So it's now almost 30 years after Chernobyl, so if I read this naively:
> When this photo was taken, 10 years after the disaster, the Elephant’s Foot was only emitting one-tenth of the radiation it once had.
the Elephant's foot will currently have 1/1000th of the original radioactivity it had right after the disaster, and 10 years from now it will be down to 1/10,000th. At that rate it would be indistinguishable from background radiation within a century or so (just guesstimating here, but that's a lot of powers of 10 -- I'm probably being pessimistic).
I'm guessing that this is wrong, though, and that the radioactivity from longer half-life radionuclides will eventually start to dominate and the "effective half-life" will be much longer.
Does anyone have any idea how long it will be until Chernobyl blends into the background radiation?
Total activity decrease in realistic "atomic waste" is not at all exponential.
Try a simple example:
Take a mixture of two isotopes. The one isotope has a half-life of 1 year and there's so much of it, that the activity is 10 decays/second. There's also a second isotope in the mix, with a half-life of 100 years, but there's 100 times as much of it, so that in total, you also get 10 decays/second.
After 10 years, the first isotope will be down to 2^-10, so only 1/1000th is left, it will be hardly measurable. But the second one will have decayed only 1/10th of a half-time, almost everything is still there: You are now down to half of the original activity.
It's more complicated than that. As you point out, you don't have just one isotope, you have a whole grab bag of stuff. Here's the wrench in the works that adds the complexity, when a radioactive isotope decays it doesn't just go away, it decays into another isotope, sometimes one that is also radioactive and with its own half life.
What yoU end up with is a system of differential equations, which are actually easy to solve if you know how, but that level of calculus is beyond what most folks have studied.
Anyway, a situation that tends to be common is that you have one sort of longer lived isotope which ends up producing another isotope which decays fairly fast along a multi-step chain. This ends up producing a fairly high level of radiation for a significant time in a pseudo steady state. But it depends on the details.
I did a bit more reading, and found this crazy and scary graph. It's under "Uranium-232 Series Activity" near the bottom of this paper[1]. It shows that gamma ray output from U-238 increases > 5x a year after U-238 is first refined, and stays higher than originally was for >100 years.
It's due to the decay products of U-238 (and their decay products) all producing radiation that adds up to more than the original's.
In fact the base nuclear fuels are almost extraordinarily safer than the products of their use, speaking from a nuclear perspective alone. Nuclear fuel that is stable enough to be useful as a reactor fuel has such a long half-life (usually on the order of billions of years) that it's only very weakly radioactive. But the fission products formed from the fission of the fuel are much much more radioactive.
>I'm guessing that this is wrong, though, and that the radioactivity from longer half-life radionuclides will eventually start to dominate and the "effective half-life" will be much longer.
Exactly. From a report on Chernobyl [0]: "Most of the decrease [in radiation] in the coming years will be at only the rate of the physical half-life of 137Cs." Cesium-137 has a half-life of 30 years [1], so if we use the number given in the article (10,000 roentgens/hour) the dose is apparently 434 million times background radiation, 23 microroentgens/hour [2]. It would take over a millennium to reduce Cesium-137 by a factor of 434 million[3]
That's the Elephant's Foot, though. Randall Munroe cites Chernobyl as having 6 millisieverts/hour on average[4]. That's 3000 times background radiation [2], or a 350-year wait before Chernobyl emits the same amount [5].
This is obviously a simplification, though. Plutonium isotopes were released too [0], which have a much longer half-life (thousands of years). It's possible those small amounts of plutonium will emit enough radiation to make Chernobyl have noticeably higher radiation levels than the background dose for much longer.
A final caveat: I'm not an expert or even a devoted amateur. Your question just sparked my curiosity. Although, this New York Times article [6] says scientists say it takes about 10-13 half lives for an area to recover, which is close to my 350 year figure.
> When this photo was taken, 10 years after the disaster, the Elephant’s Foot was only emitting one-tenth of the radiation it once had.
the Elephant's foot will currently have 1/1000th of the original radioactivity it had right after the disaster, and 10 years from now it will be down to 1/10,000th. At that rate it would be indistinguishable from background radiation within a century or so (just guesstimating here, but that's a lot of powers of 10 -- I'm probably being pessimistic).
I'm guessing that this is wrong, though, and that the radioactivity from longer half-life radionuclides will eventually start to dominate and the "effective half-life" will be much longer.
Does anyone have any idea how long it will be until Chernobyl blends into the background radiation?