Long-lived fission product
Evolution of radioactivity in nuclear waste 
Nuclear fission produces fission products, as well as actinides from nuclear fuel nuclei that capture neutrons but fail to fission, and activation products from neutron activation of reactor or environmental materials.
The high short-term radioactivity of spent nuclear fuel is primarily from fission products with short half-life. The radioactivity in the fission product mixture is mostly short-lived isotopes such as I-131 and 140Ba, after about four months 141Ce, 95Zr/95Nb and 89Sr take the largest share, while after about two or three years the largest share is taken by 144Ce/144Pr, 106Ru/106Rh and 147Pm. Note that in the case of a release of radioactivity from a power reactor or used fuel, only some elements are released. As a result the isotopic signature of the radioactivity is very different from an open air nuclear detonation where all the fission products are dispersed.
Medium-lived fission products 
After several years of cooling, most radioactivity is from the fission products caesium-137 and strontium-90, which are each produced in about 6% of fissions, and have half-lives of about 30 years. Other fission products with similar half-lives have much lower fission product yields, lower decay energy, and several (151Sm,155Eu,113mCd) are also quickly destroyed by neutron capture while still in the reactor, so are not responsible for more than a tiny fraction of the radiation production at any time. Therefore, in the period from several years to several hundred years after use, radioactivity of spent fuel can be modeled simply as exponential decay of the 137Cs and 90Sr. These are sometimes known as medium-lived fission products.
Krypton-85, the 3rd most active MLFP, is a noble gas which is allowed to escape during current nuclear reprocessing; however, its inertness means that it does not concentrate in the environment, but diffuses to a uniform low concentration in the atmosphere. Spent fuel in the US and some other countries is not likely to be reprocessed until decades after use, and by that time most of the Kr-85 will have decayed.
|244Cm||241Puƒ||250Cf||227Ac№||10–22 y||medium||m is
|249Cfƒ||242mAmƒ||251Cfƒ||140 y –
No fission products
|248Cm||4n+1||234U№||211–348 ky||99Tc||₡ can capture||126Sn||79Se|
|232Th№||238U№||235Uƒ№||0.7–14 Gy||fission product yield|
After Cs-137 and Sr-90 have decayed to low levels, the bulk of radioactivity from spent fuel come not from fission products but actinides, notably plutonium-239, plutonium-240, americium-241, americium-243, curium-245, and curium-246. These can be recovered by nuclear reprocessing (either before or after most Cs-137 and Sr-90 decay) and fissioned, offering the possibility of greatly reducing waste radioactivity in the time scale of about 103 to 105 years. Pu-239 is usable as fuel in existing thermal reactors, but some minor actinides like Am-241, as well as the non-fissile and less-fertile isotope plutonium-242, are better destroyed in fast reactors, accelerator-driven subcritical reactors, or fusion reactors.
Long-lived fission products 
On scales greater than 105 years, fission products, chiefly 99Tc, again represent a significant proportion of the remaining, though lower radioactivity, along with longer-lived actinides like neptunium-237 and plutonium-242, if those have not been destroyed.
The most abundant long-lived fission products have total decay energy around 100-300 KeV, only part of which appears in the beta particle; the rest is lost to a neutrino that has no effect. In contrast, actinides undergo multiple alpha decays, each with decay energy around 4-5 MeV.
Only seven fission products have long half-lives, and these are much longer than 30 years, in the range of 200,000 to 16 million years. These are known as long-lived fission products (LLFP). Two or three have relatively high yields of about 6%, while the rest appear at much lower yields. (This list of seven excludes isotopes with very slow decay and half-lives longer than the age of the universe, which are effectively stable and already found in nature; as well as a few nuclides like technetium-98 and samarium-146 that are "shadowed" from beta decay and can only occur as direct fission products, not as beta decay products of more neutron-rich initial fission products. The shadowed fission products have yields on the order of one millionth as much as iodine-129.)
The 7 long-lived fission products 
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The first three have similar half-lives, between 200 thousand and 300 thousand years; the last four have longer half-lives, in the low millions of years.
- Technetium-99 produces the largest amount of LLFP radioactivity. It emits beta particles of low to medium energy but no gamma rays, so has little hazard on external exposure, but only if ingested. However, technetium's chemistry allows it to form anions (pertechnate, TcO4-) that are relatively mobile in the environment. Tons of technetium-99 have been released into the ocean.
- Tin-126 has a large decay energy (due to its following short half-life decay product) and is the only LLFP that emits energetic gamma radiation, which is an external exposure hazard. However, this isotope is produced in very small quantities in fission by thermal neutrons, so the energy per unit time from 126Sn is only about 5% as much as from 99Tc for U-235 fission, or 20% as much for 65% U-235+35% Pu-239. Fast fission may produce higher yields. Tin is an inert metal with little mobility in the environment, helping limit health risks from its radiation.
