The die of a trillion faces

kw: analysis, radioactivity, quantum physics, chaos

I'm halfway through a book about the edges of scientific knowledge, which I'll review anon. In the meantime, two of the chapters got me thinking: one on mathematical chaos and the other on quantum randomness as it relates to radioactivity.

Mathematical chaos does not refer to utter randomness, but to mathematical process that are completely deterministic but "highly sensitive to initial conditions." Such systems are typically studied by running computer simulations, which brings out an amusing feature: many such systems are also overly prone to amplify rounding errors in the calculations. For example, numerically solving a set of stiff differential equations frequently results in the solution "blowing up" after a certain point, because the rounding errors have accumulated and overwhelm the result.

Natural systems, being analog and not digital, can be described by sets of differential equations. Digital simulations of such systems can proceed only so far before descending into nonsense. The most famous of these is forecasting the weather. Many computer scientists and meteorologists have labored for decades to produce weather models that run longer and longer, farther and farther into the future, before "losing it." So now we have modestly reliable seven-day forecasts (and Accuweather.com has the temerity to show 90-day forecasts); a decade ago or so, no forecast beyond three or four days was any good.

Quantum randomness is a beast of another color, indeed, of a different spectrum of colors! These days the classic illustration is the ultra-low-power two-slit interference pattern. You can produce a visible (and thus moderate-power) pattern with a laser pointer, a pinhole or lens, and a little piece of foil with two narrow slits a short distance apart. The pinhole or lens will spread the beam so you can see it hit both slits. On a screen a few inches behind, a pattern of parallel lines will appear, similar to this image.

The ultra-low-power version is to set this up with the lens/pinhole and the slits and the laser held in stands, and the screen replaced by sensitive photographic film. Then a strong filter is put at the laser's output, calculated to make the beam so weak that no more than one photon will be found in the space between the laser and the film at any one time. Such an arrangement requires an exposure of a few hours to get the beginnings of a record, and several days to get an image like the one above. Whereas this experiment with strong light seems to show the wave nature of light, the ultra-low-power version shows that a photon has a wave nature all by its lonely self!

A "short" exposure of an hour or less will show just a few dots where single photons were captured by the emulsion. They appear entirely random. The longer the exposure, the more a pattern seems to emerge, until a very long exposure will produce a clear pattern. The pattern shows that you can predict with great precision what the ensemble of many photons will do, but you cannot predict where the next photon to pass through the apparatus will strike the film.

Radioactivity also obeys certain quantum regularities (I hesitate to write "laws"). Half-life expresses the activity of a radioactive material in reciprocal terms. A long half life indicates low activity. In the book I was reading the author wrote of a little pot of uranium 238 (U-238) he bought, which contains just enough of the element to experience 766 alpha decays per minute. My first thought was to see how much U-238 he had bought. U-238 has a half life of 4.468 billion years. Working out the math, I determined that he had just over one milligram of uranium. The amount was very close, which made me suspicious that there was a typo: If he actually bought exactly one milligram, the activity would be 746 decays per minute…and that might be the true amount.

What is happening inside a uranium nucleus that leads a certain one to emit a helium (He-4) nucleus (and thus turn into thorium 234, Th-234)? Scattering experiments carried out decades ago showed that although the atomic nucleus is incredibly tiny, it is mostly empty space! I learned this as a physics student in the late 1960's. I had found it hard enough to wrap my mind around the view of an atom as a stadium with a few gnats buzzing around the periphery, centered on a heavy BB. So the protons and neutrons, while not being effectively "dimensionless" like electrons, are still much tinier than the space they can "run around" in. The propensity of proton-heavy elements such as U-238 to decay by emitting helium nuclei indicates that the protons and neutrons "run around" in subgroups.

The standard explanation is that at some point one of the He-4 nuclei "tunnels" through the "strong force barrier", finds itself outside the effective range of the force, and thus is accelerated away by electromagnetic repulsion to an energy of 4.267 MeV. What determines when it tunnels through?

Back in the chapter on chaos, the author spoke of dice with various numbers of faces, though he illustrated the randomness of a die's fall using a "normal" 6-sided die he got in Las Vegas. I guess they make them more accurate there, where large stakes are wagered on their "fairness". But dice with various numbers of faces are produced for board-based role playing games. This illustration, from aliexpress.com/, shows one such set of ten different kinds of die, ranging from 4 to 20 faces.

