6.4 A brief tutorial on radioactivity and radiation exposure units
Before discussing the amount of radioactivity released in nuclear explosions, a brief discussion of the units commonly used to quantify rates of radioactivity and its biological effects is in order. Readers familiar with units such as Curies, rads, rems, Biological Equivalent Dose, quality factors and Sieverts can skip this section.
Radioactivity is caused by nuclei undergoing decay processes such as alpha or beta decay or spontaneous fission. The rate of decay of a radioactive source depends on its mass and half-life. From equation (2.13), if you have a freshly-isolated sample of mass m grams of a radioactive material of mass number A and half-life t1/2 seconds, its decay rate, in decays per second, is given by
The superscript ‘sec’ has been added to t1/2 as a reminder of the units; there will be various conversions involved in what follows.
Two main units of decay rate are in common use. Historically, rates were quoted in ‘Curies’ (Ci), where 1 Ci = 3.7 × 1010 decays per second; this was mentioned briefly in chapter 5. This is the radioactivity of 1 g of freshly-isolated radium-226, which has t1/2 = 1599 years = 5.04 × 1010 s; check the calculation for yourself. More common in current literature is the Becquerel (Bq), named after Henri Becquerel, the discoverer of radioactivity. One Becquerel is one decay per second. This is a very low rate of decay; it is more convenient to speak in terms of millions of Becquerels (MBq); 1 MBq = 106 decays per second. Hence, 1 Ci = 37 000 MBq.
For assessing biological damage, what is important is the amount of energy deposited into a victim by the decays involved. In the following development, it is supposed for simplicity that you have ingested a radioactive source and are thereby exposed to its entire activity; in this way we can avoid dealing with geometrical factors that would be involved with an external source.
Radiologists define the ‘absorbed dose’ (AD) to be the number of Joules of energy deposited per kilogram of body mass. The energy deposited will be the product of the decay rate in Becquerels, the exposure time in seconds, and the energy per decay in Joules. Decay energies, however, are usually quoted in MeVs, so if EMeV is the decay energy in MeVs, then that in Joules will be (1.602 × 10−13) EMeV. Also, exposure times are more likely to be on the order of hours rather than seconds, so, in obvious notation, let us put tsec = (3600)thr. If the decay rate in MBq is RMBq, we can likewise write RBq = 106 RMBq. Putting these various factors together and designating the body mass as Mkg, the absorbed dose can be written as
The units of AD are formally Joules per kilogram, but in this context this unit is known as a ‘Gray’ (Gy). An older unit, the ‘rad’, was defined as an energy deposit of 100 ergs g−1; you should be able to verify that 1 Gray = 100 rads.
Different types of radiation can do more or less damage than others, even if they are of the same energy. Alpha particles, for example, are relatively heavy and can cause considerable ionization before they are slowed down, whereas beta particles (electrons) are less damaging. To account for this, radiologists have developed a scale of ‘quality factors’ or ‘damage factors’, dimensionless numbers which quantify relative damage levels. Table 6.1 lists some of these factors, which, unfortunately, are also commonly given the symbol Q even though they are not energies.
Table 6.1. Radiation damage factors.
Radiation Damage factor Q
Photons 1
Beta particles (<30 keV) 2
Beta particles (>30 keV) 1
Protons (1–10 MeV) 10–20
Neutrons (<0.02 MeV) 3–5
Neutrons (1–10 MeV);Alpha particles 10–20
Heavy ions ∼20
For assessing damage, the important number is the ‘Biological Equivalent Dose’ or BED, which is defined as the product of the absorbed dose and the damage factor:
Here again the unit is strictly Joules per kilogram, but in this context one Joule per kilogram is defined to be one ‘Sievert’ (Sv), named after Rolf Sievert (1896–1966), a Swedish medical physicist.
