The Biological Decay Chain may be my own personal concept, but I doubt that. The biological damage caused by ionizing radiation should be proportional to the energy released by decay in the body. Isotopes that are likely to be active in an average lifetime less cancer growth time, about five years, have a ionizing biological impact. The isotopes may also have poisonous chemical impact, like heavy metal poisoning, but damage due to decay energy when isotopes give of alpha, beta or gamma radiation, (there are other forms, but let's stick to the basics), cause the most negative health impact.
In the photo from Wikipedia above, you can see that a lot of stuff happens after Thorium-232 decays to radium-228. In this chain, once Thorium-232 decays, the entire resulting decay process takes less than eight years to complete, resulting in stable lead-208. To simplify the biological impact, assume that each alpha decay is five and each beta decay is one. This chain has a BHL of 32 or approximately 32,000 KeV. You will notice that there is a branch near the end of the chain. There is a little difference in energy depending on the path, but not much if you consider the whole chain.
I have written about Radon-222 before and its impact. Behind smoking, Radon is the main cause of lung cancer. It is naturally occurring and it is the greatest ionizing radiation risk. Radon-224 is more harmful because the time to stable lead is much shorter.
This is the Uranium-238/Radium-226 decay chain commonly called the Radium Chain. Things really start happening at Radium which is probably the reason. Starting at Radium, this chain has a BHL of 30 with alternate paths, it can increase to 32, though the time to stable is about four times longer, 22.5 years with a less likely start at Radium.
These are the two main decay chains since the Neptunium chain is considered extinct and the Uranium-235 chain start with a rare isotope. For the U-235 chain, the Radium 225 to stable lead is very close to the other more common chains.
Since Radon gas is more commonly inhaled, we can reduce the BHL radium energy by one alpha decay to give us a basic Radon BHL unit of 25 to compare to other isotopes. So the danger is greater if another isotope released more energy in a life time of say 70 years.
There is one thing that complicates things a little, Spontaneous Fission. Isotopes with an atomic weight of 230 and over have the possibility of under going fission which releases much more energy. Plutonium-240 is likely to under go fission outside of a reactor, but luckily Pu-240 is rare outside of a reactor.
Plutonium-240 is formed when Pu-239 absorbs a neutron. That is extremely improbable outside of a reactor but not impossible. Pu-239 can also spontaneous fission with little probability. The odds are pretty remote, but a spontaneous fission cannot be ruled out. Pu-240 has a half life of 6569 years and the probability of fission during a decay is 5 time 10^-8 or 1/500000000, that is a low probability which I consider negligible.
Note: For the nuclear purists, spontaneous fission is negligible as a biological factor. If you are trying to build a bomb, don't neglect it or your bomb will fizzle like North Korea's. Weapons grade Plutonium has less than 7% Pu-240 and the complex geometry of Plutonium based bombs is due to billions of Pu-240 atoms that are to expensive to remove. I may have to do a post on commercial nuclear waste and how it doesn't make good bombs.
To compare the relative dangers you have to consider two things, the energy and the probability that the energy will be released inside of the body in a normal human lifetime. The main consideration is the half life and quantity, to determine the probability of decay energy.
Plutonium-239 has a half life of about 24,000 years with one alpha decay of any significant probability since it decays to Uranium-235 with a half life of 700 million years. Since Radon WILL decay to stable in a human lifetime if ingested early in life and Pu-239 has a probability of 0.3 percent of decaying in a human lifetime (70/24,000) with 1/5 the energy (5 versus 25), Pu-239 is 0.06 percent as likely to cause biological damage as Radon.
For Strontium-90 with a half life of 29 years and two beta decays to stable Zirconium-90, compared to radon it is 2/25 or 8 percent as likely to cause biological damage.
Iodine-131 with a half life of 8 days and one beta decay to stable Xenon-131, it is also 8 percent as likely to cause biological damage as radon.
Note that in the comparisons, if the half life of the isotope is less than 70 years, average human life time, the ratio of the energy determines the comparable risk.
Just to round things off assume the comparison is ten percent instead of eight percent, then ten times more of Strontium-90 or Iodine-131 ingested than normal Radon ingested from background would give you the same cancer risk. The types of cancer would be different, Strontium-90 is likely to cause bone cancer or leukemia, Iodine-131 thyroid cancer and Radon lung cancer, but the chance of cancer would be close using the Radon BHL.
