Now to go look up the decay rate on nuclear stuff. My evening is full. My heart is empty.
Geo
It varies a bit depending on what the fuel mix is, but a close approximation often used in nuclear weapon planning for fall out, is that the exposure rate decreases exponentially at an exponent of -1.8 (or very close to that value). The short hand rule of thumb is that for every 7 fold increase in time, the exposure rate decreases by approximately a factor or 10.
Once the reactor shuts down (the emergency scram) the decay products begin this exponential decay. 7 hours after the shut down the radiation intensity of the decay products would be about 10% of its initial value, 7x7 hrs (2 days) after shut down the radiation intensity would be 1% or the original value. After 2 weeks 0.1% of the original value. As you can see the initial decay rate is very rapid, but begins to slow down as only the long half life isotopes are left.
The fission products in an operational reactor are a bit different than a nuclear weapon because the fission process is spread out over time, rather than all happening at a single moment in time. As a result the decay products from fission that occurred weeks or months ago, are in a much later stage of decay that the decay products of fission that occurred just moments before the shut down. As a result the decay is not as abrupt as it would be for a weapons fall out.
This however only applies to the full load of decay products from nuclear fission. In this sort of situation you get fractionation where only certain radio nuclides are mobile enough to get out of the reactor.The nobel gasses decay very rapidly (which accounts for the sharp but brief spikes in radiation as a puff of material escapes the containment. The two most prominent radio nuclides are Iodine 131 which has a 1/2 life of 8.02 days (ie every 8.02 days half of the remaining I 131 ceases to be radioactive). This is easily absorbed by the body and concentrated in the thyroid gland, and is the reason behind issuing potassium iodide tablets to flood the body with non-radioactive iodine to minimize uptake of radioactive iodine.
The second important isotope is Cesium Cs 137 which is a beta and moderate energy gamma emitter but has a half life of 30.17 years, so it takes a significant time to decay away to nothing. Medically it acts much like potassium and the good news is that it washes out of the body fairly quickly, taking only about 70 days for 1/2 of it to be excreted if any is ingested.
The third important radio isotope is probably strontium 90 which has a 1/2 life of 28.8 years. Only about 20% - 30% of the strontium 90 ingested is actually absorbed by the body. The bad news is that it is treated by the body as an analog of calcium and gets deposited in the bones. Its biological half life is about 18 years. Since it mimics calcium, the source of a persons calcium intake impacts how much Sr 90 they will absorb. Persons who get most of the calcium from milk products will take up less Sr 90 than people that get most of their calcium from vegetables, because the cow that makes the milk, preferentially filters out some of the Sr 90.
One of the problems with cooling the reactor core and rods with sea water, is that common salt when irradiated with neutrons captures neutrons and converts to a radioactive isotope Na 24. Sodium 24 has a short half life of 15 hours but it is a gamma emitter so the salt in the sea water could create a new short lived radiation hazard if it is exposed to high neutron irradiation in the core. I am not sure if the neutron flux in the shut down reactor is high enough for this to be an issue there or in the spent fuel rod pool, as I do not know how much fission occurs in the fuel rods in the cooling pool. It is obviously below the threshold to support a chain reaction but it may be high enough to activate some of the salt in the sea water.
Larry