Notes on nuclear "waste" and radiation exposure (Howard Cork Hayden)

Notes on nuclear “waste” and radiation exposure Howard C. Hayden Emeritus Physics Professor, University of Connecticut September 11, 2017 Introduction The most common question people bring up with respect to nuclear power is, “What do you do with the waste?” The answer requires discussion of three broad topics: the nature of uranium fission, radiation shielding, and the relationship between radiation and health.

The first section in this discussion will therefore be about the nature and the quantity of the high-level radioactive byproducts of uranium fission. The so-called “waste” from a nuclear reactor is different from the waste from burning coal. In the latter case, the waste (fly ash, bottom ash, and carbon dioxide, and so forth) are all separated from the coal from which they originated. Nuclear “waste”, the radioactive by-products of uranium fission remain within the fuel rods (with the exception of some trivial amounts of xenon, which is a gas). Most of what is deemed by the public as “waste” is actually fuel, and much of the radioactive by-product is actually useful in various industries. The two types of waste also vary dramatically in quantity. The quantity of coal-combustion by-products produced in the US is well over 100 million tons per year. The radioactive by-products of uranium fission are a million times smaller, at about 100 tons per year. It is intensely radioactive.

The second section will discuss the nature of shielding and its evident effectiveness.

By large measure, the most radioactivity at nuclear power stations occurs within the reactors, even though the “waste” from twenty to forty years of operation remains on site. The full-time employees of the power station receive trivial amounts of exposure because the shielding protects them from the radiation. How does that shielding work?

The EPA, the NRC, and other agencies assume that exposure is an additive quantity.

That is, if your exposure from one event is A, from another event is B, from another, C, and so on, the agencies regard your “cumulative exposure” as A +B +C … Similarly, if a million people each receive some exposure A, the agencies say that the “population exposure is 1,000,000*A. The third section will present a simple mathematical proof that there is nothing inherently additive about radiation exposure.

Radioactive “waste” from power reactors The first matter is to identify what the waste is and where it comes from. A reactor starts with a fresh fuel load containing uranium, 97% of which is U-238 and 3% of which is U-235. (Sometimes the fuel mixture is different, but that issue is of no concern here.)

If a U-235 atom absorbs a neutron that happens by, it becomes a U-236, an atom which Page 1

lasts only an instant before flying apart (fissioning) into two different atoms of lower mass, called X and Y in Eq. (1). The reaction produces a large amount of energy, two or three free neutrons, and the two daughter atoms, X and Y. The energy is the desired product; the neutrons can be absorbed by other atoms, thereby feeding the chain reaction, and the atoms X and Y are usually radioactive. They X and Y—the fission fragments—are the high-level nuclear waste.

The U-238 does not participate in fission directly. However, it can absorb neutrons to become U-239 which shortly decays by beta emission into plutonium-239. The Pu239 actually fissions better than U-235, and is used up as rapidly as it is created once an equilibrium is achieved as shown in the second line of Eq. (1).

U 235  n  U 236  X  Y  (2  3)n Pu 239  n  Pu 240  X ' Y ' (2  3) n

(1)

The atoms X' and Y' resulting from Pu-239 fission are largely the same as X and Y of U235 fission and will be treated here as if they were identical. The atoms X and Y in Eq. 1 are from the middle of the periodic table, so to speak. For example, X might be strontium, and Y might be cesium. In fact, about 20 different atomic species are possible, and within species, many isotopes are possible, for a total in excess of 200.

Most of them are radioactive. In fact, those atoms are the high-level radioactive waste (HLW). Another by-product is transuranics, atoms beyond uranium in the periodic table, such as Pu-239, Pu-240, and others. These products generally have very long half-lives, and are a small fraction of the mass of the fission fragments. Following the radioactivity levels of so many fission fragments, with all their separate half-lives, and their decay chains involving other radioactive atoms is yeoman’s work. The best general reference probably is Bernard Cohen’s 1997 article in Scientific American [1]. Details about half-lives, decay processes, and production of fission fragments can be found in the Chart of the Nuclides [2].

