A physicist from Lawrence Livermore Labs has been restoring old nuclear bomb detonation footage. This seems to me to be an incredibly valuable task because all of the original footage was shot on film, which is currently in the process of decaying and falling apart. There have been no open air nuclear bomb detonations on planet Earth since probably the 1960s, which is good… except that people are in the process of forgetting exactly how bad a nuclear weapon is. The effort of saving this footage makes it possible for people to know something about this world-changing technology that wasn’t previously declassified. Nukes are sort of mythical to a body like me who wasn’t even born until about the time that testing went underground: to everybody younger than me, I suspect that nukes are an old-people thing, a less important weapon than computers. That Lawrence Livermore Labs has posted this footage to Youtube is an amazing public service, I think.
As I was reading an article on Gizmodo about this piece of news, I happened to wander into the comment threads to see what the echo chamber had to say about all this. I should know better. Admittedly, I actually didn’t post any comments castigating anyone, but there was a particular comment that got me thinking… and calculating.
Here is the comment:
Nuclear explosions produce radioactive substances that are rare in nature — like carbon-14, a radioactive form of the carbon atom that forms the chemical basis of all life on earth.
Once released into the atmosphere, carbon-14 enters the food chain and gets bound up in the cells of most living things. There’s still enough floating around for researchers to detect in the DNA of humans born in 2016. If you’re reading this, it’s inside you.
This is fear mongering. If you’ve never seen fear mongering before, this is what it looks like. The comment is intended to deliberately inspire fear not just in nuclear weapons, but in the prospect of radionuclides present in the environment. The last sentence is pure body terror. Dear godz, the radionuclides, they’re inside me and there’s no way to clean them out! I thought for a time about responding to this comment. I decided not to because there is enough truth here that anyone should probably stop and think about it.
For anyone curious, the wikipedia article on the subject has some nice details and seems thorough.
It is true the C-14 is fairly rare in nature. The natural abundance is 1 part per trillion of carbon. It is also true that the atmospheric test detonations of nuclear bombs created a spike in the C-14 present in the environment. And, while it’s true that C-14 is rare, it is actually not technically unnatural since it is formed by cosmic rays impinging on the upper atmosphere. For the astute reader, C-14 produced by cosmic rays forms the basis of radiocarbon dating since C-14 is present at a particular known, constant proportion in living things right up until you die and stop uptaking it from the environment –a scientist can then determine the date when living matter died based on the radioactive decay curve for C-14.
Since it’s not unnatural, the real question here is whether the spike of radionuclides created by nuclear testing significantly increases the health hazard posed by excess C-14 above and beyond what it would normally be. You have it in your body anyway, is there greater hazard due to the extra amount released? This puzzle is actually a somewhat intriguing one to me because I worked for a time with radionuclides and it is kind of chilling all the protective equipment that you need to use and all the safety measures that are required. The risk is a non-trivial one.
But, what is the real risk? Does having a detectable amount of radionuclide in your body that can be ascribed to atomic air tests constitute an increased health threat?
To begin with, what is the health threat? For the particular case of C-14, one of a handful of radionuclides that can be incorporated into your normal body structures, the health threat would obviously come from the radioactivity of the atom. In this particular case, C-14 is a beta-emitter. This means that C-14 radiates electrons; specifically, one of the neutrons in the atom’s nucleus converts into a proton by giving off an electron and a neutrino, resulting in the carbon turning into nitrogen. The neutrino basically doesn’t interact with anything, but the radiated electron can travel with energies of 156 keV (or about 2.4×10^-14 Joules). This will do damage to the human body in two routes, either by direct collision of the radiated electron with the body, or by a structurally important carbon atom converting into a nitrogen atom during the decay process if the C-14 was part of your body already. Obviously, if a carbon atom turns suddenly into nitrogen, that’s conducive to organic chemistry occurring since nitrogen can’t maintain the same number of valence interactions as carbon without taking on a charge. So, energy deposition by particle collision, or spontaneous chemistry is the potential cause of the health threat.
