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Radioactivity: sieverts and other units

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.

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reader netudiant said...

Thank you for an informative post.
The section on Grays and Sieverts deserves to be highlighted. It illuminates the scale of the problem very well.

The complicating factors in this instance is that the plant workers are operating in a severely damaged facility, where much of the equipment is damaged or nonfunctional and where much of the grounds is littered with potentially very radioactive debris from the massive explosions that have racked the four reactors. All this against a backdrop of massive devastation and probable personal tragedy from the tsunami.
These workers are still on the job, even though they are certainly aware that they are dancing with death. They are surely aware that their efforts may not be enough, particularly if the spent fuel tanks boil dry, but they are not giving up. True Japanese, they deserve our admiration and respect.


reader sillyfingers said...

Thank you, Lubos,
My children are in Tokyo. This carefully presented information in most appreciated.


reader Eelco said...

"But don't forget that ionizing radiation is unhealthy for the life of an individual at any amount."

This is not true. The dose-response model you are using in your calculations is a linear no-threshold model; it has been falsified many times over by empirical data and understanding of the biological response to ionizing radiation.

DNA repair mechanisms are nonlinear and adaptive. Pretty much all damage is repaired, up until a point where the repair emzymes get saturated with work. But that doesnt happen fast; the natural background radiation varies by orders of magnitude, but cancer rates dont. We have quite some leeway. Doses which are not out of the same ballpark as the background radiation, and which are non-spikey in nature relative to the response-time of adaptation mechanisms (less than an hour), dont cause any problems at all.

Another close analogy: if I spend just an hour naked in the sahara, I will regret it for the next months, if not for the rest of my life. If I get the same radiation dose by means of ten hours of watery sunshine, no comparable effect results.

Youd want to be wearing your suit right now if working near these reactors, but just a few kilometers away, people have other things to worry about. Certainly nobody in Tokio is going to die because of this. The worst case scenario for these plants is entirely unexciting; as long as the core material doesnt get blown out, which unlike tjernobyl is just as likely to happen to these reactors as to your refridgerator, this is all a storm in a glass of water.


reader Francisco said...

I've just read this at the Washington Post today. Based on the information you gave us on this post, the situation as they describe it looks pretty grim to me.

Radiation levels reach new highs as conditions worsen for workers

http://tinyurl.com/68u55br


reader Luboš Motl said...

Hi Francisco, what you read it the Washington Post about the "10 million times normal radiation" has been simply bullshit.

The media call this bullshit a mistake (click) but I think it's much more likely that it was deliberately fabricated to make Chicken Littles such as yourself excited.


reader Francisco said...

Hi Lubos,
I’m not trying to be chicken little, not my style, but this thing is getting worrisome.

From the BBC article reporting the retraction of the 10 million times error:
http://www.bbc.co.uk/news/world-asia-pacific-12875327

“The operators of a stricken Japanese nuclear plant have apologised for a “mistake” in reporting a radiation spike 10 million times above normal.”

All right, but they also say this in the same article:

"A spokesman for Japan’s nuclear watchdog, Hidehiko Nishiyama, said the level of radiation in puddles near reactor 2 was confirmed at 1,000 millisieverts an hour."

“It is an extremely high figure,” Mr Nishiyama said.

They don’t tell us how much this is over "normal" and don't tell us how much normal is.

They want us to do the work ourselves. So, according to Wikipedia:
“Average individual background radiation is 0.00023mSv/hr,” http://en.wikipedia.org/wiki/Sievert

Ok, So 1000 divided by 0.00023 is 4.3 million.

It's not 10 million times above normal. It’s only 4.3 million times above normal.

That does not sound too reassuring to me. The other day you were saying that 400 mSv per hour is huge. Well, how about 1000?

I certainly wish I am wrong, but this doesn’t look good at all, and I am beginning to believe we are not being told what is really going on there, or maybe nobody has much of a clue. How can so much radiation be getting out? and how are they going to keep crews working on the cooling with this kind of radiation?


reader Luboš Motl said...

Hi Francisco, 1000 is 2.5 times higher than 400, whether 1000 mSv/hour is huge or not. It's huge for me.

However, this is a radiation reading near a reactor - which dangerously affects a few dozens of squared kilometers around the plant.

The surface of the Earth is 510 million squared kilometers. I don't know what's the point for the whole globe to talk about a couple of reactors that are almost certainly ruptured but that will almost certainly not explode to release most of their dirty stuff into the atmosphere.

It's a trouble for the local worker, a few buildings that are broken and that store some stinky poohs that the nuclear boy may send away.