Put two thoughts together, and you can get some interesting products. Can the randomness of alpha decay be related to the randomness of a tumbling die? We can set up a model system with a box of cubical, 6-sided dice, perhaps 100. Here are the steps:

1. Cast the dice on a table top (with raised sides so none fall off, perhaps).
2. Remove each die that shows a 6.
3. Return the rest to the box.
4. Repeat from step 1.

I did this a few times, stopping each run after 16 trials. Here are two results:

100, 81, 69, 58, 49, 41, 35, 30, 24, 21, 18, 14, 11, 9, 8, 6, 5
100, 90, 78, 64, 53, 46, 37, 31, 26, 22, 18, 15, 12, 10, 9, 8, 7

The calculated half life of these dice, with "activity" of 1/6 per throw, is 4.16 throws. As seen above, small number statistics cause a certain variation, so that after four throws, 49 and 53 are left; after 8 throws, 24 and 26; and so forth. If instead you use 20-sided dice, the half life would be 13.9 throws.

This led me to think of the He-4 (alpha particle) "cores" bouncing around inside the strong-force boundary around a U-238 nucleus as being governed by a die with an immense number of faces, perhaps a trillion. Rather than numbers from one to a trillion on the faces, the only thing that matters is the "get out of here" face, which we might consider to be green (for "go"), the rest being red. On average, once per trillion "bounces" the die momentarily has its green face at the boundary, and the alpha particle flies free. Since the decay constant for U-238 is ln(2)/half life of 4.468 billion years, or one decay yearly per 6.45 billion nuclei, a trillion-sided die would imply a "bounce" time of about two days. The actual transit time for an "orbiting" He-4 is closer to 10^-18 sec, which implies a die with a whole lot more than a trillion faces; say, ten trillion trillion faces.

Can it be that quantum randomness and mathematical chaos are related? Could one cause the other … in either direction?!?

That is as far as I have taken these ideas. I don't know (does anyone?) whether the internal, dynamic structure of a large nucleus is dominated by lone nucleons, by clusters such as He-4 and others, or what. The lack of decay products other than alpha particles, except in cases of spontaneous fission, for nuclei that are proton-rich, indicates that any nucleic clusters don't exceed the He-4 nucleus in size (and beta decay is a subject for another time!).

Countering the China syndrome

kw: book reviews, nonfiction, radiation, radioactivity

A couple of years ago, in answer to fears expressed by friends and relatives, I posted Uranium 101, to explain what we should fear and what we should not fear, about Uranium and the possible release of radiation in Japan after the earthquake and tsunami.

I am gratified to read a comprehensive summary and explanation of these matters in Radiaton: What it is, What You Need to Know, by Robert Peter Gale, M.D., and Eric Lax. The authors discuss the sources of background radiation, and the things we do that add extra radiation exposure, such as getting X-rays and CT scans, flying, and smoking. That's right, smoking increases exposure to radiation. Tobacco plants do not take up uranium from the soil, but the "daughter elements" radium (4 million times as radioactive as uranium) and polonium (5,000 times as radioactive as radium) do get into the tobacco leaves, and into cigarettes. If this really worries you, but you can't stop smoking, do this: the half life of polonium is 138 days, so just stockpile your smoking materials, write dates of purchase on the packages, and don't use them for 4 years. Then the polonium content will be less than 1/1000 of what it was when you bought it.

OK, back from digression. Americans living at sea level are exposed to 3-4 mSv (millisieverts) of radiation yearly. Higher elevations take us above some of the protective atmosphere, so nationwide, the average is about 6 mSv. When you fly in a jet plane at 36,000 ft, you are above 3/4 of the atmosphere, so more space radiation reaches you. However, now you are shielded from most of the radiation coming upward from the ground. Still, you receive a lot more radiation during each hour of flight than you get from the X-ray backscatter scanner at the airport. Better news: many airports are replacing the X-ray scanners with T-ray scanners, which cannot cause harm.

