Comparison of Nuclear Accidents versus Nuclear Bombs: Part 2--Nuclear Weapons

Types of Hazards from Nuclear Weapons

I got a lot of information from this old (but still very informative) publication on the detailed effects of nuclear weapons: The Effects of Nuclear Weapons

I will divide the hazards of a nuclear weapon into three parts:

1. Initial explosion. For a nuclear weapon, the initial detonation can be thought of as a very large conventional explosion “plus”. That is, it has all the characteristics of a regular explosion at a very large scale (heat, shock wave, shrapnel, etc.) plus a super powerful burst of thermal, gamma and neutron radiation. Nuclear weapons are far hotter than conventional weapons. This initial radiation burst has two practical consequences:
1. A significant number of people at a certain distance from ground zero may survive the initial blast, but be partially “cooked” by the heat and radiation. This causes internal damage to victims of a unique kind.
2. Nuclear weapons detonated in or above a city will cause everything flammable within a certain radius to burst into flames. Following this, gale-force winds will rush towards the center of the explosion to replace the air displaced upwards by the fireball / mushroom cloud. This will usually cause massing firestorms which will act as a secondary source of death and destruction after the initial blast.
2. Near-term elevated environmental external radiation caused by the initial fallout. This is the “afterglow” of the nuclear explosion. Due to the intense radiation (via some mechanisms I will get into shortly), the immediate vicinity of a nuclear explosion will experience elevated radiation levels, which can cause significant health issues merely by being in the area and being exposed to the radiation.
3. Long-term radioactive pollution, in the form of various radioactive by-products that can be absorbed into the body and cause various types of damage via internal radiation.

In order to to an apples-to-apples comparison with a nuclear meltdown or a dirty bomb, we would like to be able to specify the relative proportion each of these three hazards has to each other and to the known power of a specific weapon. That is, given a specific kiloton rating of a nuclear weapon, on what scale would we expect to see each of these types of hazards?

This turns out to be a very difficult question to answer in general terms. Figuring out the initial blast radius and expected damage from a nuclear explosion is not too difficult, but the other two hazards depend on much less easy-to-determine factors. I’m going to explain the factors here, but be aware that this will lead to a very wide range of possible conclusions depending on the circumstances.

Blast Radius

The number of people killed by an explosion is going to be directly related to the total area of the explosion. The total area affected by the initial explosion of a nuclear weapons is directly related to the power of the weapon, but it is not linearly proportional to that power. That is, a nuclear weapon that is 10 times as powerful as another one will not have a blast radius that is 10 times as large, nor even an affected area that is 10 times as large.

The reason for this is easy to see with a little bit of visual imagination. An explosion is a 3-D event; the energy from the explosion begins in the center and radiates out in all directions. In an idealized world, the affected space of the explosion is a sphere. The affected area on the ground will be (roughly) the shadow of this sphere. This means that while the volume of a nuclear explosion is going to be directly proportional to the power of the bomb, the radius will be (roughly) related to the cube root of the power of the bomb and the area will be (roughly) related to the cube root of the power of the bomb, squared.

In practical terms, there are some modifications to this because of reflection effects–the sphere gets squashed and spread out, as it were. The real-world factor between bomb yield and radius is actually the 2.5th root rather than the cube root. This means, for example, that if you increase the power of a nuclear bomb by 15 times, the affected area will only be about 8.5 times as large. Likewise, a 100 fold increase in power will yield only a 40 fold increase in affected area, a 1000 fold increase in power will yield only a 250 fold increase in affected area, and so forth.

Initial Fallout

For this section of the post, you should recall what has already been said about types of radiation in this blog post: “Key Points You Need to Know When Talking About Energy: Radiation”--namely, that neutron radiation has the capability of making other things radioactive. Neutrons released from the explosion slam into whatever they randomly hit. Sometimes, this will cause the neutron to become absorbed by the atom with which it collides. When this happens, that atom is now an unstable form of the same element: a radioactive isotope. Matter thus subjected to intense neutron radiation is said to be have “induced activity”. For such material, it is then only a matter of time before its unstable atoms break down and re-releases those absorbed neutrons again.

After a nuclear explosion, matter that is highly radiated by the intense neutron radiation of the nuclear fireball will be given this “induced activity”, and will subsequently immediately begin releasing decay radiation–a sort of radiation “echo” of the initial explosion.

It is important to understand that this radioactive material is of a different kind (for the most part) than the radioactive by-products of the fission reaction itself. The initial blast of fission is caused by high-neutron count isotopes of heavy actinides: plutonium, uranium, etc. These materials have a very long radioactive life, because their atoms are composed of such large, unstable clumps of protons and neutrons. When radioactive plutonium decays, it splits up into several by-products which are still large and unstable; it will end up going through a long series of decays (emitting radiation all the while) before it finally reaches a stable state.