A Sievert is a lot of exposure; if you are exposed to an acute dose of 5 Sv you will likely die if you are not treated. In everyday life, you should never have occasion to be exposed to even a small fraction of a Sievert. In view of this, a more convenient unit is the ‘rem’, an abbreviation of ‘radiation equivalent man’. One rem is defined to be 1/100 of a Sievert. (Financial analogy: if a rem is a cent, then a Sievert is a dollar.) Expressed in rems, equation (6.14) is
We are all exposed to background radioactivity all the time through sources such as cosmic rays, radioactive materials in soil, sea water, building materials, and even from long-lived radioactive potassium within our own bodies. For people living in the United States, the average annual exposure is about 0.5 rem, or about 5 milliSieverts (mSv), although this depends on factors such as the altitude at which you live. For people not working in the nuclear industry, the recommended annual exposure beyond this due to sources such as medical procedures is 0.1 rem; for adults who work with radioactive materials, the limit is 5 rems. It is advisable to limit your use of medical procedures such as CT scans, which can deliver a full rem of exposure. During the Chernobyl reactor accident in Ukraine in April, 1986, some workers were exposed to over 600 rems, and most died before the year was out. In contrast, the maximum estimated one-year exposure around the Fukushima site has been estimated at about 2 rems, but this was in a very localized area.
The body can tolerate a fairly substantial amount of exposure without dire effects, as indicated in table 6.2. It has been estimated that the roughly 100 000 survivors of Hiroshima and Nagasaki received average radiation doses of 20 rems. This would be harmless for most healthy people, but does incur a small increased risk of developing a long-term cancer.
Exercise
Suppose that you ingest 1 g of Pu-239, which would be a very ill-advised meal. Pu-239 is an alpha-decayer (Q = 15) with a half-life of 24 100 years and EMeV = 5.1. If you have a mass of 75 kg and the Pu remains in your body for one hour, what is your BED?
Answer
135 rems.
Table 6.2. Effects of acute radiation exposure. After Glasstone [1] and Sartori [3].
Dose (rems) Symptoms, treatments, prognosis
0–100 Few or no visible symptoms. No treatment required; excellent prognosis.
100–200 Vomiting, headache, dizziness; some loss of white blood cells. No hospitalization required; full recovery in a few weeks.
200–600 Severe loss of white blood cells, internal bleeding, ulceration, hemorrhage, hair loss at ∼300 rems, danger of infection. Treat with blood transfusions and antibiotics. Guarded prognosis at low end of dose range, but probability of death ∼90% at high end of dose range. Cause of death: hemorrhage, infection.
600–1000 As 200–600 but more severe. Treatment via bone marrow transplant, but probability of death 90–100%.
1000–5000 Diarrhea, fever. Treat to maintain electrolyte balance; death in 2 days–2 weeks due to circulatory collapse.
>5000 Immediate onset convulsions and tremors. Treat with sedatives. Death in no more than 1–2 days due to respiratory failure and brain tissue swelling.
6.5 Prompt radioactivity from a nuclear weapon
In addition to their gamma-ray and neutron emissions, nuclear weapons generate enormous amounts of radioactivity. The most damaging prompt radiations are neutrons and gamma rays emitted directly by the explosion and as a consequence of neutron-capture by nitrogen molecules in the surrounding air, which creates more gamma-rays as the excited nuclei shed excess energy. From graphs appearing in chapter 8 of Glasstone and Dolan, it can be estimated that gamma-rays emitted in a 100 kt explosion will deliver a dose of about 100 rems to a slant distance of about 2500 yards; for neutrons from the same explosion, the 100 rem distance is about 2000 yards. Neutrons, however, are more difficult to shield against than gamma-rays; they have to be stopped by collisions—which tends to give rise to more gamma-rays. Beyond these sources, considerable exposure is caused by deca
ying fission products. Fortunately, many of these products have very short half-lives and so decay quickly, although some have half lives of many years. Also, since alpha and beta particles are strongly attenuated as they pass through air, radiation exposure from these causes falls off much more rapidly with distance than do thermal and shock effects. In general, if you are near enough to a nuclear explosion to suffer acute radiation exposure, you have probably been blasted or burnt to death before the consequences of that exposure will have time to manifest themselves. Despite this, radiation exposure may well be the most feared consequence of a nuclear explosion, perhaps because it is not immediately apparent.
