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I was talking to a friend of mine who is an environmentalist like me but not a big fan of nuclear power and she told me it was not a good option in the long run because of the decay of uranium. Of course this is a ridiculous argument because U-238's half-life is measured in billions of years, but nonetheless I couldn't tell her whether or not the world's reserves were shrinking in a geologic time scale. Looking at the many decay elements of U-238, I believe there may be a handful of isotopes that decay into it. And I'm certain there is a name for these elements I'm looking for, I just can't find them.

Follow-up question: given our current known reserves of transuranic elements and again taking into account their decay products, where will the greatest uranium reserves be in, say, 10 half-lives of U-238? I can barely make sense of a nuclide chart and don't even know where to begin looking for a map of these elements.

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    $\begingroup$ I think you should probably stick to the first question here, then ask the second as a completely separate followup $\endgroup$ Mar 17, 2022 at 7:31
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    $\begingroup$ The isotopes that eventually decay into a given nuclide of interest are called parent isotopes. In the case of U-235, which was the isotope I was actually looking for (I must have switched them up), they are Pa-235, Np-235 and Pu-239. $\endgroup$
    – ablon
    Mar 17, 2022 at 18:41

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Let's start with the easy question:

given our current known reserves of transuranic elements and again taking into account their decay products, where will the greatest uranium reserves be in, say, 10 half-lives of U-238? I can barely make sense of a nuclide chart and don't even know where to begin looking for a map of these elements.

10 half lives of U-238 will pass in around 45 billion years. We have only about 5 billion years before the sun starts expanding beyond Earth's orbit. Therefore, the answer to your question is "inside the sun".


Now, the main part of your question:

Of course this is a ridiculous argument because U-238's half-life is measured in billions of years

You are entirely correct. We can even calculate that. Let's ask Wolfram Alpha how much uranium will have decayed after 1000 years. This is the answer:

remaining fraction of number of particles | 99.9999845% = 0.999999845

So for all practical purposes, after one thousand years (!!), the amount of uranium in the Earth does not change (other than the uranium used for power generation).

I couldn't tell her whether or not the world's reserves were shrinking in a geologic time scale

First, note that the word "reserves" has a very specific meaning. You are probably asking simply about the quantity of uranium in the Earth. So yes, it is shrinking. The half-life of uranium is about 4.5 billion years, which happens to be the age of the earth. So the Earth currently has half of the uranium it had when it first formed.

I believe there may be a handful of isotopes that decay into it

Yes, Pu-242 will decay to U-238 with a half-life of 375000 years. Since we're more than 100 half-lives past the formation of the Earth, there is no Pu-242 left on Earth for all practical purposes. Statistically speaking, there might be a few atoms left hanging around since then, but don't put your bets on their decay for increasing the amount of U-238.

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    $\begingroup$ Despite being the most abundant natural isotope of uranium, U-238 is not particularly useful. With a natural abundance of 0.72%, U-235 is the important natural isotope for use in power & nuclear reactors in general. Using current consumption rates, apparently the world only has about 230 year supply of useful uranium. After that, if we still want to use nuclear power we'll have to use Thorium. $\endgroup$
    – Fred
    Mar 17, 2022 at 16:25
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    $\begingroup$ @Fred yes. OP commented that they meant to ask about 235U, not 238U, but it still doesn't really change the answer substantially. The numbers will change a bit, but the point is that radioactive decay is meaningless. That said, as a rule of thumb, whenever someone tells you "we have only about X years supply of Y", they are wrong by definition. I have commented and answered about this before here, on chemistry.SE, and probably other sites. $\endgroup$
    – Gimelist
    Mar 17, 2022 at 23:01
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    $\begingroup$ @Fred, U-238 is useful because it can be transmuted into Pu-239, which works just fine as a reactor fuel. $\endgroup$
    – Mark
    Mar 17, 2022 at 23:46
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    $\begingroup$ @Fred ${}^{238}\mathrm{U}$ is pretty useful... if you want a dumb, heavy ballast material. For nuclear purposes, yes you're right but as Mark commented it can be transmuted into more active isotopes. $\endgroup$ Mar 18, 2022 at 15:51
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    $\begingroup$ @Gimelist It's a pretty long wait. $\endgroup$
    – Spencer
    Mar 19, 2022 at 12:30
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The uranium present on Earth is always decreasing (barring a big delivery by an impact event--and radioactivity would be the least of our concerns then.) Yes, uranium appears in some of the decay chains--but the only naturally occurring top of those decay chains is uranium.

Yes, you can find decay chains listed with something else at the top, but that something else is either synthetic or originally came from uranium.

If you want to look at geological time scales you'll find nuclear power reduces radioactivity. All the radioactivity it produces is reasonably short lived, mining and using up the uranium will eventually show up as reduced radon exposure as all radon is produced by uranium decay.

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The question in itself is flawed.

It begins to talks about nuclear power and then focuses on U-238. The overwhelming majority of nuclear power plants today depend on U-235 which is rare. Plants using different technologies have been hampered by a mix of technical and political issues. Such is the political pressure that, chances are, we will remain with the current PWR technology for a very long time.

Since U-235 is needed also as a trigger in the other types of nuclear plants chances are that an eventual switch to heavy water or breeder reactors might start when it will be too late. It would be still possible to produce Nuclear energy with U-238 using particle accelerators to generate neutron beams and bombard the Uranium, but at a high cost, proposed designs never went beyond the drawing board.

So, the problem in the long will be the exhaustion of a finite resource way long before the decay could have any impact.

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