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Take a modern nuclear reactor complex. Now picture a catastrophic meltdown, not unlike Chernobyl.

But this time there is nobody around to do damage control, and all control mechanisms do fail.

The reactor breaches, causing the other reacotrs in the complex to meltdown too and they spills radioacive death all around. The windy season picks up the particles and spread them far.

A decade after the accident, there is a zone around the reactor nobody can live in.

How big should be this zone?

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    $\begingroup$ Points: 1) reactors are always built on bodies of water as a source of coolant. 2) an uncontrolled meltdown will reach the water table and then seep into that body of water. 3) contamination will now go wherever that water goes... $\endgroup$ – RBarryYoung Mar 26 '15 at 4:39
  • $\begingroup$ Reference: see Michael Swanick's "In the Drift" stories. IIRC, he had it spread 50-100 miles, N, W, and E on the wind, and all the way to the Atlantic Ocean, south down the Delaware from Philadelphia. $\endgroup$ – RBarryYoung Mar 26 '15 at 4:43
  • $\begingroup$ There are MANY systems in place to prevent this sort of thing. I think maybe 25 miles with self activated systems... $\endgroup$ – JDSweetBeat Mar 26 '15 at 14:42
  • $\begingroup$ @DustinJackson background has that the safety mechanisms failed catastrophically and there were nobody around to handle it. $\endgroup$ – Mindwin Mar 26 '15 at 17:03
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    $\begingroup$ Not very big. Consider a) there are a number of people still living in the Chernobyl exclusion zone, and b) wildlife there is much healthier there than in most of Europe, due to the exclusion of most human activity. $\endgroup$ – jamesqf Mar 26 '15 at 17:56
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Disclaimer: I'm no nuclear scientist and no physician. Just some back-of-the-envelope calculations ...

The unit of radiation is called Becquerel. The accidents in Chernobyl and Fukushima released something to the tune of 10^18 Bq each -- no need to quibble about details. In both cases humans tried to contain the release, often at the cost of their own lives, so call it 10^20 Bq for an unmitigated disaster.

After some googling, I guess that 10^6 Bq contaminate a square meter pretty thoroughly. That means 10^20 Bq are enough for 10^14 square meters -- call it a circle 7,000 miles in diameter. That's a major continent.

It is obviously nonsense to assume that radioactive material will be spread equally across the contaminated area. The center of the disaster area will be even worse than 10^6 Bq/m^2 and areas beyond the "death zone" will still be pretty bad. How quickly will the radiation fall off from the center? I don't know.

The next problem is the definition of "death zone". Lethal within a day? A week? Ten years?

But I think you can justify a 100 mile or even a 1,000 mile death zone. With hot spots beyond this limit and perhaps with lesser radiation at "lucky spots" inside.

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    $\begingroup$ I think we can safely approximate the radiation level drop with the square of the distance $\endgroup$ – Mindwin Mar 26 '15 at 17:16
  • $\begingroup$ also, on your disclaimer: I am not expecting a scienific paper with rigour to the 9th decimal place :) --- Just some numbers that I can use not to stretch the reader's suspension of disbelief (or to not need a suspension of disbelief in the first place). $\endgroup$ – Mindwin Mar 26 '15 at 17:18
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    $\begingroup$ Note that no one died of radiation effects at Fukushima. As for the danger zone a decade later, maybe a mile - just to be on the safe side. $\endgroup$ – jamesqf Mar 26 '15 at 17:59
  • $\begingroup$ @Mindwin, we're talking about matter rather than radiation. A really big lump in the center, plus windblown fallout won't be r^2. $\endgroup$ – o.m. Mar 26 '15 at 18:01
  • $\begingroup$ You're forgetting time. The stuff decays rapidly. $\endgroup$ – Loren Pechtel Mar 27 '15 at 2:12
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After your decade the radioactivity of a spent fuel assembly is 20,000 rem/hr @ 1 meter. You might have 200 of these in a big reactor--4 million rem/hr @ 1 meter if you could manage to get that close. We have an incident from Taiwan where people were living in buildings that emitted about .1 rem/day (although it decayed over time)--with the observed health effects over a decade being beneficial, not harmful. Thus I will call this a safe level. (Yes, I realize this sounds insane--all our data on the risks of radiation are based on acute exposure and this is just one of the pieces of data that suggests acute and chronic exposure have different effects.)

4 million rem/hr * 24 hr/day = ~100 million rem/day. Spread evenly over an area to produce this safe dose we have ~1 billion m^2 = a square 31 km on a side.

On timescale of months we have someone exposed to 10 rem/day with only minor health effects (he absorbed a dose that would be almost certainly lethal as a single exposure.) Spread evenly this is a square only 3.1 km on a side.

I'm not aware of any data that lets us set a low bound on a lethal zone. I would call 100 rem/hr certainly lethal--that's a mere 200m square.

In the real world you aren't going to get an even distribution within the death zone and nothing outside it--the actual death zone will be considerably smaller. I doubt it's going to extend much beyond the reactor complex itself.

As for the issue of the local water feature being contaminated--that's going to be dilute. The radioactivity might pose a cancer risk but it won't be a death zone and most of the radioactivity will be washed out to sea and diluted beyond detectability. This will make the death zone even smaller.

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