Weapons analysts divide radiation effects into two categories: initial, or ‘prompt’ exposure, and long-term or ‘residual’ exposure. There is no strict distinction between the two, but one minute after the explosion is often taken as a working definition.
‘Prompt’ amounts of radioactivity released in nuclear explosions are fantastic. In another publication, this author has estimated the immediate energy release from the Trinity test to be on the order of 14 trillion Curies from fission products alone [4]. Glasstone and Dolan (p 390) estimate the radioactivity of fission products per kiloton of energy release to be on the order of 30 billion Curies one minute after the explosion, with the mix of half-lives giving a subsequent overall decay with time proportional to time to the power −1.2. That is, if the activity at one minute after the explosion is I1, then the activity at t minutes after the explosion will be I = I1/t1.2.
As with blast and thermal effects, an individual’s exposure to (and reaction to) radioactivity is dependent on factors such as weather conditions and shielding offered by surrounding structures. While an approximate formula for prompt radiation exposure for unprotected individuals has been developed (below), it is essentially impossible to do so for the longer-term effects as they depend on many contingencies: have winds transported much of the fallout to distant locations? Can uncontaminated food and water be provided? Is medical care available? Can people be evacuated from affected areas? In what follows I will look at the prompt dose issue, and the question of the probability of developing a long-term cancer from a dose that is not acutely lethal.
For an unprotected person a distance d miles from a warhead of yield Y kilotons, the prompt dose received, in rems, can be estimated very roughly with the expression [5]
This expression probably overestimates the exposure in that it derives from an expression valid for hydrogen bombs, for which only about 50% of the energy released is from fission reactions. For a 20 kiloton bomb at 2 miles, Dprompt ∼ 0.6 rems, an almost harmless amount (table 6.2). To receive a 500 rem dose from such a weapon one would have to be at a distance of about 0.83 miles, for which equation (6.4) predicts a shock overpressure of over 8 psi. For a 100 kt yield at d = 2000 yards = 1.14 miles, equation (6.16) predicts ∼ 220 rems, in line with the sum of the gamma and neutron exposures read from the Glasstone and Dolan graphs mentioned above; the overpressure in this case would exceed 10 psi.
Even if you do not receive an immediately harmful dose of radiation, there is a statistical chance that you will eventually die from a radiation-induced cancer. In medical parlance, this would be counted as an excess cancer death. This terminology reflects the statistic that some 20% of the population will die of cancer even if they have never been exposed to any excessive human-caused radiation. (The percentage varies by location and sub-populations, but a blanket average of 20% will serve for making estimates.) Thus, of a group of 100 000 people, we can expect that some 20 000 will die of cancer in the normal course of events. What, then, is an individual’s excess probability of dying by cancer if they have been exposed to some man-made radiation? The effects of ionizing radiation on humans and animals have been extensively studied, and a definitive publication in this regard, The Biological Effects of Ionizing Radiation, has been prepared by the United States National Academy of Sciences. While there is some ‘noise’ in the statistics and one might find slightly different numbers from different sources, the overall result can be summarized with a simple rule: for every 100 rems worth of radiation dosage, your chance of dying by cancer increases to about 24%. If a population of 100 000 acquired 100 rem exposures (a lot of exposure), then some 24 000 would be expected to die of cancer, that is, there would be 4000 excess deaths. This can be expressed as
For a 1 rem dose, this model predicts 40 excess deaths for a population of 100 000. Of course, it would be impossible to tease out which individual deaths of the (nominal) 20 040 were actually caused by the exposure. Also, these calculations exclude any other causes of death such as accidents, murders, and other medical conditions. By this model, the statistic quoted above that some 100 000 survivors of Hiroshima and Nagasaki received average radiation doses of 20 rem implies some 800 excess deaths in comparison to the estimated 100 000 killed by blast, burns, and acute radiation (chapter 5).