The worries are already vastly smaller than they were at the peak, and they will continue to fade away. But they will probably continue to a comparable extent for weeks or months. But I don't think it's right for the whole world to observe every radiation reading from Fukushima 1 that gets out. It's ultimately not the world's job.

It's the job of the people over there and it's a hard job. They're also maximally trying to protect themselves against the radiation. So far none of them has died, as far as I know. I find it plausible that some of them will. That would still be negligible relatively to the tens of thousands of tsunami fatalities.

Cheers
LM


reader Luboš Motl said...

By the way, Francisco, you're mixing apples with oranges. The original message was about the contaminated water's radiation being 10 million times the normal values - in the same reactor.

The correct figure is 100 thousand, not 4.3 million. Your calculation of 4.3 million clearly shows that you're computing a totally different ratio - one that has nothing to do with the reactor's normal state; and one that has nothing to do with the water per se. You're just confused about all the details which is why you are urged to avoid making any conclusions out of the numbers that you don't understand well enough to make rational conclusions.

Cheers
LM


reader Francisco said...

Lubos, I attribute the misunderstanding to the pranky Gods of semantics, and to sloppy, rushed journalism. It would have been helpful if they had defined what they meant by “normal” from the start. When they came up with the “10 million times over normal” statement, the only definition of “normal” that made sense to arrive at that figure would be normal background radiation (even though the correct figure would be “only” about 4 million times). From the reports I am reading now, some refer to normal as what would be normal for water in the facility, and others refer to normal as that which is within the limit of what is considered safe (which of course varies according to circumstances, urgency, exposure time, etc).

Still, the 1,000 mSv/hr figure is being repeated in recent reports, such as this NYT article today
http://www.nytimes.com/2011/03/29/world/asia/29japan.html?partner=rss&emc=rss

“Radiation measuring 1,000 millisieverts per hour was detected in water in an overflow tunnel outside the plant’s Reactor No. 2”

At the beginning of this crisis, I was taking it pretty lightly too, and thought they would control the situation soon, and that the alarm was somewhat exaggerated. But the way it has been unfolding makes me think the problem is much bigger than we thought, and they are trying to downplay it. During the Chernobyl mess they withheld information about the seriousness of what had happened as long as they could. I think it’s a given that power companies faced with a mess like this will always try to downplay the seriousness of the situation, everywhere.

As has been mentioned elsewhere, the solution of entombing the problem reactor under many tons of concrete is one that will not be considered, mainly because it would be a huge embarrasment. But it is a legitimate question to ask how long they allow water to keep overflowing with that level of contamination before the sarcophagous option is considered?

I wish a judgment on nuclear safety concerns were as easy to make as judgment on the nonsense of CO2-induced climate alarmism. But it's not. Nor can you compare these types of accidents with any natural or man-made catastrophe, no matter how big, for the simple reason that in a natural catastrophe you can go back the following day and start cleaning up and rebuilding, whereas with a mess of the Chernobyl type, your only option is to evacuate the area, which will be uninhabitable for a long time. I understand there are some abandoned cities and villages in the Ukraine that have been overgrown by forests, Pompeiis for future historians, where life in the Soviet era has been preserved for posterity. That may have some value, but every other aspect of it is depressing and spooky.

I am not (in principle) against nuclear power, but I think it is the kind of industry whose regulation must be held to such lofty standards that it may be beyond our capability to adequately control it. And if we can’t control it to those standards, messes will occur.


reader Luboš Motl said...

Dear Francisco,

I completely agree that the "tomb solution" should never be taken off the table as long as there are some new radioactive surprises. And I also agree that some people could feel embarrassed which is the main reason it won't be considered too easily.

Moreover, it's not "quite" trivial to create the tomb. They're dealing with smaller problems - e.g. how to store the radioactive water - and even with these simpler problems (why don't they just bring some new tanks over there?), they seem a bit confused. On the other hand, they don't have the world's resources to act because they still consider it a local problem with a few buildings, and I think they're mostly right.

I also think it's likely that the 1000 mSv/h figure for the reactor area is valid. It still allows one to live for many hours - and it's just a few meters around the place that everyone knows is really dirty.

The fuel has partially melted. So the vicinity of the reactor is inevitably resembling the radioactivity inside the reactor a little bit. Just some guess: do you know what's the radioactivity in Sieverts per hour inside the reactor core?

It's normal in physics when things differ by many orders of magnitude. One needs to be expert to figure out which "order of magnitude" is actually threatening.

In the Czech media, the reporting is much more balanced than what I see in the world. The media actually like to quote e.g. nuclear technology professors, who describe that the concentrations of Cs and I in the seawater are actually not really dangerous, etc.

Meanwhile, the Tokyo radioactivity is pretty much back to the normal levels.

Cheers
LM