t/t_0)" may be expressed as a power of one-half, namely as "(1/2)^(t/t_{1/2})" where "t_{1/2}" is the half-life of the nucleus, equal to "ln(2)*t_0". The half-life is the time after which one half of the material decays and one half survives.
The half-lives of various species of nuclei span a vast spectrum of time scales - from tiny fractions of seconds to billions of years; many nuclei (especially the important ones, the "survivors") are exactly stable, too (because they have nothing to decay to which would be energetically possible). Where does this diversity of time scales come from? Well, it's one of the magic features of quantum mechanics. You may imagine that e.g. an alpha-particle (a helium-4 nucleus), one that eventually escapes the large nucleus when it decays via alpha decay, is confined by a potential wall.
Classically, it couldn't escape (just like you can't walk through the wall) but quantum mechanically, there is a nonzero probability of quantum tunneling, i.e. the process in which it temporarily visits the classically forbidden region - the wall - and then it appears away from the original nucleus. The probability of quantum tunneling per unit nuclear time goes like "exp(-V)" where "V" is a number describing the potential barrier. This exponential decrease follows from the exponential behavior of the wave function inside the barrier - that's the counterpart of the oscillating wave function when the allowed kinetic energy is negative (which means that the momentum has to be imaginary).
It's not shocking that "V" may sometimes be 20 and sometimes 100, depending on the exact force fields created by the other parts of the nucleus. While 20 and 100 are pretty similar, "exp(-20)" and "exp(-100)" are vastly different numbers - and it is this difference that can create lifetimes that are astronomically longer than the characteristic time scale of nuclear physics (the latter is something like 10^{-24} seconds). Radioactivity is a living proof of the quantum fact that you can ultimately walk through the wall.
Some half-lives
Let us enumerate a couple of nuclei and their half-lives. The nuclei are denoted by a word such as "uranium" that determine the number of protons in the nucleus - and also the same number of electrons needed to produce a neutral atom (which is why those words dictate the chemical properties). For example, the word "uranium" always means that the nucleus has "Z=92" protons; see the periodic table. After the hyphen, we usually add a number "A" counting the total number of nucleons (neutrons plus protons). The number of neutrons doesn't affect the chemical properties (because chemistry is all about the electron clouds and electrons only care about the charge of the nucleus) but it hugely influences the nuclear properties which is what we discuss here.
Uranium is the primary fuel for conventional nuclear power plants. It naturally comes in two key isotopes, uranium-238 and uranium-235. The former is "ordinary" while the latter is "more special". When we talk about the enrichment of the nuclear fuel, we are talking about increasing the fraction of uranium-235 in the material. That's needed to produce nuclear bombs etc.
Uranium-238 has half-life of 4.5 billion years and uranium-235 has half-life of 0.7 billion years. They're very long-lived, indeed - the lifetimes are comparable to the current age of the Universe so a big percentage of the uranium would survive if it were created right after the Big Bang (however, in the real universe, most of the heavy elements are created inside stars and other astrophysical objects). The lifetimes sensitively depend on the number of neutrons. A beginner could think that e.g. uranium-239 has to be similar to uranium-238; however, its half-life is 23 minutes (compare with the billions of years of its friends) which is why it's clearly not included in the rocks that have been around for billions of years.
In reactors, one creates lots of other messy stuff. Plutonium-239 has half-life of 24 thousand years and another isotope, uranium-233, has half-life of 160 thousand years. Those things decay much more quickly than the uranium isotopes. One typically gets lung cancer from this kind of junk and we will discuss similar issues momentarily.
However, the nuclear reactors produce a lot of radioactive material whose lifetime is much shorter than those thousands of years. Let's jump to the opposite extreme, the short-lived nuclei, and discuss the health effects at the same time.
Health and nuclear lifetimes
You often encounter iodine-131 whose half-life is just 8 days. That means that it decays mercifully quickly. What about the animals like us? We have the thyroid gland somewhere in the neck and you know that "iodine is healthy". So this element is being stored and used over there. The thyroids can't really tell the difference between iodine-127 which is completely stable and healthy and the radioactive iodine-131 - their chemical properties are pretty much identical because they only depend on the number of protons, not neutrons.
So the thyroids just absorb the radioactive eight-day iodine-131 if there's a lot of it around. It decays in your body and typically causes thyroid cancer, a frequent diseases around Chernobyl. A way to fight this threat is to eat lots of ordinary healthy iodine-127 (in iodide tablets) and put the imported radioactive iodine-131 into a comparative disadvantage (an overcrowded market).
Strontium-90 is another bastard that emerges from such nuclear reactions. Its half-life is 29 years. If you eat it or absorb it, only 3/4 of it are excreted. The rest is searching for your bones - because it has similar chemical properties as calcium - and because it may stay there for quite some time, it is somewhat likely to cause things like bone cancer or leukemia (some blood cells are produced by bones etc.).
Similarly, caesium-137 has lifetime of 30 years. It's similar to strontium-90 but their fate in the body is very different. This caesium nucleus imitates potassium which is why it spreads across the muscles of your body. It stays in your body for 70 days or so. A treatment is a chemical called Prussian blue with the idealized formula Fe7(CN)18⋅14H2O. Whatever is the reason, this compound may bind to the caesium nuclei and help you to remove it from your body soon.
