Answer to Question #13910 Submitted to "Ask the Experts"

This has been circulating on Facebook: https://www.instagram.com/p/CLlpt08DScs/?utm_source=ig_embed.

The claim: Keeping a hundred million people in an isolated place for eight hours will kill them in 20 minutes due to the natural radiation present in human bodies. Can you confirm whether this claim is indeed true or is it false and why?

The claim being made, or at least the inference, of death to the 100 million enclosed individuals as a consequence of exposure to radiation from internally deposited naturally occurring radionuclides, is completely false. I shall explain why below. The second part of your comments as to the Health Physics Society Ask the Experts website being a source of some referenced information is correct, and the information available there is correct. However, that information simply talks about the quantities of various radionuclides present in the body; it does not provide any specific methodology for estimating doses to individuals.

If it were possible to assemble 100 million people into a very closely spaced standing group, we would likely require an area of seven to eight square miles with people standing up back-to-back, belly-to-belly, and other orientations closer than comfortable. This is still not the optimum geometry to deliver dose most efficiently, but to optimize geometry for maximum dose it would be required to pile up the people in a great cylindrical mound with the height approximately equal to the diameter of the circular base. In such an artificial but demonstrative situation we can estimate the maximum possible dose to an individual in the group by invoking a principle called energy spatial equilibrium (ESE) in which the energy emitted per unit mass of tissue is equal to the energy deposited per unit mass of tissue; radiation dose is measure in units of energy deposited per unit mass of tissue. This principle applies when a radioactive material is distributed uniformly in a very large volume of material; neglecting the small spaces between individuals, our hypothetical group would be much greater than what would be required for ESE.

To demonstrate the relevant calculation, we shall use only the natural radionuclide potassium-40 ( ⁴⁰K), since it would account for most of the dose, and we shall initially consider only the gamma radiation since the beta radiation affects a given individual but is not penetrating enough to leave the body and irradiate anyone else (we will account for it later). In a typical 70 kg person, the expected amount of ⁴⁰K is 4,260 becquerel (Bq), which represents 4,260 atoms disintegrations (d) per second; this translates to 60.86 d s^-1 per kg. In 0.1067 of the decay events, one gamma (γ) ray of energy 1.461 million electron volts (MeV) is emitted. The expected dose rate to tissue, D, in units of Gray (Gy) under ESE conditions is calculated:

D = (60.86 d s^-1  kg^-1)(0.1067 γ d^-1)(1.461 MeV γ^-1)(1.6 x 10^-13 J Mev^-1)(1 Gy per J kg^-1)(3600 s h^-1)(8 h) = 4.4 x 10^-8 Gy.

This value of absorbed dose represents a very tiny dose resulting from all the gamma radiation emitted by and among all the people. For completeness, we should note that the ⁴⁰K in each individual also emits beta radiation to the extent of 0.500 MeV of energy per disintegration (based on beta energy of 0.561 MeV and a yield of 0.8927). While one individual's beta particle emission does not affect any other individual's dose, the beta radiation, assumed to be distributed uniformly among all the soft tissues of the body, would impact every individual's dose. Using a calculation similar to above, the added dose to each individual would be about 1.4 x 10^-7 Gy, about three times higher than the gamma dose estimated above. The beta dose is higher than the gamma dose because, although the gamma energy is about three times higher than the beta energy, the yield of the beta radiation is more than eight times greater than the gamma yield. It is relevant to know that more than three quarters of this still very small dose accrues to the individual whether he/she is alone or in a crowd. The presence of the crowd increased the total dose somewhat from the gamma radiation, although a significant part of the gamma dose would have come from a given individual's own burden of ⁴⁰K.

The final result is that the eight-hour dose to an individual is 4.4 x 10^-8 Gy + 1.41 x 10^-7 Gy = 1.85 x 10^-7 Gy. The whole-body dose expected to kill 50% of an exposed population within 30 days of irradiation is about 450 Gy, a number 2.4 billion times larger than the calculated value. For perspective, the calculated dose of 1.85 x 10^-7 Gy represents about two hours' worth of typical exposure to external background radiation that each of us experiences routinely and more-or-less continuously.

So how did the cited source arrive at such a ridiculous conclusion? The link you give does not show how the determination was made, but I can guess at the sort of thing that might have been done. For example, someone may have consulted our website (hps.org) and found the 4.26 x 10³ Bq of ⁴⁰K per individual and multiplied this value by the 100 million people to get a total ⁴⁰K content of 4.26 x 10¹¹ Bq. If one then treated this as if it were a consolidated small source irradiating an individual standing in contact with or very close to the source, one could easily get numbers consistent with the statement made. Of course, such a calculation would be meaningless because it would not be based on the real distribution of the ⁴⁰K.

It is regretful that the kinds of assertions you have referenced are so commonplace on the internet. I am pleased to hear that you are among the truth speakers trying to diminish their credibility. I hope this helps.

George Chabot, PhD, CHP