# How come nuclear waste is so radioactive when uranium is relatively stable with an extremely long half life?

Natural uranium has a half life of 4.5 billion years. Representing with the expression $$m(0.5)^{\frac{x}{(4.5\times10^9 \times 364)}}$$, where $$x$$ is in days and $$m$$ is the initial mass of uranium. In one day, only $$4.2 \times 10^{-11} \%$$ decays into thorium. It would take around $$2.4 \times 10^{13}$$ atoms for one alpha particle to be generated. About $$\pu{4E-11 mol}$$. Assuming $$\pu{5 MeV}$$ per alpha particle. With $$\pu{1.6021773E-13 J}$$ in a $$\pu{MeV}$$. It would take $$\pu{2.5E2 mol}$$ of uranium or $$\pu{6 kg}$$ of uranium directly aimed at a point with theoretically $$0$$ loss of energy to achieve just a single Sievert. Then how is it possible that it is leaking $$\pu{10 Sv}$$ an hour at Fukushima reactor 1, an approximate of $$240$$ per day. That would be an equivalent to $$1.4$$ tons of pure uranium with $$0$$ theoretical power loss all directly channeled through retroreflectors and a focusing array all with 100% efficiency, channeling all the alpha decay into a single point onto the detector. I just can't wrap my head around this.

TLDR: How come nuclear power plants release so much radiation when uranium is so relatively stable?

• The whole point of fission reactors is that you extract energy by turning uranium into not-uranium. It's the not-uranium which can be many orders of magnitude more radioactive. Commented Nov 25, 2022 at 23:50
• Also, nuclear power plants have very little to do with natural uranium. Commented Nov 26, 2022 at 0:12
• @IvanNeretin Unless they use heavy water moderator, but such designs like CANDU are not used much. Commented Nov 26, 2022 at 0:29
• How can a question about radioactivity be on-topic on a chemistry site? Shouldn't it involve electrons? Commented Nov 26, 2022 at 23:18
• @PeterMortensen Questions on radioactivity is very much on topic here. Commented Nov 27, 2022 at 6:26

The radioactivity associated with nuclear waste does not come from naturally occurring uranium, but from products associated with processing and using uranium. First off, uranium as it occurs in nature is not really nuclear fuel. It must be enriched in the more radioactive but more fissionable (and thus better energy source) uranium-235, leaving behind the more stable uranium-238, or uranium-238 is converted to more useful fuels such as plutonium-239.

Then after the fission process, what is left behind includes isotopes of strontium, caesium, and the aforementioned plutonium, which are the main contributors to the hazardous radioactivity of the waste.

From the National Resources Council:

During the fission process, two things happen to the uranium in the fuel. First, uranium atoms split, creating energy that is used to produce electricity. The fission creates radioactive isotopes of lighter elements such as cesium-137 and strontium-90. These isotopes, called "fission products," account for most of the heat and penetrating radiation in high-level waste. Second, some uranium atoms capture neutrons produced during fission. These atoms form heavier elements such as plutonium. These heavier-than-uranium, or "transuranic," elements do not produce nearly the amount of heat or penetrating radiation that fission products do, but they take much longer to decay. Transuranic wastes, sometimes called TRU, account for most of the radioactive hazard remaining in high-level waste after 1,000 years.

Radioactive isotopes eventually decay, or disintegrate, to harmless materials. Some isotopes decay in hours or even minutes, but others decay very slowly. Strontium-90 and cesium-137 have half-lives of about 30 years (half the radioactivity will decay in 30 years). Plutonium-239 has a half-life of 24,000 years.

• I rolled back part of the previous edit. The text in the indented block is a direct quotation, and caesium was spelled without the "a" in the quoted material. Commented Nov 26, 2022 at 22:54

Radioactive isotopes (radionuclides to be more correct) are thermodynamically able to change into another nuclide, this decay has to be an exothermic event. For example if we consider beta decays for nuclides with mass numbers of 130. It is clear that Cadmium-130 atoms can be transformed by beta decay into lower energy atoms such as tellurium-130 by beta decay. But Xenon-130 is unable to convert itself into cesium-130.