In normal terms, the carbon-nitrogen chemistry routes for damage are not accounted for in radiation damage health effects simply because of how radiation is usually encountered: you need a lot of radiation in order to have a health effect, and this is usually from an exogenous source, that is, provided by a radiation source that is outside the body rather than incorporated with it, like endogenous C-14. This would be radiation much like the UV radiation which causes a sunburn. Heath effects due to radiation exposure are measured on a scale by a dose unit called a ‘rem.’ A rem expresses an amount of radiation energy deposited into body mass, where 1 rem is equal to 1.0×10^-5 Joules of radiation energy deposited into 1 gram of body mass. Here is a table giving the general scale of rem doses which causes health effects. People who work around radiation as part of their job are limited to a full-body yearly dose of 5 rem, while the general public is limited to 0.1 rem per year. Everybody is expected to have an environmental radiation dose exposure of about 0.3 rem per year and there’s an allowance of 0.05 rem per year for medical x-rays. It’s noteworthy that not all radiation doses are created equal and that the target body tissue matters; this is manifest by different radiation doses being allowed to occur to the eyes (15 rem) or the extremities, like the skin (50 rem). A sunburn would be like a dose of 100 to 600 rem to the skin.
What part of an organism must the damage affect in order to cause a health problem? Really, only one is truly significant, and that’s your DNA. Easy to guess. Pretty much everything else is replaceable to the extent that even a single cell dying from critical damage is totally expendable in the context of an organism built of a trillion cells. The problem of C-14 being located in your DNA directly is numerically a rather minor problem: DNA actually only accounts for about 3% of the dry mass of your cells, meaning that only about 3% of the C-14 incorporated into your body is directly incorporated into your DNA, so that most of the damage to your DNA is due to C-14 not directly incorporated in that molecule. This is not to say that chemistry doesn’t cause the damage, merely that most of the chemical damage is probably due to energy deposition in molecules around the DNA which then react with the DNA, say by generation of superoxides or similar paths. This may surprise you, but DNA damage isn’t always a complete all-or-nothing proposition either: to an extent, the cell has machinery which is able to repair damaged DNA… the bacterium Dienococcus radiodurans is able to repair its DNA so efficiently that it’s able to subsist indefinitely inside a nuclear reactor. Humans have some repair mechanisms as well.
Cells handling radiation damage in humans have about two levels of response. For minor damage, the cell repairs its DNA. If the DNA damage is too great to fix, a mechanism triggers in the cell to cause it to commit suicide. You can see the effect of this in a sunburn: critically radiation damaged skin cells commit suicide en mass in the substratum of your skin, ultimately sacrificing the structural integrity of your skin, causing the external layer to sough off. This is why your skin peels due to a sunburn. If the damage is somewhere in between, matters are a little murkier… your immune system has a way of tracking down damaged cells and destroying them, but those screwed up cells sometimes slip through the cracks to cause serious disease. Inevitably cancer. Affects like these emerge for ~20 rem full body doses. People love to worry about superpowers and three-arm, three-eye type heritable mutations due to radiation exposure, but congenital mutations are a less frequent outcome simply because your gonads are such a small proportion of your body; you’re more likely to have other things screwed up first.
One important trick in all of this to notice is that to start having serious health effects that can be clearly ascribed to radiation damage, you must absorb a dose of greater than about 5 rem.
Now, what kind of a radiation dose do you acquire on a yearly basis from body-incorporated C-14 and how much did that dose change in people due to atmospheric nuclear testing?
I did my calculations on the supposition of a 70 kg person (which is 154 lbs). I also adjusted rem into a more easily used physical quantity of Joules/gram (1 rem = 1×10^-5 J/g, see above.) One rem of exposure for a 70 kg person works out to an absorbed dose of 0.7 J/year. An exposure sufficient to hit 5 rems is 3.5 J/year while 20 rem is 14 J/year. Beta-electrons from c-14 maximally hit with 2.4×10^-14 J/strike (150 keV) with about 0.8×10^-14 J/hit on average (50 keV).
In the following part of the calculation, I use radioactive decay and half-life in order to determine the rate of energy transference to the human body on the assumption that all the beta-electron energy emitted by radiation is absorbed by the human body. Radiation rates are a purely probabilistic event where the likelihood of seeing a radiated electron is proportional to the size of the radioactive atom population. The differential equation is a simple one and looks like this:
This just means that the rate of decay (and therefore electron production rate) is proportional to the size of the decaying population where the k variable is a rate constant that can be determined from the half-life. The decay differential equation is solved by the following function:
This is just a simple exponential decay which takes an initial population of some number of objects and reduces it over time. You can solve for the decay constant by plugging the half-life into the time and simply asserting that you have 1/2 of your original quantity of objects at that time. The above exponential rearranges to find the decay constant:
Here, Tau is the half-life in seconds (I could have used my time as years, but I’m pretty thoroughly trained to stick with SI units) and I’ve already substituted 1/2 for the population change. With k from half-life, I just need the population of radiation emitters present in the body in order to know the rate given in the first equation above… where I would simply multiply k by N.