On the other hand, if a silicon or manganese atom absorbs a neutron, it will become radioactive only for as long as it takes to re-emit that neutron (or otherwise decay). Induced radiation is therefore much more short-lived than heavy-isotope, fission by-product radiation.

Magnitude of the initial fallout variable

What is the rough magnitude of this initial fallout, compared to the yield of the particular nuclear weapon? This depends on how much material is irradiated, and what the strength of that radiation is. The strength of the radiation is directly proportional to the yield of the bomb, so this part of the factor will scale with the size of the explosion in general. However, the amount of material that is irradiated depends very highly on where the bomb explodes. A surface or very near surface detonation will cause massive amounts of dirt, dust, and debris to be sucked up into the mushroom cloud and hence into the core of the irradiation in the nuclear fireball. An aerial detonation, on the other hand, will gather up a much smaller amount of material and thereafter release a much smaller amount of particulate fallout.

The difference between an aerial and ground detonation is very large, changing the amount of initial fallout by some huge amount. And here, unfortunately, I have found a large amount of uncertainty, due to how nuclear testing has taken place. For the most part, we have avoided testing with true ground detonations, either detonating in the air using a metal tower, detonating underground, or in water. Data on true ground explosions is therefore not really available. (ref. The Effects of Nuclear Weapons, section 9).

I think we can get a bit of a handle on the variability by seeing the type of variation that happens within a fallout zone. Because of the effects of wind and terrain, fallout doesn’t happen evenly across a whole area, and areas of up to 10 times as much as average the amount of radiation have been observed in discrete “pockets” in the terrain where dust and debris collected because of wind and terrain patterns. In a hand-wavey way, then, I think this kind of justifies a variation of total initial fallout between air bursts vs. ground blasts of up to 10x.

Area affected by the initial fallout: a rough estimation

There is a useful rough approximation for the area expected to be impacted by fallout of a nuclear surface blast, available here: The Effects of Nuclear Weapons, p. 9.93. To use the diagram and table provided there, you map the “rads/hr” map in the diagram to the location in question, scaling the width of the plume to the actual wind speed of your example (the baseline is given for 15 mph). What I want to point out is that the length and width of the resulting ellipsoid shape are both given in terms of the yield of the bomb, raised to approximately the 1/2 power. The total affected area is therefore going to be roughly linearly proportional to the yield of the bomb. Keep in mind, however, that whatever rough estimate you get from this method is going to be roughly predictive of the amount of total fallout, given the variability in amount of material that ends up irradiated by the bomb based off of how it is detonated.

Durability of the initial fallout predictable

Acknowledging the wide variability in total fallout, can we nevertheless estimate how long the direct radiation from the afterglow of a nuclear explosion is likely to be problematic? In fact we can, for two reasons. First, while the amount of radioactive material generated by the explosion is proportional to the power of the bomb, yet–as we just noticed–the area over which the material is dispersed is also going to be roughly proportional to the power of the bomb. This means that the total area affected by this initial fallout is going to vary according to the power of the explosion, but the intensity of the resulting immediate fallout radiation is going to be rather consistent even between blasts of very different power.

Second, the time it takes for this radiation to dissipate is controlled by exponential decay. The rule of thumb (for the first six months after an explosion) is that for any given radiation intensity in an area of immediate fallout, a seven-fold increase of time interval will cause the amount of radiation to decrease by ten-fold. After six months, the falloff happens even more rapidly.

This exponential decay means that even fairly large variations in the initial intensity of the radiation will reduce to very similar small amounts in very similar time periods. Supposing you did have a full 10 times as much initial radiation from a particular type of nuclear explosion–well, all you would need to do is wait a week and the levels from the more potent blast will be down 1/10th and be merely equal to the amount the cleaner blast produced one day ago. Once you get beyond six months past the time of the initial fallout, there will be very little practical difference between residual radiation of this shorter-lived type.

In conclusion, I think we can say that the initial fallout from a nuclear weapon will present a very varied initial amount of radioactive fallout, but that the effects are going to be very similar in the near to mid-term: evacuate the area affected, and come back when the levels have become safe again, which will be a matter of some weeks or months.

Long term fallout effects

While the majority of the radioactive by-products of a nuclear explosion decay very rapidly after the initial period of danger (on the time scale of hours, days, or weeks for the most part), some radioactive elements present more medium-term and long-term hazards. The initial load of radioactivity from fallout is strong enough to cause health problems even as external sources of radiation–enough radiation can penetrate your skin to cause real health problems in the immediate aftermath of a nuclear explosion.