We will direct our attention to the amount of radwaste produced when a power station produced 1 GW of electricity around the clock for one full year. The electrical energy generated in one year is 1000 MW  31.6 million seconds/yr = 3.16  1016 joules, but because the efficiency of converting heat to electricity is only about 35%, the actual energy released is about three times as great, namely about 9  1016 joules. Using E = mc2 to determine the amount of mass m that is converted to 9  1016 joules, we find that all of that energy results from the conversion of a mere kilogram of mass to energy.

The energy released during the fission of a single uranium atom (or plutonium) is about 200 MeV (million electron-volts). The energy equivalent of an atomic mass unit (1 u  c2, converted to the energy unit MeV) is 931.5 MeV, from which we know that the energy equivalent of a U-236 is 220,000 MeV. Therefore, the mass of the uranium is 1,100 times the mass that is converted to energy. (We will leave precision to the experts who deal with the fuel; for our purposes, we will regard that factor as 1,000).

Alternatively, the lost mass may be regarded as about 1/1000th of the mass of the uranium. The conclusion is that a 1-GW power plant operating around the clock for a year converts one kilogram into energy, and does so by converting 1,000 kg (one metric ton, of one tonne) of uranium into radioactive fission fragments, whose mass is, therefore, 1,000 kg.

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By the time the 3% U-235 is used up (spent), an approximately equal amount of U238 has also been used up through the plutonium cycle. In all, then, the spent fuel rods contain 94% U-238 and 6% radioactive by-products, X and Y. So how much HLW is there? There is about one tonne of actual HLW, but it is embedded in about 16 tonnes of uranium (also known as fuel). The fuel “rods” are actually tubes of zirconium, which have their own weight, and the (eventual) stainless containers add more weight. Of course, the mixture can be recycled by removing the waste from the fuel, but that is known by the dreaded word reprocessing.

Half-lives Another aspect of nuclear power that the public seems to find frightening is that some radioactive isotopes have long half-lives. If anybody takes that notion seriously, they should be deathly afraid of their own oxygen that has a half-life of infinity (a.k.a, forever). It should be stressed that the activity of a sample is inversely proportional to the half-life. The shorter the half-life, the faster the sample’s activity decreases. In a reactor, there are some isotopes that have such short half-lives that if they were magically hand-delivered from inside the reactor to somebody working in the office, the activity would be zero by the time they arrived.

Conversely, the longer the half-life, the less radioactive the species is. For example, plutonium-239 (half-life = 24,000 year) is only 0ne-fifteenth as radioactive as radium226 (half-life = 1600 years), given an equal number of atoms in the sample. We are using the traditional definition of activity here: the number of nuclear transitions per second.

Types of radiation We retain the traditional descriptors of radiation types—alpha, beta, gamma—used by early scientists who had yet to figure out what they were. The least penetrating were alpha rays, which turned out to be nuclei of helium atoms. When a radioactive sample was placed in a tube of mercury (inverted, like in a barometer), helium accumulated at the top. Radium-226, U-238, Th-232, and many other isotopes find it energetically easier to eject two protons and two neutrons as a bunch rather than any individual proton or neutron. (Think of coarse sandpaper taking large chunks of wood without expending energy to take them apart.) Typical energies for alphas is about 4 MeV. Next were beta particles that turned out to be ordinary electrons. In this case, a neutron in a nucleus breaks apart into a proton that remains in the nucleus and an electron that is ejected. The energies of betas are in the range of tens of keV to several MeV. A related type of decay is positive-beta, that is, the emission of a positron, which is an antiparticle to an electron. It comes from neutron-poor nuclei such as lanthanum130, which has 57 protons and 73 neutrons, as opposed to stable La-139 which has 82 neutrons. The process is that by some energetic process a proton ejects its charge, Page 3

becoming neutral. (La-130 decays to stable barium-130 with 56 protons, 74 neutrons.)

The ejected positron quickly collides with an electron causing mutual annihilation, with the release of about 1.1 MeV. The only people ever exposed to positrons are those undergoing a cancer diagnosis technique known as Positron Emission Tomography (PET scans, for short).

Gamma rays are pulses (photons) of electromagnetic radiation, in the family of radio waves, infrared, visible light, and ultraviolet (in the low-eV range), but of much higher energy (up to a few MeV). They are excess energy shed during alpha, beta, and fission reactions.

