Tobo, fair play to you for doing some research. Without knowing exactly what the waste comprises of initially ad not knowing the radiation flux history of the material they speak of its a bit difficult to take them to task, however it could be seen as at least misguiding to a reader.
You need to understand that the activity, is a measure of the amount of radiation given off by a material in a given time, the number of counts or clicks per minute registering on a geiger counter for instance (Unit - bequerel [new si] curie [old].
This is not the radiation dose however or half life.
It is important to know not only the number of decay events (clicks) per unit time, but also what type of radiation is given off and what tissues were exposed (using industry std calcs) you can arrive at a "dose equivalent(Ht)" which is a measure of the energy of the dose absorbed by the body, weighted by the type of radiation(Units - gray [new si] rad [old]), and using more calcs to arrive at "effective dose equivalent" a measure of the biological effect of the radiation weighted according to the tissue types affected, testes, thyroid, breast etc(Unit - Sievert [new si] rem [old]). This is the critical health safety measurement, monitored by personal film badges worn by radiation workers etc. Geiger counters can NOT tell you what your Effective Dose Equivalent is, or what your actual absorbed dose is!
There are three commonly considered types of radiation, Gamma - high energy (electromagnetic wave)ionising radiation (no mass), very penetrating, will pass through a foot or more of concrete or inches of lead, this is the stuff that frys you.
Beta (particle radiation), high speed electron or the opposite positron, (with some mass, not much)still very penetrating and requires maybe upto an inch of lead shielding fry's but also sometimes knocks or smashes the molecules in exposed tissues.
And lastly, Alpha (particle radiation) which you could stop with a piece of paper, however, Alpha radiation is a Helium atom with (compared to gamma and beta radiation)huge mass and therefore momentum, when ejected at high speed from the nuclei of decaying atoms.
The large size of the alpha particle compared to the gamma wave and beta particle is the reason why it is so easiy stopped; it almost always hits a molecule or atom of the material it is traveling through. Gamma and Beta being much much smaller, and a bit zippier, can slip through the 90% space between the nuclei of most materials.
So although alpha rad doesn't require inches of lead shielding it is more damaging to tissue if it isn't stopped. Particles breathed in or ingested that are alpha emitters have a very high incidence of causing cancers. Potentially only one alpha particle need be emitted from an internalised particle (close to tissue, lung etc)to cause damage that starts the cancer growing.
Half life, is the amount of time taken for half of the atoms in a radioactive substance to have decayed into a daughter isotope. If A decays to B, half life is the time taken for half of atoms (nuclide) A to have changed into atoms (nuclide) B. The remaining half of A will take (probablistically)the same time again to reduce by one half (leaving a quarter of A left) and so it continues, halving the number of A's remaining in each successive half life time, until no A is left. The decay curve is initial very steep, half of A has to have decayed in the half life, hence high activity, but this falls off rapidly since each successive half life, only has half the number of atoms decaying (activity)compared to the previous halving. I can't really simply explain to you why you don't have to actually wait 4.5 x 10^9 years to notice a big drop in activity, its all connected with it being a quantum process and there being mind numbingly large numbers of atoms even in a gram of matter.
In each transmutation A to B of the decay process, radiation is given off. Since radioactive decay is controlled by quantum effects, it can NOT be predicted, that is you can NEVER know or say when an individual atom will decay it might be the first or the last or anywhere in between. So if you could look at all the atoms in a material at the same time, you could not predict from this the total rate of activity at that time, however, the average or probablistic rate is never the less measurable.
Of course this does mean that the possibility of all the atoms decaying in a half life, decay simultaneously must also exist and for that matter any other combination of decay event timings you care to invent. But because we are dealing with such large sample numbers, the probability of such events occurring is so vanishingly small as to be effectively zilch probability.
Half lives can therefore only be established by measuring activity. And the activity of a material will depend largely on the combined effect of all the daughter nuclides within a material at any particular time which proceeds in a probablistically determinable manner.
If you were to say to a nuclear scientist, that's U238 waste over there, he would look at it and see the waste not as U238 but what it actually is comprising of all the nuclides in the U238 decay series (see below) in varying amounts.
The daughter nuclides (B) of the original parent nuclides (A) will continue to decay themselves, so that a sequence or series of daughter nuclides (isotopes) are formed until finally the decay process finishes with a stable isotopic nuclei, often Lead. Each of the successive nuclides in the decay series will have a different half life, which can be from micro seconds or less to days, years, decades upwards.
The information you have is a little misleading in that it subtly suggests that the material in question is going from very very dangerous highly active to not so dangerous over a period of decades which is kind of true, but,...I'll try an anology to explain.
Imagine you are going to be shot by firing squad, the squad has 50 riflemen, the bullets leave the rifle and less than a second later bits of you are flying in all directions and your dead. Your mate tied to the post next on the other hand has two riflemen facing him, same high velocity bullets as the 50 squad. They aim pull the trigger and, with exactly a 25th of the fire power of your firing squad, your mates head explodes. Same lethality. Could have saved 48 bullets for the next lot up against the wall (my vote New York wanker bankers!)
So the 50 man squad represents fresh Reactor fuel rods kicking off huge amounts of radiation rapidly. If you stood next to the real stuff for more than a couple of minutes your almost certainly dead. Internal organs fried and massive cellular damage, though you may linger for a few days, fate would be sealed. The spent reactor fuel after storage in water tanks for decades, is represented by the two man squad, there isn't anywhere near as much radiation given off per unit time, but, its still plenty enough to do serious damage to your head!
So starting from a very high rate, which is vastly more than needed to give you a serious health problem, and going to a much much lower rate of activity, does not inevitably lead to a lessening of the risks to human or ecological health.
Half Life
A half-life is the period of time taken for half of a radionuclide mass to decay to it next most stable form
U238 4.5 x 10^9 years Pu239 2.4 x 10^4 years
An example of Decay series
U238 > alpha > Th234 > beta > Pa234
Pa234 > beta > U234 > alpha > Th230
Phew, I think that about explains it, sorry if I dragged over stuff you already know.
onepot
Ps. Check out Poloniumm 210 toxicity.
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