Again, plutonium-239 has half-life of 24 thousand years. It is really a primary "fuel", playing a similar role to uranium-235 (the thing whose concentration you or Mahmoud increase if you or he "enriches" the uranium). It causes lung cancer but fortunately, those things have only been tested at the end of the war and shortly afterwards.
Dosage
We often want to say how much radiation some bodies have received - what is the radiation level near the Fukushima power plant or in Tokyo. The standard unit is mathematically equivalent to J/kg, "Joule per kilogram" (kilogram of your body; Joule of energy received by ionizing radiation).
However, it's desirable to distinguish the physical amount of energy and its biological impacts. So we never use the J/kg unit in this form; instead, we use two different units which are formally equal to J/kg but appear in different contexts: gray (1 Gy) and sievert (1 Sv). Also, the unit of "1 rem = 0.01 sievert" is sometimes being used; "rem" stands for "Röntgen equivalent man".
One gray is the actual amount of ionizing energy that is absorbed by the tissue; one sievert measures the amount of impact on your issues in such a way that 1 Gy = 1 J/kg in the form of x-rays, gamma rays, electrons, positrons, and muons brings exactly 1 Sv to the tissue. These are the radiation types with particles of low (or vanishing) rest masses.
However, the health impact of other kinds of radiation on the bodies is often greater. So for protons, 1 Gy gives you 2 Sv of damage and similarly for neutrons - with energies above 2 MeV or below a few keV. However, neutrons with intermediate energies between 0.1 and 2 MeV make 1 Gy equivalent to as much as 20 Sv, just like alpha particles and heavy nuclei.
Do you still follow me? One gray is the objective measure for the energy of ionizing radiation but one gray from heavy-nuclei-like may give you as much as 20 Sievert.
How many sieverts...
OK, check e.g. this page by Richard Muller. Yes, it's the same man at Berkeley who is building the BEST surface temperature record these days.
A main punch line is that 3 Sv is what causes a 50% of death within a month if untreated. Below 1 Sv, you won't see any "guaranteed" short-term impact. But don't forget that ionizing radiation is unhealthy for the life of an individual at any amount.
If you don't want to remember too many numbers, just remember that a few sieverts are already on the sure path to death. Imagine that one death is equivalent to 5 Sv. So the figures with the units of one sievert, when divided by 5, approximately give you the probability of death as a consequence of the ionizing radiation.
So "a few millisieverts" mean something like one permille probability of death. The most typical equivalent dose you get from the natural background at a generic place of the Earth is 2.4 millisievert per year. Because I defined the death to be 5 Sv, 2.4 millisievert (per year) is the 0.05% probability of death caused by the radiation (per year).
You see that the lifetime from the background radiation is comparable to 2,000 years. Because the human life expectancy is around 70 years, it follows that about 1/30 of the deaths should be due to cancer from the background radiation - which is therefore about 1/10 of the total number of cancer cases because about 1/3 of people may be dying of cancer.
Back to Japan
Today, near the worst reactor building in Fukushima, they detected 400 millisieverts per hour: this figure was ultimately confirmed by IAEA (which was, until very recently, trying to downplay all radiation risks in Japan - a fact that may be related to the current Japanese leader of IAEA, Yukiya Amano). I want you - including all fellow big fans of nuclear energy - to understand that this is just a huge number. We have quantified one death to be 5 sieverts above: and the kids playing next to the reactor receive 0.4 sieverts per hour. Thank you, you're welcome.
If you spend twelve hours by playing in the vicinity of the worst reactor of the Fukushima power plant, you will probably die. And if you die, who will continue to fight against the meltdown threats? Between the reactor buildings 2 and 3, the equivalent dose is 0.03 Sievert per hour. That will give you 150 hours of life over there - unless you are protected in some way.
Of course, it's much more important what the radiation levels will be in the nearby large towns - and I don't even want to use the word Tokyo in this paragraph. But be sure that if the radiation level in Tokyo or another city managed to jump to something like a millisievert per hour, or even per day (and it would be sustained for a day), that would mean that 1/5,000 of the population of the city would ultimately die as a consequence of the exposure during the hour (except for those who would manage to die earlier because of another reason) unless they were successfully kept indoors all the time.
These are not negligible doses - the kind of events that Greenpeace loves to hype. These are genuinely dangerous doses for the people who work for the nuclear power plant, to say the least. Nuclear energy was sensibly calculated to be a low-risk source of energy, given the expected number of dangerous earthquakes etc. However and sadly, those old probabilities have to be replaced by the conditional probabilities right now: we already know that a very damaging earthquake has taken place near such power plants...
Just to end up with some relatively good news: a millisievert per hour is (so far?) insanely far in Tokyo. They measured 0.8 microsieverts per hour. I defined one death per person to be 5 Sv, so 0.8 microsieverts per hour means 0.16 ppm (parts per million) death per person and per hour. Multiply it by 37 million people in the Tokyo metro area and you get 6 deaths in the city per hour (or 150 deaths per day or so, if the radiation remains elevated). That's nonzero but won't be measurable statistically and will remain hugely smaller than the casualties of other lethal threats.
Hopefully... Boiling water in a storage pool wouldn't be a good source of new hopes, however.