Shielding There is a very famous alpha-scattering experiment that was done by Ernest Rutherford and his students. They knew that alphas don’t penetrate matter very far, so they took the most malleable metal on the planet—gold—and made it thinner and thinner until alphas were able to penetrate it. We won’t go into the measurements, but the message here is that alphas can be stopped by just about anything. Typically, they can be stopped by a piece of paper. In air, they can travel a few centimeters.

Beta particles are electrically charged, and the same mass as the electrons they encounter in material. Therefore, they can be stopped by a few millimeters of metal.

Gammas are the most penetrating of the radioactively emitted “particles.” Whereas alphas and betas deposit all of their energy within a short distance, gammas have great penetrating power. Indeed, a gamma whose energy is in excess of about 100 keV will pass through a human body and deposit only part of its energy therein. A 1-MeV gamma and a 100-keV gamma (or x-ray) result in the same exposure to a human. The two gammas have the same linear energy transfer (LET), energy deposited per unit of path length through the body.

Radiation protection, therefore consists mainly of assuring that alpha- and betaemitters are neither ingested nor inhaled, and shielding to stop gammas. Gammas, being electromagnetic radiation, interact primarily with the electrons in matter, because they usually don’t have enough energy to affect nuclei. As they traverse matter, gammas collide with (if that can be considered appropriate vocabulary) electrons along the path, imparting small amounts of energy to each (and occasionally a lot to one). People generally know that lead is a good absorber of x-rays, but the reason does not pertain to any magical property of lead. It simply has a high density of electrons. Water, concrete, bricks, aluminum, steel, and other materials also attenuate gammas; it simply takes more thickness along the path from the source to (say) the human who needs the shielding.

Most of the radiation at a power plant occurs in the reactor. The shielding consists of the water in the reactor vessel, the steel walls of the vessel, and the thick concrete and rebar walls of the containment building. Moreover, distance plays a role, since the intensity drops off with the distance R from the source as 1/R2, regardless of shielding.

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Fresh radwaste, ensconced in fuel rods, is stored in stainless steel containers immersed in water to carry away heat. As the radiation diminishes with age, the stainless steel containers can be stored in open air which is then adequate to carry away heat. Largely because of inaction by the federal government, the vast majority of spent fuel rods are stored at the power stations that generated them. The containers are adequate to reduce the gamma radiation to barely measurable levels.

The LNT The Linear-No-Threshold (LNT) model is commonly used by the Environmental Protection Administration (EPA) and the Nuclear Regulatory Commission (NRC) to predict possible outcomes of radiation exposures. Specifically, it says that the likelihood of a cancer resulting from exposure is directly proportional to the amount of exposure (the dose). To be specific, the model says that the straight line in the dose-response graph extends all the way down to the zero-dose, zero-response point (0,0).

0

Figure 1: Schematics of the linear-response models. Left: The linear nothreshold (LNT) model in which response is directly proportional to the dose.

Right: The linear-threshold (LT) model in which response varies linearly with dose, after a threshold is reached.

The contentious part of the LNT is about the response at very low doses: are very low doses actually hazardous? We need to discuss the data on both axes.

What is the importance of the possible offset from the (0,0) point (see Figure 1)? It is simply this: the population of the US is about 300 million. If you assume that some minuscule radiation exposure to the population will cause a cancer in one person in 100,000 people, then there will be 3,000 cancers in the US. Never mind that there are already over 590,000 annual deaths due to cancer in the US. The 3,000 presumed deaths add to it, and our regulators get upset about that, and impose stringent, expensive rules on the nuclear industry (and the health industry as well) to be careful.

If the dose-response curve shows a threshold—that is, a dose below which there is no harmful response—then the stringent rules become unnecessary. Nuclear power becomes, perforce, cheaper.

In some cases, the stringent rules are not only expensive, but actually harmful. For example, in Fukushima, there were over 1,000 evacuation-related deaths to escape radiation doses that were far below levels naturally occurring elsewhere. Japan decided to shut off all nuclear reactors and get the electricity from more-polluting, imported Page 5

high-cost fuels. The effect on Japan’s economy is on-going, with its untoward effects of poverty on health.

Another dose-response curve is the hormesis model, in which the response on the graph is negative in the low-dose region. That is, a small dose is beneficial instead of harmful. And what if a small dose of radiation actually reduces cancer incidence instead of causing more cancer?