While most fission products decay relatively rapidly, longer-lived ones can present hazards far from the site of a nuclear explosion if they are borne by winds and settle out over agricultural and animal-feeding areas and thus eventually enter the food chain. Of particular concern in this regard is cesium-137, which has a 30 year half-life. The chemistry of cesium is similar to that of potassium, which is readily absorbed by the human body.
It was remarked above that federal regulations in the United States recommend an annual dosage limit of 0.1 rems above background sources. By the above excess-deaths model, exposing the entire country of 320 million people to 0.1 rems would be expected to lead to some 12 800 excess deaths on an annual basis. In comparison, about 30 000 people die in traffic accidents annually, plus about the same number from gunshot wounds.
These calculations may seem rather abstract if you are not in the vicinity of a radiation hazard. But they could be of very real interest to civil officials who might have to decide if, say, a reactor accident warrants an evacuation. A mass evacuation will inevitably lead to some deaths by traffic accidents and psychological stress. Will the nominal number of excess deaths prevented by an evacuation be worth the ones that will be immediate and obvious?
References
[1] Glasstone S and Dolan P J 1977 The Effects of Nuclear Weapons (Washington: United States Department of Defense and Energy Research and Development Agency) http://www.deepspace.ucsb.edu/wp-content/uploads/2013/01/Effects-of-Nuclear-Weapons-1977-3rd-edition-complete.pdf
[2] http://blog.nuclearsecrecy.com/wp-content/uploads/2012/10/1944-Bethe-and-Christy-Memorandum-on-the-Immediate-After-Effects-of-the-Gadget.pdf
[3] Sartori L 1983 Effects of Nuclear Weapons Phys. Today 36 (3) 32–41
[4] Reed B C 2016 Chernobyl and Trinity – Counting the Curies Federation of American Scientists Public Interest Report 69 12–5 https://fas.org/wp-content/uploads/2016/12/PIR-2016_v3.1_small.pdf
[5] Broyles A A 1982 Nuclear explosions Am. J. Phys. 50 586–94
IOP Concise Physics
The Manhattan Project
A very brief introduction to the physics of nuclear weapons
B Cameron Reed
* * *
Chapter 7
Legacy
By the time of the bombings of Hiroshima and Nagasaki, the Manhattan Engineer District had consumed about $1.9 billion in funding, and had employed nearly a half-million people in constructing and operating its various factories and laboratories. Decades later, the scale and dramatic success of the MED make it easy to forget that it was in many ways a very close call: the Project might equally well have made no contribution to ending the war. Even a few weeks delay in producing bombs beyond when they were ready might have led to very different post-war circumstances had the Japanese surrendered before an invasion by either or both of America and Russia was underway. If an invasion had happened and then bombs had become available, perhaps several might have been used in tactical as opposed to strategic roles. But these speculations are counterfactual and their answers unknowable; we cannot rewind
and replay history. In the end, the Project succeeded in producing bombs which had roles in ending the war—and which have left enormous legacies.
These legacies will be with us for decades to come. They include America’s postwar military power and political influence, the enormously expensive Cold War, the thousands of nuclear weapons still extant today, ongoing weapons development programs in potentially unstable countries, the threat of nuclear terrorism, costs of remediating environmental damage at weapons-production and testing sites, and public apprehension with nuclear energy. No other twentieth-century scientific/technological development has had such a profound impact on human affairs. In this section I briefly examine some of these legacies.
7.1 Postwar proliferation, tests, and deployments
In post-war years, advances in weapons design led to the development of both smaller-yield ‘tactical’ (battlefield-scale) warheads and larger-yield ‘strategic’ warheads which could be mounted on a wide variety of delivery vehicles, including bombers, land-, sea-, and submarine-based missiles, landmines, artillery projectiles, terrain-following cruise missiles, torpedoes, and air-to-air, air-to-ground, and earth-penetrating missiles carried by aircraft. In the early 1950s, weapon yields took a quantum leap with the development of fusion-based ‘hydrogen bombs’, which used fission bombs as their triggers.
The Manhattan Project Page 11