Many people are afraid of all kinds of radiant energy. The electromagnetic spectrum is very, very wide, and only about half of it (in logarithmic terms) is harmful. Too see how wide, we need to talk units. Two sets of units are used, wavelength and energy per photon. Wavelength is used for the longer, less energetic photons, and energy is used to discuss the higher energy, very short-wave photons. The "center" of the spectrum is visible light, and in this region, both units are used depending on the reason for discussing them. So let's start with visible light, and the near-visible regions of near infrared and near ultraviolet.

The limits of normal vision are considered to be at wavelengths of 400 nm at the blue end, and 700 nm at the red end. Actual visual response at these limits is about 0.4% of the response to yellow light near 580 nm. The unit nm is the nanometer, or a billionth of a meter. To convert to energy, the proportionality constant is 1,293.7 eV-nm, and we divide this number by the wavelength to get energy. So blue-limit light's energy per photon is 1,239.7/400 = 3.1 eV, and at the red limit, it is 1,239.7/700 = 1.77 eV. The eV is the electron-volt, the energy an electron has when accelerated by a 1-volt potential. Old CRT type TV sets used an electron gun with about 30,000 volts, so the electrons were hitting the front plate with an energy of 30,000 eV, usually shown as 30 KeV, for Kilo-eV. We'll get back to this.

Near-infrared (NIR) is typically considered to range from 700 to 5,000 nm, AKA 0.7-5 µ (microns; the "consistent" term micrometer hasn't really caught on). Near-ultraviolet (NUV) ranges from 400 to 280 nm, the range of UV that can easily pass through the atmosphere. It has two components, UVA and UVB, with a cutover at 315 nm. UVC that you may have read about is the germicidal UV used in hospitals, ranging down to about 240 nm, where the atmosphere blocks it even over short distances, such as across a room. The UVA-UVB cutoff has an energy of 3.94 eV. Organic chemical bonds have energies in this range, which makes UVA and UVB risky for our skin. The thinner ozone layer is letting through a little UVC from the Sun, also, which is why sunblock is needed more now than in the past. The energy of UVC is at least 4.43 eV per photon, and it can damage exposed skin quickly.

Energetic as these wavelengths may be, they are not ionizing radiation. That takes a lot more energy per photon. Although the C-C bonds in organic materials can be broken by UVC, that produces free radicals, not ions. True ionization needs at least 10 eV/photon, or a wavelength shorter than 124 nm. This is the boundary between Far UV and "soft" X-rays. The X-rays used by your dentist are generated by an electron beam hitting a tungsten anode at 70,000 volts. They have a range of energies peaking at about 40 KeV. These are called medium X-rays, while hard X-rays are in the range above 100 KeV. Such X-rays are used by industrial inspection X-ray machines.

Remember the CRT TV? It produces small amounts of rather soft X-rays at about 20-25 KeV. That's why parents used to tell their children to stay farther from the TV set. Today's flat-screen TV's, whether Plasma, LCD or LED, do not produce any X-rays.

Now, how about your cell phone? Can it cause cancer? While you are talking (not listening), the phone is signaling to the tower using about 1 watt of microwave radio. While "microwave" may sound scary, that just means it is at a wavelength shorter than the UHF band used for analog TV signals (channels 13-65), in the pre-cable days. Microwaves have wavelengths over a wide range, from 1 m to 1 mm. Let's convert the shortest wavelength (most energetic) to nm and check the eV formula: 1mm = 1 million nm, so 1,239.7/1,000,000 = 0.0012 eV per photon. This is much less energetic than visible light. You'd suffer more damage by shining a flashlight into the side of your head! By the way, T-ray scanners use a wavelength near 1 mm.

Other kinds of radio use even longer wavelengths, and their tiny photon energies are why this unit is not used in this range. The longest common frequency to which we are exposed is the 60Hz signal from AC power transmission, which has a wavelength of 5,000 km. Thus the range of non-ionizing radiation is between 5,000 km and about 500 nm, a range of 1 quadrillion to 1. Now let's look at higher energies than X-ray.

There is a big gap in the spectrum of natural radiation to which we are exposed, because of blocking by the atmosphere, and because common radioactive elements produce energetic particles starting at a rather high point, though typically at a low level. Three elements form the foundation of natural radiation in Earth materials, mostly rocks: Uranium, Thorium and Potassium.