A recent letter to Physics Today [3] made a case for the threshold model: Muller’s and Stern’s approaches survive in the LNT model of today, which says that low-dose radiation increases cancer risk. However, while linearity—the “L” in LNT—was demonstrated only at high doses, the absence of a threshold has never been demonstrated. The only scientific conclusion from the data from 1949 through today is that the linear threshold (LT) model, not the LNT, is correct, and it has a low-dose threshold below which radiation is harmless. Even data from atomic-bomb survivors, the gold standard of dose-response data, do not support the LNT model; adaptive protections mitigate radiation-induced damage at low doses and low dose rates. No epidemiological studies have ever demonstrated a causal relationship between low-dose radiation exposure and carcinogenesis.

Some letters in the subsequent edition [4] of Physics Today insisted that the LNT is correct, and others insisted that it is not correct.

Dose In the medical industry, it is customary to prescribe medicines in amounts proportional to body weight. Similarly, unwanted chemicals in the body are generally considered on a per-weight basis, on the notion that the concentration of the substance is what determines the health outcome. The original measure of radiation itself was the Roentgen, defined as the amount of radiation that would produce one electrostatic unit of charge produced by x-rays in a cubic centimeter of dry air under standard temperature and pressure, later replaced by charge per unit mass.

By extension, the radiation protection community has long measured doses in radiative energy absorbed per unit mass. The older unit—ergs per gram—was the rad.

The newer (SI) international unit—the joule per kilogram—is the gray (Gy), where 1 Gy = 100 rads.

Not all types of radiation are equally damaging to cells. Scientists multiply doses by a quality factor corresponding to each type of radiation to produce a dose equivalent that has the same damaging effect as x-rays of a certain energy (100 keV). The dose equivalent units are the rem and the sievert (Sv) respectively. Again, the two units differ by a factor of 100: 1 Sv = 100 rems; 1 mSv = 100 mrem, etc.

Implicit in those definitions is the recognition that there is something inherently different between (say) 1 joule absorbed by 10 kilograms and 1 joule absorbed by 1000 kilograms. The difference is, of course, that the body can “handle” low doses better than

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high doses. In other words, the body can repair damage if it is not too concentrated.

New cells can be created by replicating healthy cells nearby.

Another important aspect of radiation doses is the time interval over which the radiation is absorbed. A dose that is lethal to 50% of the people who receive it suddenly (the LD50) has only about a 5% chance of causing cancer if the dose is spread out over a long time. A summer’s worth of beach sunlight received from sunlamps in a few hours is lethal, Response In a laboratory situation, it is easy to infer doses accurately, so the position on the horizontal axis of the dose-response graph can be accurately determined. Cell damage (response) can easily be determined under a microscope.

For non-laboratory situations, one must infer both the dose and the response, and both variables carry some uncertainty. Only for very strong doses can you determine the hazard, and even that is not so easy. For example, in the bombings of Hiroshima and Nagasaki, there were something like 100,000 survivors who received near-fatal doses, yet it took sophisticated statistical techniques to find that a few hundred cancers resulted from the radiation, against a background of about 20,000 cancers that would have happened anyway.

The LNT model implies that doses are an additive quantity. That is, if a person receives 3 mSv/year of environmental radiation for 20 years, and 10 mSv/year (some from the environment, some from x-rays) for 2 years, the “cumulative exposure” is 80 mSv. The LNT model further implies that the exposures of many people add up to a “population exposure.” If, say, all 100,000 people in a certain city receive 3 mSv per year for 50 years, the population exposure is 100,000 people multiplied by 150 mSv, or 15,000,000 mSv, or 15,000 Sv. Then, assuming that 50 Sv (this estimate changes a bit over time) is enough to cause a cancer, some 300 cancer cases will ensue.

An important theorem: Exposure is not inherently additive.

Exposure, in the lingo of thermodynamics, is an intensive variable—like temperature, pressure, density, or specific heat—that does not increase as the quantity of matter increases. We do not add the temperature on one side of the room to the temperature on the other side to get a “total” or “cumulative” temperature, whereas the internal energy, number of molecules, and the volumes—all of which are extensive variables—of the two sides of the room are additive.