- Selenium-79 is produced at low yields and has weak radiation. Its decay energy per unit time should be only about 0.2% that of Tc-99.
- Zirconium-93 is produced at a relatively high yield of about 6%, but its decay is 7.5 times slower than Tc-99, and its decay energy is only 30% as great; therefore its energy production is initially only 4% as great as Tc-99, though this fraction will increase as the Tc-99 decays. 93Zr does produce gamma radiation, but of a very low energy, and zirconium is relatively inert in the environment.
- Caesium-135's predecessor xenon-135 is produced at a high rate of over 6% of fissions, but is an extremely potent absorber of thermal neutrons (neutron poison), so that most of it is transmuted to almost-stable xenon-136 before it can decay to caesium-135. If 90% of 135Xe is destroyed, then the remaining 135Cs's decay energy per unit time is initially only about 1% as great as that of the 99Tc. In a fast reactor, less of the Xe-135 may be destroyed.
135Cs is the only alkaline or electropositive LLFP; in contrast, the main medium-lived fission products and the minor actinides other than neptunium are all alkaline and tend to stay together during reprocessing; with many reprocessing techniques such as salt solution or salt volatilization, 135Cs will also stay with this group, although some techniques such as high-temperature volatilization can separate it. Often the alkaline wastes are vitrified to form high level waste, which will include the 135Cs.
Fission caesium contains not only 135Cs but also stable but neutron-absorbing 133Cs (which wastes neutrons and forms 134Cs which is radioactive with a half-life of 2 years) as well as the common fission product 137Cs which does not absorb neutrons but is highly radioactive, making handling more hazardous and complicated; for all these reasons, transmutation disposal of 135Cs would be more difficult.
- Palladium-107 has a very long half-life, a low yield (though the yield for plutonium fission is higher than the yield from uranium-235 fission), and very weak radiation. Its initial contribution to LLFP radiation should be only about one part in 10000 for U-235 fission, or 2000 for 65% U-235+35% Pu-239. Palladium is a noble metal and extremely inert.
- Iodine-129 has the longest half-life, 15.7 million years, and due to its higher half life, lower fission fraction and decay energy it produces only about 1% the intensity of radioactivity as Tc-99. However, radioactive iodine is a disproportionate biohazard because the thyroid gland concentrates iodine. I-129 has a half-life nearly a billion times as long as its more hazardous sister isotope iodine-131, therefore with a shorter high life, I-131 is approximately a billion times more radioactive than the longer lived I-129. Together with the longer more stable nature(longer half life) of I-129, and its lower decay energy, than its sister isotope I-131, I-129 is only about a billionth as radioactive as I-131.
LLFP radioactivity compared 
In total, the other six LLFPs, in thermal reactor spent fuel, initially release only a bit more than 10% as much energy per unit time as Tc-99 for U-235 fission, or 25% as much for 65% U-235+35% Pu-239. About 1000 years after fuel use, radioactivity from the medium-lived fission products Cs-137 and Sr-90 drops below the level of radioactivity from Tc-99 or LLFPs in general. (Actinides, if not removed, will be emitting more radioactivity than either at this point.) By about 1 million years, Tc-99 radioactivity will have declined below that of Zr-93, though immobility of the latter means it is probably still a lesser hazard. By about 3 million years, Zr-93 decay energy will have declined below that of I-129.
Nuclear transmutation is under consideration as a disposal method, primarily for Tc-99 and I-129 as these both represent the greatest biohazards and have the greatest neutron capture cross sections, although transmutation is still slow compared to fission of actinides in a reactor. Transmutation has also been considered for Cs-135, but is almost certainly not worthwhile for the other LLFPs.
- Nuclear Wastes: Technologies for Separations and Transmutation. National Academies Press. 1996. ISBN 978-0-309-05226-9.
- "The Nuclear Alchemy Gamble: An Assessment of Transmutation as a Nuclear Waste Management Strategy".
- Note: This is the heaviest isotope with a half-life of at least ten years before the "Sea of Instability".
- Note: Radium (element 88) is actually a sub-actinide, but it immediately precedes actinium (89) and follows a three element gap of instability after polonium (84) where no isotopes have half-lives of at least ten years (the longest-lived isotope in the gap is radon-222 with a half life of less than four days). Radium's longest lived isotope, at 1600 years, thus merits inclusion here.
- Note: specifically from thermal neutron fission of U-235, e.g. in a typical nuclear reactor.