First and foremost, we cannot avoid Potassium (symbol K). The human body contains 0.25% K. Thus, I weigh 200 lbs (91 kg), so my body contains half a pound of potassium, or about 0.23 kg. The radioactive isotope of potassium is K-40, and makes up 0.0118% of the total, or 0.027 g; just over 1/40th of a gram. That isn't much, and K-40 is weakly radioactive, with a half life of 1.28 billion years. But that 40th of a gram is about 4x10²⁰ atoms, of which nearly 7,000 decay each second. Now we get to energy. K-40 decays by the beta process, ejecting an electron or positron (it can do either, to become either Ca-40 or Ar-40, both of which are stable). The ejected particle has an energy of 1.3 or 1.5 MeV (million eV), some 1,000 times as energetic as a hard X-ray. It also produces energetic photons with an energy of 0.5 or 1.5 MeV. The beta particle stays in the body, while the gamma photon can exit, meaning that during a hug (or sleeping together) we receive some gamma radiation from our partner!

K-40 gamma radiation is near the low end of the range of natural radioactivity, but is not the lowest. Uranium and Thorium in the soil, particularly in areas with a lot of granite, produce energetic alpha particles, but these are absorbed by almost anything, such as a sheet of paper. A typical room with gypsum sheetrock contains a tenth of a gram of U and half as much Th, but their alpha radiation is stopped by the paper and the paint on the wall. Not so their gamma photons, which are actually in the hard X-ray region, at 48 KeV and 59 KeV respectively. Also, they have long half lives, 1.41 billion years for Th-232 and 4.51 billion years for U-238.

What about Radon? When U-238 emits an alpha particle, it becomes Th-234. That emits a beta particle (24 day half life) to become Pa-234 (Protactinium), and the chain continues. After a few more decays, Radium (Ra-226) is produced, which has a half life of 1,600 years. After an alpha emission, the next daughter element is Radon, specifically Rn-222, with a half life of 3.8 days. This is a gas, and is a concern everywhere there are soils derived from granitic rock (most of the U.S.). Radon is the primary cause of lung cancer in nonsmokers. Although it produces gamma radiation, with an energy of 500 KeV, it is the 5 MeV alpha particle, with nothing to stop it, that damages the lung. In sum, the ionizing range of radiations goes from about 10 eV to about 10 MeV, and there are cosmic rays with much higher energies. This is about a million-to-one range, a much smaller part of the entire spectrum than the non-ionizing range.

All this, a combination of salient facts from the book plus things I knew or dug out of the literature, set the stage. When you put everything together, people worldwide experience a background radiation level of 2.5-8 mSv. That is a combination of exposure to K, U and Th in soils and rock, to Rn in the air, to Ra in some rocks, and a contribution from solar radiation more-or-less blocked by the atmosphere and depending mainly on the elevation above sea level. That unit, milliSieverts, is a complex measure of the potential damage from ionizing radiation. The radiation of your cell phone is ZERO mSv, because it is not ionizing. A dental X-ray is in the range of 0.005 mSv, or about 0.1 mSv for a set of 18 over your full mouth. If you live in Florida, with little granite, and your background exposure is 3 mSv, you'd have to get 30 sets of dental full-mouth X-rays in one year to double your dose. Of course, that is skewed because most of it would be to your head, particularly if the dental technician puts a lead shield on you like mine does.

CT scans are another situation entirely. A chest-abdomen spiral scan totals 50-60 mSv, equal to 5-10 years of background radiation for most of us. This is the greatest radiation exposure most of us will ever have. When your doctor orders a CT scan, make sure it is for a good reason!

The authors of Radiation dwell much on what was learned from the casualties and survivors of the Hiroshima and Nagasaki nuclear explosions. This sets another baseline, the high end of survivable exposure. The LD50 (lethal dose for 50% of victims) for whole-body radiation dosage is 5 Sv or 5,000 mSv. That's only about 100 CT scans! However, that is a single-event dose; little is yet known about doses spread over years or decades. It seems the body can repair radiation damage up to a point.