The rate of the transformation (radioactive decay) is proportional to the number of the nuclei of the radionuclide in question. While with exceptionally high decay energies the decay rate is often higher, there not a clear relationship between decay energy and rate of decay. Things like odd vs even proton / neutron numbers and magic numbers are important.

The rate constant for the reaction is normally written as "lambda" the value of the constant varries greatly between very large (such as beryllium-8) and very small (such as thorium-232, bismuth-209 and plutonium-244).

The activity (A in Bq which is events per second) is given by the equation

A = lambda N

Where N is the number of atoms

You calculate lambda by dividing ln(2) by the half life in seconds

When fission of uranium or plutonium atoms occurs a vast range of different nuclides are created. The final decay products of these range from zinc through to the middle of the lanthanide series. You can imagine that a very wide range of different nuclides exist in the decay chains of the different initial fission products. If we consider if a zirconium-110 nucleus is formed by the fission process, all the radionuclides in the decay chain which leads to palladium-110 have short half lives (less than 15 seconds). So if a short pulse of fission such as a nuclear bomb detonation occurs then all the atoms with the mass of 110 will have decayed to the palladium in about two minutes.

If we were to make a solution of enriched uranium nitrate and deliver a strong neutron pulse to it and then five seconds later we were to separate the ruthenium from this mixture then the specific activity of the ruthenium in terms of Bq per mole would be exceptionally high. But given a minute or so then the radioactivity level of the ruthenium in the neutron bombarded uranium will be far lower.

Now if we were to leave uranium after a dose of neutrons and leave it it for millions of years then the vast majority of the fission products will decay away and then the radioactivity of the uranium will be larger than the fission products. There is a place in Africa where a series of natural nuclear reactors operated many millions of years ago. The vast majority of the fission products and the transuranium elements (such as plutonium) formed by these prehistoric reactors have decayed away to either stable nuclides (in the case of fission products) or uranium in the case of the plutonium which the reactor formed.

In the samples of the African fossil reactor materials clear signs of nuclear fission exist, while for a while (a long time ago) the fission product radioactivity was far greater than the either the uranium or plutonium radioactivity. The fission product radioactivity and then the plutonium radioactivity have no decayed away. Leaving the slowly decaying uranium still in the samples.

• We have enough information on the rate at which that natural reactor worked to say that the fission product radioactivity was higher? Commented Nov 26, 2022 at 21:54
• If anyone wants to look up this reactor, look for Oklo, Gabon.
– Dan
Commented Nov 28, 2022 at 0:48

As said in the comments, the whole point of fission reactors is that you extract energy by turning uranium into something else and that "something else" is much more radioactive than uranium itself. The nuclear waste can be categorized according to their radioactivity:

• low-level waste (LLW)
• intermediate-level waste (ILW)
• high-level waste (HLW)

The vast majority of the waste (90% of total volume) is considered LLW which contributes to 1% of the total radioactivity. On the other hand, HLW accounts for 3% of the total volume of waste, but contains 95% of the total radioactivity.

The HLW is primarily both uranium fuel that has been used in a nuclear power reactor and is "spent" or no longer efficient in producing electricity (Spent fuel is thermally hot as well as highly radioactive and requires remote handling and shielding) and the fission products (why the fission product is radioactive is mentioned in Oscar's answer).

When the nucleus splits, most of the energy is released immediately and carried off by coolant to do useful work. This energy continues to be released for thousands of years after the atom splits. This delayed emissions mean that nuclear waste is still highly radioactive. Even the afterglow heat that is produced is what makes the waste hazardous.

The amount of HLW worldwide is currently increasing by about 12,000 tonnes every year. A 1000-megawatt nuclear power plant produces about 27 t of spent nuclear fuel (unreprocessed) every year.

References:

• A point worth making is that we don't have any choice about the products of uranium fission being much more radioactive than the starting fuel. The laws of physics decide that. Commented Nov 27, 2022 at 16:59