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What happens if all the carbon-14 atoms in a persons body decays at once? Would they die or will they be unaffected?

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There is about 1 radioactive $^{14}$C atom for every $10^{12}$ $^{12}$C atoms. With a half-life of 5730 years, this means there are usually about 0.2 decays per gramme of carbon per second.

Carbon is about 18% of your body mass, so an 80 kg adult would have about 14 kg of carbon and $7\times 10^{14}$ $^{14}$C atoms. If these all decayed in say one second, the dose rate would be $1.9\times 10^4$ Ci

To estimate the effects, we could assume all the beta particles are absorbed and that each has an energy of about 0.1 MeV. This gives an absorbed energy of just 11 Joules of energy. Totally negligible in energetic terms.

In terms of absorbed radiation the quantity is about 11 J/80 kg = 0.14 Grays and for beta particles, roughly the same number of Sieverts, i.e. 140 mSv.

This is roughly the same radiation dose you would get from $\sim$20 CT scans or about the same as a few decades worth of exposure to ambient radiation in the environment and is enough to raise your long-term cancer risk slightly (a few per cent) but likely not enough to cause acute radiation poisoning.

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    $\begingroup$ +1 for actually looking at the radiation dose $\endgroup$
    – mic_e
    Nov 8, 2021 at 16:45
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    $\begingroup$ +1 CT scans vary a lot, though - 140mSv is actually a pretty large dose, and is about 70 times higher than a simple head CT scan (about 2mSv). Other types of CT scan (ie: heart-attack diagnosis, abdomen/pelvis) can be higher and closer to the value you're quoting (around 14mSv). 140mSv is actually almost three times the annual exposure limit for US radiation workers (50mSv). The Fukushima 50 had a number of workers that received doses in the 100-180mSv range, so that's maybe the closest comparison for OP to consider. $\endgroup$
    – J...
    Nov 8, 2021 at 17:36
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    $\begingroup$ @ProfRob I'd say it's a bit more serious than that, especially as an acute dose. A few decades of background radiation happens over a long time. All at once, though, is a different matter. Two plant workers at Fukushima, for example, were exposed in an accident to 170-180mSv and had to be taken to hospital for radiation burns. That's a bit more than an abstract few-percent increase in future risk - that's a serious acute effect. 140mSv is a big dose, especially when it's coming from inside the body. $\endgroup$
    – J...
    Nov 8, 2021 at 17:47
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    $\begingroup$ @ProfRob I agree your numbers are in line with current medical knowledge. I'm just saying that OP's circumstance is highly irregular and not the type of exposure that medical science has a lot of experience with (ie: entire body becoming acutely radioactive). That the mode of exposure is so different, and is absorbing dose inside all the body's critical organs, we might expect the physical consequences to fall on the pessimistic side of our stochastic models. $\endgroup$
    – J...
    Nov 8, 2021 at 20:35
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    $\begingroup$ For C-14 decay, $\lambda\approx 3.8332×10^{-12}\,s^{-1}$. So the probability of all $7×10^{14}$ atoms decaying in 1 second is incomprehensibly small. The base 10 log of the probability is $\approx-8×10^{15}$. If you wrote the probability itself in a font with characters 1 mm wide, the zeros would stretch over 53 AU. $\endgroup$
    – PM 2Ring
    Nov 8, 2021 at 21:14
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Carbon-14 has a relative abundance to Carbon-12 of about 0.0000000001% (one part per trillion). The average human body has about 15 kg of Carbon give or take, meaning about 1.5 micrograms of Carbon-14. That's 107 nanomoles of carbon, or about 6.444×10^16 atoms (1/3000th a grain of sand). When a Carbon-14 atom decays into a Nitrogen-14 atom via beta decay, it loses 0.001% of its mass in the form of an electron and kinetic energy (156.5 keV of kinetic energy to be precise). The total amount of kinetic energy released into the body if all 6.444×10^16 atoms in it were to decay would be 1.6 kJ.

It's hard to say exactly how much damage that would do to the body, but it would definitely do something. That's about the energy your body releases in 15 seconds, so the damage that would be done entirely depends on how quickly the decay happens. If its over a few seconds, likely nothing would happen. If its instantaneous, that would be like a very sudden hotflash that could damage some tissue, though even that wouldn't kill you. The dangerous thing you'd have to worry about is cancer. To give perspective, only about 20 atoms of carbon would decay in a given cell, and only a 20% chance that in a given cell one of those would be in a DNA molecule. About 1 in every 5 of your cells will likely have a single base pair destroyed, meaning one letter of your genetic code. While these happen all the time, if this scenario occured over one second, it would be about 200,000 times higher than the normal rate of mutation per second. That wouldn't guarantee cancer of course, but I wouldn't volunteer for this to happen to me any time soon.

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    $\begingroup$ The carbon doesn't go missing, it just becomes a nitrogen atom with approximately the same mass. Any molecule with one of the carbons would be damaged yes, but thats only a very small fraction of molecules. As I say in my answer, 1 in ever 5 cells will have a DNA molucule that will be effected. $\endgroup$ Nov 8, 2021 at 9:09
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    $\begingroup$ You can correct your energy output to $1.6$ kJ $(49.5/156.5) = 0.5$ kJ. Make a rough approximation that your body is made of water, The specific heat of water is $4186$ kJ/kg/$^o$C. Assume you used Wikipedia's average human mass value of $62$ kg. Then that much energy would raise your temperature $1.6$ micro$^o$C. $\endgroup$
    – mmesser314
    Nov 8, 2021 at 15:07
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    $\begingroup$ Compared this other answer on this page, your estimate of the carbon-14 mass is higher by a factor of 100, and your estimate of the total decay energy is higher by a factor of 1000. You have (v1) at least one unit conversion error: “kilo” times $10^{-12}$ is “nano,” but you go from kilograms of carbon to micrograms of carbon-14. I haven’t done the energy calculation, but give it a second look. $\endgroup$
    – rob
    Nov 8, 2021 at 16:00
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    $\begingroup$ One trillionth of 15 kG is not 1.5 micrograms, it is 15 nanograms. That's off by a factor of 100. $\endgroup$ Nov 8, 2021 at 16:38
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    $\begingroup$ This answer is busted. $\endgroup$
    – TonyK
    Nov 8, 2021 at 17:21
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More important than the radiation dose is that the Carbon-14 would decay to Nitrogen-14 and random proteins, cellular structures, RNA and DNA would no longer function. There might be secondary effects, such as The Bends, a.k.a decompression sickness, from nitrogen in the blood, or other diseases. I would hesitate to predict anything but a painful lingering death.

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    $\begingroup$ I doubt you'd get the bends from 14 nanograms of nitrogen. $\endgroup$
    – PM 2Ring
    Nov 8, 2021 at 20:47
  • $\begingroup$ OK, then. I read the previous answers and I was more impressed with the possible biological effects than radiation. Maybe we need a volunteer, but how could this be accomplished? $\endgroup$
    – Wastrel
    Nov 9, 2021 at 0:33

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