The authors stress several times, when a doctor prescribes any kind of radiation beyond a simple X-ray, you need to ask what the exposure is, as compared to background (stated in mSv or in milli-Grays, which is equivalent). If the doctor can't state that, or won't, you need a different doctor! The doctor also should be able to explain the expected benefit and how it outweighs the risk of the radiation dose, whether from a CT scan, radiation applied to a cancer, or an ingested or injected radioisotope for some therapeutic or test purpose. This is a general rule, but is particularly important regarding such therapies and tests: if your doctor can't or won't explain, get a new doctor!

Finally, I have to tout nuclear power generation. The authors make it clear that we are much more likely to get radiation-induced cancer from coal burning power plants than from nuclear power plants. There are radioactive elements in coal, and they go right into the air when coal is burned. Also, the slag remaining from burnt coal contains heavy metals and other toxins, and these don't have a half-life like U or Ra, so they are toxic forever and ever. A nuclear power plant produces a few tons of high-level radioactive waste per year. A coal fired power plant produces hundreds or thousands of tons of toxic waste per year. The waste dump for a single coal plant could be used to store all the output from all U.S. nuclear plants for decades or centuries, and not run out of room. Just put the canisters on pallets on the ground, fence it off, and guard the stuff.

Really, we ought to be recycling spent uranium. 95% of its energy is still in there, just "poisoned" by the fission products. The problem isn't scientific; the science and technology are well known and safe. The problem is political. Even better, we ought to be using breeder reactors, to turn U-238, which won't "fizz", into Pu-239, which will. There's 140 times as much U-238 as there is U-235, the usual fuel. I suggest having the U.S. Navy oversee the design, construction and operation of nuclear power plants. They've been running aircraft carriers and submarines with nuclear power for more than half a century, and they seem to be able to do it without meltdowns or other accidents.

OK, I really like this book, and got quite inspired as you can see above. Without minimizing or distorting the risks, the authors make it clear that current fears about radiation are unfounded. Knowledge is the enemy of unwarranted fear. This book belongs on everybody's reading list.

It may be radio, but is it active?

kw: book reviews, nonfiction, science, physics, radioactivity, history

Click on this image to see the details more clearly. In ultra-brief form it embodies knowledge that led to a couple dozen Nobel prizes from 1901 to the 1930s.

In each small chart, the horizontal axis is the Proton number (the Atomic Number), Z, and the vertical axis is the Neutron number, N. Atomic Mass, A, is Z+N. Therefore, in the lower left Uranium Series, The starting point is U²³⁸: Z=92, N=146 and A=238.

A careful look reveals that three of the four series begin with or pass through a Uranium isotope, and all four begin with or pass through a Thorium isotope. All pass through at least Radium, Radon, Polonium, and Lead isotopes, as well as a few others. Three end at the stable isotopes of Lead, 206, 207 and 208, while the fourth ends at Thallium 205. In an alpha-beta decay scheme, one of those four isotopes must be the end result.

These are the end result. Where did we learn all this? That is the subject of Radioactivity: A History of a Mysterious Science by Marjorie C. Malley. Beginning with the discovery of "Uranium rays" that affected photo emulsions in 1896, scientists labored to learn, step by step, of the different "rays" and "emanations" of uranium, thorium and their decay products, which were initially given names like "Uranium X" and "Mesothorium".

A marvelous feature of the book is to immerse us in the time, using the terms current as the discoveries were being made. As the various radioactive "rays" were discovered, there were periods of years during which, for example, the alpha "ray" was misunderstood because, while its bending by a magnet could not at first be discerned, it was stopped by paper, unlike the x-rays to which it was being compared. Eventually the trichotomy was discerned: alpha equals fast-moving He⁺⁺, beta equals electron, and gamma equals extra-powerful x-ray. Then the fun began! If heavy atoms "radiated" by emitting helium, the helium particle (this was before the neutron was known) must be a building block of atomic nuclei. Only much later were protons and neutrons found.

Before isotopes were discerned (I hesitate to say, discovered), confusion reigned. We now know that "Radium" referred to Ra²²⁶, while Actinium X, Mesothorium I and Thorium X referred to other isotopes of Radium. They could not be chemically separated, and it was only by measuring the atomic mass of radioactively-produced substances that they could be told apart until the invention of the mass spectrograph in 1919.