To do this calculation, the half-life of C-14 is known to be 5730 years, which I then converted into seconds (ick; if I only care about years, next time I only calculate in years). This gives a decay constant of 3.836×10^-12 emissions/sec. In order to get the decay rate, I also need the population of C-14 emitters present in the human body. We know that C-14 has a natural prevalence of 1 per trillion and also that a 70 kg human body is 16 kg carbon after a little google searching, which gives me 1.6×10^-8 g of C-14. With C-14’s mass of 14 g/mole and Avagadro’s number, this gives about 6.88×10^14 C-14 atoms present in a 154 lb person. This population together with the rate constant gives me the decay rate by the first equation above, which is 2.639×10^3 decays per second. Energy per beta-electron absorbed times the decay rate gives the rate of energy deposited into the body per second on the assumption that all beta-decay energy is absorbed by the target: 2.639×10^3 decays/sec * 2.4×10^-14 Joules/decay = 6.33 x 10^-11 J/s. For the course of an entire year, the amount of energy works out to about 0.002 Joules/year.
This gets me to a place where I can start making comparisons. The exposure limit for any old member of the general public to ‘artificial’ radiation is 0.1 rem, or 0.07 J/year. The maximum… maximum… contribution due to endogenous C-14 is 35 times smaller than the allowed public exposure limits (for mean energy, it’s more like 100 times smaller). On average, endogenous C-14 gives 1/100th of the allowed permitted artificial radiation dose.
But, I’ve actually fudged here. Note that I said above that humans normally get a yearly environmental radiation dose of about 0.3 rem (0.21 J/year)… meaning that endogenous C-14 only provides about 1/300th of your natural dose. Other radiation sources that you encounter on a daily basis provide radiation exposure that is 300 times stronger than C-14 directly incorporated into the structure of your body. And, keep in mind that this is way lower than the 5 rem where health effects due to radiation exposure begin to emerge.
How does C-14 produced by atmospheric nuclear testing figure into all of this?
The wikipedia article I cited above has a nice histogram of detected changes in the environmental C-14 levels due to atmospheric nuclear testing. At the time of such testing, C-14 prevalence spiked in the environment by about 2 fold and has decayed over the intervening years to be less than 1.1-fold. This has an effect on C-14 exposure specifically of changing it from 1/300th of your natural dose to 1/150th, or about 0.5%, which then tapers to less than a tenth of a percent above natural prevalence in less than fifty years. Detectable, yes. Significant? No. Responsible for health effects…… not above the noise!
This is not to say that a nuclear war wouldn’t be bad. It would be very bad. But, don’t exaggerate environmental toxins. We have radionuclides present in our bodies no matter what and the ones put there by 1950s nuclear testing are only a negligible part, even at the time –what’s 100% next to 100.5%? A big nuclear war might be much worse than this, but this is basically a forgettable amount of radiation.
For anybody who is worried about environmental radiation, I draw your attention back to a really simple fact:
The woman depicted in the picture above has received a 100 to 600 rem dose of very (very very) soft X-rays by deliberately sitting out in front of a nuclear furnace. You can even see the nuclear shadow on her back left by her scant clothing. Do you think I’m kidding? UV light, which is lower energy than x-rays, but not by that much… about 3 eV versus maybe 500 eV, is ionizing radiation which is absorbed directly by skin DNA to produce real radiation damage, which your body treats indistinguishably from how it treats damage from particle radiation of radionuclides or X-rays or gamma-rays. The dose which produced this affect is something like two to twelve times higher than the federally permitted dose that radiation workers are allowed to receive in their skin over the course of an entire year… and she did it to herself deliberately in a matter hours!
Here’s a hint, don’t worry about the boogieman under the bed when what you just happily did to yourself over the weekend among friends is much much worse.