Once this radiation has died down to a power level at which your skin is an adequate protection against most of the damage it may cause, the concern then shifts to those radioactive materials still present which may be ingested or inhaled into and then persist in the body. Now, most of the radioactive materials in fallout can be ingested or inhaled; however, what is particularly damaging are those materials that have some specific use in living bodies, or which chemically mimic elements that have such specific uses.

The elements that are particularly problematic here are iodine-131, strontium-90, and cesium-137. Iodine is used by the body and when ingested, tends to accumulate in the thyroid gland. Strontium is in the same column of the periodic table of elements as calcium, and is therefore absorbed into your bones in the same way if you ingest it. Likewise, cesium is chemically similar to potassium and will be absorbed by your body in the same way. All of these elements can also be absorbed by animals and then re-emitted into the food supply, the most worrisome pathway being milk from cows ingesting contaminated food.

Amounts of radioactive material which would not be dangerous in the open environment can still cause significant health issues if collected directly into your vulnerable tissues and not eliminated rapidly. Each of these problematic materials have been shown to cause cancers of various types.

Of these three materials, iodine is more of a short-to-medium term danger. It has a half-life of about 8 days, so it decays away into irrelevance fairly quickly.  In terms of practical considerations, iodine-131 really should be counted more as a problem of the late "Initial Fallout" stage, rather than a true long-term effect.

Cesium and strontium, on the other hand, both have a half-life of about 30 years. They need to be considered a risk, therefore, for a much longer time.

Quantity of Cesium and Strontium

What quantity of cesium and strontium can be expected, based on the power of the nuclear bomb exploded? For fission bombs, this is not too difficult to ascertain. As a rough estimate, a fission bomb will generate about 125 pounds of radioactive isotopes per megaton of yield (see The Effects of Nuclear Weapons, p.9.12). About 6.3% of that will be cesium-137 (about 7.9 pounds) and about 4.5% will be strontium-90 (about 5.6 pounds). (Ref. “Fission products by element”)

However, most tactical weapons nowadays are not pure fission bombs, and here, unfortunately, we are forced to admit a lot of uncertainty. In this case, the amount of cesium and strontium produced is determined to a large extent by the specific type of explosion that is generated, and hence by the design of the bomb. Producing a nuclear explosion is not actually a simple procedure and typically involves a carefully designed sequence of explosions, rather than a single one. In a typical H bomb, the fission reactions that generate the cesium and strontium are mostly due to the flash-irradiation of a depleted uranium shell around the first fission reaction (which triggers a second fission explosion, which triggers the final fusion explosion). 

So to really know how much cesium and strontium you can expect from such a bomb, you need to know what percentage of the explosive energy of the bomb comes from fission as opposed to fusion, and in order to know *that*, you need to specific details about the design of the bomb.

Unsurprisingly, I have been unable to find the required detailed schematics for constructing an H-bomb online that would enable me to nail down specifics for this question.

In general, what I have read indicates that fusion bombs tend to be cleaner than fission bombs, but not as much as you might think or want. I would suggest, as a quick-and-dirty rule of thumb, that we just estimate the fallout products of a fusion bomb to be roughly half of what an equivalent yield fission bomb would be--"The Effects of Nuclear Weapons" makes just this estimate at one point. But I have to admit that this is just a very rough estimate.

Effects of Cesium and Strontium

I should note something important here: it appears that the health effects of these long-term nuclear products have been negligible, so far as we can tell from those few instances of real-life fallout impacting real people that we have observed. Now, this is a very small set of instances--basically, Hiroshima and Nagasaki, the Marshall Island bombing exposure incident, and Chernobyl, and I think that's it.  Almost all of the *demonstrated* adverse health effects from radioactive fallout in these cases has come from iodine-131, not from the cesium or strontium. (see The Effects of Nuclear Weapons, section 9).

So we don't really have enough data to *know* how much cesium and strontium pollution from a nuclear weapon or nuclear accident is enough to cause significant adverse health effects in the long-term.

Summary

The effects of the detonation of a nuclear weapon can then be summarized as follows:

1. Short term, a massive radius of destruction, proportional to the size of the bomb.
2. Medium term, a large area of dangerous fallout, which will render some area unsafe for a period of time, possibly for months but not for years. Iodine-137 is the biggest issue once a few weeks have elapsed from the time of the explosion.
3. Long term, a certain amount of dangerous materials (primarily cesium-137 and strontium-90) deposited in the environment: about 8 pounds of cesium-137 per megaton of fission explosion, and maybe 4ish pounds per megaton of H-bomb explosion, and about 5.5 and 2.75 pounds of strontium-90, respectively. These amounts, however, do not seem to entail a lot of health consequences that we know about, given our admittedly limited experience.

This gives us a frame of reference with which to compare the consequences of a nuclear meltdown, which will be the next entry in this series.