Radioactivity discoveries helped elucidate quantum theory. For example, the energy of emitted alpha particles was related to total intensity, or inversely related to half life. For uranium, for example, we find that isotopes with half lives of a minute or a few minutes have alpha energies near 7MeV, half lives of a few days go with energies near 6MeV, half-lives of years to thousands of years go with energies near 5MeV, and half-lives in the millions- to billions of years imply alpha energies of 4.5 MeV or less. The phenomenon of quantum tunneling and exponential statistics, coupled with Heisenberg's Uncertainty Principle, eventually explained such patterns.

Throughout the book, we learn of the persons who worked all this out, of their labors, theories, missteps and discoveries. Of course, the Curies are the most famous, and Roentgen and Becquerel and Rutherford not far behind. The roll call of famous pre-1920 physicists and chemists numbers in the dozens, and many received Nobel Prizes. Marie and Irène Curie stand out as the only mother and daughter to both receive a Nobel Prize, while the two William Braggs, father and son, received a joint Prize in 1915.

The dangers of handling radioactive materials were slow to be realized. Several persons induced radium burns in their skin, but longer-term effects went unknown for decades. As late as 1960 children touring uranium-producing facilities were given vials or capsules containing yellowcake, or pure U₃O₈. Both my mother and I received such souvenirs. In my case, I carried the capsule in my pocket for a few weeks before putting it in a dresser drawer. Later I gave it to a geology professor for use as a standard material in his radiation lab (by 1971 it was almost impossible to obtain uranium compounds). I don't know if carrying a strong gamma-emitter like that had anything to do with the cancer I had forty years later; it occurred at a location in my colon next to the pocket in which I carried the capsule at age 12.

By the time the Manhattan Project and similar European efforts were undertaken, the decay chains illustrated above were well known, and Radioactivity as a discipline had been subsumed into Nuclear Physics and Particle Physics. The focus of study turned to those few isotopes that could be stimulated to fission, the basis of nuclear power plants and atomic bombs. In the public mind these overshadow other advances such as nuclear medicine and radionuclide imaging and therapy, and even the tiny speck of an alpha-emitter in a smoke detector (It is a tiny enough amount that even if you dug it out and ate it, you'd suffer little harm).

We live in the post-Atomic age. Nuclear power plants are on the wane, particularly after a few melt-downs in recent years and the disaster last year in Japan. Yet much of modern life would be unthinkable without the discoveries of more than a century ago, when the understanding of how atoms worked was turned upside down, starting with a few pieces of photographic film fogged by proximity to uranium ore.

Uranium 101

kw: observations, radioactivity

In the wake of the likelihood that a lot of radiation might be released from the damaged nuclear reactors in Japan, I'd like to address some common fears.

First, the danger is real, but it will probably be limited. If a total meltdown occurs, let us remember that Uranium metal is twice as dense as Lead, and nearly all of it will melt its way downward, until it is dissipated to the point that it can't sustain a chain reaction. Then it will cool off. However, some fraction of a percent of the total core will react with air and steam in the early stages, and this amounts to several grams of Uranium. Plus, because the reactor has been running for some time, the breakdown products of Uranium fission could amount to a few percent of the total, and these are more volatile. The most risky is an isotope of Iodine, which is why the Japanese government has been giving people Iodine pills. Having extra Iodine in the body will reduce the amount of radio-Iodine that the body can absorb, reducing long-term risk.

Uranium itself is only weakly radioactive. The half life of U238 is 4.6 billion years. Compare this with the most common isotope of Radium, with a half life of 1,200 years. It is four million times as radioactive as Uranium. Enriched Uranium has a little stronger activity, but still in the billion-year range, because U235 has a half life of 0.7 billion years.

What few people know is that Uranium is found in small amounts almost everywhere. Common granite (got a granite countertop?) contains 3 parts per million Uranium. That is three grams per tonne. It is present at about one part per million in ordinary Gypsum board, AKA drywall, or a gram per tonne. An ordinary room contains a tenth of a tonne of drywall in its walls. However, the paper and paint on the wall completely stop the main radiation the Uranium emits.