Note: Just to make this perfectly clear, ten times is on an atom to atom basis, counts is a different issue.
Plutonium-239 at 0.06 percent as likely as radon to cause harm, is barely statistically significant on an atom to atom basis. Radionuclides with half lives greater than 24,000 years would produce insignificant risk in small quantities compared to radon.
The amount of these longer lived radionuclides is then the issue. This is where the dose meters come in with a little qualification. Dose meters record what your body is exposed to not what is ingested. For this purpose ingestion would be by consumption, inhalation or direct absorption into the blood stream. Inhalation and direct absorption more directly compare. With consumption, only a percentage consumed makes it into the blood stream. Food limits then have a built in safety factor since they do not consider the percentage absorbed. Strontium-90 when consumed in food is 20 percent absorbed, Plutonium between 1 and 5 percent absorbed. Inhalation is the greatest likely danger and most directly comparable to Radon which is primarily inhaled.
Cesium-137 is a common fallout isotope with a half life of 30 years and a beta decay to stable Barium-137. There are a couple routes to stable Barium with a comparison energy of about 1.25. 1.25/25 equals 5 percent as likely as Radon at the same quantity. Cesium is more likely absorbed into the blood stream through consumption, so there is not extra safety factor.
So how well does this radon biological half life factor work? If you consider Strontium and Iodine, ten times the quantity produces equal risk, so ten times normal Radon is the cancer threshold where you would be equally likely to develop cancer. Ten times background is the prudent limit for normal safety. At this ten times limit the counts per minute or second would be roughly equal to background, so twice background would be the possible statistically significant threshold if measuring absorbed radiation.
Measuring absorbed radiation is complicated. Only some of the Radon would be measured, about a fifth because of the delay in the chain, so exposed radiation, the real counts that can be measured, would result in five times two or ten times normal background in counts to meet the threshold.
If measuring food, the normal background is approximately 100 Becquerel per kilogram. Ten times normal is 1000Bq/kg would be the implied limit by the radon BHL, which compares will with most national standards which are less than or equal to 1000 Bq/kg. For exposure limits, ten times background would be 1 Microsievert per hour in Japan or about 9 milliSieverts per year.
So the Radon biological half life standard does not change any limits, it only offers a better indication on the amounts of different radionuclides based on half life and energy required to add significant risk.
I need to double check my math, but this may give a better perspective of radiation risk than the banana dose.
For a double check, the radon decay energy to stable lead is close enough. While Radon-222 takes over 22 years to decay, the 25 is reasonable as a basic reference. To compare with another radionuclide, determine the probable decays in 70 years, that does not have to be exact. Then divide that energy (as an integer)by 25 to get a raw percentage. If the half life of the radionuclide is much greater than 70 years, divide 70 by the half life and multiply that by the probable energy in integer form divided by 25. That gives a fair conservative estimate of the relative harm of that radionuclide compared to common radon.
This may seem incorrect because of the horror stories. For example Uranium miners may have a higher cancer risk, but that is more likely due to the variety of radionuclides in the ore or pitch blend, which includes a good deal of radium. Radium alpha decays to radon so a comparison to Radium-226 with a half life of 1600 years would be (70/1600)times (30/25) yields 0.043 times 1.2 equals 0.0525 or 5.25 percent. With Radium-223, which has a very short half life, that comparison would be 30/25 or 20 percent greater chance than radon. Radium-224 would also be 20 percent greater as an estimate. Radium-228 would be 35/25 or 140 or 40 percent greater risk. Brazil nuts contain Radium-226 and are not considered a cancer risk in reasonable quantities. If they contained significant amounts of Radium-228,-224 or -223, they would be.
The decay chains with half life and energy are available online in several places. For this post I used Wikipedia Decay Chain.
As far as the ten time natural background for Cesium, Strontium and Iodine radionuclides, the ingested should be reasonably conservative. The external exposure relationship may be debatable, but should be conservative because those radionuclides are beta emitters.
Another thing that makes the Radon Biological half life comparison conservative it that Cesium-137 for example has an actual biological half life of under 120 days.
I may try and make a comparison chart, but the isotopes covered should give you an idea of how to make your own rough estimate of risk.
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