To understand why exposure is an intensive variable, imagine a one-kilogram mass of leg muscle exposed to one mJ of x-radiation. The exposure—absorbed energy per unit mass, one mJ/kg—is 1 mGy. Now, mentally separate the one-kg mass into two halfkg masses, each receiving 1 mGy (½ mJ divided by ½ kg for both “halves”). Can we add

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the two 1-mGy exposures to get 2 mGy? Of course not. Q.E.D. Exposure is an intensive variable and is not inherently additive.

Notwithstanding that radiation dose is an intensive variable, the people involved in radiation safety still add doses to get cumulative doses for individuals and population doses for large groups of people. These statistical sums are basically proxies for probabilities that cancers or other untoward effects will result. The underlying assumption (acknowledged or not) is that the probabilities are additive. Well, in statistics, some probabilities are additive and some are not. For example, if your body heals after some accident that has 50-50 odds of killing you, and you have another accident of the same kind, the chance of death from the second accident is 50%, not 100%, as you would get if the probabilities were additive.

Now we return to the dose-response curves. It is perfectly possible for a straight line derived from data at high doses to seem to extrapolate right down to (0,0), as shown in Figure 2, where the dots might represent radiation doses to various individuals and the corresponding response (gastrointestinal illness, skin reddening, or other effect, somehow quantified). Even with proper accounting of propagation of error—how uncertainties in the data affect both the slope of the line and its intercept—the extrapolation to the (0,0) point is subject to uncertainty. Direct measurement—not presumption—near the (0,0) point is necessary.

RES PON SE

DOSE

Figure 2: Extrapolating from high doses back toward zero dose is not a good way to determine whether there is a threshold. For example, the LD50 for radiation is about 4.5 Gy, whereas annual exposure from background radiation is around 0.003 Gy, and incremental radiation from a high-altitude crosscountry flight is in the range of 0.000 03 Gy. At this point, I must defer to experts with direct experience in dose-response curves.

For example, at a meeting of the Doctors for Disaster Preparedness in Omaha (www.ddponline.org), Dr. Mohan Doss of the Fox Chace Cancer Center gave an excellent presentation of the failures of the LNT, from which much of the following discussion is derived. He presented evidence to show that the incidence of cancer decreases with dose, up to a limit of about 10 mGy/year (1000 mradyear). Similarly, whereas the government recommends radon remediation when the indoor level is 4 pCi/liter1, lung cancers decrease with increasing radon concentration up to well beyond 4 pCi/liter.

Doss corrected the atomic bomb survivor data (subtracting observed cancer rate from 1

pCi = picocurie. 1 Ci = 3.7 * 1010 disintegrations per second, the approximate activity of a gram of radium; 4pCi/liter = 0.148 disintegrations per second per liter of air.

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background cancer rate, as should have been done decades ago), and showed a decided hormesis effect, the J-shaped curve in Figure 3. He also presented similar data for many other known dose-response cases, for example bone sarcomas in radium-dial painters.

Figure 3: Excess relative risk versus colon dose for atomic bomb survivors.

Cancer is, alas, largely a failure of the immune system. Cells of the body are continuously being damaged and repaired, so suppressing the immune system increases the likelihood of cancer. Low doses of radiation evidently stimulate the immune system, with the result that there is a real hormesis effect. Any dose below about 100 mGy (10,000 mrads) can be considered safe.

[1] Bernard Cohen, “The disposal of radioactive waste from fission reactors,” Scientific American [June 1997] [2] Chart of the Nuclides, https://www.nuclidechart.com/xcart/ [3] Jeffry A. Siegel, Charles W. Pennington, and Bill Sacks, “Low-dose radiation exposure should not be feared,” Physics Today 69(1), 12 (2016); online at http://dx.doi.org/10.1063/PT.3.3037 [4] J. S. Levinger, “The linear no-threshold theory: Readers weigh in,” Physics Today 69(7), 10 (2016); online at http://dx.doi.org/10.1063/PT.3.3037Radiation Exposure Howard Hayden is Prof. Emeritus of Physics, UConn He lives in Pueblo West, CO, and has published The Energy Advocate since 1996 Contact: corkhayden@comcast.net

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