The Uranium in your environment is the largest component of the background radiation of 3 millisieverts (3 mSv) per year that we all absorb. How does this compare with other exposures? A full-mouth set of dental x-rays gives you a quick dose of 0.15 mSv, or some 5% of the yearly background. A CT scan, by contrast, produces a dose of about 10 mSv, or three years of background all at once. This is considered a safe dose if not repeated more often than once every two years. During the five years after my cancer operation, I had a CT scan yearly. The early detection was considered an acceptable risk.

What kind of dose would a meltdown produce? For those nearest the event, it could be truly grave: hundreds of mSv per day. This is why evacuation is going on. For the next continent downwind (America), the worst case is expected to be an extra mSv or two per month for a year or more, which is like getting a yearly CT scan, or two. However, the more likely scenario from a partial meltdown that gets contained, similar to the Three Mile Island experience, is an extra mSv or two total during the first year, then nothing more. Even people who are most susceptible to radiation would not be considered at any great risk from that. It would be like moving to Denver, where there is an extra half to one yearly mSv from cosmic rays because of altitude.

An even better scenario, assuming there is some kind of meltdown and release, is for very rainy weather to wash most of the stuff from the skies before it spreads around the globe. I'm glad March and April are rainy months in the Northern hemisphere!

Warming from the inside

kw: earth, history, geology, radioactivity

It didn't require much sideways thinking, after yesterday's post about uranium and radioactive decay, to recall the history of these elements in the Earth. The age of the planet is 4.5 billion years (Gy), and even these long-lived isotopes must have changed over time. One question that comes up sometimes in Freshman Earth Science courses is, "How much does radioactivity affect the Earth's temperature?" A more thoughtful student may also ask whether it was much greater in the past.

The short answer to the first question is, "Not much." In spite of a century of intensive Geological exploration, the total heat flow from Earth's interior is known only within a factor of about 2, as between 30 and 60 Terawatts (3-6x10¹³W). A commonly accepted figure it 40 TW. About 75% of this is thought to be radiogenic heat.

This diagram, representing a view toward the upper end (60TW), has radiogenic heating near 52TW, and gives the breakdown by the four isotopes that contribute significantly. The source of the image is this Jrank article. In spite of this diagram, the article's author, David Rothery, considers the total heat flux from Earth's interior to be closer to 40 TW.

Let us first compare that to solar influx. The Solar Constant (which is variable in a narrow range) is about 1,350 W/m², or 1.35x10⁹ W/km². The Earth's nominal radius is 6,370 km, so it intercepts 1.275 km² of sunlight, a total of 1.72x10¹⁷ W. One-third of this is reflected outright by clouds and ice, leaving about 1.1x10¹⁷ to reach the ground and heat the surface. Divide this by 40 TW, and we see it is 2,800 times the internal heat flow.

Now, whether radiogenic heating is 52 TW, as shown in this diagram, or closer to 30 TW (0.75x40 TW), it doesn't contribute much heat compared to the Sun. How about in the past? The diagram shows that when Earth first came together, radioactive heating from these four isotopes was 8x what it is today. There were other short-lived isotopes that no doubt added significantly to this, but they didn't last long and we have no evidence how abundant they were 4.5 billion years ago (Ga).

Now, the Sun was 40% fainter then, but we don't know how much of its radiation reached the surface. At least during the Hadean period, between 4 and 4.5 Ga, when the entire planet was molten, there were not likely any water clouds in the atmosphere, but we don't know what the atmosphere was like. Still, the radiogenic heat probably never supplied more than about 1/400th of Solar heat. It has never been much of a factor in the planet's temperature.

However, today it supplies about 3/4 of the energy that drives plate tectonics. The other quarter is remnant primordial heat and the heat of crystallization as the outer liquid core slowly freezes onto the solid inner core. Two billion years ago, radiogenic heat was more than twice what it is today, and I expect that plate tectonics ran at a brisker clip. There was also more volcanism than today.

Can we predict the future? I don't have a good handle on how much internal heating is required to keep plate tectonics going. Without it, the biosphere and atmosphere would change a lot, and the continents would erode down to just below sea level, leaving an ocean planet. If the critical value is half of today's amount (this is a wild guess), we can predict that such a level will be reached in about two more billion years. That's the time we have left to figure out how to live on an ocean planet, or how to leave the planet altogether. Given humanity's tendency to procrastinate, it probably isn't enough time!